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1) How fast can you rotate a "rigid" disc of a radius of 1 km? When you consider that the max speed of the circumference is 1% of c or 3000km/sec then this is approx 500 revolutions per second.

[[Mod. note -- In general a rotating object will break up (i.e., the internal stresses caused by the rotation will exceed the material's structural strength) if its tip velocity exceeds (up to a factor of order unity) the speed of sound in the object. For most solids the sound speed is between 1 and 10 km/s. -- jt]]

2) a more difficult question is: is there length contraction in respect to the radius? You can "easily" detect that when you have a grid in the rest frame and the disc "floats" above this grid centered around the axis of rotation.

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>	2) a more difficult question is: is there length contraction in respect to the radius?

AFAIK the mostly agreed solution of this so-called Ehrenfest paradoxon is:

The material of the disk itself is not length-contracted, since this is not possible without destroying the disk. However, this has the effect that seen from a disk-riding observer, the disk material seems to be stretched, since the yardsticks of this observer undergo a length contraction. The result is that for the disk-riding observer, the circumference of the disk is stretched, i.e. is greater then 2pi r, where r is the disk radius. This means that the disk-riding observer observes a non-Euklidian spatial geometry for the disk.

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This becomes clearer if one considers not a solid disk, but rather a bunch of radial hairs in the form of a disk: as the rotation rate increases the individual hairs become further apart, as measured by a comoving observer at the end of some hair.

Of course in practice no material is anywhere close to being strong enough for this to be important or measurable.

Tom Roberts

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No, "seen from a disk-riding observer" is wrong. This observer will not see his own yardstick contracted. You have to invoke a stationary observer for that! And that observer will also see that distance markers along the circumference of the disk still are unchanged compared to the stationary circumference circle (otherwise the disk would not fit on the original circle, which it does in the situation we are describing).

This in turn means that also the disk-riding observer will see the mismatch between his yardstick and the markers (worldlines of markers cannot coincide in one frame and have mismatch in another). But the disk-riding observer will explain this as a correct yardstick and a stretched disk.

To judge the mechanical stresses in the disk the disk- riding observer is best positioned. In his inertial frame he sees the material of the disk at rest (albeit with some rotation and in a gravity field). The fact that the disk seems stretched to hime means that there really is a mechanical stretching force in the material.

...

>	circumference of the disk is stretched, i.e. is greater then 2pi r, where r is the disk radius. This means that the disk-riding observer observes a non-Euklidian spatial geometry for the disk.

If he uses a disk-fixed coordinate system, that is.. Another option for his coordinates would be an inertial frame with the momentary speed of his point on the rim.

-- Jos

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>>

AFAIK the mostly agreed solution of this so-called Ehrenfest paradoxon is: The material of the disk itself is not length-contracted, since this is not possible without destroying the disk. However, this has the effect that seen from a disk-riding observer, the disk material seems to be stretched, since the yardsticks of this observer undergo a length contraction.

>	No, "seen from a disk-riding observer" is wrong. This observer will not see his own yardstick contracted.

I did not write that the observer sees his own yardstick contracted. I wrote his yardstick is contracted (seen from an inertial frame in which the disk is rotating, but not translating). As the disk-riding observer sees his own yardstick non-contracted, i.e. having normal length, he instead measures the circumference of the disk being stretched, when he measures the circumference using his yardstick.

>	You have to invoke a stationary observer for that!

That is exactly what I did. Without mentioning it explicitly because I thought that would be clear.

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>	popular, literature. See, for example, http://casa.colorado.edu/~ajsh/sr/contraction.html#cartwheel and check out the Lorentz-contracted cartwheel. -P.H.]

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This raises the practicle question: which one of these two effects will win if the disk has some elasticity which will allow its radius to be stretched (by centrifugal effect) or to be contracted (by circumferential stress).

Is there a fixed ratio between these opposing effects? Or can the contraction win for some value of disk size and rotation speed? (One would expect centrifugal expansion to win for simple laboratory-sized experiments..)

>	but is really due to the circumference remaining 2*pi*R while its length to the rotating observer is larger).

Remaining 2*pi*R _for the stationary observer_, you mean. (Be careful with absolute claims in relativity.)

-- Jos

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>	This raises the practicle question: which one of these two effects will win if the disk has some elasticity which will allow its radius to be stretched (by centrifugal effect) or to be contracted (by circumferential stress).

The only way to answer this question is by performing different experiments with different materials. If the outcome is different than you can see how difficult this whole issue is. When you introduce concepts like stress and elasticity the whole issue becomes a physical problem. This raises the question to what extend when you study only length contraction (of a rod) is stress involved. For example does it make a difference if you push or pull an object.

> >	but is really due to the circumference remaining 2*pi*R while its length to the rotating observer is larger).

>	Remaining 2*pi*R _for the stationary observer_, you mean. (Be careful with absolute claims in relativity.)

IMO when you study length contraction you should only (?) do this from the viewpoint of one frame.

Nicolaas Vroom

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>>>	[Moderator's note: Keep in mind that the Lorentz contraction is not real, but is simply how a quickly moving object appears.

>>	What do you mean not real? Do you mean it is not physical? Is Time Dilation real i.e. physical?

>	It is not real in that no stress or strain on the object results. Consider: it depends on relative velocity. More than one observer can look at the object with different relative velocities, and see different length contractions. Which one is real?

The one that occurs in the applied inertial frame. If you denote only frame-independent phenomena as "real", then you are right, Lorentz contraction is not real then.

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What do you mean with "is not real"? Length contraction is real in that sense that in an inertial frame S, relative to which a body is moving, the length of the body is shorter than in the body's rest frame S'.

In addition, length contraction is not the way how the moving body appears. Take e.g. a moving ball. Lorentz contraction makes it ellipsoid-shaped, however, when watching the moving ball, one sees it still bullet-shaped, due to effects of light propagation. Those effects are described here:

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When you observe a sun eclipse in reality, dependent about the distance from the moon to the earth it is possible to see the limb of the Sun around the Moon. As such the moon appears larger and smaller. This is all a visible illusion and physical there is no difference in size involved.

>	It is not real in that no stress or strain on the object results. Consider: it depends on relative velocity. More than one observer can look at the object with different relative velocities, and see different length contractions.

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If you do not believe the theory of relativity or the theory of elastic deformation, _then_ your only way to answer the question is by performing experiments. (But this may not be the situation for the audience you are addressing here..)

>	If the outcome is different than you can see how difficult this whole issue is.

Different from what? (The outcome, I mean!)

>	When you introduce concepts like stress and elasticity the whole issue becomes a physical problem.

But not fundamentally different from designing a skyscraper, or any mechanical structure.

-- Jos

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Good comment. Many people DO regard anything that is frame-dependent to be "not real". I don't subscribe to that belief: I think that length contraction and time dilation (and, more generally, simultaneity) are all real for a given observer. I certainly don't regard them to be any kind of "illusion" or "meaningless appearance".

-- Mike Fontenot

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>

The first question to answer what type of material is rigid and what is non-rigid. AFAIK rigid material does not experience length contraction. The only way to find this out is by performing real experiments. Please visit: https://www.nicvroom.be/wik_Born_rigidity.htm#ref2 What this shows are three outcomes of almost the same experiment. In fact this is the most simple experiment to demonstrate length contraction without any clocks. In each experiment there is one train at rest and one is moving.

You are considering linear motion there, i.e. translation, not rotation like for the rotating disk. For linear motion, it is immediately clear that length contraction always occurs, independent from the properties of the material. This result follows from Lorentz transformation, or, what might be easier to understand, from considering a Minkowski diagram, like this one:

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There is no possible material that is rigid, because that would imply an infinite speed of sound. And, of course, no material ever observed comes close to being rigid.

>	AFAIK rigid material does not experience length contraction.

This is just plain wrong. "Length contraction" does not affect any physical object, it is a geometrical projection that affects how relatively moving observers MEASURE the object. Such measurements cannot possibly affect the object itself. And, of course, there can be many differently-moving observers who measure different values for the "length contraction" of the object, but it clearly has a single actual length.

Yes, all those sloppy authors that say "moving clocks run slow" and "moving rods get shortened" are WRONG. They ought to say "moving clocks are observed to run slow", and "moving objects objects are observed to be shortened". Because neither the clock nor the rod is affected in any way, but their words say that they are. But my phrases are not perfect, either, as one might interpret them as saying these phenomena are merely appearance, and that isn't correct, either. Bottom line: sound bites cannot capture the subtleties of relativity.

>	The only way to find this out is by performing real experiments.

First you must understand this correctly by learning what the words you use actually mean. In particular, "length contraction" does not mean what you apparently think it means. You are probably similarly confused by "time dilation".

I always put those two phrases in quotes because those names are very poor, and do not accurately describe the actual phenomena. But they are solidly established historically.

>	[... repetitions of the above mistake]

Tom Roberts

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The problem is that the words "real" and "physical" are ambiguous, and mean different things to different people (and in different contexts, and...).

For instance, "time dilation" and "length contraction" are not "real" in the sense that they modify or affect the object in question. But they are "real" in the sense that these phenomena can have observable, physical consequences (e.g. pion beams ~ 1 km long exist; electrons moving in wires generate magnetic forces that drive motors).

As I have said so often, understanding subtle concepts like relativity requires precision in thought and word. The above exchange falls woefully short of what is required. For instance, the Moderator's "appears" does not seem to subsume the fact that pion beams ~ 1 km long exist -- if "time dilation" was merely "appearance" they could not exist. So there is more substance here than those words capture....

[Moderator's note: I agree with all you say in this post and the previous one, except, perhaps, here: Adopting your terminology, the correct formulation should be: "pion beams are observed to be ~ 1 km long". If you are referring to the fact that they are observed to travel farther than one would expect from their speed and lifetime, then what is involved is time dilation (from our point of view) and/or length contraction (from their point of view); pions are clocks and rulers just like anything else. -P.H.]

Gregor Scholten said:

>	If you denote only frame-independent phenomena as "real" [...]

One reasonable meaning of "real" is "serves as a viable and useful model of some physical phenomenon". If that is the meaning used, then only coordinate- independent quantities can be "real" (because coordinates are arbitrary human constructs, and Nature does not use them).

Mike Fontenot said

>	I don't subscribe to that belief: I think that length contraction and time dilation (and, more generally, simultaneity) are all real for a given observer.

I don't think it makes sense for "reality" to be observer dependent like that. But I also think your words are too ambiguous to be useful.

Tom Roberts

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But velocities are of no significance in basic theories.

Objects, which, in conventional terms, rotate at highest physical possible velocities are the electrons in high angular momentum states.

Its funny to observe that their speed in the 1-particle projection Dirac space is nearly infinite because the current four vector in spherical relativistic coordinates, as the cofactor of the angular momentum, correctly transforms covariantly in the same way as if the proper speed four-vector of a material point object would be measured in proper time and not coordinate time.

This is of course a rock solid principle of covariantly Lorentz invariant fomulation of questionable physical terms like velocities of basically wavelike phenomena.

--

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I elaborate on my statement in the section entitled "Empirical Determination of the Current Age of a Distant Perpetually-Inertial Person" of my webpage

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I agree with you that rigid material (by difinition) does not exists. IMO the reason is that it requires instantaneous communication.

> >	AFAIK rigid material does not experience length contraction.

>	This is just plain wrong. "Length contraction" does not affect any physical object, it is a geometrical projection that affects how relatively moving observers MEASURE the object.

What you indirectly indicate (?) that when you have an observer at rest in front of an object/train at rest and a moving object/train which passes directly infront of the object/train at rest that the observer can never observe any (physical) length contraction when both trains are in front of him. (Assuming that both objects have the same length at rest)

>	Such measurements cannot possibly affect the object itself.

I fully agree. Performing a measurement does not physical change the object being measured. The issue ofcourse is that the apparatus used by the moving observer in order to measure should not undergo any physical change. As such in order to study physics you should not use different relative moving observers.

>	And, of course, there can be many differently-moving observers who measure different values for the "length contraction" of the object, but it clearly has a single actual length.

IMO it does not make sense to use the results of different observers if they measure different values for the same object.

>	Yes, all those sloppy authors that say "moving clocks run slow" and "moving rods get shortened" are WRONG. They ought to say "moving clocks are observed to run slow", and "moving objects are observed to be shortened".

Clifford M.Will at page 273 writes (Was Einstein right):
"On the other hand it is rather difficult effect to see experimentally because it is hard to accelerate macroscopic rods to high enough velocities to make the effect noticeable."

At page 271 he writes: "The observational evidence for time dilation is overwhelming." My understanding is that in order to demonstrate this you only need one observer and two clocks. The moving clock should run behind when both meet again.

> >	The only way to find this out is by performing real experiments.

>	First you must understand this correctly by learning what the words you use actually mean. In particular, "length contraction" does not mean what you apparently think it means. You are probably similarly confused by "time dilation".

My understanding is that time dilation is a physical effects i.e. that moving clocks run slower. My understanding for length contraction is much less clear. I thought (this is for me a question) that length contraction is also a physical effect. If it is not but implies different "observers" which have all different speeds (using moving clocks which all run differently) relative to the object being measured my solution would be to use only one frame and one set of synchronised clocks.

Nicolaas Vroom

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>	But they are "real" in the sense that these phenomena can have observable, physical consequences (e.g. pion beams ~ 1 km long exist; electrons moving in wires generate magnetic forces that drive motors).

Only physical processes can influence other physical processes.

>

[Moderator's note: etc If you are referring to the fact that they are observed to travel farther than one would expect from their speed and lifetime, then what is involved is time dilation (from our point of view) and/or length contraction (from their point of view); pions are clocks and rulers just like anything else. -P.H.]

If pions behave (physical) different under different (physical) conditions than if the law that describe these processes is called time dilation than time dilation (as a description of a process) is real.

At the same time physics becomes difficult when in order to describe (study) time dilation also length contraction is involved and when length contraction is described (studied) also time dilation is involved. IMO both should be studied independently of each other and when that is not possible clearly be indicated why. This implies that you should study moving objects i.e. length (contraction) without moving clocks.

Nicolaas Vroom

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>	Nothing happens to the fast-moving object.

The issue of course is what happens physical with the length of the rod when the speed approaches the speed of light. The question ofcourse is if this also a symmetrical issue.

> > >

Yes, all those sloppy authors that say "moving clocks run slow" and "moving rods get shortened" are WRONG. They ought to say "moving clocks are observed to run slow", and "moving objects are observed to be shortened".

> >	Clifford M.Will at page 273 writes (Was Einstein right): "On the other hand it is rather difficult effect to see experimentally because it is hard to accelerate macroscopic rods to high enough velocities to make the effect noticeable."

>	Both true, but the Will quote isn't relative to the one above.

The question is what are the details (observations and or measurements) involved to decide that the length of the moving rod is shortened. Accordingly to M.Will such an experiment is difficult. The most difficult is quantitative.

> >	My understanding is that time dilation is a physical effects i.e. that moving clocks run slower.

>

Note that in this case, the observers with each clock has a different experience, as the change in direction can be noticed. (Sometimes it is said that this involves acceleration---which it must---and thus needs GR to understand---which it doesn't. It isn't the magnitude of the acceleration, or any integral over it, which matters, but rather the path length.

In principle you can perform the whole experiment without acceleration and only by using clocks at a constant speed.
That means you need 3 Clocks. Clock A is at rest. Clock B moves away from A. and Clock C moves back to A.
Clock B is set equal to A when they meet. Clock C is set equal to B (later) when they meet. The difference between A and C is linear function of the path way.
However that does not mean that acceleration is not involved. In order to get moving clocks you always need acceleration and this acceleration can change the behaviour of the clocks and explain what is observed.

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Not in relativity. In relativity (both GR and SR), "time dilation" is a geometrical projection, and no clock is ever affected.

>	My understanding for length contraction is much less clear.

Hmmmm. Clarity does not equate to correctness. But in relativity, "length contraction" is also a geometrical projection, and no object is ever affected. It is merely projection onto a different axis than "time dilation"; other than that the two are the same.

>	Only physical processes can influence other physical processes.

OK, as long as you include geometrical properties and relationships in the set of "physical processes". That is, of course rather unusual, so it would be better to abandon this sound bite.

Example: you can carry a ladder through a narrow doorway in some orientations but not others; if you seek a "cause" for this, ultimately you will be forced to accept geometrical relationships (yes, the ladder collides with the door-frame in some orientations, but WHY does it collide?). Ditto for the "cause" of a bullet putting a hole through the target some times, and sometimes not. Etc.

>	[... other confusions and misconceptions]

Note, please, that the twin paradox does NOT demonstrate "time dilation". Rather, it demonstrates a DIFFERENT geometrical property: the path length between two points can be different for different paths between them. The two points are the twins separating and rejoining; the stay-at-home twin moves inertially between them, and the traveling twin does not -- the difference in their ages (elapsed proper times) is just the difference in path length for these two paths through spacetime. The fact that the traveling twin moved non-inertially is important; the amount of acceleration is not -- what matters is the total path length.

In short: "time dilation" and "length contraction" are differential relationships valid at individual points; both are simple geometrical projections. Path length, on the other hand, is an integral property and applies to paths, not points.

Tom Roberts

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In relativity, the time between two events read off from the hands of a moving clock on given curved worldline by any observer is the length of that arc of the worldline

Period

Never there will arise any dispute between observers concerning proper time intervalls. The synchronisation procedures of their laboratory clocks do not enter the definition.

That fact makes the difference between length contraction determined by passages times of the two ends with clocks at rest, length dialation with two comoving clocks and time dilation. Per definition time dilation is the hand rotation rate ratio of a single moving clock and a single clock at rest. There is no ambiguity in observation of time at rest for of a full round completed on the moving clocks face.

--

Roland Franzius

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That may be true. But what does it practically means when you perform an experiment. Does this imply that the time of two clocks which are the same at the start of an experiment can be different at the end?

>

Period

>	That fact makes the difference between length contraction determined by passages times of the two ends with clocks at rest, length dialation with two comoving clocks and time dilation.

This sentence is not clear. Do you always need clocks to determine length contraction?

>	Per definition time dilation is the hand rotation rate ratio of a single moving clock and a single clock at rest.

Is this number always less than 1?

>	There is no ambiguity in observation of time at rest for of a full round completed on the moving clocks face.

Tricky sentence.

Nicolaas Vroom

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Edwin F. Taylor and John Archibald Wheeler
"Spacetime Physics", 2nd Ed.
W. H. Freeman, 1992,
ISBN 0-7167-2326-3 (hardcover)
0-7167-2327-1 (paperback)

N. David Mermin
"Space and Time in Special Relativity"
McGraw-Hill, 1968
Waveland Press, 1989
ISBN 0-88133-420-0 (paperback)

Even though it's nominally about general relativity, you can also get a lot of insights into special relativity from

Robert Geroch "General Relativity from A to B"
University of Chicago Press, 1978,
ISBN 0-226-28863-3 (hardcover),
0-226-28864-1 (paperback)

Op donderdag 26 maart 2015 09:07:11 UTC+1 schreef Tom Roberts:

>	On 3/18/15 3/18/15 10:31 AM, Nicolaas Vroom wrote:

> >	My understanding is that time dilation is a physical effects i.e. that moving clocks run slower.

>	Not in relativity. In relativity (both GR and SR), "time dilation" is a geometrical projection, and no clock is ever affected.

Understanding starts by performing experiments. Experiments with moving clocks are described in "Was Einstein right" by Clifford M. Will at the pages 54 to 61. (Chapter The gravitational Red Shift of Light and Clocks) At page 56 we read: "Thus time dilation makes the flying clock run slowly relative to the ground clock"
This is in conflict with your claim that "no clock is ever affected" The next step is to explain this (physical?) behaviour.

> >	My understanding for length contraction is much less clear.

>	Hmmmm. Clarity does not equate to correctness. But in relativity, "length contraction" is also a geometrical projection, and no object is ever affected. It is merely projection onto a different axis than "time dilation"; other than that the two are the same.

The issue is first to what extend you can demonstrate length contraction without moving clocks. At page 273 of the mentioned book is written that these experiments are difficult.

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Yes, of course. Real experiments have been performed that display this difference.