Is relativity remain unchanged?

[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?

 

[Mentz114]

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

 

[Dale]

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?

 

[HallsofIvy]

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.

 

[sanjibghosh]

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

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

 

[Mentz114]

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

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.

 

[sanjibghosh]

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?

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?

 

[Ich]

We start with the observation that there is an invariant speed.
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.

 

[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

 

[Vanadium 50]

The answer to that question is "no".

 

[Dale]

if information can not travel with 'c' then what are the transformation equations?

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.

 

[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

 

[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.

 

[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.

 

[sanjibghosh]

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.

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)

 

[sanjibghosh]

The answer to that question is "no".

why?

 

[Dale]

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.

 

[neopolitan]

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.

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.

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:

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

Then using Mona's perspective:

distance_Mona (Mona-E) = distance_Mona (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:

• distance_Mona (Stan-E) and distance_Stan (Stan-E), and
• distance_Stan (Mona-E) and distance_Mona (Mona-E)

Mathematically:

• distance_Mona (Stan-E) = conversion factor * distance_Stan (Stan-E), ...... (3)
• distance_Stan (Mona-E) = conversion factor * distance_Mona (Mona-E) ...... (4)

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

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

therefore:

distance_Mona (Stan-E) = conversion factor * distance_Stan (Stan-E) = conversion factor * ( distance_Stan (Mona-E) + v.distance_Stan (Mona-E) / s )

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



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

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

therefore:

distance_Stan (Mona-E) = conversion factor * distance_Mona (Mona-E) = conversion factor * ( distance_Mona (Stan-E) - v.distance_Mona (Stan-E) / s )

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



Substituting (6) into (5):

distance_Mona (Stan-E) = conversion factor * conversion factor * distance_Mona (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) distance_Stan (Mona-E) = ( distance_Mona (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.distance_Mona (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 realize 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

 

[Dale]

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.

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.

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.

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.

 

[Vanadium 50]

However, it is contrary to an enormous amount of evidence to consider that light does not carry information

Particularly to consider this on the internet, where the very considering is happening thanks to optical cables!

 

[neopolitan]

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.

Gotcha, but the OP was considering a vastly different invariant speed/speed of information.

My original question to you, Dale, was more about about the angle of the worldline of light pulses. If the invariant speed is the speed of information and is less than the speed of light (which we all agree is not possible since information is carried by light), then I would have thought that the angle of the world line of light pulses would be greater than 45 degrees.

Now this is based on the assumption that "invariant speed" is more than just the "speed which is the same in all inertial frames" but is also a feature of the relationship between spatial dimensions and the temporal dimension. The equation:

S² = (ct)² - x² - y² - z²

would become (assuming s is the invariant speed):

S² = (st)² - x² - y² - z²

It is for this reason that I would think that the world line for things that travel faster than s would have an angle of greater than 45 degrees. It wouldn't be the case if I misunderstood what you meant by "invariant speed"

cheers,

neopolitan

 

[Dale]

I explicitly said that I was not answering the OP as posed, but was re-posing the question in a manner that was consistent with experimental evidence. But yes, the worldline for a hypothetical tachyon has an angle greater than 45º.

 

[neopolitan]

I explicitly said that I was not answering the OP as posed ...

However, what the OP posed has interesting possibilities, at least historically.

I've often wondered how (and when) we could have otherwise come to our current understanding of at least special relativity.

For example, if Einstein died in childbirth, it is entirely like that Lorentz would have got the ticket since a paper he wrote indicated that he had independently cottoned onto the idea that his equations explained the Michelson Morley failed experiment (apparently at the time, it was not generally recognised that Einstein's SR explained it).

I think that if Hubble's work had come out a couple of decades earlier, it is possible that SR could have been arrived at from the understanding that the universe is expanding the way it is.

I also think that, if Galileo had thought about it, a similar fashion to the OP, he would have realized that information is not transmitted instantaneously. He certainly understood that the speed of light is not infinite (he conducted an experiment which concluded that light travels 10 times faster than sound) - http://en.wikipedia.org/wiki/Speed_of_light#Early_attempts".

In any event, if Galileo had gone through the process that I laid out in https://www.physicsforums.com/showpost.php?p=2103428&postcount=18" (noting that you don't have to use "the speed of information" which just makes things more awkward - you can and should use the speed of light), then he would have arrived at the Lorentz transformations and the basics of Special Relativity.

That means that we could have had SR a little under 300 years earlier than we did.

Naturally, everything becomes a lot clearer in retrospect. Galileo had enough troubles supporting Copernicus, let alone putting forward his own crazy theory about how everything is relative. While this may sound a little more like philosophy than physics, it was philosophy (more specifically philosophy's intellectually challenged cousin "theology") that was holding back physics at that time.

cheers,

neopolitan

 

[nathatanu0]

but if in some media "s" is the ultimate speed and through this the information can travel and no more than that speed... then it is obvious that "s" will remain invariant... because we are using "s" for highest precision to measure "s" itself... as its the highest speed with which information can travel in that media... so "s" will be invariant speed...in that space time of the media...(if observers are confined inside the media)... then "s" will be definitely a property of that space-time (the media)... so for the observers confined in that media... "c" of STR should have to be replaced by "s" in that media... for the sake of Physics of the people inside...
if m not to wrong!

 

[Al68]

but if in some media "s" is the ultimate speed and through this the information can travel and no more than that speed... then it is obvious that "s" will remain invariant... because we are using "s" for highest precision to measure "s" itself... as its the highest speed with which information can travel in that media... so "s" will be invariant speed...in that space time of the media...(if observers are confined inside the media)... then "s" will be definitely a property of that space-time (the media)... so for the observers confined in that media... "c" of STR should have to be replaced by "s" in that media... for the sake of Physics of the people inside...
if m not to wrong!

It would depend on why the speed was limited to "s". For example, the speed of information travel in air is limited to less than c, yet c is still the invariant speed.

 

[Dale]

but if in some media "s" is the ultimate speed and through this the information can travel and no more than that speed... then it is obvious that "s" will remain invariant... because we are using "s" for highest precision to measure "s" itself... as its the highest speed with which information can travel in that media... so "s" will be invariant speed...in that space time of the media...(if observers are confined inside the media)... then "s" will be definitely a property of that space-time (the media)... so for the observers confined in that media... "c" of STR should have to be replaced by "s" in that media... for the sake of Physics of the people inside...
if m not to wrong!

I don't really buy this argument. Let's say that you have a completely opaque material (perfect blackbody) with a speed of sound of 100 m/s. Then information can only move through that material at a speed of 100 m/s. But in a frame where it is moving at 1 m/s a sound wave will propagate at ~101 m/s in one direction and ~99 m/s in the other. Therefore the speed of information is not invariant.

 

[nathatanu0]

@Dalespam

you must remember the fact that deriving Lorentz transformation "the isotropy of space and homogeneity of time" was assumed... and now you are violating that here... now tell me one thing when space-time is curved... STR is valid? no! then how this "s" STR u expect to be valid... then u've to bring "s" GTR here! I hope u agree... one thing u think once... u keep the space-time isotropic & homogeneous... flat... and then u see, we are measuring everything in terms of that "s" speed... so its obvious that "s" will remain invariant... !

@Al6
if speed of information in air is limited to "c" then how does "c" enter into the story?? "c" is speed of what then...if the ultimate information speed is limited to speed less than "c"? One more thing... I'm talking about a media... as I've described at the beginning of this reply... @Dalespam... like the media Einstein himself considered... yeah definitely "s" will depend upon what kind of media we are in... but if there is no way to know it... by the inhabitant living inside that media... a perfectly isotropic in space and homogeneous in time media...

... I'll wait for your reply... may be I'm completely wrong...!

 

[Dale]

you must remember the fact that deriving Lorentz transformation "the isotropy of space and homogeneity of time" was assumed... and now you are violating that here...

You are correct that isotropy and homogeneity are assumed in deriving the Lorentz transform, but I am not violating that here at all. The wave equation in a moving medium is both homogenous (translate your initial conditions and your coordinate system and you get the same equation) and isotropic (rotate your initial conditions and your coordinate system and you get the same equation).

 

[Dale]

However, what the OP posed has interesting possibilities, at least historically.

I've often wondered how (and when) we could have otherwise come to our current understanding of at least special relativity.
...
In any event, if Galileo had gone through the process that I laid out in https://www.physicsforums.com/showpost.php?p=2103428&postcount=18" (noting that you don't have to use "the speed of information" which just makes things more awkward - you can and should use the speed of light), then he would have arrived at the Lorentz transformations and the basics of Special Relativity.

That means that we could have had SR a little under 300 years earlier than we did.

Hi neopolitan, http://arxiv.org/abs/0806.1234v1" is a paper that you might enjoy on the subject. I just found it and have only made it part way through, but so far he seems to agree with your conclusion though his derivation is different.

 

[Al68]

@Al6
if speed of information in air is limited to "c" then how does "c" enter into the story?? "c" is speed of what then...if the ultimate information speed is limited to speed less than "c"?

Well, the speed of information propagation is limited to about 0.9997c in air, 0.75c in water. c is the invariant speed of the universe, and is the theoretical speed of light in a perfect vacuum, which doesn't exist.

The speed limit for information transfer is dependent on both c and the refractive index (for light) of the medium.

 

[sanjibghosh]

one thing that i can tell you ,in refractive medium the macroscopic speed of light is c/n .but microscopically, the speed of light is c, because the medium is nothing but a arrangement of atoms and vacuum.so the light travel though medium by absorption and emission proses or any other interaction with electrons. in between this two (abs. & emission) light still has speed c. the photons travel through medium with speed c.
if photon has speed less than c then the observer outside medium will realize that rest mass of the photon is non zero.
is it true Dalespam,neopolitan,and other people also?
but i have no enough information that,all words that i told are completely true.this is my realization +little knowledges(information).

 

[Ich]

Dalespam, there has been a https://www.physicsforums.com/showthread.php?t=282828"discussing this paper.
AL68, the speed of light in media is no limit for information transfer, see http://en.wikipedia.org/wiki/Cerenkov_radiation" .

 

[Al68]

AL68, the speed of light in media is no limit for information transfer, see http://en.wikipedia.org/wiki/Cerenkov_radiation" .

Not in an absolute sense, but it is if the info is carried via light in that medium. For example, if a light signal is sent through water, it will propagate at 0.75c. But the event signal could be sent via a different medium to the same destination faster. My point was that the actual propagation speed of information is not c. It is always less than c.

 

[sanjibghosh]

what about my last post?
please reply...

 

[neopolitan]

what about my last post?
please reply...

I was a little lost about what you were trying to say. Can you have a go at rephrasing?

cheers,

neopolitan

 

[sanjibghosh]

I was a little lost about what you were trying to say. Can you have a go at rephrasing?

cheers,

neopolitan

I have a problem about the speed of light in refractive medium. if the speed of light in that medium is less than 'c'. then the observer who standing outside the medium will realize that the rest mass of photon (moving in the medium) is non-zero. because the speed of the photon is less than 'c' with respect to the outside-observer.
so i conclude that the speed of photon in that medium is not less than 'c' and introduce the idea of absorption and then emission by the atoms in the medium .within this a-e(absorption-emission) there is a little time delay ,and therefore when we calculate the speed of light within the medium we see that it is less than 'c'.
but actually the speed of light is just 'c', microscopically .because when we will see the photon within medium in between two a-e, a-e proses we will still observe that speed is 'c'. during a-e proses the photon is no longer a photon, it was just absorbed by atom.

 

[Ich]

ZapperZ promotes a https://www.physicsforums.com/showpost.php?p=899393&postcount=4" . I'd say it's a bit more complicated even in the case of weak coupling, but I'm not an expert.

 

[neopolitan]

I have a problem about the speed of light in refractive medium. if the speed of light in that medium is less than 'c'. then the observer who standing outside the medium will realize that the rest mass of photon (moving in the medium) is non-zero. because the speed of the photon is less than 'c' with respect to the outside-observer.
so i conclude that the speed of photon in that medium is not less than 'c' and introduce the idea of absorption and then emission by the atoms in the medium .within this a-e(absorption-emission) there is a little time delay ,and therefore when we calculate the speed of light within the medium we see that it is less than 'c'.
but actually the speed of light is just 'c', microscopically .because when we will see the photon within medium in between two a-e, a-e proses we will still observe that speed is 'c'. during a-e proses the photon is no longer a photon, it was just absorbed by atom.

That's certainly what I understand to be the case. In a vacuum the photon travels at c, even in the micro vacuum between the atoms in a crystal lattice, liquid or gas (and even some solids, we can see through paper after all). But yes, when you get absorption of a photon, all bets are off. The photon emitted is not the same one which was absorbed.

You could say "the speed of a photon is c" and then no longer need to say "in a vaccuum".

I tried to find a nice authoritative reference which explicitly discussed this process, but Google pretty much just pointed me back to physics forums (there are a few other threads on the topic, such as https://www.physicsforums.com/archive/index.php/t-104317.html").

cheers,

neopolitan

 

[JesseM]

It's possible this was posted already, but post #4 on the Physics Forum FAQ sticky thread has a good explanation of what's going on in QM terms when photons slow down traveling through a medium.

 

[neopolitan]

It's possible this was posted already, but post #4 on the Physics Forum FAQ sticky thread has a good explanation of what's going on in QM terms when photons slow down traveling through a medium.

If I am reading that right, the photon is not actually absorbed, but "almost absorbed" and re-emitted, with a delay.

the lattice does not absorb this photon and it is re-emitted but with a very slight delay

Is it the same photon? I guess the question may seem a bit non-sensical because there is nothing to distinguish one photon from any other photon, except to allow the informal statement "photons travel at c" and if you could meaningfully say there is photon prior to prior to interaction with lattice ions, photon during interaction with lattice ions and photon after interaction with lattice ions.

An alternative might be to say that "light travels at c when not interacting with matter", which is the same as "in a vaccuum" but indicates that it is the interaction which slows light down, rather than "not being in a vaccuum". (In other words, if the photon did not interact at all with some hypothetical medium, then it could maintain a speed of c even if it was not in a vaccuum.)

cheers,

neopolitan

 

[sanjibghosh]

to,
neopolitan
is it a meaningful question that "if the speed of light in that medium is less than 'c'. then the observer who standing outside the medium will realize that the rest mass of photon (moving in the medium) is non-zero."

 

[neopolitan]

to,
neopolitan
is it a meaningful question that "if the speed of light in that medium is less than 'c'. then the observer who standing outside the medium will realize that the rest mass of photon (moving in the medium) is non-zero."

No, I don't think so. When it is actually travelling, the photon travels at c and you observer will be happy that the photon has zero rest mass. The average speed of the photon across the medium is a different thing if it is being stopped every now and then and semi-absorbed into lattices.

I can see that your observer might make the assumption of a non-zero rest mass for the photon, if ignorant of what was happening in the medium. But this does not amount to realising a "fact" that that the photon has a non-zero rest mass.

cheers,

neopolitan

 

[JesseM]

If I am reading that right, the photon is not actually absorbed, but "almost absorbed" and re-emitted, with a delay.

The language is slightly confusing, but I think the article is saying that the vibrational modes of the lattice do absorb photons, but in some cases they are permanently absorbed and their energy converted to heat, in other cases they are re-emitted in short order.

A solid has a network of ions and electrons fixed in a "lattice". Think of this as a network of balls connected to each other by springs. Because of this, they have what is known as "collective vibrational modes", often called phonons. These are quanta of lattice vibrations, similar to photons being the quanta of EM radiation. It is these vibrational modes that can absorb a photon. So when a photon encounters a solid, and it can interact with an available phonon mode (i.e. something similar to a resonance condition), this photon can be absorbed by the solid and then converted to heat (it is the energy of these vibrations or phonons that we commonly refer to as heat). The solid is then opaque to this particular photon (i.e. at that frequency). Now, unlike the atomic orbitals, the phonon spectrum can be broad and continuous over a large frequency range. That is why all materials have a "bandwidth" of transmission or absorption. The width here depends on how wide the phonon spectrum is.

On the other hand, if a photon has an energy beyond the phonon spectrum, then while it can still cause a disturbance of the lattice ions, the solid cannot sustain this vibration, because the phonon mode isn't available. This is similar to trying to oscillate something at a different frequency than the resonance frequency. So the lattice does not absorb this photon and it is re-emitted but with a very slight delay. This, naively, is the origin of the apparent slowdown of the light speed in the material. The emitted photon may encounter other lattice ions as it makes its way through the material and this accumulate the delay.

It may also be that the word "absorb" has the connotation of permanent absorption, I don't know. If not, maybe that last bolded sentence should be rewritten to say "So the lattice does not permanently absorb this photon and it is re-emitted but with a very slight delay."

 

[neopolitan]

The language is slightly confusing, but I think the article is saying that the vibrational modes of the lattice do absorb photons, but in some cases they are permanently absorbed and their energy converted to heat, in other cases they are re-emitted in short order.

It may also be that the word "absorb" has the connotation of permanent absorption, I don't know. If not, maybe that last bolded sentence should be rewritten to say "So the lattice does not permanently absorb this photon and it is re-emitted but with a very slight delay."

I guess you would have to confer with ZapperZ.

The bottom line seems to be that there is a significant difference between absorption and reemission by an atom and absorption and reemission by a lattice. I could think that there is a process where capture of a photon is required before it can be absorbed, so it would be either capture-absorb, if the frequency is right, or capture-release, if it isn't. The "checking" process would not be instantaneous (although it may be so damn quick it is close enough for government work, like a Planck time), so delays would thus be added.

If neither lattice nor photon have memory, then the photon would be repeatedly captured and released while in the lattices area of influence. That would result in a significant overall delay. (For this to work the medium could not be nothing but lattice, but rather mostly vaccuum.)

cheers,

neopolitan

 

[v2kkim]

I prefer the wording almost captured to absorb/re-emit, because in case absorb/re-emit it is very hard to guarantee the light keep the same direction, but light keep exactly same direction in a crystal.