# Is the speed of light always 299 792 458 m / s

1. Nov 28, 2012

### Bjarne

The speed of light is measured to 299 792 458 m / s and 1 meter defined to 1/299 792 458 of the speed of light.

Let us assume that A live at the top of a skyscraper and B in the cellar the past 10 billion years.
After 10 billion years B’s clock have “lost” 10 second due to different gravitational influence, compared to A’s clock.

10 billion years ago 2 photons was leaving a star 10 billion light years away and hit A and B at the same moment 10 billion year after.

B would now say that he measured the time it took for the photon to reach earth, to 10 second less than A measured.

B would therefore claim that either the speed of light must have been traveling faster than 299 792 458 m / s, or local distance (where B is) must be stretching or contracting proportional with the stretch of time.

Which option is correct, and what proves it ?

2. Nov 28, 2012

### Staff: Mentor

Length contraction.

Proof? It can't be proven with that experiment, each would have to locally measure the speed of light and measure that it is C. Then they would know the distance has to be different.

Please don't make this about the recursiveness of the definitions. That is not a confounding factor.

3. Nov 28, 2012

### Staff: Mentor

Neither, really (B, in the cellar is still subject to some gravitational effects so will get a different result from a hypothetical observer in a gravity-free vacuum). But as you've stated the problem, there's no way of "proving" that any of them are correct or not - we just have a bunch of very slightly different measurements, all multiplied by 10 billion to exaggerate the differences.

To completely understand their observations, they must both measure the local speed of light; they'll both get the same result. Then they can assume that that value is also the speed of the light traveling from the distant galaxy, see whether that assumption leads to an internally consistent theory that also matches experimental evidence. Only then can they accept the explanation that A and B experienced different amounts of gravitational time dilation.

(And you are still free to try to construct a completely different theory if you want to... but given the experience of the past century with relativity, this is unlikely to be a good use of your time).

4. Nov 28, 2012

### Staff: Mentor

Why would he make either claim? Depending on personal inclination and unspecified details B could also attribute the difference to:
A different simultaneity convention
Different paths of the photons through spacetime
Different paths of A and B through spacetime
A's clock is wrong
B's clock is wrong
Etc.

The math can be interpreted many ways, but the important thing is that GR makes correct predictions about experimentally measured results.

5. Nov 29, 2012

### Bjarne

B is counting 10 second less, and the explanation is "length contraction" of the distance to the source that 10 billion years ago emitted the photon, according to GR.

I guess that according to GR this must mean that 1 local meter by B (in the cellar) is longer, compared to 1 meter at the top of the skyscraper. And this is why the distance B would measure is shorter (contracted).
I mean in reality the distance to the source (10 billion km away) is not changing, - it would be illogical if it was, - but what instead happens is that B experience some kind of optical change due to change of space time ( deformation of space)..

Or how can we be more specific to understand “length contraction” in this case?

6. Nov 29, 2012

### Staff: Mentor

Saying "optical change" implies to me that you think it is an illusion. It isn't. Length is just different for different observers, just like time and speed....and even color.

7. Nov 29, 2012

### Bjarne

Right, and as I wrote this must mean that 1 meter is not the comparable same for A and B (?)

8. Nov 29, 2012

### Staff: Mentor

Depends how you do the comparison. This is something that you didn't clearly specify in your previous thread either.

9. Nov 29, 2012

### Bjarne

This is off course not possible to confirm because A and B cannot be both at the top of the building and in the cellar of the skyscraper to compare whether 1 meter is the comparable same, - in these 2 different space time realities. Anyway that should not mean this is a dead end. What is wrong by chosen the most logical conclusion..(?)

We know speed of light is the "same" for both A and B.

We also know speed for both A and B

Speed * Time = Distance.

The result is that the time it took the 2 photons to reach the skyscraper is 10 less second seen from B’s perspective compared to A’s observation..

The first simple mathematical conclusion is therefore that length cannot be the same.

But the most logical conclusion must be the 2 photons must be assumed to have hit the same skyscraper “in the same moment” – I mean if both A and B would see the same supernova 10 billion LY away, - the light B would receive would not be delayed 10 seconds compared to A.
So fare I believe we are on safe ground.

Furthermore the most logical conclusion must also be that the “real distance” (doesn’t matter how it is measured and by who) – is NOT changing. I mean if I would take the elevator to the top of a building, - this is not changing the “real distance” to the Sun etc...

Based on such simple logical conclusions, the only way left, whereby distances in this case possible can be different, - is if the way they are measured, - which off course must mean 1 meter is not comparable the same, - for both A and B. (or ?)

10. Nov 29, 2012

### Staff: Mentor

Leaving aside the nonsense about different realities, you have it completely backwards. The problem is not that it is impossible to make this comparison, it is the opposite. There are many ways to make the comparison, so you have to specify exactly how you plan on doing it. I suggested several different ways in our previous conversation.

I already proposed several alternative conclusions.

The problem is that you think that this question is meaningful as posed, and it isn't. You must specify how you propose to compare the meter at A to the meter at B.

Btw, the whole discussion about the light from the star has little to do with the comparison of meters local at A and meters local at B since the bulk of the path of the light is not local to either A or B. It is a "red herring".

Last edited: Nov 29, 2012
11. Nov 29, 2012

### Bjarne

I am not sure whether I understand what you mean.
Regarding whether a deeper understanding of the “length contraction phenomena” - possible could be caused due to that 1 meter not is the comparable same for A and B (at the top of the skyscraper compared and at the cellar) ? - I cannot see any method to either confirm or reject this. Can you (really) ?
I think it is impossible to measure / prove, since the device to measure it cannot be in 2 different space-time realities at the same time, and this is as I see it necessary.

Yes that’s right, a different thread. – But the thought-experiments was much too “complicated”
SR was overlapping GR , and I was more confused after the discussion as before.
The thought experiment in this threat is far more simple, - at least to my opinion.

Right, you suggested…
1. A different simultaneity convention
2. Different paths of the photons through space-time
3. Different paths of A and B through space-time
4. A's clock is wrong
5. B's clock is wrong
6. Etc.

Sorry, by in my ears none of these sounds, - like the most logical conclusion.

Option 1 - A different simultaneity convention.
If you mean this should be responsible for the whole time-difference between A and B (?)
If so that would also mean that B would see photons from a supernova (billion LY away) several seconds true delayed compared to A.
Will A and B see see the 2 photon's in the same moment?, - I believe so. Disagreement must be relative insignificant compared to the measured time difference (by A and B)..
So, to a certain degree I guess YES, - but insignificant compared to the relative large time difference measured by A and B during a period of 10 billion years.

Option 2. - Different paths of the photons through space-time
To a certain degree YES, but insignificant compared to the relative large time difference measured by A and B during a period of 10 billion years.
I mean imagine a supernova not only was 10 billion LY away but for example 1.000.000.000LY (and the Universe is 'bit' older than now) .
2 photons leaving a supernova that long distance away, would not only cause few second difference but cause many hours’ time measurement difference (seen from A and B's perspective) .
I assume such 2 photons anyways would hit the skyscraper (top and cellar) at the same moment .
We are not only talking about split second differences, - but much more than that.
I cannot imagine that A can see the supernova from first floor, after that go to the top and here have to wait 1 hour before he can see it here too, - due to something serious had happen to the photon's path.

Option 3 - Different paths of A and B through space-time
To a certain degree YES, but insignificant compared to the relative large time difference measured by A and B.

It is the same kind of problem as option 2, - we are dealing with a relative large time difference, increasing during billions of years. - This should make it possible to ignore all insignificant factors.

Option 4+5
Wrong Clock’s ?
This aspect of GR / SR have past plenty test / GPS etc..

We can even simplify the thought-experiment further
Imagine one neutrino, travelling the same distance, first hitting the skyscraper from right above, (and detected at the upper floor,) and a split second later detected in the cellar.
Now relative motion of A and B, - or – “traveling by different paths” - cannot be significant options or at least very insignificant.

And still A and B would far from agree about the distance the neutrino had traveled since it started 10 (or 100.000.000) billion LY away.

So we are back where we started; - is it possible to reach a logical and deeper difination of ; what is length contraction ?
How many true options are there?
I mean several options must be possible, - logical – to shut out.

Last edited: Nov 29, 2012
12. Nov 29, 2012

### nitsuj

Oh that's easy, it's width widening

A meter stick as measured by you (comparably at rest) rockets off a boomerang trajectory at a significant chunk of c.

on it's return towards you in impales your body; sorry just trying to bring these separate physical realities together.

how much length passes through you; a full meter?

13. Nov 29, 2012

### Staff: Mentor

There is no such thing as one singular "real distance" just as there is no such thing as "absolute time". If I measure the Earth's distance to the sun and get 90 million miles and you measure it and get 80 million miles using a similar method but experiencing relativistic effects, both are "real".

14. Nov 29, 2012

### arindamsinha

Would it be valid to explain it in this way?
• B is in higher gravity, so his 'seconds' are slightly longer than A's (say x%)
• For the same reason, B's 'meter' is also slightly longer than A's, and by the same proportion (x%)
Therefore when B computes the speed of light, which has units of 'meters' per 'second', the effects cancel out, and he gets the same numerical answer as A?

15. Nov 29, 2012

### Bill_K

Spacetime is locally Minkowskian at every point. The local speed of light is the same everywhere. The diameter of a hydrogen atom is the same, and the frequency of its spectral lines are the same. So from B's local point of view, nothing has contracted, neither time nor space. And c is c.

The only question then is how A views B's experiments. He does so using his own Schwarzschild coordinates, r, t, θ and φ. A interprets the velocity of a light ray moving in the radial direction to be its coordinate velocity, dr/dt. In the azimuthal direction he interprets it as r dφ/dt. Neither of these is equal to c. Furthermore they are not equal to each other. A believes the speed of light down in the well is not c, and not isotropic either.

16. Nov 29, 2012

### Staff: Mentor

This is nonsense. In GR there are not two separate realities, there is only one. There is only one interpretation of one theory (the many worlds interpretation of QM) which contemplates multiple realities, and then the device is automatically in an infinite multitude of realities, not just one.

It is a complicated topic. I am sorry that you wound up confused, but I think that is largely because you are deliberately attempting to impose a non-mainstream viewpoint and are resistant to learning anything contrary to your preconceived notions.

Nevertheless, they are valid and logically possible which means that we are not forced to make the conclusion you suggest.

You acknowledge that the effect is present. That it is insignificant is a quantitative argument that needs to be supported mathematically.

Again, you agree that the effects are present. To claim that they are insignificant is a quantitative argument requiring math.

Yes. GPS in fact treats the orbiting clocks as wrong and corrects them.

I agree, several are possible, which is why you must always specify the details.

Again, the light from the star is irrelevant to the comparison of the meters at A and B.

17. Nov 30, 2012

### Bjarne

Corrrect
I was just trying to explain that seen from any overall perspective - "the distance" - "it self" - (between the Earth and the distant star) is not changing, - (regardless which overall observer that would measure it), - the disagreement between A and B, is rather due to a "local" different space time deformation / reality perception.
I fully agree to that.
But still the point is what happens to 1 meter, - I guess the same thing.

Let say A would use a lot of effort putting a measurement tape between the Sun and the Earth. Everybody could now see that the distance was exactly 1,5E11 meter, so as A predicted.

But B is skeptical, he would say, seen from his cellar perspective, - (due to length contraction), - the distance must be 10 meter less. Something very basic must be wrong with A’s measurement tape.

It must be crystal clear that B never would be able accept that A's total measurement to the Sun is correct.
If A's total measurement not is correct (seen from B's perspective), - he must most likely also have failed to measure 10% of the path to the Sun, - and also failed to measure 1% of the path.

In the end of the day it comes down to that B would say to A, - I don't trust your ruler is exactly 1 meter. Prove it to me.

A's definition of 1 meter is the time interval of 1/299,792,458 of a second, - So what is exactly wrong with that?

I think the definition of one meter is always correct = 1/299,792,458 of a second
BUT it must be relative to the local time-dilation.
Which mean a short second = a short meter, - and a relative longer second = a proportional longer meter. That would be the most simple and logical way to exactly settle the disagreement.

Such conclution should not come as a surprise, because space is curving, - illustrated by the stretching rubber sheet.
So when space is ‘stretching’ towards a field of gravity, and time also, - I cannot see what prevent such logical conclusion, - There should as I see it not be any conflict to that

Last edited: Nov 30, 2012
18. Nov 30, 2012

### nitsuj

Does this point have any purpose? It seems to me to be of an opinion of interpretation, for example with russ' one measures distance as 80 million miles an other measures the same points as 90 million miles. That is two separate physical realities. I can even do the math 90-80 = 10 see they're not the same length.

I appreciate the perspective that the interval is the same, and stands as a "true" measure of spacetime, in turn one physical reality. But i don't think that is your point with calling different measures of length time of the same physical reality. To reword my point of view, the Twins are different ages, at one point they experienced different physical realities...comparably.

Last edited: Nov 30, 2012
19. Nov 30, 2012

### Staff: Mentor

This is not correct. There is no such thing as the distance "itself". There is only the distance according to a specified reference frame/coordinate system. And that does change wrt different systems.

Again, the answer depends on the method of comparison. What experiment would B accept as a method of comparison?

I don't know why this concept is so hard for you to understand. I thought you understood it after our previous conversation on the same topic.

20. Nov 30, 2012

### Staff: Mentor

No, they are not different realities, they are merely different perspectives on the same reality. The point is that there is no such thing as distance by itself. Only distance relative to some coordinate system. So the fact that distance relative to A is not equal to distance according to B does not imply multiple realities.

Even in non relativistic physics this happens with some quantities. Would you say Newtons universe implies a different reality for each Newtonian reference frame?

Last edited: Nov 30, 2012