1 relativistic gamma factor maximum

20-JUN-2021 hello -

I find a maximum value for the Lorentz gamma factor, gamma = ((1-((v)^2/c^2))^(1/2))^-1 = 54794158.005943767726, for a relative velocity v = 299792457.99999997 m/s. For an electron with mass m_e = 510998.91 ev/c^2 and momentum p_e=m_ev the max velocity is v_e = p_e/m_e = 299792457.9999999404 m/s. Plugging v_e into the gamma equation yields the same gamma max. Computing a higher velocity past the eighth decimal place does not change the gamma value either; until it blows up as gamma = inf.

Is there a good turn of phrase to explain this limit?

Cheers, mj horn

[[Mod. note -- I think "floating-point rounding errors" is the phrase you're looking for. If v/c is very close to 1, then the formula for gamma tends to be very sensitive to rounding errors, causing the sorts of anomolous behavior you noticed.

The computation can be reorganized to be less sensitive to rounding errors, but the easy solution is to just use brute force, i.e., use higher precision in the computation. For example, software systems such as Sage, Maple, and Mathematica can all easily do computations in higher precision than standard C "double" (which typically gives about 16-digit accuracy). For example, in Sage:

sage: gamma(v_over_c) = 1/sqrt(1 - v_over_c^2)
sage: gamma(1 - 1/(10**20)) 100000000000000000000/199999999999999999999*sqrt(199999999999999999999)
sage: n(gamma(1 - 1/(10**20)), digits=50) 7.0710678118654752440261212905781540809584467771981e9
sage:

As to what relevance this has for *physics*: the current record for the highest-energy cosmic ray has a gamma factor of over 10**20, corresponding to v/c of over 1 - 10**-40. -- jt]]

2 relativistic gamma factor maximum

mark horn schrieb:

>	[[Mod. note -- I think "floating-point rounding errors" is the phrase you're looking for. If v/c is very close to 1, then the formula for gamma tends to be very sensitive to rounding errors, causing the sorts of anomolous behavior you noticed.

3 relativistic gamma factor maximum

Thomas -

Thank you. Excellent reference to have, as I plod forward with the machine on my back.

Best, m

4 relativistic gamma factor maximum

On Monday, June 21, 2021 at 4:01:07 AM UTC-4, mark horn wrote:

>

20-JUN-2021 hello - I find a maximum value for the Lorentz gamma factor, gamma = ((1-((v)^2/c^2))^(1/2))^-1 = 54794158.005943767726, for a relative velocity v = 299792457.99999997 m/s. For an electron with mass m_e = 510998.91 ev/c^2 and momentum p_e=m_ev the max velocity is v_e = p_e/m_e = 299792457.9999999404 m/s. Plugging v_e into the gamma equation yields the same gamma max. Computing a higher velocity past the eighth decimal place does not change the gamma value either; until it blows up as gamma = inf. Is there a good turn of phrase to explain this limit? Cheers, mj horn [[Mod. note -- I think "floating-point rounding errors" is the phrase you're looking for. If v/c is very close to 1, then the formula for gamma tends to be very sensitive to rounding errors, causing the sorts of anomolous behavior you noticed. The computation can be reorganized to be less sensitive to rounding errors, but the easy solution is to just use brute force, i.e., use higher precision in the computation. For example, software systems such as Sage, Maple, and Mathematica can all easily do computations in higher precision than standard C "double" (which typically gives about 16-digit accuracy). For example, in Sage: sage: gamma(v_over_c) = 1/sqrt(1 - v_over_c^2) sage: gamma(1 - 1/(10**20)) 100000000000000000000/199999999999999999999*sqrt(199999999999999999999) sage: n(gamma(1 - 1/(10**20)), digits=50) 7.0710678118654752440261212905781540809584467771981e9 sage: As to what relevance this has for *physics*: the current record for the highest-energy cosmic ray has a gamma factor of over 10**20, corresponding to v/c of over 1 - 10**-40. -- jt]]

21-JUN-2021

Thanks so much. I'll chalk up another one to the unreasonable effectiveness of my ignorance to lead me astray.

thanks again, m

5 relativistic gamma factor maximum

On 6/21/21 3:01 AM, mark horn wrote:

>

[...]

For extended-precision arithmetic, rather than "Sage, Maple, and Mathematica", people may find it easier to use Python and its decimal module. It provides arbitrary-precision decimal arithmetic using standard Python arithmetic operators and functions. It defaults to 28 significant digits, well beyond double-precision floating point.

>>>	from decimal import * two = Decimal(2) Decimal.sqrt(two) Decimal('1.414213562373095048801688724') getcontext().prec = 50 Decimal.sqrt(two) Decimal('1.4142135623730950488016887242096980785696718753769')

Tom Roberts

6 relativistic gamma factor maximum

Tom Roberts schrieb:

>	On 6/21/21 3:01 AM, mark horn wrote:

>>

[...]

>	For extended-precision arithmetic, rather than "Sage, Maple, and Mathematica", people may find it easier to use Python and its decimal module.

Alternatively, you can use the oldest scientific programming language, Fortran.

7 relativistic gamma factor maximum

This has as a second advantage (besides using a language from the days when Einstein and Feynman were still alive) that with those declared variables you can actually compute things in a fast way, since Fortran is a compiled language while Python is interpreted.

(Apparently Thomas thinks the first advantage should already be decisive, and perhaps it should, but just for completeness..)

-- Jos

[Moderator's note: Einstein died in 1955, while the first version of Fortran was released in 1957. So not quite, though Fortran development might have already started while Einstein was still just alive. Interesting that you mention Feynman of all people. At Los Alamos, he developed a sort of human compiler where complex tasks were executed by noting something on a card and passing it to another person who calculated something on a mechanical calculator, added the result, and passed it on to another person, and so on. In principle, one could implement a Fortran compiler this way, as the standard doesn't specify how the compiler actually has to be built, though in practice it is always on an electronic digital computer. Fortran, which has seen several updates since 1957, is still widely used for scientific computing. --P.H.]

8 relativistic gamma factor maximum

Op maandag 21 juni 2021 om 10:01:07 UTC+2 schreef toadast...@gmail.com:

>	20-JUN-2021 I find a maximum value for the Lorentz gamma factor, gamma = ((1-((v)^2/c^2))^(1/2))^-1 = 54794158.005943767726, for a relative velocity v = 299792457.99999997 m/s.

That calculation is 'correct' using c = 299792458.00000000 m/s

>	For an electron with mass m_e = 510998.91 ev/c^2 and momentum p_e=m_ev the max velocity is v_e = p_e/m_e = 299792457.9999999404 m/s.

That calculation is simple, but that is not the issue.
How do you know that m_e = 510998.91 ev/c2 and
how do you know that p_e = m_e*v = 15319361264220,749544464964
How are both calculated i.e measured by means of experiment.

>	As to what relevance this has for *physics*: the current record for the highest-energy cosmic ray has a gamma factor of over 10**20, corresponding to v/c of over 1 - 10**-40. -- jt]]

The physics behind this question is very important, because how do you know that the speed cosmic ray is almost the same as the speed of light but smaller and not larger? What I want to know is how are both speeds established?

Ofcourse you could claim that the speed of light is constant. In that case you get a new question: How do you know that the distance of a photon travelled in 1 second is slightly more than the distance of the cosmic ray i.e. 299792458.00000000 m versus 299792457,99999999999700207542 m using v/c = 1 - 10**-20 How is that established by means of experiment? or observation?

IMO this is difficult. It means that if both signals are emitted simultaneously the photon should arrive before the cosmic ray

9 relativistic gamma factor maximum

Nicolaas Vroom schrieb:

>	Ofcourse you could claim that the speed of light is constant.

The way that the SI units are defined now, the speed of light in vacuum is indeed constant. If you measure anything else than 299792458 m/s, recalibrate your measurement devices.

10 relativistic gamma factor maximum

In article <4062c54b-7af6-4f3a...@googlegroups.com>, Nicolaas Vroom writes:

>

Maybe this document gives a glue, because it mentions Supernova 1987A https://www.abc.net.au/science/articles/2011/11/25/3376138.htm Neutrino's win but Einstein has not lost yet "but the supernova observations showed that neutrinos and photons generated at the same time by the supernova, 160 thousand light years away, arrived here at the same time as well." But if they arrive simultaneously here how do you know that they were emitted simultaneously overthere?

The fact that they arrived at roughly the same time sets strong upper limits on the mass of the neutrinos involved. For some types of neutrinos, those were (maybe still are) the best limits. A supernova is not an instantaneous event, and for various reasons the light and neutrinos are not produced at exactly the same time or, more importantly, cannot freely travel from the same time, so some discrepancy is expected. It's not clean enough to use for the type of test which you have in mind.

11 relativistic gamma factor maximum

In article , Thomas Koenig writes:

>	Nicolaas Vroom schrieb:

> >	Ofcourse you could claim that the speed of light is constant.

>	The way that the SI units are defined now, the speed of light in vacuum is indeed constant. If you measure anything else than 299792458 m/s, recalibrate your measurement devices.

The speed of light is now a defined quantity, that is true. However, that is merely a practical matter. If the speed of light really were variable, that could still be detected just as easily as before the redefinition. Suppose that the speed of light did drop by a measurable amount. People would not immediately redefine the length of everything because of that.

Many other SI units were recently redefined, so they are "exact" in that sense. The same caveats apply.

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On 6/26/21 5:36 AM, Jos Bergervoet wrote:

>	[...] with those declared variables you can actually compute things in a fast way, since Fortran is a compiled language while Python is interpreted.

While true, this is a red herring, except for very-old-school programmers who don't understand how to use Python [#]. Modern software development involves using libraries rather than coding stuff yourself. Python libraries numpy and scipy are every bit as fast as FORTRAN when using arrays for large computations. When not using arrays, and for small computations, Python is faster than humans, which is usually all that matters.

[#] Hint: if you ever loop over the elements of an array in Python, you are probably doing it wrong, or at least very inefficiently. (Does not apply to small lists.)

The real win for Python, however, is in improved programmer productivity compared to Fortran. As any serious programmer learns the basics of a new language in a day or two, this improved productivity applies even if you don't already know Python. (Except for tiny, one-off projects.)

There are situations where languages like Fortran or C++ are appropriate, mostly when dealing with legacy libraries, or building a large software edifice.

Tom Roberts

13 relativistic gamma factor maximum

On 21/06/27 9:38 AM, Tom Roberts wrote:

>	On 6/26/21 5:36 AM, Jos Bergervoet wrote:

>>	[...] with those declared variables you can actually compute things in a fast way, since Fortran is a compiled language while Python is interpreted.

>	While true,

Thank you for the confirmation. (As I wrote, I mentioned this advantage merely for completeness.. It does, however, seem to raise some deeper questions.)

>	this is a red herring, except for very-old-school programmers who don't understand how to use Python [#]. Modern software development involves using libraries rather than coding stuff yourself.

This description may be accurate, but how do we know that "modern" software development is any better than this old-school variety where "stuff" is actually coded? (We should restrict the question to applications in physics of course, to keep it somewhat on-topic..)

>	Python libraries numpy and scipy are every bit as fast as FORTRAN when using arrays for large computations.

This brings us to the core of the matter. How do you know that progress (in computational physics) will only require combining things that have already been programmed? We know that advances in mathematics are often driven by physics. Wouldn't that also apply to numerical mathematics, requiring us to go beyond what is in any existing library?

How did, for instance, the development of symplectic integrators go? (NB: I'm purely asking out of curiosity, I don't claim that this proves anything I said, it just seems to be a relevant, recent development.) If I look for discussions about actual code, I see various languages being used, it surely also includes Fortran.

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Tom Roberts schrieb:

>	The real win for Python, however, is in improved programmer productivity compared to Fortran.

I would like to refer everybody to

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Op zaterdag 26 juni 2021 om 22:07:42 UTC+2 schreef Thomas Koenig: That is the problem. The issue is: I have to measure the speed of light and I have to measure the speed of an electron v_e or of a cosmic ray. The question is how do you do that in an uniform way in both cases so that other people can repeat these experiments?

The result for the gamma ray should be in the order of 299792457,999999999997 m/sec. That means the experiments should be done very accurate. The speed of light should be 299792458 m/sec in vacuum.

But suppose that I can not measure the speed of light in a vacuum and result I get case (1) 299792457,9 m/sec or case (2) 299792458,1 m/sec Both results give me a headache, because they are wrong. In case (1) the speed is too small and in case (2) too large. Now suppose that the results my experiments with a gamma ray are in case (1) 299792457,8995 m/sec or in case (2) 299792458,0995 m/sec

In both cases (1) and (2) ofcourse I can calculate a gamma factor, but that is simple mathematics. IMO the most important question to answer is: what is the standard way to measure the speed of light, of an electron or of a cosmic ray.

A more advanced question is what to do in case the speed of cosmic ray is higher than the speed of light i.e 299792458,0995 m/sec versus 299792458 m/sec in vacuum.

Nicolaas Vroom.

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Phillip Helbig (undress to reply) wrote:

>	In article , Thomas Koenig writes:

> >	Nicolaas Vroom schrieb:

> > >

Ofcourse you could claim that the speed of light is constant.

> >	The way that the SI units are defined now, the speed of light in vacuum is indeed constant. If you measure anything else than 299792458 m/s, recalibrate your measurement devices.

>	The speed of light is now a defined quantity, that is true. However, that is merely a practical matter. If the speed of light really were variable, that could still be detected just as easily as before the redefinition.

It is incredible how much misunderstanding there is on such a simple subject.
To clear things up: The speed of light cannot 'really' be variable. Why? In order for the speed of light to be measurable at all we need to define both a length and a time unit. Now this can be done in many different ways.
For example, we can define the second on basis of a seconds pendulum, or on basis of the vibrations of a quartz crystal, or on basis of some atomic hyperfine transition, or.... With some thought you can figure out how those definitions scale, when fundamental constants vary. (different of course, the pendulum has a G in it, the other second definitions don't) Likewise for length units, like platinum bars, atomic wavelengths, stabilised lasers, the AU, etc.)

Now if some, or all of the fundamental constants vary, so does the measured c, depending on how we set up the definitions of the length and time units. (with all kinds of possible answers) This 'measured' c is not something to do with nature, it depends on our -human- measurement definitions.

Now it should be obvious to anyone with any sense of how physics should be done that the units of time and length should be chosen in mutually compatible ways. (so differing by a factor of c) So, with the right definitions of units c cannot possibly be variable.

Or, saying the same in different words: c is not really a fundamental constant of nature in any way that makes -physical- sense. It is merely a conversion factor between units. You could just as well ask how 5280 feet/mile is going to change with the age of the universe,

Jan

17 relativistic gamma factor maximum

Op zondag 27 juni 2021 om 00:57:19 UTC+2 schreef Phillip Helbig (undress to reply):

>	In article <4062c54b-7af6-4f3a...@googlegroups.com>, Nicolaas Vroom writes:

>>>	As to what relevance this has for *physics*: the current record for the highest-energy cosmic ray has a gamma factor of over 10**20, corresponding to v/c of over 1 - 10**-40.

> >	The physics behind this question is very important, because how do you know that the speed cosmic ray is almost the same as the speed of light but smaller and not larger? What I want to know is how are both speeds established? (*1)

> >	Maybe this document gives a glue, because it mentions Supernova 1987A https://www.abc.net.au/science/articles/2011/11/25/3376138.htm Neutrino's win but Einstein has not lost yet

>

The fact that they arrived at roughly the same time sets strong upper limits on the mass of the neutrinos involved. For some types of neutrinos, those were (maybe still are) the best limits. A supernova is not an instantaneous event, and for various reasons the light and neutrinos are not produced at exactly the same time or, more importantly, cannot freely travel from the same time, so some discrepancy is expected.

>	It's not clean enough to use for the type of test which you have in mind.

That is the question. What I want to know is a clear description of the tests in order to measure the speed of light, of an electron and of a gamma ray. IMO these tests, the description of, involve high uniform accurate measurements and should be performed in a standard way.
For example, I expect they should all be done in vacuum. If that is possible, than they can each be compared with the standard speed of light c in vacuum. If that is not possible than they at least all should be done under the same conditions. But that raises a problem, related to the value of the speed of light, (not in vacuum) that can be expected and is accepted.

IMO these issues are more important than the calculation of gamma.

I agree with you that part of the problems are related to the (simultaneous or not) production of these 'particles'

Nicolaas Vroom.

[[Mod. note -- This topic is a bit tricky, because to measure a speed in meters/second, we need to know what a meter is, and what a second is. The SI definition of a second is fairly straightforward: "The second is defined as being equal to the time duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the fundamental unperturbed ground-state of the caesium-133 atom."

18 relativistic gamma factor maximum

In article <1pbi21w.1t8rob81hgck0aN%nos...@de-ster.demon.nl>, nos...@de-ster.demon.nl (J. J. Lodder) writes:

>	Phillip Helbig (undress to reply) wrote:

>>	In article , Thomas Koenig writes:

>>>	Nicolaas Vroom schrieb:

>>>>	Of course you could claim that the speed of light is constant.

>>>	The way that the SI units are defined now, the speed of light in vacuum is indeed constant. If you measure anything else than 299792458 m/s, recalibrate your measurement devices.

>>	The speed of light is now a defined quantity, that is true. However, that is merely a practical matter. If the speed of light really were variable, that could still be detected just as easily as before the redefinition.

>	It is incredible how much misunderstanding there is on such a simple subject.

I agree. :-)

>	To clear things up: The speed of light cannot 'really' be variable.

It is true that the metre is now defined as the distance travelled by light in a certain time and thus by definition the speed of light is constant. However, the metre (and the second) used to be defined differently than they are now. Back then, it was certainly possible, in principle, to detect a change in the speed of light. One could perform the same experiment today. Nature doesn't know what the current SI definitions are.

The metre is now defined as it is a) as a practical matter and b) because we assume that the speed of light is constant. If the speed of light did change, i.e. of one does observations like those of R�mer, Fizeau, etc., using, say, pendulum clocks as a reference, and notice that it changes, then one has measured the change. The consequence would not be to point to the SI definition and say that it cannot change, therefore we must modify other definitions (perhaps even periodically if the speed of light depends on time), but rather would be to realize that our assumptions in the current definition of the metre are wrong and must be changed.

Think about the definition of the metre and kilogram. Why are the original definitions not used? One reason is because on noticed that the mass of the reference kilogram has actually changed with time. By your logic, that should not have been possible, since, by definition, the reference kilogram has a mass of exactly one kilogram. Nevertheless, the change was detected.

19 relativistic gamma factor maximum

On 21/06/29 8:41 AM, J. J. Lodder wrote:

>	Phillip Helbig (undress to reply)

>>	In article , Thomas Koenig

>>>	Nicolaas Vroom schrieb:

>>>>	Ofcourse you could claim that the speed of light is constant.

>	It is incredible how much misunderstanding there is on such a simple subject.

I think there are several reasons for it. See below..

>	The speed of light cannot 'really' be variable. Why? In order for the speed of light to be measurable at all we need to define both a length and a time unit.

Indeed we can agree that basically this is determined by the metric of space. Any massless field will have a propagation speed defined by the metric, but any measurement of speed also has to use that metric. So the result is fixed.

This should make clear that a change cannot be observed using the local metric, but not everyone will agree that this means it cannot 'really' change.

We know that seen from another point in space, the speed of light can be different if space-time is curved (as it usually is..) You may then claim that it is only an 'apparent' slowing down if e.g. light falls into a black hole, but then we only change the discussion to the meaning of 'apparent' and 'really'. We can't maintain that it is unobservable, in that case.

Obviously, by specifying the "locally observed speed of light" this problem is avoided, but if you do not want to talk about different points in space or in time, then it becomes a bit too obvious that 'change' cannot be observed, it looks a lot like not wanting to observe it, then..

Finally, it's also conceivable that the photon mass at some point in the future will become nonzero, theoretically (another theory says that this has already happened).

All these things explain the ongoing discussion, I think..

-- Jos

20 relativistic gamma factor maximum

On 6/29/21 1:49 PM, Jos Bergervoet wrote:

>	Indeed we can agree that basically this is determined by the metric of space. Any massless field will have a propagation speed defined by the metric, but any measurement of speed also has to use that metric. So the result is fixed.

You mean the metric of spacetime (not space). And this applies only to a massless field -- there is no fundamental reason for the photon to be massless, it's just that its mass is observed to be consistent with zero and an extremely tiny upper limit (< 10^-18 eV).

>	This should make clear that a change cannot be observed using the local metric, but not everyone will agree that this means it cannot 'really' change.

The constancy of the vacuum speed of light applies only locally, so everyone who understands the issues will agree for a massless field. But of course that's the rub -- we don't really know whether the photon field is truly massless.

>

We know that seen from another point in space, the speed of light can be different if space-time is curved (as it usually is..) You may then claim that it is only an 'apparent' slowing down if e.g. light falls into a black hole, but then we only change the discussion to the meaning of 'apparent' and 'really'. We can't maintain that it is unobservable, in that case.

That's just an argument over the meanings of words. Moreover it's an argument that never comes up because the constancy of the vacuum speed of light applies only locally.

All this only applies to massless fields, and we don't really know whether the photon field is truly massless. Of course we never will....

Tom Roberts

21 relativistic gamma factor maximum

Op woensdag 30 juni 2021 om 21:37:22 UTC+2 schreef Tom Roberts:

>	On 6/29/21 1:49 PM, Jos Bergervoet wrote:

> >	Indeed we can agree that basically this is determined by the metric of space. Any massless field will have a propagation speed defined by the metric, but any measurement of speed also has to use that metric. So the result is fixed.

>	You mean the metric of spacetime (not space). And this applies only to a massless field -- there is no fundamental reason for the photon to be massless, it's just that its mass is observed to be consistent with zero and an extremely tiny upper limit (< 10^-18 eV).

How is this mass observed? Or should I write upper limit?

> >	This should make clear that a change cannot be observed using the local metric, but not everyone will agree that this means it cannot 'really' change.

>	The constancy of the vacuum speed of light applies only locally, so everyone who understands the issues will agree for a massless field.

What are the issue?

>	But of course that's the rub -- we don't really know whether the photon field is truly massless.

Is it possible to measure this photon field?

Is it not true, that when it is possible to measure the energy of a light pulse, that then individual photons also have energy, and as a consequence individual photons also have a mass?

This implies when a star emits light it also emits mass.

> >

We know that seen from another point in space, the speed of light can be different if space-time is curved (as it usually is..) You may then claim that it is only an 'apparent' slowing down if e.g. light falls into a black hole, but then we only change the discussion to the meaning of 'apparent' and 'really'. We can't maintain that it is unobservable, in that case.

>	That's just an argument over the meanings of words. Moreover it's an argument that never comes up because the constancy of the vacuum speed of light applies only locally.

Does that implies that globally, considering a light pulse (explosion) emitted over a long distance, that its speed is not constant?

Is this text from Wikipedia true?: "Photons are massless,[a] so they always move at the speed of light in vacuum, 299792458 m/s (or about 186,282 mi/s). [a] The photon's invariant mass (also called "rest mass" for massive particles) is believed to be exactly zero. This is the notion of particle mass generally used by modern physicists. The photon does have a nonzero relativistic mass, depending on its energy, but this varies according to the frame of reference."

Nicolaas Vroom

22 relativistic gamma factor maximum

On 6/28/21 8:28 AM, Nicolaas Vroom wrote:

>	I have to measure the speed of light and I have to measure the speed of an electron v_e or of a cosmic ray.[...]

Before worrying about that, you should first study significant digits, experimental resolutions, and errorbars. That will give you perspective about your questions. Your example numbers are unrealistic and unworkable, which that study would teach you to avoid.

>	A more advanced question is what to do in case the speed of cosmic ray is higher than the speed of light i.e 299792458,0995 m/sec versus 299792458 m/sec in vacuum.

That study will also teach you how to handle this -- such a measurement is OK and not unexpected, as long as your measurement resolution is about 0.04 m/sec or larger.

Tom Roberts

23 relativistic gamma factor maximum

On 6/29/21 1:41 AM, J. J. Lodder wrote:

>	[...] The speed of light cannot 'really' be variable. [...]

You make far too many assumptions to be reasonable.

Certainly the (vacuum) speed of light COULD vary, it's just that in the world we inhabit, with current technology, it is observed to not vary significantly (when measured using standard clocks and rulers at rest in some locally inertial frame). But it certainly is possible that in the future we will develop technology with greatly improved resolution and discover that it actually does vary in the world we inhabit. It is also possible we will never find it varies -- science is a JOURNEY, not a destination.

Yes, c is really a units conversion factor, IN THE SPACETIME MODEL. And yes, it is not possible for the symmetry speed of Lorentzian manifolds to vary. But the restriction you imagine is on that symmetry speed, and not really on the (vacuum) speed of light -- there is no fundamental reason why light must propagate at the symmetry speed.

Note that it is an historical accident that we call the symmetry speed of Lorentzian manifolds by the name "the speed of light" (with "vacuum" implied). Light really has nothing to do with it.

Tom Roberts

24 relativistic gamma factor maximum

Phillip Helbig (undress to reply) wrote:

>	In article <1pbi21w.1t8rob81hgck0aN%nos...@de-ster.demon.nl>, nos...@de-ster.demon.nl (J. J. Lodder) writes:

> >	Phillip Helbig (undress to reply) wrote:

>>>	In article , Thomas Koenig writes:

>>>>	Nicolaas Vroom schrieb:

>>>>>

Of course you could claim that the speed of light is constant.

>>>>	The way that the SI units are defined now, the speed of light in vacuum is indeed constant. If you measure anything else than 299792458 m/s, recalibrate your measurement devices.

>>>	The speed of light is now a defined quantity, that is true. However, that is merely a practical matter. If the speed of light really were variable, that could still be detected just as easily as before the redefinition.

>>	It is incredible how much misunderstanding there is on such a simple subject.

>	I agree. :-)

> >	To clear things up: The speed of light cannot 'really' be variable.

>	It is true that the metre is now defined as the distance travelled by light in a certain time and thus by definition the speed of light is constant. However, the metre (and the second) used to be defined differently than they are now.

Certainly, the definitions have changed several times even.

>	Back then, it was certainly possible, in principle, to detect a change in the speed of light.

Yes, but what would this mean? [1] The changes would have depended on the particular -human- choices made for the definitions of those units. And even so, my point stands. The only physically sound way of defining those independent length and time units is to chose them in mutally compatible ways. (so with a factor c between them, for example both based on atomic hyperfine structure)

>	One could perform the same experiment today.

That's another common misunderstanding. Those experiments -are- done routinely in standards labs. Only the name differs, they are nowadays called: 'the calibration of a secondary meter standard'.

>	Nature doesn't know what the current SI definitions are.

A forteriori, nature doesn't know what units are at all. All units are LGM or human inventions.

>	The metre is now defined as it is a) as a practical matter and b) because we assume that the speed of light is constant.

We assume nothing about that. We define it to be the case. (and take the consequences, if any, somewhere else)

>

If the speed of light did change, i.e. of one does observations like those of R�mer, Fizeau, etc., using, say, pendulum clocks as a reference, and notice that it changes, then one has measured the change. The consequence would not be to point to the SI definition and say that it cannot change, therefore we must modify other definitions (perhaps even periodically if the speed of light depends on time), but rather would be to realize that our assumptions in the current definition of the metre are wrong and must be changed.

Certainly. If yesterday's pistons won't fit tomorrow's engines we must overhaul all of our physics.

>	Think about the definition of the metre and kilogram. Why are the original definitions not used? One reason is because on noticed that the mass of the reference kilogram has actually changed with time.

Not really. All that we can say is that we can't reproduce the relative mass of certain chunks of metal as accurately as we thought we could. (reasons mostly unknown) That's why the kilo is now locked to Planck's constant, with, one hopes, better reproducibility.

>	By your logic, that should not have been possible, since, by definition, the reference kilogram has a mass of exactly one kilogram. Nevertheless, the change was detected.

See above, no. The other so-called kilograms may have changed instead. Only if all metal kilograms drift in the same way wrt Planck there will be a new problem.

Jan

[1] For your amusement: there is creationist folklore about the speed of light. Taking a handful of the very first measurements from the 19th century (with large errors)

25 relativistic gamma factor maximum

Phillip Helbig (undress to reply) wrote:

>	In article <1pbi21w.1t8rob81hgck0aN%nos...@de-ster.demon.nl>, nos...@de-ster.demon.nl (J. J. Lodder) writes:

>>	Phillip Helbig (undress to reply) wrote:

>>>	In article , Thomas Koenig writes:

>>>>	Nicolaas Vroom schrieb:

>>>>>

Of course you could claim that the speed of light is constant.

>>>>	The way that the SI units are defined now, the speed of light in vacuum is indeed constant. If you measure anything else than 299792458 m/s, recalibrate your measurement devices.

>>>	The speed of light is now a defined quantity, that is true. However, that is merely a practical matter. If the speed of light really were variable, that could still be detected just as easily as before the redefinition.

>>	It is incredible how much misunderstanding there is on such a simple subject.

>	I agree. :-)

>>	To clear things up: The speed of light cannot 'really' be variable.

>	It is true that the metre is now defined as the distance travelled by light in a certain time and thus by definition the speed of light is constant. However, the metre (and the second) used to be defined differently than they are now.

Certainly, the definitions have changed several times even.

>	Back then, it was certainly possible, in principle, to detect a change in the speed of light.

Yes, but what would this mean? [1] The changes would have depended on the particular -human- choices made for the definitions of those units. And even so, my point stands. The only physically sound way of defining those independent length and time units is to chose them in mutally compatible ways. (so with a factor c between them, for example both based on atomic hyperfine structure)

>	One could perform the same experiment today.

That's another common misunderstanding. Those experiments -are- done routinely in standards labs. Only the name differs, they are nowadays called: 'the calibration of a secondary meter standard'.

>	Nature doesn't know what the current SI definitions are.

A forteriori, nature doesn't know what units are at all. All units are LGM or human inventions.

>	The metre is now defined as it is a) as a practical matter and b) because we assume that the speed of light is constant.

We assume nothing about that. We define it to be the case. (and take the consequences, if any, somewhere else)

>

If the speed of light did change, i.e. of one does observations like those of R�mer, Fizeau, etc., using, say, pendulum clocks as a reference, and notice that it changes, then one has measured the change. The consequence would not be to point to the SI definition and say that it cannot change, therefore we must modify other definitions (perhaps even periodically if the speed of light depends on time), but rather would be to realize that our assumptions in the current definition of the metre are wrong and must be changed.

Certainly. If yesterday's pistons won't fit tomorrow's engines we must overhaul all of our physics.

>	Think about the definition of the metre and kilogram. Why are the original definitions not used? One reason is because on noticed that the mass of the reference kilogram has actually changed with time.

Not really. All that we can say is that we can't reproduce the relative mass of certain chunks of metal as accurately as we thought we could. (reasons mostly unknown) That's why the kilo is now locked to Planck's constant, with, one hopes, better reproducibility.

>	By your logic, that should not have been possible, since, by definition, the reference kilogram has a mass of exactly one kilogram. Nevertheless, the change was detected.

See above, no. The other so-called kilograms may have changed instead. Only if all metal kilograms drift in the same way wrt Planck there will be a new problem.

Jan

[1] For your amusement:
there is creationist folklore about the speed of light. Taking a handful of the very first measurements from the 19th century (with large errors) they conclude that the speed of light varies enormously. And (you could not possibly have guessed it of course) so enormously that the apparent age of the universe of billions of years fits precisely with the creation of the earth 6000 years ago.

26 relativistic gamma factor maximum

Op dinsdag 29 juni 2021 om 08:51:03 UTC+2 schreef Nicolaas Vroom:

>	Op zondag 27 juni 2021 om 00:57:19 UTC+2 schreef Phillip Helbig: Nicolaas Vroom. [[Mod. note -- This topic is a bit tricky, because to measure a speed in meters/second, we need to know what a meter is, and what a second is.

That is correct

>

"The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second." So with this definition, the speed of light is necessarily exactly 299 792 458 meters/second. Experiments to "measure the speed of light" (e.g., by timing a light pulse over a measured distance) are actually measuring a *length* (in meters). E.g., if your measurement shows that it takes light 100 nanoseconds to travel a certain distance, then what you've really done is measure that distance to be (as 100e-9 seconds * 299 792 458 meters/second) = 29.9792458 meters.

That is the measurement by person "A" in vacuum. What that means that "A" first places two markers a certain distance away and then sends a light signal between those two markers.
What "A" measures is that it takes 100 nanoseconds to travel that distance. His conclusion is that the distance is 29.9792458 meters.

Suppose "B" does 'exactly' the same, but "B" measures that it takes less than 100 nanosecs and his is conclusion is that the distance is 29.9792458 meters.

Is that physical possible? In order for "B" to perform the experiment he has to rely on a very detailed description (supplied by "A" or ?), on how to perform this experiment. For example it should tell you how to measure the time (everywhere in the universe) and give a clear definition exactly what a vacuum is.
This type of information is of critical importance to calculate the distance travelled by a light pulse and secondly to establish if that distance is everywhere the same. Implying that the speed of light is a physical constant and also everywhere the same. (Personally I doubt that)

The same type of description is also required if you want to measure the speed of an electron or a cosmic ray. In that case you first have to measure the 'fixed' distance using a light pulse, secondly you have to measure the time t2 it takes for the cosmic ray to travel that same 'fixed' distance. Dividing the 'fixed' distance by t2 gives you the speed of the cosmic ray.

Nicolaas Vroom

27 relativistic gamma factor maximum

Op dinsdag 29 juni 2021 om 20:49:55 UTC+2 schreef Jos Bergervoet:

>	On 21/06/29 8:41 AM, J. J. Lodder wrote:

> >	It is incredible how much misunderstanding there is on such a simple subject.

>	I think there are several reasons for it. See below..

> >	The speed of light cannot 'really' be variable. Why?

Why can the speed of light not be different in different places in the universe

> >	In order for the speed of light to be measurable at all we need to define both a length and a time unit. ...

The time unit is the most tricky if the method to measure time involves light signals and when you want to use time to measure the speed of light. This looks like circular reasoning.

>	Indeed we can agree that basically this is determined by the metric of space.

Exactly what is determined by the metric of space? This raises also the question how is this metric measured.

>	Any massless field will have a propagation speed defined by the metric, but any measurement of speed also has to use that metric. So the result is fixed.

This also looks like circular reasoning.

In Newtonian context the first thing you have to observe the objects studied (positions and speeds) during a certain period. Important is: That these observations require the speed of light. Secondly using Newton's Law you can calculate the masses of the objects studied. That calculation does not require the speed of light

>	This should make clear that a change cannot be observed using the local metric, but not everyone will agree that this means it cannot 'really' change. We know that seen from another point in space, the speed of light can be different if space-time is curved (as it usually is..)

I assume when objects are involved. Tricky sentence. What means seen? Normally seen implies the speed of light.

>	All these things explain the ongoing discussion, I think..

The ongoing discussion involves both the speed of light and the speed of a cosmic ray. The issue is to describe how both are defined and how both are actual measured in a clear and unambiguous manner. That is not easy.

Nicolaas Vroom

28 relativistic gamma factor maximum

In article , Nicolaas Vroom writes:

>	Op woensdag 30 juni 2021 om 21:37:22 UTC+2 schreef Tom Roberts:

> >	On 6/29/21 1:49 PM, Jos Bergervoet wrote:

> > >

Indeed we can agree that basically this is determined by the metric of space. Any massless field will have a propagation speed defined by the metric, but any measurement of speed also has to use that metric. So the result is fixed.

> >	You mean the metric of spacetime (not space). And this applies only to a massless field -- there is no fundamental reason for the photon to be massless, it's just that its mass is observed to be consistent with zero and an extremely tiny upper limit (< 10^-18 eV).

>	How is this mass observed? Or should I write upper limit?

The upper limit comes from the observed accuracy of the inverse-square law. Also, if photons had rest mass, then photons of different energies would travel at different speeds. That effect is used to set limits on neutrino masses.

>	Is it not true, that when it is possible to measure the energy of a light pulse, that then individual photons also have energy, and as a consequence individual photons also have a mass?

E = mc^2 so in that sense photons have mass...

>	This implies when a star emits light it also emits mass.

...and as a result the mass of a star decreases when it emits light.

The question is whether the rest mass is zero.

> > >

We know that seen from another point in space, the speed of light can be different if space-time is curved (as it usually is..) You may then claim that it is only an 'apparent' slowing down if e.g. light falls into a black hole, but then we only change the discussion to the meaning of 'apparent' and 'really'. We can't maintain that it is unobservable, in that case.

> >	That's just an argument over the meanings of words. Moreover it's an argument that never comes up because the constancy of the vacuum speed of light applies only locally.

>	Does that implies that globally, considering a light pulse (explosion) emitted over a long distance, that its speed is not constant?

Look up "Shapiro delay".

>

Is this text from Wikipedia true?: "Photons are massless,[a] so they always move at the speed of light in vacuum, 299792458 m/s (or about 186,282 mi/s). [a] The photon's invariant mass (also called "rest mass" for massive particles) is believed to be exactly zero. This is the notion of particle mass generally used by modern physicists. The photon does have a nonzero relativistic mass, depending on its energy, but this varies according to the frame of reference."

Yes.

29 relativistic gamma factor maximum

Nicolaas Vroom wrote:

>	Op dinsdag 29 juni 2021 om 08:51:03 UTC+2 schreef Nicolaas Vroom:

> >	Op zondag 27 juni 2021 om 00:57:19 UTC+2 schreef Phillip Helbig: Nicolaas Vroom. [[Mod. note -- This topic is a bit tricky, because to measure a speed in meters/second, we need to know what a meter is, and what a second is.

>	That is correct

> >

"The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second." So with this definition, the speed of light is necessarily exactly 299 792 458 meters/second. Experiments to "measure the speed of light" (e.g., by timing a light pulse over a measured distance) are actually measuring a *length* (in meters). E.g., if your measurement shows that it takes light 100 nanoseconds to travel a certain distance, then what you've really done is measure that distance to be (as 100e-9 seconds * 299 792 458 meters/second) = 29.9792458 meters.

>

That is the measurement by person "A" in vacuum. What that means that "A" first places two markers a certain distance away and then sends a light signal between those two markers. What "A" measures is that it takes 100 nanoseconds to travel that distance. His conclusion is that the distance is 29.9792458 meters. Suppose "B" does 'exactly' the same, but "B" measures that it takes less than 100 nanosecs and his is conclusion is that the distance is 29.9792458 meters. Is that physical possible? In order for "B" to perform the experiment he has to rely on a very detailed description (supplied by "A" or ?), on how to perform this experiment. For example it should tell you how to measure the time (everywhere in the universe) and give a clear definition exactly what a vacuum is. This type of information is of critical importance to calculate the distance travelled by a light pulse and secondly to establish if that distance is everywhere the same. Implying that the speed of light is a physical constant and also everywhere the same. (Personally I doubt that) The same type of description is also required if you want to measure the speed of an electron or a cosmic ray. In that case you first have to measure the 'fixed' distance using a light pulse, secondly you have to measure the time t2 it takes for the cosmic ray to travel that same 'fixed' distance. Dividing the 'fixed' distance by t2 gives you the speed of the cosmic ray. Nicolaas Vroom

Eh, I don't want to increase your confusions further, but all accurate laboratory 'speed of light' measurements were done using --standing waves--. No propagation timing involved,

Jan

30 relativistic gamma factor maximum

Tom Roberts wrote:

>	On 6/29/21 1:41 AM, J. J. Lodder wrote:

> >	[...] The speed of light cannot 'really' be variable. [...]

>	You make far too many assumptions to be reasonable. Certainly the (vacuum) speed of light COULD vary, it's just that in the world we inhabit, with current technology, it is observed to not vary significantly (when measured using standard clocks and rulers at rest in some locally inertial frame).

That's where you are mistaken. There is no such thing as a god-given 'standard clock' or 'standard ruler'.

>	But it certainly is possible that in the future we will develop technology with greatly improved resolution and discover that it actually does vary in the world we inhabit.

A meaningless statement.
If variation is found we will have to discover (or decide!) what it is that varies. (speed?, rulers?, clocks?, all three?, some 'fundamental' 'constant'?)

>	It is also possible we will never find it varies -- science is a JOURNEY, not a destination.

Empty ideology.
This is not a matter that can be settled by means of naive empiricism, by just 'measuring' the 'speed of light',

Jan

31 relativistic gamma factor maximum

Thomas Koenig wrote:

>	Nicolaas Vroom schrieb:

> >	Ofcourse you could claim that the speed of light is constant.

>	The way that the SI units are defined now, the speed of light in vacuum is indeed constant. If you measure anything else than 299792458 m/s, recalibrate your measurement devices.

Nonsense. In the SI as it stands it is impossible in principle to measure the speed of light,

Jan

32 relativistic gamma factor maximum

Tom Roberts wrote:

>	On 6/29/21 1:49 PM, Jos Bergervoet wrote:

> >	Indeed we can agree that basically this is determined by the metric of space. Any massless field will have a propagation speed defined by the metric, but any measurement of speed also has to use that metric. So the result is fixed.

>	You mean the metric of spacetime (not space). And this applies only to a massless field -- there is no fundamental reason for the photon to be massless, it's just that its mass is observed to be consistent with zero and an extremely tiny upper limit (< 10^-18 eV).

> >	This should make clear that a change cannot be observed using the local metric, but not everyone will agree that this means it cannot 'really' change.

>	The constancy of the vacuum speed of light applies only locally, so everyone who understands the issues will agree for a massless field. But of course that's the rub -- we don't really know whether the photon field is truly massless.

Why this insistence on photons being or not being 'truly' massless? It is nothing but a red herring. All troubles that might arise from a non-zero photon mass are easily killed in advance by adding 'in the limit of infinite frequence' to the definition of the speed of light.

Since the photon mass cannot be measured, even the longest radio waves that we can make still have an 'infinite' frequency.

> >

We know that seen from another point in space, the speed of light can be different if space-time is curved (as it usually is..) You may then claim that it is only an 'apparent' slowing down if e.g. light falls into a black hole, but then we only change the discussion to the meaning of 'apparent' and 'really'. We can't maintain that it is unobservable, in that case.

>

That's just an argument over the meanings of words. Moreover it's an argument that never comes up because the constancy of the vacuum speed of light applies only locally. All this only applies to massless fields, and we don't really know whether the photon field is truly massless. Of course we never will....

Indeed, and of course not. A photon mass corresponding to a wavelength of the size of the universe cannot be measured in principle. Our poor photon has only a few decades left to have mass in,

Jan

33 relativistic gamma factor maximum

In article <1pbx3kk.jywko91341fc9N%nos...@de-ster.demon.nl>, nos...@de-ster.demon.nl (J. J. Lodder) writes:

>	Tom Roberts wrote:

> >	On 6/29/21 1:41 AM, J. J. Lodder wrote:

> > >

[...] The speed of light cannot 'really' be variable. [...]

> >	You make far too many assumptions to be reasonable. Certainly the (vacuum) speed of light COULD vary, it's just that in the world we inhabit, with current technology, it is observed to not vary significantly (when measured using standard clocks and rulers at rest in some locally inertial frame).

>	That's where you are mistaken. There is no such thing as a god-given 'standard clock' or 'standard ruler'.

> >	But it certainly is possible that in the future we will develop technology with greatly improved resolution and discover that it actually does vary in the world we inhabit.

>	A meaningless statement. If variation is found we will have to discover (or decide!) what it is that varies. (speed?, rulers?, clocks?, all three?, some 'fundamental' 'constant'?)

> >	It is also possible we will never find it varies -- science is a JOURNEY, not a destination.

>	Empty ideology. This is not a matter that can be settled by means of naive empiricism, by just 'measuring' the 'speed of light',

One could measure the speed of light via several different types of rulers and clocks, or by measuring wavelength and frequency, or whatever, in the lab. It is theoretically possible that the speed of light could change with time and that we could measure it.

The fact that the speed of light is now a defined quantity does not somehow magically make it impossible to make a measurement which was possible with the original SI definitions.

Obviously, if such a change were detected, then it would be a good idea to change the definition of the metre.

34 relativistic gamma factor maximum

In article <1pbx48j.1xmowyy1fnnxmfN%nos...@de-ster.demon.nl>, nos...@de-ster.demon.nl (J. J. Lodder) writes:

>	Thomas Koenig wrote:

> >	Nicolaas Vroom schrieb:

> > >

Ofcourse you could claim that the speed of light is constant.

> >	The way that the SI units are defined now, the speed of light in vacuum is indeed constant. If you measure anything else than 299792458 m/s, recalibrate your measurement devices.

>	Nonsense. In the SI as it stands it is impossible in principle to measure the speed of light,

Because, for practical reasons, the metre is now defined as the distance light travels in a certain time. That is our definition, which Nature doesn't know about. We cannot magically influence Nature by changing definitions.

With time, more and more SI units have been defined via fiat values of constants of Nature. This is a purely practical matter, because we ASSUME that they do not change with time. The definitions are also coupled with experiments which are relatively easy to reproduce.

Back when the metre was defined as 1/10,000,000 of the distance from north pole to equator along the meridian through Paris, that did not somehow make it impossible to measure the change in the size of the Earth with time.

***

35 relativistic gamma factor maximum

On 7/5/21 6:49 AM, Nicolaas Vroom wrote:

>	Op woensdag 30 juni 2021 om 21:37:22 UTC+2 schreef Tom Roberts:

>>	[...] there is no fundamental reason for the photon to be massless, it's just that its mass is observed to be consistent with zero and an extremely tiny upper limit (< 10^-18 eV).

>	How is this mass observed? Or should I write upper limit?

36 relativistic gamma factor maximum

Op maandag 5 juli 2021 om 20:45:32 UTC+2 schreef Phillip Helbig:

>	In article , Nicolaas Vroom writes:

> >	Op woensdag 30 juni 2021 om 21:37:22 UTC+2 schreef Tom Roberts:

> > >

That's just an argument over the meanings of words. Moreover it's an argument that never comes up because the constancy of the vacuum speed of light applies only locally.

> >	Does that implies that globally, considering a light pulse (explosion) emitted over a long distance, that its speed is not constant?

>	Look up "Shapiro delay".

37 relativistic gamma factor maximum

On 7/7/21 3:31 AM, J. J. Lodder wrote:

>	Tom Roberts wrote:

>>	Certainly the (vacuum) speed of light COULD vary, it's just that in the world we inhabit, with current technology, it is observed to not vary significantly (when measured using standard clocks and rulers at rest in some locally inertial frame).

>	There is no such thing as a god-given 'standard clock' or 'standard ruler'.

Of course. Such standards are determined by humans. Organizations such as ISO have been created to agree upon such standards and publish them.

It OUGHT to be obvious that a standard clock measures its elapsed proper time using standard seconds, and a standard ruler measures distance using some standard of length, such as meters.

>>	But it certainly is possible that in the future we will develop technology with greatly improved resolution and discover that it actually does vary in the world we inhabit.

>	A meaningless statement. If variation is found we will have to discover (or decide!) what it is that varies. (speed?, rulers?, clocks?, all three?, some 'fundamental' 'constant'?)

My statement is not meaningless: if the speed of light is measured to vary, then it is certainly varying -- DUH!

Whether something else is also varying is a different question; to date no significant variation has been found in any of the things you mention. Such measurements have excellent accuracy, 9 or more significant digits.

>	This is not a matter that can be settled by means of naive empiricism, by just 'measuring' the 'speed of light',

How else could one detect a variation in the speed of light????

Tom Roberts

38 relativistic gamma factor maximum

On 7/7/21 12:20 PM, J. J. Lodder wrote:

>	Tom Roberts wrote:

>>	The constancy of the vacuum speed of light applies only locally, so everyone who understands the issues will agree for a massless field. But of course that's the rub -- we don't really know whether the photon field is truly massless.

>	Why this insistence on photons being or not being 'truly' massless?

Because it is an important aspect of whether the (vacuum) speed of light varies. In our current best models of the world, nonzero photon mass and a varying vacuum speed of light are equivalent (either both are valid or both are invalid).

>	All troubles that might arise from a non-zero photon mass are easily killed in advance by adding 'in the limit of infinite frequence' to the definition of the speed of light.

But a) we don't do that, and b) that would make it impossible to actually measure the speed of light, one could only measure it approximately -- hopeless for such a fundamental aspect of the world we inhabit, and one used in so much technology.

The correct way to deal with a nonzero photon mass is to distinguish between the two quite different meanings of c:
1) the vacuum speed of light
2) the symmetry speed of Lorentzian manifolds
If (1) is found to vary, no fundamental revolution in physics is involved, we just start using a nonzero photon mass [#]. If (2) is found to vary, it would refute every theory of physics we have today.

[Historically, in 1905 this distinction was not known and Einstein intermixed them inappropriately. His second postulate is actually about (2), not (1). Today we consider SR to be a theory of geometry, not electrodynamics (the subject of his 1905 paper).]

[#] See Proca theory.

>	Since the photon mass cannot be measured, even the longest radio waves that we can make still have an 'infinite' frequency.

This is just plain wrong: a) The photon mass has been measured many times; at present the best measurements are consistent with zero and an upper limit of 10^-18 eV. b) EM waves with frequencies from kilohertz to terahertz have been measured -- NONE are "infinite".

>	A photon mass corresponding to a wavelength of the size of the universe cannot be measured in principle.

Hmmmm. Mass does not "correspond" to wavelength in any way.

Tom Roberts

39 relativistic gamma factor maximum

On 7/5/21 1:45 PM, Phillip Helbig (undress to reply) wrote:

>	In article , Nicolaas Vroom writes:

>>	tindividual photons also have energy, and as a consequence individual photons also have a mass?

>	E = mc^2 so in that sense photons have mass...

That is not mass in any sense, that is ENERGY.

>>	This implies when a star emits light it also emits mass.

No, the light it emits carries no mass.

>	...and as a result the mass of a star decreases when it emits light.

Yes, even though the light itself carries no mass. As the star emits light with total energy E, the star's mass decreases by m, with E=mc^2. This is what that equation actually means, not your misinterpretation above.

>	The question is whether the rest mass is zero.

"Rest mass" is an archaic term. Today "mass" refers to the norm of an object's 4-momentum. In the object's rest frame that corresponds to its energy [#]. The "c" in E=mc^2 is just a units conversion factor; physicists often use units with c=1 and omit "c" from equations. So, for instance, the PDG now lists particle masses in Ev, not the older Ev/c^2.

[#] This of course does not apply to light, which has no rest frame. "Rest mass" could never apply to light; mass does, and is zero.

Tom Roberts

40 relativistic gamma factor maximum

Op maandag 12 juli 2021 om 19:18:57 UTC+2 schreef Nicolaas Vroom:

>	Op woensdag 7 juli 2021 om 19:20:49 UTC+2 schreef Phillip Helbig:

> >	Because, for practical reasons, the metre is now defined as the distance light travels in a certain time. That is our definition,

>	[[Mod. note -- An old nautical saying is "never go to sea with two chronometers; always take one or three".

In process control the best way to implement redundancy is: triple redundancy.

>

In this context, that means that people doing precision timing & clock development often use an an ensemble of co-located clocks (typically 5-10 are used), all of similar construction and method-of-operation, so that they can inter-compare the clocks. Since all the clocks in the ensemble are co-located, they should all record the same elapsed-time readings; more accurately, any differences in their elapsed-time readings can be ascribed to clock drifts (errors). Inter-comparing the clocks can thus give a statistical estimate of the clocks' accuracy If any clock is an outlier in the ensemble, it's flagged as not-working-properly (a.k.a "broken").

I fully agree with you. But the experiment we are discussing here is slightly different. Starting point is the text by Tom Roberts:

>	Your premise is wrong -- we do not use the speed of light to determine the unit of time. The second is defined as the duration of 9,192,631,770 cycles of the hyperfine ground-state transition of Cs-133.

That means first we use this clock to measure 1 second. This defines two moments t1 (start pulse) and t2 (stop pulse) Secondly we use these two events to transmit a light ray at t1 at position p1 and mark the position p2 (along a rod) of the light ray at t2. As described by Phillip Helbig. The length between p2 and p1 defines the standard distance of 299792458 m. The problem is that it is very difficult to establish the position p2 of the light ray at t2. What you need? is a clock at p2 and when that clock reaches 9,192,631,770 cycles the light signal should arrive from p1 simultaneous. IMO this does not work because exactly where should you place this clock? I hope that someone comes up with better detailed standard description how to perform this experiment accurate, such that others can perform the same.

Using such a standard experiment we can now perform many experiments: 1) at the same location and observe if all the distances are the same. 2) at different locations and observe if all the distances are the same. In case 1, in principle, all people should measure the same distance but I expect they will not. The major reason is inaccuracy inherent in the experiment. In case 2, all people don't have to measure the same distance. The major reason is that the speed of light is not the same in all directions, caused by gravity considerations.

Nicolaas Vroom

41 relativistic gamma factor maximum

Phillip Helbig (undress to reply) wrote:

>	In article <1pbx48j.1xmowyy1fnnxmfN%nos...@de-ster.demon.nl>, nos...@de-ster.demon.nl (J. J. Lodder) writes:

> >	Thomas Koenig wrote:

> > >

Nicolaas Vroom schrieb:

> > > >

Ofcourse you could claim that the speed of light is constant.

> > >

The way that the SI units are defined now, the speed of light in vacuum is indeed constant. If you measure anything else than 299792458 m/s, recalibrate your measurement devices.

> >	Nonsense. In the SI as it stands it is impossible in principle to measure the speed of light,

>	Because, for practical reasons, the metre is now defined as the distance light travels in a certain time. That is our definition, which Nature doesn't know about. We cannot magically influence Nature by changing definitions.

Nature doesn't know about our definitions, but we had better chose our definitions in ways that agree with what nature is like. To the best of our knowledge we live in a spacetime that is characterised by an absolute velocity, confusingly also called c. If this is indeed the case we have to choose our length and time units in accordance with this fundamental fact. (like the SI already does) If physical things (such as G or alpha for example) are indeed variable we would otherwise obtain unphysical results, such as deluding ourselves into a belief that c could be variable.

>

With time, more and more SI units have been defined via fiat values of constants of Nature. This is a purely practical matter, because we ASSUME that they do not change with time. The definitions are also coupled with experiments which are relatively easy to reproduce. Back when the metre was defined as 1/10,000,000 of the distance from north pole to equator along the meridian through Paris, that did not somehow make it impossible to measure the change in the size of the Earth with time.

This meridian of the earth thing was never more than a propaganda device. For metrological reasons anno 1800 a length standard could only be two scratches on a metal bar. A reason had to be invented to declare a particular pair of scratches on a particular better than all others. (to break all local chauvinisms) As a matter of historical fact the earth was never remeasured for obtaining a more accurate meter,

Jan

42 relativistic gamma factor maximum

Phillip Helbig (undress to reply) wrote:

>	In article <1pbx3kk.jywko91341fc9N%nos...@de-ster.demon.nl>, nos...@de-ster.demon.nl (J. J. Lodder) writes:

> >	Tom Roberts wrote:

> > >

On 6/29/21 1:41 AM, J. J. Lodder wrote:

> > > >

[...] The speed of light cannot 'really' be variable. [...]

> > >

You make far too many assumptions to be reasonable. Certainly the (vacuum) speed of light COULD vary, it's just that in the world we inhabit, with current technology, it is observed to not vary significantly (when measured using standard clocks and rulers at rest in some locally inertial frame).

> >	That's where you are mistaken. There is no such thing as a god-given 'standard clock' or 'standard ruler'.

> > >

But it certainly is possible that in the future we will develop technology with greatly improved resolution and discover that it actually does vary in the world we inhabit.

> >	A meaningless statement. If variation is found we will have to discover (or decide!) what it is that varies. (speed?, rulers?, clocks?, all three?, some 'fundamental' 'constant'?)

> > >

It is also possible we will never find it varies -- science is a JOURNEY, not a destination.

> >	Empty ideology. This is not a matter that can be settled by means of naive empiricism, by just 'measuring' the 'speed of light',

>	One could measure the speed of light via several different types of rulers and clocks, or by measuring wavelength and frequency, or whatever, in the lab. It is theoretically possible that the speed of light could change with time and that we could measure it.

That is utterly and thoroughly wrong. You can potter about with all kinds of measuring equipment, and you might see that things vary. That you have measured the speed of light to be varying must be a theoretical assumption. Your units could be changing instead. (as a result of something else changing, alpha for example)

>	The fact that the speed of light is now a defined quantity does not somehow magically make it impossible to make a measurement which was possible with the original SI definitions.

You can still do exactly the same measurements. (and in fact these are done routinely) Only the interpretation has changed. What used to be called 'a speed of light measurement' is nowadays called 'the calibration of a (secondary) meter standard'.

>	Obviously, if such a change were detected, then it would be a good idea to change the definition of the metre.

You would need a lot of much better ideas than that, such as reinventing spacetime,

Jan

43 relativistic gamma factor maximum

Tom Roberts wrote:

>	On 7/7/21 3:31 AM, J. J. Lodder wrote:

> >	Tom Roberts wrote:

> >>	Certainly the (vacuum) speed of light COULD vary, it's just that in the world we inhabit, with current technology, it is observed to not vary significantly (when measured using standard clocks and rulers at rest in some locally inertial frame).

> >	There is no such thing as a god-given 'standard clock' or 'standard ruler'.

>	Of course. Such standards are determined by humans. Organizations such as ISO have been created to agree upon such standards and publish them.

Which makes them arbitrary.

>	It OUGHT to be obvious that a standard clock measures its elapsed proper time using standard seconds, and a standard ruler measures distance using some standard of length, such as meters.

Certainly, if considered in a purely tautological sense.

> >>	But it certainly is possible that in the future we will develop technology with greatly improved resolution and discover that it actually does vary in the world we inhabit.

> >	A meaningless statement. If variation is found we will have to discover (or decide!) what it is that varies. (speed?, rulers?, clocks?, all three?, some 'fundamental' 'constant'?)

>	My statement is not meaningless: if the speed of light is measured to vary, then it is certainly varying -- DUH!

Do explain how you can 'measure' the speed of light in a -natural- way, without introducing arbitrary, human made units.

>	Whether something else is also varying is a different question; to date no significant variation has been found in any of the things you mention. Such measurements have excellent accuracy, 9 or more significant digits.

> >	This is not a matter that can be settled by means of naive empiricism, by just 'measuring' the 'speed of light',

>	How else could one detect a variation in the speed of light????

The answer is that one can't. To be able to measure anything at all you need to know what the space-time is.

The speed of light can only become variable if you begin by inventing a new space-time in which the relativity postulate does not hold. (so you have to build a new foundation for all of phyics) Next you have to work out how measurements are to be done in this new space-time, and how that relates to real physical measurements.

It is only after all that has been accomplished that you can begin to talk about measuring a variable speed of light.

Again, the problem is not faffing about with all kinds of measurement equipment. The problem is to give a meaningful interpretation, based on deeper lying concepts of space and time, of what you think that you are doing.

Jan

44 relativistic gamma factor maximum

Nicolaas Vroom wrote:

>	Op woensdag 7 juli 2021 om 19:20:49 UTC+2 schreef Phillip Helbig:

> >	In article <1pbx48j.1xmowyy1fnnxmfN%nos...@de-ster.demon.nl>, nos...@de-ster.demon.nl (J. J. Lodder) writes:

> > >

Thomas Koenig wrote:

> > > >

The way that the SI units are defined now, the speed of light in vacuum is indeed constant. If you measure anything else than 299792458 m/s, recalibrate your measurement devices.

> > >

Nonsense. In the SI as it stands it is impossible in principle to measure the speed of light,

> >	Because, for practical reasons, the metre is now defined as the distance light travels in a certain time. That is our definition,

>	Etc, You can do that, but now you create a new issue: How is this CERTAIN TIME defined and more important measured in detail in practice.

The practical answer is that the 'certain time' is effectively infinite. Precision light speed measurements were done with standing waves. (when these were still done, nowadays meter standard calibrations)

>

That is a very important issue because we can all measure the same time, but when we compare all the distances measured, (which should be identical) they are not. That means at the most 1 person measures the distance of 299792458 meters correct assuming we all measure 1 second. It is the same as the above ambiguous advice: "YOU should recalibrate your measurement device." But if my measurement also is different from all of the others how much should I adapt my time measurement device? The above raised issue about CERTAIN TIME becomes even more important if you want to measure the speed of a cosmic ray (etc).

You calibrate the wavelength of your stabilised laser, somebody else calibrates his, and when you communicate your results should agree, within statistical errors.

>	[[Mod. note -- An old nautical saying is "never go to sea with two chronometers; always take one or three".

Indeed. [OT amusement, if moderators permit] Naval chronometers could have sudden jumps in their going rates for various reasons. Take one, and you hope for the best. Take two and you go crazy when they start to diverge. (which one is right, so where am I ????) Take three and you can hope to identify the faulty one.

These were quite practical matters, literally matters of life or death. Having rounded Cape of Good Hope or Cape Horn they sailed East resp. West in the Roaring Forties, and turned North to arrive where they wanted to go. Turn to late, resp to early, would get them shipwrecked on the Australian, resp. Chilean coasts,

Jan

45 relativistic gamma factor maximum

J. J. Lodder schrieb:

>	Naval chronometers could have sudden jumps in their going rates for various reasons. Take one, and you hope for the best. Take two and you go crazy when they start to diverge. (which one is right, so where am I ????) Take three and you can hope to identify the faulty one.

"To measure once leads to knowledge. To measure twice leads to doubt. To measure three times leads to statistics."

(An unattributed Internet quote which seems to be a generalization of what you wrote).

46 relativistic gamma factor maximum

Yes, but those captains had more than statistics to worry about. Their main worry was a chronometer changing its rate in an unpredictable way. [1]

Perhaps the background for this story was Royal Navy policy. They would supply one chronometer to each RN ship, unless the captain also owned one privately. In that case they would supply two, on the ground that a second one by itself would not give additional accuracy,

Jan

47 relativistic gamma factor maximum

On 21/08/07 5:09 AM, J. J. Lodder wrote:

>	Tom Roberts wrote:

>>	On 7/7/21 3:31 AM, J. J. Lodder wrote:

... ...

>>>	This is not a matter that can be settled by means of naive empiricism, by just 'measuring' the 'speed of light',

>>	How else could one detect a variation in the speed of light????

>	The answer is that one can't.

I'm afraid you are playing a game of words.. The speed of light as defined by the maximum speed allowed by the metric can indeed not change since our units have been based on it. But the speed of light defined as the propagation speed of certain field modes of the existing quantum fields can in principle still change.

>	To be able to measure anything at all you need to know what the space-time is.

What would this resolve? Do you mean we currently don't know what space-time is so we cannot measure anything at all? Or do you mean we know what space-time is, in which case the statement would not block measuring anything?!

>	The speed of light can only become variable if you begin by inventing a new space-time in which the relativity postulate does not hold.

Why? Just suppose that some quantum field (not light itself) is in a false vacuum, and at some time it falls into the true vacuum, thereby creating (through some couplings) an effective increase in the EM permittivity or permeability of vacuum? Then light would propagate slower. But neutrino's for instance could still move at the old speed (assuming they don't couple to the filed that caused the change).

>	(so you have to build a new foundation for all of phyics) Next you have to work out how measurements are to be done in this new space-time, and how that relates to real physical measurements.

This might be true, also in my given example. Probably the meter should then be redefined based on neutrino speed and not on the speed of light, and some other practices and definitions might change as well. But how does the fact that "things would change" prove that something cannot happen?

...

>	The problem is to give a meaningful interpretation, based on deeper lying concepts of space and time, of what you think that you are doing.

Absolutely true. And then the example I gave might be ruled out as being impossible, based on some of those concepts that we are certain about. But I have not seen any reasoning here that actually does so!

-- Jos

48 relativistic gamma factor maximum

[dear moderators, the moderation software, or something else, still makes a mess of the reference headers. This makes it difficult sometimes to reply to the right person, or to see who has replied to a given posting)

Tom Roberts wrote:

>	On 7/7/21 12:20 PM, J. J. Lodder wrote:

> >	Tom Roberts wrote:

> >>	The constancy of the vacuum speed of light applies only locally, so everyone who understands the issues will agree for a massless field. But of course that's the rub -- we don't really know whether the photon field is truly massless.

> >	Why this insistence on photons being or not being 'truly' massless?

>	Because it is an important aspect of whether the (vacuum) speed of light varies. In our current best models of the world, nonzero photon mass and a varying vacuum speed of light are equivalent (either both are valid or both are invalid).

> >	All troubles that might arise from a non-zero photon mass are easily killed in advance by adding 'in the limit of infinite frequence' to the definition of the speed of light.

>	But a) we don't do that, and b) that would make it impossible to actually measure the speed of light, one could only measure it approximately -- hopeless for such a fundamental aspect of the world we inhabit, and one used in so much technology.

Your points are completely beside the subject of this sub-thread, which was the question if the speed of light can vary with -time-, and if we could in principle measure this.

>

The correct way to deal with a nonzero photon mass is to distinguish between the two quite different meanings of c: 1) the vacuum speed of light 2) the symmetry speed of Lorentzian manifolds If (1) is found to vary, no fundamental revolution in physics is involved, we just start using a nonzero photon mass [#]. If (2) is found to vary, it would refute every theory of physics we have today. [Historically, in 1905 this distinction was not known and Einstein intermixed them inappropriately. His second postulate is actually about (2), not (1). Today we consider SR to be a theory of geometry, not electrodynamics (the subject of his 1905 paper).] [#] See Proca theory.

You are discussing the by comparison trivial point whether the speed of light could depend on frequency. (through a finite photon mass for example) If so, we would measure the dispersion relation, and obtain the speed in the limit of infinite frequency. (like so many other idealisations in physics)

> >	Since the photon mass cannot be measured, even the longest radio waves that we can make still have an 'infinite' frequency.

>	This is just plain wrong: a) The photon mass has been measured many times; at present the best measurements are consistent with zero and an upper limit of 10^-18 eV. b) EM waves with frequencies from kilohertz to terahertz have been measured -- NONE are "infinite".

You are wrong in that, the photon mass has never been measured. All we have are upper limits. So -every- photon we have ever seen has an infinite frequency, as far as photon mass is concerned.

> >	A photon mass corresponding to a wavelength of the size of the universe cannot be measured in principle.

>	Hmmmm. Mass does not "correspond" to wavelength in any way.

??? \lambda = 2\pi/m, naturally, or 2\pi\hbar/mc, if you prefer plumber's units. It really does not matter how you express the characteristic for where Maxwell's equations end, as a mass, a frequency, or a wavelength,

Jan

49 relativistic gamma factor maximum

[[Mod. note -- I apologise to all for the delay in processing this article, which arrived in the moderation system on 22-Aug-2021. -- jt]]

Op woensdag 11 augustus 2021 om 18:35:46 UTC+2 schreef J. J. Lodder:

>

> >	On 7/7/21 12:20 PM, J. J. Lodder wrote:

> > >

Tom Roberts wrote:

> >

Because it is an important aspect of whether the (vacuum) speed of light varies. In our current best models of the world, nonzero photon mass and a varying vacuum speed of light are equivalent (either both are valid or both are invalid). But a) we don't do that, and b) that would make it impossible to actually measure the speed of light, one could only measure it approximately -- hopeless for such a fundamental aspect of the world we inhabit, and one used in so much technology.

>	Your points are completely beside the subject of this sub-thread, which was the question if the speed of light can vary with -time-, and if we could in principle measure this.

> >	The correct way to deal with a nonzero photon mass is to distinguish between the two quite different meanings of c:

When I was in high school my mathematical teacher (Mr Zweens) wrote down the mathematical equation: x + y + z = 3 (approximate recapulation)
Does that equation make sense?
Yes, in mathematical space at the point x=1, y=1, z=1
Next he wrote down the equation: x + y + z + w = 4
Does that equation make sense?
Yes, in mathematical space at the point x=1, y=1, z=1, w=1
He also could have written: x + y + z + t = 4. (x=1,y=1,z=1,t=1)
The reason was, because we were 'discussing' two 4D equations, and the 3D solution of these equations.
In reality: two 4D space equations and the 3D space solution. (or objects) Immediate came into my mind:
Yes, you can do all of that in mathematics, but does it physical make sense?
What I did not realize, approx 60 years ago, that I should have considerd the issues involved in the reverse order:
First comes the question: What does physical exists? What is real.
Second: How can we measure the physical reality?
And third: are there and which are the mathematical relations between these measurements?

In the text above I have the same problem:
First you must measure the speed of light. Or better, you have to describe a general accepted way, how the speed of light is measured.
If you have such a recipe, you can measure and decide if the speed of light is everywhere the same and if this speeed is the same in -time- at a specific location

The same type of problems exists between: what is mass and how is this directictly measured or calculated based on different measurements.

If you don't start with some sort of mutual agreements, similar discussions will go on and on, forever.

Nicolaas Vroom

50 relativistic gamma factor maximum

On 21/08/29 8:04 PM, Nicolaas Vroom wrote:

>	[[Mod. note -- I apologise to all for the delay in processing this article, which arrived in the moderation system on 22-Aug-2021. -- jt]]

[[ Is there a processing speed limit? And does it vary with time?! ]]

...

>>	... the subject of this sub-thread, which was the question if the speed of light can vary with -time-, and if we could in principle measure this.

... ...

>	First you must measure the speed of light. Or better, you have to describe a general accepted way, how the speed of light is measured.

But we have that! Observing the propagation of light using length and time units based on the propagation of light. The outcome is fixed.

>	If you have such a recipe, you can measure and decide if the speed of light is everywhere the same and if this speeed is the same in -time- at a specific location

The only way to change it is to abandon the accepted definition (which always keeps the speed fixed). And perhaps this could happen, if for instance all speeds in physics suddenly became 10% higher, except light. Then most physicists would be open to the idea that actually we should change this definition.

>	The same type of problems exists between: what is mass and how is this directictly measured or calculated based on different measurements.

There it is even more complicated since the word has undergone a change in meaning. "Mass" without qualifier used to be the total mass (so in those days E=mc^2 was always true, people said mass would increase with velocity). But today the word "mass" by default means "rest mass", and you have to specify "kinetic mass" or "total mass" if you mean one of those. (So now E=mc^2 is wrong for moving particles!)

Fortunately we do not (yet?) have such a shift in meaning for "speed".

-- Jos

51 relativistic gamma factor maximum

In article , Jos Bergervoet writes:

> >	First you must measure the speed of light. Or better, you have to describe a general accepted way, how the speed of light is measured.

>	But we have that! Observing the propagation of light using length and time units based on the propagation of light. The outcome is fixed.

> >	If you have such a recipe, you can measure and decide if the speed of light is everywhere the same and if this speeed is the same in -time- at a specific location

>

The only way to change it is to abandon the accepted definition (which always keeps the speed fixed). And perhaps this could happen, if for instance all speeds in physics suddenly became 10% higher, except light. Then most physicists would be open to the idea that actually we should change this definition.

Indeed. It could happen. It has happened. The metre used to be defined as 1/10,000,000 of the quadrant of the meridian through Paris. The second used to be defined as a certain fraction of a year. These definitions were changed. Why? In part because other definitions can be reproduced with greater accuracy, but also because they can change. Of course, it would have been silly to say that since the definition of the metre is fixed, the size of the Earth, or the length of the year, could not change, even in principle.

> >	The same type of problems exists between: what is mass and how is this directictly measured or calculated based on different measurements.

Like some other units, the kilogramme has recently been redefined. Why? In part because the standard kilogramme in Paris was losing mass. So, it was possible to detect it, even though it was the standard.

The Universe does not care how we define our units. Certain quantities either vary or they don't. We cannot prevent them from varying by using them to define a unit. When we are REASONABLY SURE that something does not vary (at least not detectably over interesting timescales), as a purely PRACTICAL matter one can define units in terms of constants of nature such as the speed of light.

52 relativistic gamma factor maximum

Phillip Helbig (undress to reply) wrote:

The problem with your position is that you postulate that what has to be shown, namely that there is such a thing as the speed of light, and that it is a constant of nature.

As far as we know now there is no such a thing. We can formulate all known laws of nature in such a way that the speed of light doesn't occur in any of them.

What remains is that the 'speed of light' is an artefact caused by maladroit choices in the definition of our unit systems. It has no more physical reality than Boltzmann's constant, or the impedance of the vacuum.

If you want to have a 'speed of light' as a constant of nature you must invent new, and fundamentally different laws of physics in which there is such a thing,

Jan

53 relativistic gamma factor maximum

In article <1peqwo1.1pvreq6wg61gwN%nos...@de-ster.demon.nl>, nos...@de-ster.demon.nl (J. J. Lodder) writes:

Please explain. There are various sources of light. We can measure a distance. We can measure a time. Thus, we can measure a speed. We find that the speed of light is always the same. Similar results for the speed of sound at a given temperature and pressure.

Your position seems to be that the speed of light is merely a conversion factor, and might as well be set to 1 (not uncommon in some fields of physics). However, that is possible only if the speed of light is a constant of nature. Thus, it seems to me that you are the one making the assumption that the speed of light is some fundamental physical quantity.

Yes, it is possible to have units where the speed of light is just a conversion factor, or is 1, or whatever, but that is possible only if it IS a constant of nature.

54 relativistic gamma factor maximum

On 21/08/31 7:26 AM, Phillip Helbig (undress to reply) wrote:

>	In article <1peqwo1.1pvreq6wg61gwN%nos...@de-ster.demon.nl>, nos...@de-ster.demon.nl (J. J. Lodder) writes:

>>	Phillip Helbig (undress to reply) wrote:

>

>>

The problem with your position is that you postulate that what has to be shown, namely that there is such a thing as the speed of light, and that it is a constant of nature. As far as we know now there is no such a thing. We can formulate all known laws of nature in such a way that the speed of light doesn't occur in any of them. What remains is that the 'speed of light' is an artefact caused by maladroit choices in the definition of our unit systems. It has no more physical reality than Boltzmann's constant, or the impedance of the vacuum. If you want to have a 'speed of light' as a constant of nature you must invent new, and fundamentally different laws of physics in which there is such a thing,

>	Please explain. There are various sources of light. We can measure a distance. We can measure a time. Thus, we can measure a speed. We find that the speed of light is always the same. Similar results for the speed of sound at a given temperature and pressure.

This may again just show the ambiguity of the question, due to mixing up the two concepts:
1) The maximum speed allowed by the metric.
2) The propagation speed of a certain quantum field.

If we talk about 1) then changing the speed of light is changing the scale factor ratio between the time dimension and the space dimensions. That's only slightly less strange than changing the scale factor between one of the space dimensions and the other two. Why would one do it? How could it ever be justified? (But still, I can't see why there absolutely never would be a reason for it..)

If we talk about 2) then changing the (self) interaction of the quantum fields (e.g. by vacuum decay, auxiliary fields, etc.) could obviously change the propagation speed of its particles. But in our currently used field theories this would probably only give the photon a mass, so it would still leave the high-energy limit of the speed the same, coinciding with definition 1) of the concept. (Other theories, where this is not necessarily the case may exists, of course..)

>

Your position seems to be that the speed of light is merely a conversion factor, and might as well be set to 1 (not uncommon in some fields of physics). However, that is possible only if the speed of light is a constant of nature. Thus, it seems to me that you are the one making the assumption that the speed of light is some fundamental physical quantity. Yes, it is possible to have units where the speed of light is just a conversion factor, or is 1, or whatever, but that is possible only if it IS a constant of nature.

And it would be similar to using the meter to measure length, height and width, instead of having 3 different units. It's not *obviously* correct, only correct if the universe is absolutely isotropic. So do we accept that as a given? What exactly *can* we accept as given?

-- Jos

55 relativistic gamma factor maximum

Phillip Helbig (undress to reply) wrote:

>

In article <1peqwo1.1pvreq6wg61gwN%nos...@de-ster.demon.nl>, nos...@de-ster.demon.nl (J. J. Lodder) writes: Please explain. There are various sources of light. We can measure a distance. We can measure a time. Thus, we can measure a speed. We find that the speed of light is always the same. Similar results for the speed of sound at a given temperature and pressure.

OK, I'll try to write a tutorial.

>	Your position seems to be that the speed of light is merely a conversion factor, and might as well be set to 1 (not uncommon in some fields of physics).

Not just my position, the position of the people who decide about those kind of things, at places like NIST and BIPM and ..., with the approval of the CGPM. So the position of every competent physicist.

And not just some fields of physics, all of physics. (at least in principle, and as far as we know now) This position will not need to be changed until new laws of nature are discovered. In other words, it is not just theoretically pleasing, it is empirically adequate.

>	However, that is possible only if the speed of light is a constant of nature. Thus, it seems to me that you are the one making the assumption that the speed of light is some fundamental physical quantity.

There is no such thing as the speed of light, (as a physical constant) just like there is no such thing as the impedance of the vacuum. These things are artefacts of clumsy unit systems.

>	Yes, it is possible to have units where the speed of light is just a conversion factor, or is 1, or whatever, but that is possible only if it IS a constant of nature.

It is the only unit system we have nowadays. We could in priciple abolish the meter completely, and agree to express all distances in (nano)seconds. The meter is kept only for practical reasons of convenience and backward compatibility.

Jan

56 relativistic gamma factor maximum

On 21/08/31 2:01 PM, J. J. Lodder wrote:

>	Phillip Helbig (undress to reply)

... ...

>>	Your position seems to be that the speed of light is merely a conversion factor, and might as well be set to 1 (not uncommon in some fields of physics).

>	Not just my position, the position of the people who decide about those kind of things, at places like NIST and BIPM and ..., with the approval of the CGPM.

But are decisions from places like NIST and BIPM (even those with approval of the CGPM) of eternal validity? (In general, I mean.. have all such decisions as of yet been found to remain unchallenged and unchanged indefinitely?)

>	So the position of every competent physicist.

57 relativistic gamma factor maximum

What you are really debating is the process of science. In order to do anything we must have some framework of ideas we are working with, that we assume are valid. In order for alarge group of scientist to work together they must all talk the same "language", i.e. have the same framework of assumed theory. Otherwise we are debating kinetic energy vs phlogiston. That just doesn't work.

Just because we have an assumed theoretical framework doesn't mean that it is correct and cast in concrete, only that it is the current best understanding. As more experiments are performed and more physical facts revealed we may come to realize that some aspect of our assumed theoretical framework is not quite correct. Or someone may come up with a different framework that is compelling enough that everyone adopts it. Examples include quantum mechanics, relativity, Maxwell's Equations, Newton's Laws, etc.

It is the task of the revolutionary to convince the mainstream consensus that the new idea is better. That is usually a bit hard because so many people become emotionally invested in the consensus framework, but if the new idea truely has value and is supported by experimental evidence than it will eventually prevail.

Rich L.

58 relativistic gamma factor maximum

Jos Bergervoet wrote:

>	On 21/08/31 2:01 PM, J. J. Lodder wrote:

> >	Phillip Helbig (undress to reply)

>

... ...

> >>	Your position seems to be that the speed of light is merely a conversion factor, and might as well be set to 1 (not uncommon in some fields of physics).

> >	Not just my position, the position of the people who decide about those kind of things, at places like NIST and BIPM and ..., with the approval of the CGPM.

>	But are decisions from places like NIST and BIPM (even those with approval of the CGPM) of eternal validity? (In general, I mean.. have all such decisions as of yet been found to remain unchallenged and unchanged indefinitely?)

Of course not, subject to possible change by next CGPM. However, looking back, it is remarkable how cumulative it all has been, with ever increasing reproducibility of units and precision of measurement.

> >	So the position of every competent physicist.

>	Really? https://www.azquotes.com/picture-quotes/quote-science-is-the-belief-in-the-ignorance-of-experts-richard-p-feynman-35-30-25.jpg>

59 relativistic gamma factor maximum

On 21/09/02 9:34 AM, J. J. Lodder wrote:

>	Jos Bergervoet wrote:

>>	On 21/08/31 2:01 PM, J. J. Lodder wrote:

>>>	Phillip Helbig (undress to reply)

>>

... ...

>>>>	Your position seems to be that the speed of light is merely a conversion factor, and might as well be set to 1 (not uncommon in some fields of physics).

>>>	Not just my position, the position of the people who decide about those kind of things, at places like NIST and BIPM and ..., with the approval of the CGPM.

>>	But are decisions from places like NIST and BIPM (even those with approval of the CGPM) of eternal validity? (In general, I mean.. have all such decisions as of yet been found to remain unchallenged and unchanged indefinitely?)

>	Of course not, subject to possible change by next CGPM.

So you agree that speed of light being "merely a conversion factor" could possibly be revoked by a next CGPM. So no proof here..

>	However, looking back, it is remarkable how cumulative it all has been, with ever increasing reproducibility of units and precision of measurement.

If you find that remarkable, you probably agree that it doesn't *have to* be like that. And indeed, when Michelson and Morley did *not* find variation in the speed of light that was quite disruptive. So no proof here..

>>>	So the position of every competent physicist.

>>	Really? https://www.azquotes.com/picture-quotes/quote-science-is-the-belief-in-the-ignorance-of-experts-richard-p-feynman-35-30-25.jpg

>	What did -he- measure?

Who cares? No-one says the speed of light has recently changed or is about to change anytime soon. Nothing has to be measured, our only question is whether it can change in principle. we just have to look at what flexibility there is in our definitions and theories.

>	Anyway, it is a highly misleading statement, when taken out of context. You may want to read the original, in context of 'education science', at http://www.feynman.com/science/what-is-science/

That question "what is science" is an excellent context for the current discussion here! So I do not see what your context worries are..

>	And just my opinion: I doubt very much whether Feynman would say the same thing again, were he alive today.

Why? Feynman's worry: "there is a considerable amount of intellectual tyranny in the name of science." (10 lines before the end) is at least as relevant today as it was then! As long as politics and commerce abuse the word "science" for their purposes this will not change.

>	Anyway, if you want to actually measure things in physics you don't have a choice. A measurement is a measurement only if it can be traced back, at least in principle, to a standard kept by NIST, BIPM, etc.

I think a measurement is a measurement only if (enough) decoherence occurs between a set of different sub-spaces of the total Hilbert space, while at the same time relatively phase-constant saddle-points remain around some pointer states. (But I'm quite willing to consider any other non-anthropocentric definition, regardless of what NIST, BIPM, etc. have written down!)

>

>>>	And not just some fields of physics, all of physics. (at least in principle, and as far as we know now) This position will not need to be changed until new laws of nature are discovered.

>>	But that usually happens every few decades, or even within a few years.. so doesn't that lead to the opposite conclusion than the one you want?

>	Really? For the behaviour of 'ordinary' matter, under 'ordinary' circumstances, (which is what the CGPM deals with)

But *you* brought in the CGPM! This thread was only dealing with the question whether the speed of light can change in principle, so certainly not constrained to "ordinary circumstances."

...

>	nothing fundamentally new has happened since the Dirac equation and the Pauli Principle were established. ...

I believe that is debatable, but it is a bit off-topic..

-- Jos

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Richard Livingston wrote:

>

What you are really debating is the process of science. In order to do anything we must have some framework of ideas we are working with, that we assume are valid. In order for alarge group of scientist to work together they must all talk the same "language", i.e. have the same framework of assumed theory. Otherwise we are debating kinetic energy vs phlogiston. That just doesn't work. Just because we have an assumed theoretical framework doesn't mean that it is correct and cast in concrete, only that it is the current best understanding. As more experiments are performed and more physical facts revealed we may come to realize that some aspect of our assumed theoretical framework is not quite correct. Or someone may come up with a different framework that is compelling enough that everyone adopts it. Examples include quantum mechanics, relativity, Maxwell's Equations, Newton's Laws, etc. It is the task of the revolutionary to convince the mainstream consensus that the new idea is better. That is usually a bit hard because so many people become emotionally invested in the consensus framework, but if the new idea truely has value and is supported by experimental evidence than it will eventually prevail.

Well, no, not really. We were discussing measurement, at the limits of what can be measured. These are very practical matters, and even to philosophers there are limits to how much you can philosophise on counting fringes, or weighing blocks of metal. This really is expert territory.

Apart from that, it is noticable, at least to me, that the great philosoper-kings of science, such as Popper, Kuhn, Lakatos, and so on are becoming a thing of the past too. And their exemplars to philosophise about, Galileo, Newton, Einstein etc. are even farther removed from us.

As to for new wannabee revolutionaries, there has been a noticeable scarcity of succesful ones. There is no shortage of magnificent schemes, such as (super)string theories/landscapes, but they have all bogged down in self-generated problems, and failed to deliver the goods. No GUT or TOE in sight, not even an idea of why \alpha has the value it has.

All there is on offer are multiverses and anthropic principles, and philosophising about it that boils down to 'the grapes hang too high, and they are probably sour anyway', so we really shouln't even imagine that they exist at all,

Jan

-- Judged by the ordinary criteria of uniqueness and elegance, String Theory has gone from being Beauty to being the Beast. And yet the more I think about this unfortunate history, the more reason I think there is to believe that String Theory is the answer. (Leonard Susskind)

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> >

The problem with your position is that you postulate that what has to be shown, namely that there is such a thing as the speed of light, and that it is a constant of nature. If you want to have a 'speed of light' as a constant of nature you must invent new, and fundamentally different laws of physics in which there is such a thing,

>	Please explain. There are various sources of light. We can measure (1) a distance. We can measure (2) a time. Thus, we can measure a (3) speed.

Yes we can measure a speed and a distance and using both calculate a speed. This is rather straight forward when you want to calculate the speed of a car , but very difficult when you want to calculate the speed of light or the speed of a neutrino. The main problem is the reference frame.

The first step is to describe exactly how (1) and (2) are measured such that we all can perform the same experiment and compare the results (at different locations or circumstances). To measure the time you can use two atomic clocks, but than you have to agree how to synchronise these clocks.

To measure the distance you could start with two points A,B, a fixed distance apart. Next you can define a point C halfway between these two points AB and issue a synchronisation flash from C towards A and B. But the question is do both pulses arive simultaneous? Next you can issue a pulse from point A and measure the arriving time t1 of that pulse at point B. You can do the reverse from B to A and measure t2. The question is: Are these two arriving times t1 and t2 (durations) the same? If they are you can calculate c. If they are not you have a problem.

Next you want to do with the same with a neutrino? Is that physical possible. IMO the best strategy is first to calculate the speed of light at that location and use the points (A,B) to measure the speed of a neutrino. This strategy is not simple.

A whole different approach is when you start with the assumption that the speed of light is every where the same. In that case you can start with a fixed number of counts n between the two atomic clocks. That means n * c gives you the distance you need for example 100m. The problem is where is point B, where should you place the second atomic when you want to send a pulse from A to B and the distance is 100m? That means, when when you send the pulse from A and the count is m, that when the pulse arrives at B the count should be m+n.

The only way to do that is by 'approximation' i.e that means first you try point B1 which gives n1, then a pair B2,n2 next B3,n3 etc, etc The final point Bx with nx, closest to n is the solution. This whole approach, measuring a distance and assuming that the speed of light is constant is also not simple.

In this case, because the speed of light is everywhere the same, you don't have to repeat this exercise in the reverse direction.

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Of course it is possible, and it is, at least in principle, simple. And it has been done, in the CERN neutrino velocity experiment, with (at first) disastrous results.
The distance CERN-Gran Sasso was measured by triangulation, using GPS. The clocks were synchronised, again using GPS. So the whole experiment was based on timing, using (many) communicating atomic clocks.
The experiment was a direct comparison of the speed of the neutrinos and the speed of light. (the distance was measured in [light-]seconds)

As you probably know all went well, up to the timing at the entrance of the Gran Sasso tunnel. The supposed faster than light speed of the neutrinos was due to a delay in an improperly fastened optical connector. The deeper fault in the set-up was that they should have had at least a dual link for bringing the timing into the mountain,

Jan

[snip other observers] The experiment measures v_{neutrino}/v_{light}, which is a dimensionless world scalar, so all observers should find the same result. (note that E_{neutrino} >> m_{neutrino}) THere is no way to measure v_{neutrino} in some absolute way, independently of assumptions about the speed of light.

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In article <384f2c33-591d-4297...@googlegroups.com>, Leaving aside the issues that the speed of light is now constant by definition (a few decades now) and that we believe that it is constant in all frames (more than a century now), as far as normal measurements go, there is really no problem. Ole R�mer measured the speed of light via timing the eclipses of Jupiter's satellites. Fizea measured it with two gears.

Bringing back the other issues, we could of course still measure the speed of light with those old methods, and if it did actually change with time, we would notice it, despite the facts that it is now defined to be constant and that we believe that it is constant. I don't think that likely; my point is merely that we cannot prevent the speed of light from changing simply by defining it to be constant. Rather, it is defined to be constant as a practical matter because we have evidence that it is.

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[[Mod. note -- Please limit your text to fit within 80 columns, preferably around 70, so that readers don't have to scroll horizontally to read each line. I have rewrapped the lines in this article. -- jt]]

Op vrijdag 17 september 2021 om 06:16:55 UTC+2 schreef Phillip Helbig (undress to reply):

>	c to be constant and that we believe that it is constant. I don't think that likely; my point is merely that we cannot prevent the speed of light from changing simply by defining it to be constant. Rather, it is defined to be constant as a practical matter because we have evidence that it is.

If that is true you should explain us what that evidence is. I prefer to write: because we have no evidence that it is not.

My point is mainly that if 'you' define c to be physical constant, that means that photons always have the same speed, 'you' should also define how this speed is calculated. What R�mer did (very cleverly) was to calculate the average speed of light between Jupiter and the Earth. This calculation is a mathematical description of the mechanical Sun, Earth, Jupiter system. Assuming my understanding of book "Einstein's theory of relativity" page 93 is correct.

Is his result valid for the whole of the universe? We use the speed of light to measure hugh distances. Is it realy correct to claim that this speed, along that whole path, is everywhere the same? What about the influence if 'space' is a vacuum? What about the influence of matter?

Nicolaas Vroom.

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In article , Nicolaas Vroom writes:

>	[[Mod. note -- Please limit your text to fit within 80 columns, preferably around 70, so that readers don't have to scroll horizontally to read each line. I have rewrapped the lines in this article. -- jt]] Op vrijdag 17 september 2021 om 06:16:55 UTC+2 schreef Phillip Helbig (undress to reply):

> >	c to be constant and that we believe that it is constant. I don't think that likely; my point is merely that we cannot prevent the speed of light from changing simply by defining it to be constant. Rather, it is defined to be constant as a practical matter because we have evidence that it is.

>	If that is true you should explain us what that evidence is. I prefer to write: because we have no evidence that it is not.

OK, but that is a linguistic/philosophical issue which detracts from the main argument.

>

My point is mainly that if 'you' define c to be physical constant, that means that photons always have the same speed, 'you' should also define how this speed is calculated. What R�mer did (very cleverly) was to calculate the average speed of light between Jupiter and the Earth. This calculation is a mathematical description of the mechanical Sun, Earth, Jupiter system.

Right. But his speed agrees with other measurements.

>	Is his result valid for the whole of the universe?

That is indeed an assumption, but we have no evidence that it is not true. People have investigated cosmological models with a variable speed of light.

>	We use the speed of light to measure hugh distances. Is it realy correct to claim that this speed, along that whole path, is everywhere the same?

The speed of light in a vacuum is the same (and is the same no matter who measures it). There is no evidence that that is not true.

>	What about the influence if 'space' is a vacuum?

If it is not a vacuum, the speed is less.

>	What about the influence of matter?

General relativity describes that. It is a matter of taste whether one interprets some phenomena as slowing the speed of light or increasing the distance.

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68 relativistic gamma factor maximum

He didn't imply that everything therefore has to be as we currently think it is. So what would it prove here?

>>	And indeed, when Michelson and Morley did *not* find variation in the speed of light that was quite disruptive. So no proof here..

>	Finding that some of the 'constants' of nature' (the real ones like alpha, not a pseudo like c) are indeed variable will be far more disruptive than Michelson ever was.

If you agree that what happened was disruptive then why couldn't disruptive things happen again? Perhaps even more disruptive..

..

>>>>>

So the position of every competent physicist.

>>>>	Really? https://www.azquotes.com/picture-quotes/quote-science-is-the-belief-in-the-ignorance-of-experts-richard-p-feynman-35-30-25.jpg>

>>>	What did -he- measure?

>>	Who cares? No-one says the speed of light has recently changed or is about to change anytime soon. Nothing has to be measured, our only question is whether it can change in principle. we just have to look at what flexibility there is in our definitions and theories.

>	That's easy. Our present theories say that we live in a spacetime in which space and time are the same thing. [1] (apart from historical accidents with our choices of units) This is the most rigid aspect of all our theories, IMHO.

I tend to agree, but still it's a theory..

>	We'll break everything else first, if it would be necessary to break things.

Agreed as well, but still we might have to break it..

>	[snip more of the 'Feynman on science education' sideline]

No sideline at all! You brought in the argument from authority with this "position of every competent physicist" claim, and that made Feynman's dissenting view on this matter totally relevant.

>	Start another thread about it if you wish to continue.

Relevant for *this thread* because of reasoning used in this thread!

...

>>>	Anyway, if you want to actually measure things in physics you don't have a choice. A measurement is a measurement only if it can be traced back, at least in principle, to a standard kept by NIST, BIPM, etc.

>>

I think a measurement is a measurement only if (enough) decoherence occurs between a set of different sub-spaces of the total Hilbert space, while at the same time relatively phase-constant saddle-points remain around some pointer states. (But I'm quite willing to consider any other non-anthropocentric definition, regardless of what NIST, BIPM, etc. have written down!)

>	Another red herring. Quantum measurement has nothing to do with it.

On the contrary, quantum mechanics is the only theory that can shed a light on it, since it is the theory we currently believe to be the best we have. (Coming to think of it, the Feynman propagator *is superluminal*, slightly. Just to keep Feynman in the thread, of course..)

And also if you want any real proof for your (seemingly quite reasonable) claim that "space and time are the same thing", you might need something like string theory to describe how space and time dimensions emerge to begin with, what determines the number of each of them, and why they are, or aren't, "the same thing".

-- Jos

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>	We seem to live in a universe that is ruled by law, rather than a lawless or a chaotic one.

We are part of world that is constantly changing. This world can be divided into parts that behave more or less identical. For example 'everywhere' in the univerese are galaxies. [2]

>	Why this is the case is, as Einstein said, a complete mystery.

Why this is the case nobody knows. It is a 'fact' based on observations.

> > >

That's easy. Our present theories say that we live in a spacetime in which space and time are the same thing. [1] [1] This follows from the fact that we can eliminate c completely from all laws of physics by means of a suitable choice of units.

[1] is in conflict with [2] above.

The problem with spacetime is that we define a line segment which connects two events t1 and t2.
This line segment defines the start and end point of a light signal. The problem is that line segment c*dt does not physical exist.
The main problem is an unambigous definition of the points x1,y1,z1,t1 and x2,y2,z2,t2 of the two events in space.
That means an event in our Galaxy and in Andromeda Galaxy. That means you need a clear definition how these events are measured.

This problem would be simpler if one reference frame and one clock is used.

Spacetime is in fact a mathematical approach. To set c to 1 (and to make it a physical constant) does not 'solve' the issues involved.

Nicolaas Vroom.

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Science deals with chemical, mechanical, biological and medical processes. All these processes involve change. The descriptions of processes we can call laws.

>	(and their consequences) Astronomers, looking back in time, can see that the laws of physics have not changed. (in any way that they can detect)

A whole different issue is the validity of these laws. For example, it will be interested to investigate, if in the atmosphere of the three exoplanets of Alpha Centauri, also organic compounds can be detected, identical as here on earth. If, that is the case, we may conclude that there is similar type of life possible, as here on earth. It is also possible, that we can expect there a different type of life. And if that finally is the case, then we have to modify our present laws.

> >	This problem would be simpler if one reference frame and one clock is used. Spacetime is in fact a mathematical approach. To set c to 1 (and to make it a physical constant) does not 'solve' the issues involved.

>	Precisely the point of Kant. There is nothing to 'solve'. Mathematics must come before all physical theory.

The first step is to make observations. This includes instruments to observe. The second step is to make a physical model. This is important to identify different parts or subprocesses and how they influence each other. The third step is to quantify and to use mathematics.

A good example to study is to answer the question: What is faster the speed of light or the speed of a neutron? Also, here there are two different situations: We can qualify or quantify.
If we want to 'qualify' we have to perform an experiment which emits simultaneous a short beam of neutrons and a short beam of photons and 'observe' which arrives the first.
If we want to 'quantify' we have to do the same to 'qualify', but besides that, we have to measure the distance travelled and the time of emission and detection using two synchronised clocks in both path ways. This is important in order to compare the results.

>	Without a well-understood mathematical framework, you can't even begin measuring things.

We should start with a good physical framework, before we can measure anything.

>	(beyond the most naive level) This still holds, despite the mathematical framework having been changed from Euclidean geometry to relativistic Riemannian geometry,

WE must understand what that physical means.

Just a thought: We must understand, how it is possible, that at any moment in time all the planets in the universe move around a star. This has nothing to do with mathematics. Part of the solution is that the universe is not empty, but 'filled' with photons, radiation and gravitons.