Invariance of c

[AbstractDreamer]

Special Relativity is formulated from an assumption: 

2. Second Postulate (Invariance of c)

There exists an absolute constant  \(0<c<\infty\) with the following property. If A, B are two events which have coordinates \((x_{1},x_{2},x_{3},t)\) and \((y_{1},y_{2},y_{3},s)\) in one inertial frame \(F\), and have coordinates \((x'_{1},x'_{2},x'_{3},t')\) and \((y'_{1},y'_{2},y'_{3},s')\) in another inertial frame \(F'\), then

\( \sqrt { (x_{1}-y_{1})^{2}+(x_{2}-y_{2})^{2}+(x_{3}-y_{3})^{2} )}=c(s-t) \) if and only if \( \sqrt {(x'_{1}-y'_{1})^{2}+(x'_{2}-y'_{2})^{2}+(x'_{3}-y'_{3})^{2})}=c(s'-t') \).

It appears this postulate makes no limitations on \((s-t)\) even if it is on a cosmological coordinate time scale.  Assuming local c was first measured around  400 years ago and hasn't changed since, why should we assume that it was also the same 13 billion years ago, and will be the same 13 billion years in the future? 

Can we prove that c has always been invariant and will always be invariant? 

Can we prove that this is true for any and all inertial frames of reference.  Given an inertial frame of reference at location in space at the edge of our observable universe, how do we prove that the speed of light here in the Milky Way, as measured using units of time and distance from over there, will be the same c as they are experiencing over there? 

 

 

Edited June 1, 2018 by AbstractDreamer
latex probs

[Strange]

You seem to be mixing two separate ideas here. One is that the speed of light is invariant: the same in all frames of reference. This has been tested (every test of SR confirms this).

The other is that the speed of light is constant. This is harder to test (impossible to test directly). However, the value of the speed of light is fundamental to many things in physics. So if it changed, we should see some effects. (I am fairly sure I have seen something about this being tested, but can't find anything right now.

So it appears the speed of light is both constant and invariant. 

[AbstractDreamer]

Invariant means it doesn't vary.  Constant means it stays the same.  Essentially, in language, the two words are synonyms and have the same meaning.  I'm not mixing up two separate ideas here, I'm asking two separate questions, though I might be using the wrong words.  But now I understand in physics semantics invariance is specifically related to a transformation reference and constant is related to a time reference.  However I had hoped my explanation was clear what I was asking, but maybe not.

a) If c is invariant in all frames of spatial reference - including extra-galactic distances.  How has this been tested?  If every test of SR has been done over relatively short distances, doesn't that leave an obvious question to be answered?

b) If c is constant in all frames of time reference - including a long time ago and a long time in the future.  If it has changed, what effects might we see?

[Strange]

12 minutes ago, AbstractDreamer said:

Essentially, in language, the two words are synonyms and have the same meaning.

Not in physics, though. They are used to describe different and (as far as I know) independent things. One or other (or neither) could be true. It happens that they both are.

Note that "constant" doesn't just refer to changes over time but to any changes (if the speed of light changed for any reason; then all observers would still measure it to be the same; i.e. it would still be invariant).

Maybe someone else has better answers to your questions....

Edited June 1, 2018 by Strange

[beecee]

We have observational evidence  of length contraction and also time dilation: I pretty sure they both denote and require an invariant "c" 

Invariant over time?, what reason do we have to presume that "c"changes over time? How about the other physical constants?

Edited June 1, 2018 by beecee

[YaDinghus]

9 minutes ago, beecee said:

We have observational evidence  of length contraction and also time dilation: I pretty sure they both denote and require an invariant "c" 

Invariant over time?, what reason do we have to presume that "c"changes over time? How about the other physical constants?

A change in c would be quite a drastic change in the laws of nature. The only time I can imagine this happening is the first planck time after the big bang, but that doesn't mean that this would have been the case. 

[swansont]

1 hour ago, AbstractDreamer said:

Invariant means it doesn't vary.  Constant means it stays the same.  Essentially, in language, the two words are synonyms and have the same meaning. 

Invariant means it doesn't change under a coordinate transform. Constant means it doesn't change in time, or position. 

c is constant and invariant. Energy, for example, is constant but frame-dependent, so it is not invariant.

1 hour ago, AbstractDreamer said:

 

I'm not mixing up two separate ideas here, I'm asking two separate questions, though I might be using the wrong words.  But now I understand in physics semantics invariance is specifically related to a transformation reference and constant is related to a time reference.  However I had hoped my explanation was clear what I was asking, but maybe not.

a) If c is invariant in all frames of spatial reference - including extra-galactic distances.  How has this been tested?  If every test of SR has been done over relatively short distances, doesn't that leave an obvious question to be answered?

b) If c is constant in all frames of time reference - including a long time ago and a long time in the future.  If it has changed, what effects might we see?

As has already been stated, c shows up in a lot of places. One is in the fine structure constant (alpha). If c was varying in time or position, it would show up as a change in electromagnetic coupling. We have pretty stringent limits on both. We observe spectra from distant galaxies, and don't see the changes you would expect if alpha was varying. We can look at different atoms in atomic clocks and see that alpha isn't changing in time, both within experimental limits, of course. (meaning the experiments place a very small upper bound on possible changes) 

[Strange]

47 minutes ago, YaDinghus said:

The only time I can imagine this happening is the first planck time after the big bang, but that doesn't mean that this would have been the case. 

I remember seeing something like that suggested as an alternative to inflation. 

[AbstractDreamer]

1 hour ago, beecee said:

We have observational evidence  of length contraction and also time dilation: I pretty sure they both denote and require an invariant "c" 

Length contraction and time dilation are both predicted by special relativity, and proved to real phenomena through experimental tests.  Both also rely on c being "constant" and "invariant" - over the limitations of the tests.    None of this am I questioning.

1 hour ago, beecee said:

Invariant over time?, what reason do we have to presume that "c"changes over time? How about the other physical constants?

I have no evidence whatsoever to presume c changes over time.  I'm asking what evidence is there prove it doesn't, to make it the 2nd postulate of special relativity.

I don't have knowledge of these tests, and do not understand these limitations. 

It is my guess that these test were not - can not - be done on EM radiation that is older than 400 years, because humans did not start testing until 400 years ago. 

• I'm not talking about measuring the velocity of an EM radiation being measured today, here at velocity c originating from the source a 10 billion years ago,
• I'm talking about measuring the velocity of EM radiation a few billion years ago - as it was THEN 10 billion years ago.

It is also my guess is that these tests were not - can not- be done on EM radiation further than 0.0019 light years from earth, as that is the distance that Voyager 1 (the furthest spacecraft to date) has managed to reach. 

• I'm not talking about measuring the velocity of an EM radiation being measured today, here at velocity c originating from a source 10 billion light years away
• I'm talking about measuring the velocity of EM radiation 10 billion light years away - as it is NOW, over THERE, from HERE, 10 billion light years away.

 

13 minutes ago, swansont said:

As has already been stated, c shows up in a lot of places. One is in the fine structure constant (alpha). If c was varying in time or position, it would show up as a change in electromagnetic coupling. We have pretty stringent limits on both. We observe spectra from distant galaxies, and don't see the changes you would expect if alpha was varying. We can look at different atoms in atomic clocks and see that alpha isn't changing in time, both within experimental limits, of course. (meaning the experiments place a very small upper bound on possible changes) 

Showing up in a lot of places, and there being a lot of evidence that c is constant and invariant I don't disagree.  But logically, that simply does not prove that in ANY inertial frame of reference and ALL time coordinates that it is invariant and constant.  We observe spectra from distant galaxies yes.  But we can only observe them today at time t=now.  Which of course is the same c as it was since experiments began 400 years ago.  Looking at alpha today is not looking at alpha a long time ago nor is it looking at alpha a long way away.

Is there any proof that if c was not constant or not invariable, that special relativity is necessarily wrong and not simply incomplete?

What would happen if c is invariant and constant, but simply a different value?  Are there any theories or equations that would cease to work?  Would that change anything about the laws of physics?

1 hour ago, YaDinghus said:

A change in c would be quite a drastic change in the laws of nature. The only time I can imagine this happening is the first planck time after the big bang, but that doesn't mean that this would have been the case. 

Why would it drastically change the laws of nature, if these changes were simply beyond anything that might affect you?  Unless you were to travel a cosmologically long distance or time away, you wouldn't know any different.

 

 

[beecee]

27 minutes ago, AbstractDreamer said:

Length contraction and time dilation are both predicted by special relativity, and proved to real phenomena through experimental tests.  Both also rely on c being "constant" and "invariant" - over the limitations of the tests.    None of this am I questioning.

I have no evidence whatsoever to presume c changes over time.  I'm asking what evidence is there prove it doesn't, to make it the 2nd postulate of special relativity.

You want to prove a negative? Secondly, science isn't about "proof" ...It's about scientific theories that are the best explanation at the time, and are open for possible modification and or total change: Of course those scientific theories such as SR GR and the BB, that continue to explain and make successful predictions, do gain in certainty over time.

It is a postulate of SR because it is required to explain length contraction and time dilation.

• Quote

  I don't have knowledge of these tests, and do not understand these limitations. 

  It is my guess that these test were not - can not - be done on EM radiation that is older than 400 years, because humans did not start testing until 400 years ago. 

  YaDinguhs answered that quite well I thought as follows......

• Quote

  YaDinguhs

  A change in c would be quite a drastic change in the laws of nature. The only time I can imagine this happening is the first planck time after the big bang, but that doesn't mean that this would have been the case. 

   

Quote

Showing up in a lot of places, and there being a lot of evidence that c is constant and invariant I don't disagree.  But logically, that simply does not prove that in ANY inertial frame of reference and ALL time coordinates that it is invariant and constant.

Again scientific theories are not about proof. Read the first answer.

Edited June 1, 2018 by beecee

[Strange]

28 minutes ago, AbstractDreamer said:

But logically, that simply does not prove that in ANY inertial frame of reference and ALL time coordinates that it is invariant and constant. 

That is not really how science works. We can say, for example, that electrons have a charge of e without testing every single electron in the universe.

30 minutes ago, AbstractDreamer said:

We observe spectra from distant galaxies yes.  But we can only observe them today at time t=now.  Which of course is the same c as it was since experiments began 400 years ago.  Looking at alpha today is not looking at alpha a long time ago nor is it looking at alpha a long way away.

That IS looking at alpha hundreds, thousands or even billions of ears in the past.We are looking at the processes with generated the photons.

31 minutes ago, AbstractDreamer said:

Is there any proof that if c was not constant or not invariable, that special relativity is necessarily wrong and not simply incomplete?

If the speed of light were not invariant, then tests of special relativity would not match the predictions (which are based on c being invariant).

People would love to find evidence that SR is wrong or incomplete and so tests have been done to extraordinary levels of accuracy and they are perfectly consistent with the speed of light being invariant.

33 minutes ago, AbstractDreamer said:

Why would it drastically change the laws of nature, if these changes were simply beyond anything that might affect you?  Unless you were to travel a cosmologically long distance or time away, you wouldn't know any different.

Because c is a factor in so many things (e=mc², for an obvious example) so the nuclear fusion processes in distant stars  would be different than in modern stars. And we don't observe that.

 

[AbstractDreamer]

11 minutes ago, beecee said:

You want to prove a negative? Secondly, science isn't about "proof" ...It's about scientific theories that are the best explanation at the time, and are open for possible modification and or total change: Of course those scientific theories such as SR GR and the BB, that continue to explain and make successful predictions, do gain in certainty over time.

It is a postulate of SR because it is required to explain length contraction and time dilation.

Again scientific theories are not about proof. Read the first answer.

You are entirely missing my point.  You're attacking me with all the usual "science is not about proof" spiel, even though it might be a mistake I have made in my comments, is not the message I'm trying to convey.

I have valid questions on the invariance and constance of c, and instead of trying to answer them or tell me why they are not valid, you are trying to school me on what science is about.

Telling me to read your first answer when you yourself haven't understood mine is frustrating.  But I will say it again.

Length contraction and time dilation are both predicted by special relativity, and proved to real phenomena through experimental tests.  Both also rely on c being "constant" and "invariant".  This does NOT necessarily mean that if c was NOT invariant or NOT constant under special circumstances, that time dilation and length contraction would no longer be real phenomena under other circumstances.  

[swansont]

44 minutes ago, AbstractDreamer said:

 It is my guess that these test were not - can not - be done on EM radiation that is older than 400 years, because humans did not start testing until 400 years ago. 

Light traveling at c takes time to get here. If the galaxy was a billion LY away when the photon was sent, the photon is a billion LY old (ignoring expansion effects here), not 400 years old.

 

Quote

 

Showing up in a lot of places, and there being a lot of evidence that c is constant and invariant I don't disagree.  But logically, that simply does not prove that in ANY inertial frame of reference and ALL time coordinates that it is invariant and constant.  We observe spectra from distant galaxies yes.  But we can only observe them today at time t=now.  Which of course is the same c as it was since experiments began 400 years ago.  Looking at alpha today is not looking at alpha a long time ago nor is it looking at alpha a long way away.

The frequency of the emitted photon is dictated by the value of c (and other constants) at the time it was emitted. Seeing the expected value of frequency, in relation to other expected values, tells us that c has not changed with time or distance.

Quote

Is there any proof that if c was not constant or not invariable, that special relativity is necessarily wrong and not simply incomplete?

What would happen if c is invariant and constant, but simply a different value?  Are there any theories or equations that would cease to work?  Would that change anything about the laws of physics?

If c were different and other constants unchanged, then alpha would be different, and atoms would behave differently. Nuclei would behave differently.

 

 

 

[Strange]

2 minutes ago, AbstractDreamer said:

Length contraction and time dilation are both predicted by special relativity, and proved to real phenomena through experimental tests.  Both also rely on c being "constant" and "invariant".  This does NOT necessarily mean that if c was NOT invariant or NOT constant under special circumstances, that time dilation and length contraction would no longer be real phenomena under other circumstances.  

But until you can define what those "special circumstance" are and make a prediction of the effect they have and then propose an experiment to test it, you are not doing science.

You can imagine all sots of things might be possible. Maybe the speed light changes when we are not measuring it. Or perhaps it is not invariant on very short timescales. Or maybe ...

But if you have no evidence for these random ideas, and no way of testing them, and all the evidence we currently have shows the opposite, then the speculation is a bit pointless.

[swansont]

5 minutes ago, AbstractDreamer said:

 

I have valid questions on the invariance and constance of c, and instead of trying to answer them or tell me why they are not valid, you are trying to school me on what science is about.

You have been given several answers and it looks like you have misunderstood the implications of them

 

[beecee]

4 minutes ago, AbstractDreamer said:

You are entirely missing my point.  You're attacking me with all the usual "science is not about proof" spiel, even though it might be a mistake I have made in my comments, is not the message I'm trying to convey.

I don't believe I am. Science is not about proof. It is about the scientific method, observational and experimental evidence, and supporting theories based on that.

Quote

I have valid questions on the invariance and constance of c, and instead of trying to answer them or tell me why they are not valid, you are trying to school me on what science is about.

No, I told you why "c'is invariant, and I also referred you to another answer by another. 

Quote

 

Telling me to read your first answer when you yourself haven't understood mine is frustrating.  But I will say it again.

Length contraction and time dilation are both predicted by special relativity, and proved to real phenomena through experimental tests.  Both also rely on c being "constant" and "invariant".  This does NOT necessarily mean that if c was NOT invariant or NOT constant under special circumstances, that time dilation and length contraction would no longer be real phenomena under other circumstances.  

 

 Length contraction and time dilation are evidenced. This tells us that "c"is invariant.

 

 

[AbstractDreamer]

1 minute ago, Strange said:

That is not really how science works. We can say, for example, that electrons have a charge of e without testing every single electron in the universe.

That IS looking at alpha hundreds, thousands or even billions of ears in the past.We are looking at the processes with generated the photons.

If the speed of light were not invariant, then tests of special relativity would not match the predictions (which are based on c being invariant).

People would love to find evidence that SR is wrong or incomplete and so tests have been done to extraordinary levels of accuracy and they are perfectly consistent with the speed of light being invariant.

Because c is a factor in so many things (e=mc², for an obvious example) so the nuclear fusion processes in distant stars  would be different than in modern stars. And we don't observe that.

 

But I'm not asking to test every electron in the universe.  I'm not asking to test every inertial frame of reference.  I'm asking to test ONE inertial frame of reference 10 billion light years away.

It is NOT looking at alpha as it was then billions of years ago.  It is looking at alpha today that has already aged billions of years.

If the speed of light were invariant under circumstances beyond that tests for special relativity, then none of the tests would fail to match predictions.

 

 

[Strange]

1 minute ago, AbstractDreamer said:

But I'm not asking to test every electron in the universe.  I'm not asking to test every inertial frame of reference.  I'm asking to test ONE inertial frame of reference 10 billion light years away.

You can't. SR only applies locally. You need to use GR to compare frames of reference on that scale. And GR has been amazingly successful in that regard.

1 minute ago, AbstractDreamer said:

It is NOT looking at alpha as it was then billions of years ago.  It is looking at alpha today that has already aged billions of years.

Nonsense. Alpha determines the behaviour of the atoms that emitted the light.

2 minutes ago, AbstractDreamer said:

If the speed of light were invariant under circumstances beyond that tests for special relativity, then none of the tests would fail to match predictions.

Correct. But then you need to come up with a model for what those circumstances are and how it would change the predictions of SR. 

Without that you are just imaging that there might be invisible flying unicorns in some part of the world we haven't explored yet.

[swansont]

6 minutes ago, AbstractDreamer said:

But I'm not asking to test every electron in the universe.  I'm not asking to test every inertial frame of reference.  I'm asking to test ONE inertial frame of reference 10 billion light years away.

 

We can't do that. But demanding impossible tests isn't going to get you anywhere.

We're limited to the test we can actually perform, and they tell is that alpha is the same as it was billions of years ago, in all directions, and is not currently changing here.

6 minutes ago, AbstractDreamer said:

It is NOT looking at alpha as it was then billions of years ago.  It is looking at alpha today that has already aged billions of years.

Yes, it is. That's when the interactions that produced the photons occurred.

 

[beecee]

13 minutes ago, AbstractDreamer said:

It is NOT looking at alpha as it was then billions of years ago.  It is looking at alpha today that has already aged billions of years.

It certainly is looking at Alpha as it was billions of years ago. We are effectively looking into the past every time we look at the night sky.  All due to the finite invariant nature of light and the vast distances involved.

Let me also add that each frame of reference is as valid as each other. eg: In another frame, Alpha may have gone supernova, while we see it as it was millions/billions of years ago, and will keep seeing it for millions/billions of years until we see it go supernova.

Edited June 1, 2018 by beecee

[AbstractDreamer]

7 minutes ago, swansont said:

Light traveling at c takes time to get here. If the galaxy was a billion LY away when the photon was sent, the photon is a billion LY old (ignoring expansion effects here), not 400 years old.

 

The frequency of the emitted photon is dictated by the value of c (and other constants) at the time it was emitted. Seeing the expected value of frequency, in relation to other expected values, tells us that c has not changed with time or distance.

If c were different and other constants unchanged, then alpha would be different, and atoms would behave differently. Nuclei would behave differently.

 

 

 

The photon is a billion years old, but the MEASUREMENT is 400 years old of a photon that has aged a billion years.  It is NOT the measurement of the photon a billion years AGO.

By frequency do you mean intensity?  What is the equation that is dictated by c?  What are the other constants are involved?

[StringJunky]

6 minutes ago, AbstractDreamer said:

By frequency do you mean intensity?  What is the equation that is dictated by c?  What are the other constants are involved?

Frequency is the number of wave oscillations in a second.

[AbstractDreamer]

14 minutes ago, Strange said:

But until you can define what those "special circumstance" are and make a prediction of the effect they have and then propose an experiment to test it, you are not doing science.

You can imagine all sots of things might be possible. Maybe the speed light changes when we are not measuring it. Or perhaps it is not invariant on very short timescales. Or maybe ...

But if you have no evidence for these random ideas, and no way of testing them, and all the evidence we currently have shows the opposite, then the speculation is a bit pointless.

I already have defined those special circumstances.  When time is a long time ago, or a long time in future.  Or when distance is a long way away.  I'm not here to do science, i'm here to ask questions about science.

Its not a random idea.  It taken from the 2nd postulate of special relativity where there is no limitation stated on (s-t), nor is there any limitation on inertial frames of reference.  I am simply questioning those limitations.  You have already hinted that during inflation, there are some theories to a varying speed of light.  So when t=very early on, physics were different and special relativity fails, but the postulates do not reference these limitations either.

 

[YaDinghus]

1 hour ago, AbstractDreamer said:

2 hours ago, YaDinghus said:

A change in c would be quite a drastic change in the laws of nature. The only time I can imagine this happening is the first planck time after the big bang, but that doesn't mean that this would have been the case. 

Why would it drastically change the laws of nature, if these changes were simply beyond anything that might affect you?  Unless you were to travel a cosmologically long distance or time away, you wouldn't know any different.

I might have said it in another thread. c is not only the speed of light, it is the speed of causality. And it affects every interaction involving everything, because it is in the basic relationship of Mass, Momentum and Energy. Since Energy is a conserved quantity as long as there is a conserved symmetry, and changing c would change Energy, you would necessarily break symmetry, which only happens at force unification and diversification thresholds - major changes in the laws of physics. We are quite confident that c has not changed after the first planck time after the big bang.

[AbstractDreamer]

17 minutes ago, Strange said:

You can't. SR only applies locally. You need to use GR to compare frames of reference on that scale. And GR has been amazingly successful in that regard.

Nonsense. Alpha determines the behaviour of the atoms that emitted the light.

Correct. But then you need to come up with a model for what those circumstances are and how it would change the predictions of SR. 

Without that you are just imaging that there might be invisible flying unicorns in some part of the world we haven't explored yet.

No, flying unicorns is crazy.  Variable c is within the domain of questionable physics.