### Is The Speed of Light Everywhere the Same?

 1 Nicolaas Vroom Is The Speed of Light Everywhere the Same? Wednesday 30 november 2016 2 J. J. Lodder Re :Is The Speed of Light Everywhere the Same? Thursday 1 december 2016 3 Gregor Scholten Re :Is The Speed of Light Everywhere the Same? Monday 5 december 2016 4 Nicolaas Vroom Re :Is The Speed of Light Everywhere the Same? Friday 9 december 2016 5 Lawrence Crowell Re :Is The Speed of Light Everywhere the Same? Sunday 11 december 2016 6 Gregor Scholten Re :Is The Speed of Light Everywhere the Same? Sunday 11 december 2016

### 1 Is The Speed of Light Everywhere the Same?

From: Nicolaas Vroom
Datum: Wednesday 30 november 2016
On Wednesday, 16 November 2016 06:48:37 UTC+1, Gregor Scholten wrote:
 > Nicolaas Vroom wrote:

 > > Should this document not be updated to reflect the opinion that the (vacuum) speed of light is not always c, specific when gravitation is important?
 > Feel free to add a section "The speed of light in General Relativity".

The answer on the question: Is the speed of light everywhere the same? should be: No This answer reflects the idea that light i.e. photons is a physical process and is in accordance with the most common situation. The cause that the speed of light changes is gravity.

To consider the speed of light constant for practical reasons is a different subject.

In the above mentioned document, which starts with the original text, my comments are at the end. Each comment has a "number" or id. It is easy to jump forward and backward between both sections

It is easy to write that the speed of light in an inertial frame is everywhere the same (without giving the details how the speed is measured) but what is the purpose of such a claim if you want to simulate a whole galaxy?

Nicolaas Vroom

[Moderator's note: In any realistic galaxy simulation, the non-constancy of the speed of light is negligible compared to the other approximations made. -P.H.]

### 2 Is The Speed of Light Everywhere the Same?

From: J. J. Lodder
Datum: Thursday 1 december 2016
Nicolaas Vroom wrote:

 > On Wednesday, 16 November 2016 06:48:37 UTC+1, Gregor Scholten wrote:
 > > Nicolaas Vroom wrote:
 >
 > > > Should this document not be updated to reflect the opinion that the (vacuum) speed of light is not always c, specific when gravitation is important?
 > > Feel free to add a section "The speed of light in General Relativity".
 > I think if any we should first investigate this document: http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLigh/speed_of_light.ht
ml

Jan

### 3 Is The Speed of Light Everywhere the Same?

From: Gregor Scholten
Datum: Monday 5 december 2016
Nicolaas Vroom wrote:

 >> > Should this document not be updated to reflect the opinion that the (vacuum) speed of light is not always c, specific when gravitation is important?
 >> Feel free to add a section "The speed of light in General Relativity".
 > I think if any we should first investigate this document: http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLigh/speed_of_
l
 > ight.html I have written my comments in a separate document: https://www.nicvroom.be/speed_of_light_FAQ_comments.htm The answer on the question: Is the speed of light everywhere the same? should be: No

You're wrong. The correct answer is: the question is not sufficiently precise to be answered in a meaningful way. The question lacks of the definition of the quantity "speed".

In Newtonian physics as well as in Special Relativity, one could find the following definition of speed trivial:

"Take an inertial frame (x,y,z,t). Take two points on the trajectory of a body, having the coordinates

(x0,y0,z0,t0)

and

(x0 + dx, y0 + dy, z0 + dz, t0 + dt)

Then the quantity

\vec v = (vx, vy, vz) = (dx/dt, dy/dt, dz/dt)

is the speed vector of the body between both points with respect to the considered inertial frame, and the quantity

v = |\vec v| = \sqrt(vx^2 + vy^2 + vz^2)

is the absolute value of the speed of the body with respect to that inertial frame."

However, taking General Relativity into account, this definition becomes obsolete, because one can no longer apply the concept of a inertial frame, except in SR limit. In GR, there are two possible definitions of speed:

- Speed defined with respect to a local inertial frame. This is defined by replacing the concept of "inertial frame" from the upper definition by the concept of "local inertial frame".

- Speed defined with respect to some general coordinate system. This is defined by replacing the concept of "inertial frame" from the upper definition by the concept of "coordinate system".

According to the first definition, the speed of light is everywhere the same according to GR. According to the second definition, the speed of light may vary, but this is little meaningful because the construction of a coordinate system is arbitrary, and therefore, the resulting value for the quantity "speed" is arbitrary, too.

 > It is easy to write that the speed of light in an inertial frame is everywhere the same (without giving the details how the speed is measured) but what is the purpose of such a claim if you want to simulate a whole galaxy?

None, presumably. But when asking the question "Is the speed of light everywhere the same?" you do not restrict yourself in any way to consider the simulation of a galaxy.

If you want to restrict yourself to such a consideration, you should rather ask "When programming a simulation of a galaxy, do I have to consider the speed of light as being constant or as varying?". The correct answer then would be: as varying.

### 4 Is The Speed of Light Everywhere the Same?

From: Nicolaas Vroom
Datum: Friday 9 december 2016
On Monday, 5 December 2016 13:37:43 UTC+1, Gregor Scholten wrote:
 > Nicolaas Vroom wrote:
 > > The answer on the question: Is the speed of light everywhere the same? should be: No
 > You're wrong. The correct answer is: the question is not sufficiently precise to be answered in a meaningful way. The question lacks of the definition of the quantity "speed".

Maybe a better question is: Is the speed of light going from A to B always the same? or: Is the speed of light influenced by gravity (mass)

 > In Newtonian physics as well as in Special Relativity, one could find the following definition of speed trivial: "Take an inertial frame (x,y,z,t). Take two points on the trajectory of a body, having the coordinates (x0,y0,z0,t0) and (x0 + dx, y0 + dy, z0 + dz, t0 + dt) Then the quantity \vec v = (vx, vy, vz) = (dx/dt, dy/dt, dz/dt) is the speed vector of the body between both points with respect to the considered inertial frame, and the quantity v = |\vec v| = \sqrt(vx^2 + vy^2 + vz^2) is the absolute value of the speed of the body with respect to that inertial frame."

 > However, taking General Relativity into account, this definition becomes obsolete, because one can no longer apply the concept of a inertial frame, except in SR limit. In GR, there are two possible definitions of speed: - Speed defined with respect to a local inertial frame. This is defined by replacing the concept of "inertial frame" from the upper definition by the concept of "local inertial frame". - Speed defined with respect to some general coordinate system. This is defined by replacing the concept of "inertial frame" from the upper definition by the concept of "coordinate system".

Suppose I take the tower of Pisa, as my "local inertial frame." The floor of the tower is the point x=0,y=0 The tower itself is the z azis.

 > According to the first definition, the speed of light is everywhere the same according to GR.

I can imagine that when you measure the speed of light in the horizontal (x,y) plane, that the speed of light is everywhere the same. I have a problem to consider a light signal which follows the z axis and which starts from the top also has a constant speed.

 > According to the second definition, the speed of light may vary, but this is little meaningful because the construction of a coordinate system is arbitrary, and therefore, the resulting value for the quantity "speed" is arbitrary, too.

I agree that the construction of a coordinate system is arbitrary but that means that we first have to agree on which one. The issue is than if the speed of light is constant in the selected coordinate system. For example: we could select the center of gravity of the solar system as a coordinate system. In that coordinate system, during the experiment, the "Tower of Pisa" itself moves through space. However that does not effect the outcome of the experiment nor the conclusions.

 > > It is easy to write that the speed of light in an inertial frame is everywhere the same (without giving the details how the speed is measured) but what is the purpose of such a claim if you want to simulate a whole galaxy?
 > None, presumably. But when asking the question "Is the speed of light everywhere the same?" you do not restrict yourself in any way to consider the simulation of a galaxy. If you want to restrict yourself to such a consideration, you should rather ask "When programming a simulation of a galaxy, do I have to consider the speed of light as being constant or as varying?". The correct answer then would be: as varying.

The question is much more: if the speed of light everywhere in the galaxy is the same? When the answer is: No, than I have to take that into account (in prinsiple) when I want to calculate the initial positions of the objects involved, based on observations.

Nicolaas Vroom

### 5 Is The Speed of Light Everywhere the Same?

From: Lawrence Crowell
Datum: Sunday 11 december 2016
[Moderator's note: Sometimes we do minor reformatting of posts, but there has to be a limit. PLEASE send plain-text posts without any encoding. Make sure that your post doesn't contain lines longer than 70--80 characters. Even if your software shows you line breaks, they might not be there. Sending too long lines can cause them to be encoded, which explains the strange formatting below. Yes, modern technology, MIME etc make many things possible, but this is a text-based newsgroup without HTML, embedded videos, etc. -P.H.]

The speed of light is defined in a local inertial frame or a region of space small enough to be considered flat. It is here the speed of light is defined. The speed of light is a conversion factor between distance and time. We consider space and time as different because of how we measure them, but this is our convention and not really how nature works. Light rays are then zero length lines, or curves in the case of curved spacetime, that define a projective subspace. As such the speed of light is really c = 1. We really should shake off the prejudice to see this as a quantity with units, but as really unitless. This means the speed of light is an absolute invariant. I hold the same for the Planck constant hbar that is an intertwiner between momentum and position spread Delta E Delta t = hbar/2.

If there is any variation in constants it is with gauge charges. The fine structure constant a = (1/4pi eps)e^2/hbar c is known to vary with energy according to a renormalization group flow in QED. The quantity that varies is the charge or e^2/eps with energy or transverse momenta of scatter. We can make an argument that it does not vary with time based on the uncertainty principle

Delta E Delta t = hbar/2,

where as the universe expands t --> infinity the spread in time is huge and so the energy is near zero. As a result the fine structure constant is constant FAPP. A recent measurement of the fine structure constant in QED processes in distant atom 10 billion light years away shows no variation. This means there is no variation with either time or distance or region of space.

It is also worth noting the gravitational constant switches the meaning of mass and distance. We assume that c = 1, without this nonsense of m/sec or even light years/year, and by the same we have from Delta E Delta t = hbar/2 that hbar = 1, thinking of p as a reciprocal length or with p = 2pi hbark/lambda. Momentum is the reciprocal length and the gravitational constant G has length^2 = area units then interchanges mass ~ 1/length with length. This is the meaning of r = 2m = 2GM/c^2.

LC

### 6 Is The Speed of Light Everywhere the Same?

From: Gregor Scholten
Datum: Sunday 11 december 2016
Nicolaas Vroom wrote:

 >> > The answer on the question: Is the speed of light everywhere the same? should be: No
 >> You're wrong. The correct answer is: the question is not sufficiently precise to be answered in a meaningful way. The question lacks of the definition of the quantity "speed".
 > Maybe a better question is: Is the speed of light going from A to B always the same? or: Is the speed of light influenced by gravity (mass)

No, these two question lack in the same way of the definition of "speed", by the same reasons I already pointed out.

 >> In Newtonian physics as well as in Special Relativity, one could find the following definition of speed trivial: "Take an inertial frame (x,y,z,t). Take two points on the trajectory of a body, having the coordinates (x0,y0,z0,t0) and (x0 + dx, y0 + dy, z0 + dz, t0 + dt) Then the quantity \vec v = (vx, vy, vz) = (dx/dt, dy/dt, dz/dt) is the speed vector of the body between both points with respect to the considered inertial frame, and the quantity v = |\vec v| = \sqrt(vx^2 + vy^2 + vz^2) is the absolute value of the speed of the body with respect to that inertial frame."
 > IMO if you want to establish "if the speed is constant" always at least three points should be considered

No, the two points I described are fully sufficient. "Speed being constant" then means that the resulting quantity is always the same, no matter where the two points are located.

Once again: ASCII art is really old-schooled today. You should rather draw some image.

 >> However, taking General Relativity into account, this definition becomes obsolete, because one can no longer apply the concept of a inertial frame, except in SR limit. In GR, there are two possible definitions of speed: - Speed defined with respect to a local inertial frame. This is defined by replacing the concept of "inertial frame" from the upper definition by the concept of "local inertial frame". - Speed defined with respect to some general coordinate system. This is defined by replacing the concept of "inertial frame" from the upper definition by the concept of "coordinate system".
 > Suppose I take the tower of Pisa, as my "local inertial frame."

That's logically impossible. The spacetime region covered by the tower of Pisa is not sufficiently limited to define a local inertial frame that describes that region in complete. Only a small part of the region, e.g. a single floor of the tower during some short time interval, can be described by a single local inertial frame.

 >> According to the first definition, the speed of light is everywhere the same according to GR.
 > I can imagine that when you measure the speed of light in the horizontal (x,y) plane, that the speed of light is everywhere the same. I have a problem to consider a light signal which follows the z axis and which starts from the top also has a constant speed.

That problem is due to the logical inconsistency of your assumptions. You cannot take the tower of Pisa as a local inertial frame.

 >> According to the second definition, the speed of light may vary, but this is little meaningful because the construction of a coordinate system is arbitrary, and therefore, the resulting value for the quantity "speed" is arbitrary, too.
 > I agree that the construction of a coordinate system is arbitrary but that means that we first have to agree on which one.

And since our agreement would be arbitrary, the result of our agreement would be arbitrary, too.

 > The issue is than if the speed of light is constant in the selected coordinate system. For example: we could select the center of gravity of the solar system as a coordinate system.

No, we couldn't, since that is no coordinate system. It is a single point in space, or a worldline in spacetime, but no coordinate system.

If we were in SR, i.e. in a flat spacetime, we could define a coordinate system, more precisely: a frame of reference, from that wordline, by defining time coordinate lines that are parallel to the wordline and spatial coordinate lines that are straight and orthogonal to the time coordinate lines.

In a curved spacetime, however, we cannot do that. In a curved spacetime, there is no rule defined to uniquely construct a coordinate system from just a worldline. We can construct various coordinate systems that have in common that the wordline of the center of gravity of the solar system makes up the spatial origin, but all these coordinate systems are different, and no option to prefer one of them as opposed to any other.

 > In that coordinate system, during the experiment, the "Tower of Pisa" itself moves through space.

From the various coordinate systems that have in common that the wordline of the center of gravity of the solar system makes up the spatial origin, there are many in which the tower of Pisa is NOT moving through space.

Once again: in curved spacetime, there is no such thing like a frame of reference (except locally), and therefore no coordinate system with the properties of a frame of reference.

 > However that does not effect the outcome of the experiment nor the conclusions.

The arbitrariness of the choice of the coordinate system DOES effect the conclusions.

 >> > It is easy to write that the speed of light in an inertial frame is everywhere the same (without giving the details how the speed is measured) but what is the purpose of such a claim if you want to simulate a whole galaxy?
 >> None, presumably. But when asking the question "Is the speed of light everywhere the same?" you do not restrict yourself in any way to consider the simulation of a galaxy. If you want to restrict yourself to such a consideration, you should rather ask "When programming a simulation of a galaxy, do I have to consider the speed of light as being constant or as varying?". The correct answer then would be: as varying.
 > The question is much more: if the speed of light everywhere in the galaxy is the same?

If that is the question you are asking, you do NOT restrict yourself to consider the simulation of a galaxy.

 > When the answer is: No, than I have to take that into account (in prinsiple) when I want to calculate the initial positions of the objects involved, based on observations.

You're wrong: you have to take that into account when *in the coordinate system you're using for your simulation* the speed of light turns out not to be constant.