# Invariance of the speed of light

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Suppose we want the measure the speed of light for light emanating from the Sun.

How do we do that directly?

Suppose we have an observer who has accelerated to the mid point between the Earth and the Sun (at c/2 ,as an example)

How does that observer directly measure the speed of the light it detects at that moment?

If the observer chooses 2 points separated by 1 metre and records the time of detection at each point this should allow him or her to evaluate the speed ,but if the light is first detected at the first point then is not the photon absorbed by that detector  and retransmitted to the second detector?

So if the observer evaluates the speed of light between those 2 points is that actually the same as the speed of light between the Sun and the first detector?

Is not the observer actually measuring the speed of light between the two detection points?

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11 hours ago, geordief said:

If the observer chooses 2 points separated by 1 metre and records the time of detection at each point this should allow him or her to evaluate the speed ,but if the light is first detected at the first point then is not the photon absorbed by that detector  and retransmitted to the second detector?

That doesn't matter because you can use a short pulse of light, ie. simply use many many photons instead of one, and they'll all behave the same with respect to speed. Some of the photons can be detected at the first point, and others at the second.

11 hours ago, geordief said:

So if the observer evaluates the speed of light between those 2 points is that actually the same as the speed of light between the Sun and the first detector?

Yes and no. Assuming flat spacetime, yes: It is assumed that the speed of light is the same everywhere, and that agrees with experience. With GR, not really. Measuring the speed of light from a distance, at a different gravitational potential, isn't really meaningful. The local speed of light is invariantly c. Some might say "the coordinate speed of light in a gravitational well isn't necessarily c" but "coordinate speed" might not be an accepted scientific definition.

11 hours ago, geordief said:

How does that observer directly measure the speed of the light it detects at that moment?

There's not really any theoretically accepted way to directly measure the one-way speed of light without something like the definition below. If you're using measurements of timing made at two different locations, you need a way to relate those two measurements, for example using synchronized clocks. Einstein established the definition we use to say that sync'd clocks read the same time. The definition he used in his 1905 paper on SR is (translated):

Quote

We have not defined a common “time” for A and B, for the latter cannot be defined at all unless we establish by definition that the “time” required by light to travel from A to B equals the “time” it requires to travel from B to A.

Using this you can measure the one-way speed of light between A and B because it's by definition the same as the two-way speed of light, which can be directly measured, and also because you can sync clocks at A and B, etc.

Obviously, the one-way speed of light between A and B depends on the time it takes light to go from A to B, and the time at the different locations is defined. There's no way to independently measure the time at A and B without knowing that the one-way speed of light is the same as two-way, or to measure the one-way speed of light without knowing the time at A and B. So the time of a light signal is defined to be the same in either direction.

(Of course... you could use alternative definitions as well. You could eg. put an observer C equidistant to A and B, and observe that one-way signals from A to B do take the same time as from B to A. But then you'd define (or assume) that the light from A to C takes the same as from B to C. Einstein did it right, defining instead of assuming that the time is the same, because if you used some alternative way to sync clocks in a consistent way, then you could make different assumptions on the timing of light that are true using your alternative definition of time.)

Edited by md65536
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You can use the photoelectric effect since when the light strikes metal plates they will emit photoelectrons which can be used to power a device which records the reading from an atomic clock. Given the distance between the metal plates and the readings from the atomic clocks you can calculate the speed.

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9 hours ago, md65536 said:

Yes and no. Assuming flat spacetime, yes: It is assumed that the speed of light is the same everywhere, and that agrees with experience. With GR, not really. Measuring the speed of light from a distance, at a different gravitational potential, isn't really meaningful. The local speed of light is invariantly c. Some might say "the coordinate speed of light in a gravitational well isn't necessarily c" but "coordinate speed" might not be an accepted scientific definition

What about my scenario of an observer traveling at c/2    at the mid point of A and B in the direction of B (using your terminology)?

This is flat spacetime ,I think but the frequency of  the light coming from B  is much higher than it would be if O (observer) was at rest wrt B and A.

If many photons are emitted  from B towards O and he or she detects them on two detectors (as per your suggestion) will he measure the speed  as c?

Lastly if O is accelerating towards B will this be the same as a gravitational  scenario? (Will he or she measure the speed of light as greater than c using the  2 detector method?)

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6 hours ago, geordief said:

What about my scenario of an observer traveling at c/2    at the mid point of A and B in the direction of B (using your terminology)?

This is flat spacetime ,I think but the frequency of  the light coming from B  is much higher than it would be if O (observer) was at rest wrt B and A.

If many photons are emitted  from B towards O and he or she detects them on two detectors (as per your suggestion) will he measure the speed  as c?

Lastly if O is accelerating towards B will this be the same as a gravitational  scenario? (Will he or she measure the speed of light as greater than c using the  2 detector method?)

The frequency increases (blue shifts) the faster that you move toward the light source. At c/2 gamma is about 1.15, the frequency would be 1.15 times what was emitted, if moving toward the source (or redshifted to 1/1.15 times the emitted frequency if moving away).

Everyone will measure the speed of light as c in their inertial frame. The two detectors I mentioned I was referring to A and B.

Acceleration complicates things. The equivalence principle implies that you can set up a scenario where an accelerating O measures the same things as an O in a uniform gravitational field. So...... using 2 detectors depends on a lot of stuff (which direction O's accelerating, etc). One problem is that if O is changing speeds, and the 2 detectors must detect the light at different times (the events "A detects light signal" and "B detects same light signal" are separated by a light-like interval, so there is no reference frame where they are simultaneous) then effectively you're talking about 2 different measurements made in 2 different reference frames. O changes speed in the time that it takes light to travel the distance between A and B. You'd get a "speed of light other than c" if O treats the two measurements as if they were made in a single inertial reference frame, which they weren't.

Edited by md65536
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2 hours ago, md65536 said:

The frequency increases (blue shifts) the faster that you move toward the light source. At c/2 gamma is about 1.15, the frequency would be 1.15 times what was emitted, if moving toward the source (or redshifted to 1/1.15 times the emitted frequency if moving away).

No.  The detected frequency would be 1.732 times the source frequency.  The red or blue shift is due to a combination of both The changing light propagation times and relativistic time dilation.

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37 minutes ago, Janus said:

No.  The detected frequency would be 1.732 times the source frequency.  The red or blue shift is due to a combination of both The changing light propagation times and relativistic time dilation.

Oops, right! It's the relativistic Doppler factor, not the Lorentz factor. 🤕 brain damage

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10 hours ago, md65536 said:

You'd get a "speed of light other than c" if O treats the two measurements as if they were made in a single inertial reference frame, which they weren't.

Thanks. That seems to solve the problem I had . So an observer accelerating towards a source of light needs 2 nearby  detectors and to measure a short pulse of light at each.

The closer in time he or she  collates measurements from the two detectors the closer the measurement of the light will come to c.

Do I have it?

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On 9/11/2020 at 6:48 PM, geordief said:

How do we do that directly?

Measure permittivity and permeability of the vacuum, preferably many times over in a number of different ways so as to obtain a large sample size, to reduce the overall error margin. Once you know the values for these to the desired degree of accuracy, the speed of light follows directly, given the validity of Maxwell’s equations.

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2 hours ago, Markus Hanke said:

Measure permittivity and permeability of the vacuum, preferably many times over in a number of different ways so as to obtain a large sample size, to reduce the overall error margin. Once you know the values for these to the desired degree of accuracy, the speed of light follows directly, given the validity of Maxwell’s equations.

By "directly" I  meant the particular scenario in the OP  where I wanted to physically  measure  the speed of a "passing wave" at that very instant  and linking it to its departure earlier from the source.

md65536 has persuaded me that  we can do this with 2 detectors and a pulse  of photons  so that the result can be arrived at statistically.

He also pointed out that ,for an accelerating observer ,using this method there are effectively 2 frames of reference.

I am very happy with this new understanding, which keeps me in the fold of accepting the invariance of  the speed of light (unsure before because this scenario was new to me)

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11 hours ago, geordief said:

Thanks. That seems to solve the problem I had . So an observer accelerating towards a source of light needs 2 nearby  detectors and to measure a short pulse of light at each.

The closer in time he or she  collates measurements from the two detectors the closer the measurement of the light will come to c.

Do I have it?

I think so... but I'll nitpick. I wouldn't say the observer "needs" 2 separated detectors. For example Markus's method I think involves making only local measurements. Instead I would say, that if you *are* using 2 separated detectors, you have to coordinate them properly.

Not all measurements that rely on a separation of detectors will be the same as a local measurement, just by making the separation smaller. But in this case, by making the two detectors closer, you're minimizing the time that the observer accelerates, so minimizing the effects of difference in speed, and yes getting closer to what an inertial observer measures.

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23 hours ago, Markus Hanke said:

Measure permittivity and permeability of the vacuum, preferably many times over in a number of different ways so as to obtain a large sample size, to reduce the overall error margin. Once you know the values for these to the desired degree of accuracy, the speed of light follows directly, given the validity of Maxwell’s equations.

To measure the dielectric and magnetic constants, a distance standard must be used. Is there a distance standard independent of the speed of light? The whole problem of invariance of the speed of light comes from the fact that there are no standards of distance and time independent of the speed of light in a vacuum.

But the dielectric and magnetic constants will change differently when the speed of light changes, so we can detect a change in the wave resistance of the vacuum.

Edited by SergUpstart
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2 hours ago, SergUpstart said:

The whole problem of invariance of the speed of light

Lorentz invariance isn't a problem, it's a solution to an awful lot of issues that plagued physics before relativity. Without Lorentz invariance, you wouldn't be here right now.

2 hours ago, SergUpstart said:

Is there a distance standard independent of the speed of light?

You are free to choose a distance standard in any way you want, so long as it is consistent. All laws of physics are invariant (i.e. make the same predictions) under consistent changes of units.

2 hours ago, SergUpstart said:

But the dielectric and magnetic constants will change differently when the speed of light changes, so we can detect a change in the wave resistance of the vacuum.

I highlighted the operative word for you. These quantities not being constants in vacuum is inconsistent with both Maxwell's laws, as well as quantum field theory.

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2 hours ago, SergUpstart said:

The whole problem of invariance of the speed of light comes from the fact that there are no standards of distance and time independent of the speed of light in a vacuum.

That's only because the invariance of the speed of light has been established to the point where we rely on it for our standards. The standard for distance used to be a physical artifact. The standard for time is the ground-state hyperfine transition in Cesium, which is not directly dependent on c.

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1 hour ago, swansont said:

That's only because the invariance of the speed of light has been established to the point where we rely on it for our standards. The standard for distance used to be a physical artifact. The standard for time is the ground-state hyperfine transition in Cesium, which is not directly dependent on c.

The keyword is "directly". It is affected by the Planck constant, which is uniquely related to the speed of light. Planck's constant also determines the size of the atoms, hence the size of the physical artifact.

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11 minutes ago, SergUpstart said:

The keyword is "directly". It is affected by the Planck constant, which is uniquely related to the speed of light. Planck's constant also determines the size of the atoms, hence the size of the physical artifact.

Planck's constant is related to c? How?

It is true that c shows up in many places, but for this to be a problem it has to vary by location, as well as between frames. The problem is that if it isn't, physics doesn't just break in the one or two ways you want it to. It breaks in may ways. Ways that we have good evidence that it isn't broken. Markus gave three different views of the big picture. And you have provided...nothing.

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18 minutes ago, swansont said:

Planck's constant is related to c? How? Edited by SergUpstart
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Just now, SergUpstart said:

Showing up in the same equation (for a planck unit, no less) does not make one depend on the other.

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