# Is relativity remain unchanged?

1. Feb 26, 2009

### sanjibghosh

let's the speed of light is constant(c) but any information(interaction) can not travel with 'c'. let's it is travel with the speed of sound. then ,is relativity remain unchanged?

2. Feb 26, 2009

### Mentz114

Information can travel at the speed of light. Perhaps you mean something else ?

3. Feb 26, 2009

### Staff: Mentor

The question as posed is very difficult to answer. Light carries information and there are tons of experiments that show it or that use that fact. We would have to go back to each of those experiments, change the results and then come up with a new theory that explains all of those imagined results.

Here is a different question which would not contradict any previous experiments, but should get to your underlying concern:

The mass of the photon is believed to be zero, but that is something that cannot be established experimentally. All you can do is put an upper bound on the mass. So, let's say that the next experiment to measure the mass of a photon detects a small (consistent with previous experiments) but non zero mass? Then light would not travel at c nor would the information carried by light.

Is that a suitable substitute?

4. Feb 26, 2009

### HallsofIvy

Staff Emeritus
The question "as posed" simply doesn't make any sense! There is no point in saying " let's it is travel with the speed of sound". Information can travel with any speed up to and including the speed of light. If you hear someone call your name, that's information isn't it? And it traveled to you at the speed of sound. Do you mean "suppose information could NOT travel faster than the speed of sound" or, equivalently, "suppose the speed of light was the same as the speed of sound". The fundamental concepts of relativity would not change but we would observe the results of relativity more easily.

5. Feb 27, 2009

### sanjibghosh

suppose,there is an world where information can travel only through the sound, light still exist, but can not carry any information.

Last edited: Feb 27, 2009
6. Feb 27, 2009

### Mentz114

I can't imagine such a world. Would we still be able to use our eyes ? Light is such a fundamental part of our reality that reality without it seems impossible. Not a line of thought I wish to pursue.

7. Feb 27, 2009

### sanjibghosh

but here we calculating all masses and other things with the help of 'relativity with speed of light'. if information can not travel with 'c' then what are the transformation equations?
suppose there is some system where no information can travel with c but with the speed of sound, then can i use all the transformation equation by applying the replacement c by speed of sound ?
if so, then what is the speed of light in that system?

8. Feb 27, 2009

### Ich

From this, and the principle of relativity, it can be deduced that this speed "plays the role of infinite speed", which means that no information can travel faster.
It is irrelevant whether light rays or cathode rays or sound waves happen to travel at this speed. But if you analyze the nature of these phenomena, you find that anything that travels at invariant speed must be massless and independent of a carrier medium. That's true for light and gravitation, obviously not quite for neutrinos, not really for cathode rays (electrons), and certainly not for sound waves.

9. Mar 1, 2009

### sanjibghosh

actually i want to know that if all possible interaction(under consideration) play through sound wave in some system then can i use the fact that the effective mass of particle m=m0/$$\sqrt{}(1-\gamma)$$
where $$\gamma$$=v2/s2
and s=speed of sound

Last edited: Mar 1, 2009
10. Mar 1, 2009

Staff Emeritus
The answer to that question is "no".

11. Mar 1, 2009

### Staff: Mentor

The Lorentz transform would remain unchanged. The invariant speed c is a property of spacetime, not just a property of light. In that sense calling c "the speed of light" is a historical misnomer.

12. Mar 2, 2009

### neopolitan

Hi sanjibghosh,

I think I understand your question. You are dividing up the speed of light and the maximum speed at which information may be transmitted. Now the other responders are correct in saying that light conveys information so you have an immediate problem but let's look at a situation where your "speed of information" might make sense.

"Gallilean relativity" is the simple sort of relativity that we first get taught in high school, normally we get taught something like:

s=x+vt

but with some renaming and reorganisation (s->x, x->x'), this is:

x'=x-vt

|...............|..........................................................|
|......<-------------------..s..------------------>........|
|...............|.........<-----------..x..---------->...........|

x0..............|.........................................................x1
|..............x'0........................................................x'1
....-> v ->

But, this simple relativity is based on the instantaneous transmission of information. We now know that information is speed limited (to c) and you want to know what if it were speed limited to the speed of sound (s).

You can go from Gallilean relativity to Einsteinian relativity by removing the assumption of instantaneous transmission of information. If the speed is limited to c, then you end up with the Lorentz transformations, rather than x'=x-vt (and the implied, but rarely stated, t'=t). Similarly, if the speed is limited to s, you end up with the Sanjibghoshian transformation which has s where c is in the Lorentz versions.

While this method for deriving the Lorentz transformations will arrive at a sensible sounding result, most of the other methods will fall over if you have information limited to a speed below the speed of light (since a lot of them are based on electromagnetic radiation, like the original Maxwell based derivation, Einstein's 1905 derivation and Feynman's light clock). One other derivation will arrive at the same Sanjibghoshian transformation equations (a derivation based on universal expansion, if the rate of expansion changes from c to s you can end up with the same equation) ... however, the model that this derivation is based on will then tell you that light cannot travel at faster than s.

So, you arrive back at where the other posters were at. If the transmission of information was limited below the speed of light you have a problem. Even if we use the derivation above, from Gallilean relativity to Special Relativity by removing the assumption of instantaneous transmission of information, and give the speed of transmission of information as s, you will end up being able to get information quicker than "the speed of information" since you will get light images telling you about something happening a distance away before the information could have reached you, which leads you into the same sort of potential causality problems you can get into with tachyons (theoretical faster than light particles, but in light of this discussion they could be called "faster than information particles"). A discussion elsewhere came to the conclusion that you can have only two of the following three: causality, special relativity, FTL. In your universe, you could only have two of: causality, special relativity, FTI (faster than information). The most likely candidate for exclusion is FTI.

Basically, the speeds of light and information will always be the same, and as DaleSpam said, calling the c the speed of light is a bit misleading.

In my words (not Dale's anymore), c is the fastest anything can go, it's a reflection of the ratio between the spatial dimensions and the temporal dimension. Both light and information travel as fast as they possibly can, and therefore they travel at c. It's such a fundamental that it is very difficult to imagine any way in which information could be limited to a speed below light (even if one ignored the fact that light conveys information).

cheers,

neopolitan

Last edited: Mar 2, 2009
13. Mar 2, 2009

### confinement

I understand the question sanjibghosh, and the answer is yes, as long as the sublight speed barrier (speed of sound in your example) is a true upper bound on speed, as opposed to an approximate upper bound i.e. only holds or some range of energies.

Even in the latter case we have the mainstream treatment of phonons on a lattice which will satisfy approximate lorentz symmetry, where the speed of light is literally replaced with the speed of sound in the material. This can be found in most modern condensed matter books.

14. Mar 4, 2009

### sanjibghosh

hi,
neopolitan
I'm very happy with sanjibghoshian(!!!.. ) transformation.but i do not understand clearly,so can you tell me some sources where it was discussed.

Last edited: Mar 4, 2009
15. Mar 4, 2009

### sanjibghosh

i think the limitation of 'energy range' can be explain as
when energy is low ,the most of the interaction is due to the phonon exchange .
but if the energy is large, the electromagnetic interaction is active and that's why the model does not work.

i am not sure.even i do not know whether the phonon model work at high energy range or at low energy range(good condensed matter books are not available to me)

16. Mar 4, 2009

### sanjibghosh

why?

17. Mar 4, 2009

### Staff: Mentor

There are two main formulations of SR: the traditional two-postulate formulation and the modern Minkowski geometry formulation. In the two-postulate formulation all that would be necessary to adapt it is that the second postulate would need to refer to "the invariant speed" rather than to "the speed of light". For the Minkowski geometric formulation all that would be needed is to draw the worldlines of light pulses at a less than a 45 degree angle. No changes to the Lorentz transform would be necessary for either formulation.

18. Mar 4, 2009

### neopolitan

I am not sure that Dale fully grasped one aspect of the question. It's no surprise because as I said, it is difficult to conceive of a situation where the maximum speed of information is lower than the speed of light.

What is "the invariant speed"? I'm not being silly (I hope) but pointing out that the definition in terms of the original question will have to be such that light can go faster than it. For the Minkowski space explanation, remember again that in the original question information travels at less than the speed of light, not light slower than the speed of information.

For sanjibghosh:

Think about a "stationary observer" - Stan, an "observer in motion" - Mona, and a distant event - E. Initially Stan and Mona are co-located.
- According to Stan, Mona has a constant velocity, relative to E, of v (ie in the direction of E).
- According to Mona, Stan has a constant velocity, relative to E, of -v (which means Stan is moving away from the event).
- Both observers "know" that the event they observe is the same event that the other observes.
- Both observers work on the assumption that the laws of physics are the same for both of them.

With Gallilean relativity, after a period of time - t, and assuming instantaneous transmission of information, we have:

distance (Mona-E) = distance (Stan-E) - vt

Now let's remove the assumption of instantaneous transmission of information and insert a new assumption "information travels at a constant speed of s".

We end up with a number equations, because the information about E reaches each observer at different times, t(Mona) and t(Stan) (ie time elapsed before information from E reaches Mona, according to Mona and time before information from E reaches Stan according to Stan) or t(Mona)Stan and t(Stan)Mona (ie time elapsed before information from E reaches Mona, according to Stan and time before information from E reaches Stan according to Mona). First, looking at things from Stan's perspective:

distanceStan (Stan-E) = distanceStan (Mona-E) + v.t(Mona)Stan = s.t(Stan)Stan ...................... (1)

Then using Mona's perspective:

distanceMona (Mona-E) = distanceMona (Stan-E) - v.t(Stan)Mona = s.t(Mona)Mona ....................... (2)

Now, the thing to remember here is that - according to Mona - Mona has not moved and - according to Stan - Stan has not moved and, according to both, the laws of physics apply equally to both. This last condition implies a consistent conversion factor between:

• distanceMona (Stan-E) and distanceStan (Stan-E), and
• distanceStan (Mona-E) and distanceMona (Mona-E)

Mathematically:

• distanceMona (Stan-E) = conversion factor * distanceStan (Stan-E), ........................ (3)
• distanceStan (Mona-E) = conversion factor * distanceMona (Mona-E) ........................ (4)

Taking Stan's perspective, noting that t(Mona)Stan=distanceStan (Mona-E) / s:

distanceStan (Stan-E) = distanceStan (Mona-E) + vt(Mona)Stan = distanceStan (Mona-E) + v.distanceStan (Mona-E) / s

therefore:

distanceMona (Stan-E) = conversion factor * distanceStan (Stan-E) = conversion factor * ( distanceStan (Mona-E) + v.distanceStan (Mona-E) / s )

distanceMona (Stan-E) = conversion factor * distanceStan (Mona-E) * ( 1 + v / s ) ..................................... (5)

Then taking Mona's perspective, noting that t(Stan)Mona=distanceMona (Stan-E) / s:

distanceMona (Mona-E) = distanceMona (Stan-E) - vt(Stan)Mona = distanceMona (Stan-E) - v.distanceMona (Stan-E) / s

therefore:

distanceStan (Mona-E) = conversion factor * distanceMona (Mona-E) = conversion factor * ( distanceMona (Stan-E) - v.distanceMona (Stan-E) / s )

distanceStan (Mona-E) = conversion factor * distanceMona (Stan-E) * ( 1 - v / s ) ................................ (6)

Substituting (6) into (5):

distanceMona (Stan-E) = conversion factor * conversion factor * distanceMona (Stan-E) * ( 1 - v / s ) * ( 1 + v / s )

1 = ( conversion factor )2 * ( 1 - v / s ) * ( 1 + v / s )

( conversion factor )2 = 1 / ( 1 - v2 / s2 )

conversion factor = $$1 / \sqrt{ ( 1 - v^{2} / \textit{s}^{2} ) }$$ ........................ (7)

With the appropriate use of (1), (2), (3), (4) and (7) to find out (a) what the distance between Mona and E is, according to Stan but in terms of Mona's observations and (b) what time has elapsed before Mona receives information from E, according to Stan but in terms of Mona's observations, you arrive at:

(a) distanceStan (Mona-E) = ( distanceMona (Stan-E) - v.t(Stan)Mona) $$/ ( \sqrt{ ( 1 - v^{2} / \textit{s}^{2} ) }$$

in other words

x'= ( x - v.t) $$/ ( \sqrt{ ( 1 - v^{2} / \textit{s}^{2} ) }$$

and

(b) t(Mona)Stan = ( t(Stan)Mona - v.distanceMona (Stan-E) / s2) $$/ ( \sqrt{ ( 1 - v^{2} / \textit{s}^{2} ) }$$

in other words

t' = ( t - v.x / s2) $$/ ( \sqrt{ ( 1 - v^{2} / \textit{s}^{2} ) }$$

which correspond directly with the standard Lorentz transformations:

x'= ( x - v.t) $$/ ( \sqrt{ ( 1 - v^{2} / \textit{c}^{2} ) }$$

and

t' = ( t - v.x / c2) $$/ ( \sqrt{ ( 1 - v^{2} / \textit{c}^{2} ) }$$

We started off with a speed of information with a value of s, if we started with a speed of information of c, we'd have ended up with the Lorentz transformations rather than the Sanjibghoshian transformations.

...

I do have a cleaner version of this, but I am not allowed to link what might be a questionable document. I personally don't see this derivation as revolutionary, it is merely starting from a different starting point (information is not transmitted instantaneously) to get to the same conclusions as SR does.

And yes, I do realise that the subscripts can be confusing, but SR gets a lot more confusing if you refuse to remain consistent about whose perspective you are using.

cheers,

neopolitan

PS Note that while I showed

(a) the distance between Mona and E, according to Stan but in terms of Mona's observations and
(b) the time elapsed before Mona receives information from E, according to Stan but in terms of Mona's observations,

I could have done

(a) the distance between Stan and E, according to Mona but in terms of Stan's observations and
(b) the time elapsed before Stan receives information from E, according to Mona but in terms of Stan's observations

which would have end up with the same final equations in terms of x, x', t and t'. I could do that if anyone feels cheated, but really, some work should be left for the reader

Last edited: Mar 4, 2009
19. Mar 5, 2009

### Staff: Mentor

I have no problem concieving of an information-less tachyon. In fact it is easier than one that carries information since you avoid all of the nasty causality problems. However, it is contrary to an enormous amount of evidence to consider that light does not carry information, which is why I re-posed the question as I did. I think my re-framing of the question is physically reasonable and still addresses his root concern.
The invariant speed is the speed which is the same in all inertial reference frames. I.e. it is the speed "c" in the Lorentz transform. The invariant speed is a feature of spacetime, and is not directly a feature of either light or information. The invariant speed is equal to the speed at which light propagates to current experimental precision, but future experiments could concievably determine that light propagates at a slightly different speed without any impact on the Lorentz transform.

20. Mar 5, 2009