## Is the speed of light actually constant or just always measured to be the same?

Greetings,

Sometimes I read that the speed of light is constant, and sometimes I read that it is always measured to be the same. Is it:

A - The speed of light is actually constant.

or

B - It is not constant, but is always measured to be the same due the effect of something such as time dilation? If so, what is the apparent constant speed the result of?

or

C - Is something going on similar to weird quantum phenomena. Is it that a photon does not actually exist at any particular location along it's path, and has no speed, until it is absorbed by something? For example, if a year after a photon is emitted, there is an object, which is stationary relative to the source, a light year away in the path of the photon, then the photon will be there and be absorbed. But, if instead, a year after the photon is emitted, there is an object, which is moving and experiencing time dilation, in the same place a light year away in the path of the photon, then the photon will *not* be there and will *not* be absorbed because the time dilation would cause it to measure the photon as having taken longer to travel the light year?

Thanks
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 What is the difference between something 'actually' being constant, and always measured to be constant?

 Quote by FunkyDwarf What is the difference between something 'actually' being constant, and always measured to be constant?
Something might be measured to be the same under various conditions even though that something is different, if the measuring instruments are somehow affected by the different conditions. Or for some other not thought of reason.

## Is the speed of light actually constant or just always measured to be the same?

Hey CosmicVoyager,

In a vacuum the speed of light is always measured at being 186,000 miles per second.

But when light passes through something like glass or water it slows down a little.

At the speed of light time stops, but from the photons point of view its time is normal, and the time for the rest of the universe has stopped. From the photons point of view it takes absolutely no time at all to travel a light year. The photon sees all the space in the universe as being compressed. So from the photons point of view it does not have to travel any distance.

Mentor
 Quote by CosmicVoyager B - It is not constant, but is always measured to be the same due the effect of something such as time dilation?
How would we know that the speed isn't really constant, then?

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Quote by CosmicVoyager
 Quote by FunkyDwarf What is the difference between something 'actually' being constant, and always measured to be constant?
Something might be measured to be the same under various conditions even though that something is different, if the measuring instruments are somehow affected by the different conditions. Or for some other not thought of reason.
For example, we can tell that a pendulum clock is affected by vibrations, because it disagrees with a quartz clock. In this situation, we would say that time is not actually affected by vibration. There is one clock that is right, and one that is wrong.
But in relativity, *all* clocks in the same state of motion agree. There is therefore no useful way to make the distinction between a distortion of measurement of time and an actual distortion of time.
The same considerations apply to distance as to time.
Since a speed is a distance divided by a time, there is also no way to make such a distinction when it comes to the speed of light.
 Recognitions: Gold Member Science Advisor Isn't the constant speed of light given by the wave equation derived from maxwell's equations?

 Quote by bcrowell For example, we can tell that a pendulum clock is affected by vibrations, because it disagrees with a quartz clock. In this situation, we would say that time is not actually affected by vibration. There is one clock that is right, and one that is wrong. But in relativity, *all* clocks in the same state of motion agree. There is therefore no useful way to make the distinction between a distortion of measurement of time and an actual distortion of time. The same considerations apply to distance as to time. Since a speed is a distance divided by a time, there is also no way to make such a distinction when it comes to the speed of light.
"There is therefore no useful way to make the distinction between a distortion of measurement of time and an actual distortion of time."

Hi. I am not addressing if time is distorted. We know it is. Time moves slower at faster speeds. If we know the clocks we are using to measure the speed are running slower, then we know the actual speed of what we are measuring is faster.

 Quote by CosmicVoyager "There is therefore no useful way to make the distinction between a distortion of measurement of time and an actual distortion of time." Hi. I am not addressing if time is distorted. We know it is. Time moves slower at faster speeds. If we know the clocks we are using to measure the speed are running slower, then we know the actual speed of what we are measuring is faster.
This is a bit of a misunderstanding. None of the those frames of reference are any less valid than any other. It is not like there's one guy who's stopped and his time is accurate, and every one else's time is distorted.

Time is a factor of the relative velocities between two frames of reference. There is no such thing as "a stationary frame of reference".
 Simply put, you are making a distinction without a difference. Light always travels at c. Period. There is no such thing as a "special" measurment technique that can somehow measure the "real" speed of light.

 Quote by CosmicVoyager "There is therefore no useful way to make the distinction between a distortion of measurement of time and an actual distortion of time." Hi. I am not addressing if time is distorted. We know it is. Time moves slower at faster speeds. If we know the clocks we are using to measure the speed are running slower, then we know the actual speed of what we are measuring is faster.
If A and B are moving relatively, then A will find that B's clock is slower, and B will find A's clock is slower.

I always think this is the key to understanding time dilation. It is not a transitive relation! Therefore there is no actual speed.

 Quote by CosmicVoyager Greetings, Sometimes I read that the speed of light is constant, and sometimes I read that it is always measured to be the same. Is it: A - The speed of light is actually constant.
Classical physics is spoken in the Relativity Forum. In the domain of Special Relativity the following answer holds:
No, the speed of light is not constant--not even in a vacuum. This is a common misconception here, but it is not true. In fact, it is somewhat misleading to assign a single speed to the propagation velocity of electromagnetic waves in almost any given case.

The proportionality constant, c, between space and time is--apparently--constant, but not the propagation speed of electromagnetic radiation, as can be simply shown. Only in the exceptional cases where beams of light, planar waves or other idealizations are produced, can the speed of the light be said to be c.

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 Quote by Phrak Classical physics is spoken in the Relativity Forum. In the domain of Special Relativity the following answer holds:No, the speed of light is not constant--not even in a vacuum. This is a common misconception here, but it is not true. In fact, it is somewhat misleading to assign a single speed to the propagation velocity of electromagnetic waves in almost any given case. The proportionality constant, c, between space and time is--apparently--constant, but not the propagation speed of electromagnetic radiation, as can be simply shown. Only in the exceptional cases where beams of light, planar waves or other idealizations are produced, can the speed of the light be said to be c.
Could you spell out more completely what you mean here? Are you talking about phase velocity versus group velocity? Accelerating versus nonaccelerating frames? Local versus global? The phenomena analogous to refraction and partial reflection that you theoretically get in a strong gravitational field?

The speed of light in a vacuum *is* a constant, when the words are interpreted the way that nearly all physicists interpret them.

Re accelerating versus nonaccelerating frames, which is an issue that comes up here frequently, the following may be helpful.

FAQ: Is the speed of light equal to c even in an accelerating frame of reference?

The long answer is that it depends on what you mean by measuring the speed of light.

In the SI, the speed of light has a defined value of 299,792,458 m/s, because the meter is defined in terms of the speed of light. In the system of units commonly used by relativists, it has a defined value of 1. Obviously we can't do an experiment that will remeasure 1 to greater precision. However, it could turn out to have been a bad idea to give the speed of light a defined value. For example, it would have been a bad idea to give the speed of sound a defined value, because the speed of sound depends on extraneous variables such as temperature.

One such extraneous variable might be the direction in which the light travels, as in the Sagnac effect, which was first observed experimentally in 1913. In the Sagnac effect, a beam of light is split, and the partial beams are sent clockwise and counterclockwise around an interferometer. If the interferometer is rotating in the plane of the beams' path, then a shift is observed in their interference, revealing that the time it takes light to go around the apparatus clockwise is different from the time it takes to go around counterclockwise. An observer in a nonrotating frame explains the observation by saying that the beams went at equal speeds, but their times of flight were unequal because while they were in flight, the apparatus accelerated. An observer in the frame rotating along with the apparatus says that clearly the beams could not have always had the same speed c, since they took unequal times to travel the same path. If we insist on letting c have a defined value, then the rotating observer is forced to say that the same closed path has a different length depending on whether the length is measured clockwise or counterclockwise. This is equivalent to saying that the distance unit has a length that depends on whether length is measured clockwise or counterclockwise.

Silly conclusions like this one can be eliminated by specifying that c has a defined value not in all experiments but in local experiments. The Sagnac effect is nonlocal because the apparatus has a finite size. The observed effect is proportional to the area enclosed by the beam-path. "Local" is actually very difficult to define rigorously [Sotiriou 2007], but basically the idea is that if your apparatus is of size L, any discrepancy in its measurement of c will approach zero in the limit as L approaches zero.

In a curved spacetime, it is theoretically possible for electromagnetic waves in a vacuum to undergo phenomena like refraction and partial reflection. Such effects are far too weak to be detected by any foreseeable technology. Assuming that they do really exist, they could be seen as analogous to what one sees in a dispersive medium. The question is then whether this constitutes a local effect or a nonlocal one. Only if it's a local effect would it violate the equivalence principle. This is closely related to the famous question of whether falling electric charges violate the equivalence principle. The best known paper on this is DeWitt and DeWitt (1964). A treatment that's easier to access online is Gron and Naess (2008). You can find many, many papers on this topic going back over the decades, with roughly half saying that such effects are local and violate the e.p., and half saying they're nonlocal and don't.

Sotiriou, Faraoni, and Liberati, arxiv.org/abs/0707.2748

Cecile and Bryce DeWitt, "Falling Charges," Physics 1 (1964) 3

Gron and Naess, arxiv.org/abs/0806.0464v1

 Quote by Phrak Classical physics is spoken in the Relativity Forum. In the domain of Special Relativity the following answer holds:No, the speed of light is not constant--not even in a vacuum. This is a common misconception here, but it is not true. In fact, it is somewhat misleading to assign a single speed to the propagation velocity of electromagnetic waves in almost any given case. The proportionality constant, c, between space and time is--apparently--constant, but not the propagation speed of electromagnetic radiation, as can be simply shown. Only in the exceptional cases where beams of light, planar waves or other idealizations are produced, can the speed of the light be said to be c.
 Quote by bcrowell Could you spell out more completely what you mean here?
Phase velocity.

To keep things simple I pick a single case where two planar electromagnetic waves, with electric fields in the Y direction, intersect in vacuum.

$$E_{yR} = E_{y0} sin \left( \frac{2\pi z}{\lambda_z} + \frac{2\pi x}{\lambda_x} - \omega t\right)$$

$$E_{yR} = E_{y0} sin \left( \frac{2\pi z}{\lambda_z} - \frac{2\pi x}{\lambda_x} - \omega t\right)$$

$$E_y = E_{yR}+E_{yL}$$

$$E_y = 2E_{y0} sin \left( \frac{2\pi z}{\lambda_z}-\omega t\right) cos \left( \frac{2\pi x}{\lambda_x} \right)$$

The wavelength of each contributing wave is

$$\lambda = \frac{\lambda_x \lambda_z}{\sqrt{\lambda_x^2 + \lambda_z^2}}$$

so that
$$\omega = 2 \pi c / \lambda$$
or
$$c = \omega / k \ .$$

c is the phase velocity of both components E_yR and E_yL.

Find the phase velocity, w of E_y, from k_z = 2pi/omega for lambda_x > 0.

This latex is a pain in the rear to enter and then debug. I don't think I'm going to do this again. It would far easier to attach a word document.
 Yes, it is constant-constant. The speed of light is 1, and 1 is always 1. In a sense, the speed of light plays the same role in pseudo-Euclidean (Minkowski) geometry, that infinity does in Euclidean geometry. I mean that in the sense of projective geometry - that is, in Minkowskian affine geometry, the invariant quadric is the light cone, while in Euclidean affine geometry, it is the circle at infinity x^2 + y^2 = 0. The speed of light in Euclidean geometry is the imaginary unit "i", while in Minkowski geometry it is "1". The c part is just because time and space are different and one needs a relative scale. Group-theoretically, one finds that the allowed transformations from one referent to another depend on a universal fixed velocity - that light goes at this velocity is incidental to the analysis, which would still be correct if light went at something less than c because it had a tiny mass. -drl

 Quote by bcrowell An observer in the frame rotating along with the apparatus says that clearly the beams could not have always had the same speed c, since they took unequal times to travel the same path. If we insist on letting c have a defined value, then the rotating observer is forced to say that the same closed path has a different length depending on whether the length is measured clockwise or counterclockwise. This is equivalent to saying that the distance unit has a length that depends on whether length is measured clockwise or counterclockwise.
Even though the direction is constantly changing, the moving observer has a constant speed. Why not conclude the relative light speed is c-v and c+v for the one way paths, the same as in an inertial frame?
The c speed for both directions in SR was only a definition, not a fact about light propagation, as stated by the author.

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