A relativity question regarding the speed of light

[JacobEvans]

Well I have at least an understanding of the basics of Einstein's Theories of Relativity, but one aspect confuses me.


Whenever I hear about that thought experiment that goes like "If you were on a train going 80% the speed of light, and you shined a light in front of the train, would the light appear to only move 20% the speed of light to the person on the train?"

Well I understand the idea that time would actually slow down for the person on the train as the speed of light is constant and the distance is the same, so time has to change. But can't light be slowed down if it passes through a medium (refraction)?

I understand that the thought experiment probably assumes that no air is present in front of the train, but I seem to be experiencing some cognitive dissonance as I am told both that the speed of light is so constant that time will slow down to allow light to move away at the speed of light relative to the observer, and I am told that the speed of light is almost never equal to c when it is not in a vacuum.

I know that I just have something mixed up here, as I doubt I just found a hole in TOR :lol:

But, I'm very much confused about why I'm told to seemingly contradictory statements.

I have a feeling TOR can still be used even when the light is moving in a medium, as the speed of light is constant in a medium depending on the refraction index, but would the thought experiment above have the same result if the train and light were moving in another medium such as water? Can we go faster than light if we are in a medium, but not a vacuum,?or can we never go faster than light if we are in the same medium as the light?

 

[Zylstra]

You would see it move away from you @ C. If I were in front of the train (fuck knows why i would be), looking at you I would see the beam of light approaching me @ C and you @ .8C

 

[yarps]

There's no contradiction here. The statement of Special Relativity is that the speed of light in a vacuum is the same for all (inertial) observers. The speed of light in anything else can be, and usually is, less and (I think) observer dependent.

Some additional comments.

First, you ask if it is possible to go faster than the speed of light if we are in a medium. Yes. It is possible to go faster than the speed of light in air, water or anything else even if you are in that medium. Only the vacuum speed represents a hard limit. In fact, if you travel faster than the 'local' speed of light (and are a charged particle) you will emit a type of radiation known as Cerenkov radiation; this is the light equivalent of a sonic boom.

The hole light-shining-from-a-train type thought experiments get tricky if we include refractive media. This is because I'm fairly certain that the index of refraction is an observer-dependent quantity.

One way I find quite useful for thinking about this slowing down of light is to think about it at the level of a single photon. Why would a single photon be slowed down by the presence of a non-vacuum? Well, you can think of it as interacting with the atoms - being temporarily absorbed, then re-emitted. Between interactions, the photon travels at the speed of light (in a vacuum). However, it is essentially stationary during the interactions; similar to how express trains, making fewer stops, travel faster. This picture is not perfect, but I find it a useful lie.

 

[Zylstra]

Isn't spacetime but another medium? What's to keep a properly charged particle from traveling faster than the speed of light within the fabric of spacetime?

 

[Master_Ghost_Knight]

The speed of light isn't literaly the speed of light, but rather a constant derived from the equations that were first determined in Electromagnetism in the study of light (for which light under that model must have a speed equal to that constant on exempt mediums, i.e. speed of light when it faces no interference from an medium).
I hope this answers the questions.

Curiosity: Light doesn't travel at the speed of light.

 

[scikidus]

yarps put it best: Einstein was talking about light in a vacuum.

However, when you include other media, the first thing to come to mind is friction: were you not in the vacuum of space, the friction of your train moving at .8c relative to the medium would incinerate you nearly instantaneously.

 

[JacobEvans]

I think I understand this now, my question has pretty much been answered. thanks

 

[JacobEvans]

Isn't spacetime but another medium? What's to keep a properly charged particle from traveling faster than the speed of light within the fabric of spacetime?

The particle will gain more and more mass as it accelerates requiring infinite energy.

 

[Zylstra]

The particle will gain more and more mass as it accelerates requiring infinite energy.

Infinite, or just ludicrously high?

 

[Cygnus]

Infinite, or just ludicrously high?

Infinite.

 

[Zylstra]

Infinite.

A meaningless word, in actuality. Infinite energy is clearly not needed to drive all particles, or light (indeed all 'energy' in the EM spectrum) itself would either not exist or would provide infinite energy if properly harnessed. Clearly, photons, are exempt from the assertion. As we know Einstein was wrong, it is possible that there may be other particles which can achieve the same It may prove possible to adopt tachyons or some other not-yet-known particle to carry 'information' in a means that will allow us to sidestep the issue before us.

On a side note: If I bring you the cat dead and alive, do I get double the reward?

 

[Ozymandyus]

Electromagnetic waves/photons have no mass which is why they are 'exempt'.

 

[Cygnus]

A meaningless word, in actuality. Infinite energy is clearly not needed to drive all particles, or light (indeed all 'energy' in the EM spectrum) itself would either not exist or would provide infinite energy if properly harnessed.

As Ozymandyus correctly points out, photons are massless and as such do not require an infinite amount of energy to 'travel' at c. According to Einstein, the mass of an object increases as it approaches the speed of light by M=m/[(1-v^2/c^2)^1/2]. If one takes this into account, allowing for relativistic conceptions of work and energy we quickly find that as an object of any mass approaches c, the amount of energy that must be 'added' to an object increases without limit.

Photons themselves do carry definite quantities of energy. This realization has fundamental applications in astronomy and atomic physics.

As we know Einstein was wrong, it is possible that there may be other particles which can achieve the same It may prove possible to adopt tachyons or some other not-yet-known particle to carry 'information' in a means that will allow us to sidestep the issue before us.

I'm unclear as to what you mean when you say Einstein was wrong. All of general and special relativities predictions have been tested extensively without defect.

On a side note: If I bring you the cat dead and alive, do I get double the reward?

 

[Zylstra]

If one takes this into account, allowing for relativistic conceptions of work and energy we quickly find that as an object of any mass approaches c, the amount of energy that must be 'added' to an object increases without limit.

it seems like a cheat- possible a symptom of Einstein being wrong (which we now know he was). This reminds me of the old riddle of the man chasing a tortoise- which baffled the Greeks for many years. Does he ever catch it? ( i don't recall the name of the character)

Photons themselves do carry definite quantities of energy. This realization has fundamental applications in astronomy and atomic physics.

I'm unclear as to what you mean when you say Einstein was wrong. All of general and special relativities predictions have been tested extensively without defect.

Not so. His laws do not work on the small scale. His models are incorrect- just as our current understanding of particle physics is known to be flawed by the fact that such laws do not work on the cosmic scale. We know both are wrong- but they provide the best and most accurate models yet available to us. We're still looking for a single theory that can explain the workings of trhe whole physical universe

 

[Ozymandyus]

You need to stop saying 'Einstein being wrong (which we now know he was)'. Just saying it again doesn't make it true.

Einstein wasn't right about everything, but many of his general principles and theorems will most definitely be involved in a theory of everything (when/if such a theorem is ever discovered).

You are thinking of Xeno's paradox, and it wasn't an old man, it was Achilles racing a tortise. It does not apply to this situation, and we are not claiming the existence of an actual infinity, we are claiming the impossibility of mass travelling at or above lightspeed.

 

[Pulsar]

Not so. His laws do not work on the small scale. His models are incorrect

Special relativity works perfectly fine on quantum scale, and is incorporated in relativistic quantum field theory. Gravity (and hence general relativity) is only relevant on macroscopic scale, or in extreme situations like black holes or the early universe. Since we're not talking about these extremes here, the problems between general relativity and quantum mechanics are not important.

 

[Josan]

Now, I do not know much about relativity I shall freely confess, but I have taken a look at the lorentz factor, and to me it explains why anything with mass can't travel at the speed of light, because as the velocity approches c, the energy that is needed to increase the velocity is increased, basicly for us; the energy we add to the particle has diminishing returns.

Not so. His laws do not work on the small scale. His models are incorrect- just as our current understanding of particle physics is known to be flawed by the fact that such laws do not work on the cosmic scale. We know both are wrong- but they provide the best and most accurate models yet available to us. We're still looking for a single theory that can explain the workings of trhe whole physical universe

Again... I might not know much, but I was under the impression that using the lorentz factor we could basicly use Einstein's equation to account for the small scale of things. I pulled up wikipedia to double check my suspiciouns and this is what I found.

"The approximation γ ≈ 1 + 1/2 β2 is occasionally used to calculate relativistic effects at low speeds. It holds to within 1% error for v < 0.4 c (v < 120,000 km/s), and to within 0.1% error for v < 0.22 c (v < 66,000 km/s).
The truncated versions of this series also allow physicists to prove that special relativity reduces to Newtonian mechanics at low speeds."

So we get within a 1% error with an approximation of the lorentz factor, sounds pretty watertight to me.

 

[Zylstra]

You need to stop saying 'Einstein being wrong (which we now know he was)'. Just saying it again doesn't make it true.

I say it because it's true

and it wasn't an old man

'old' is subjective

and we are not claiming the existence of an actual infinity

Yes, you are. You're saying that infinite energy would be needed

Since we're not talking about these extremes here, the problems between general relativity and quantum mechanics are not important.

A true and correct set of laws will work in every part of the physical universe, at all scales, at all times. We do not yet have such a model. The quest for the 'Theory of Everything' continues

 

[Ozymandyus]

Would be needed if there were objects with mass travelling at the speed of light. Which there are not.

That's like claiming that particles can always be divided into smaller particles so all particles are made up of infinite particles. The first part of the statement isn't true, and therefore neither is the second.

You are just completely wrong on all this stuff, you obviously won't admit it but no big deal - the facts remain unchanged.

Achilles was a semi-immortal hero and the point of the paradox was even someone as fast as Achilles cannot overtake something slow if space is considered infinitely divisible. Completely the opposite of the image of an old man trying to catch a tortise, which is why old being subjective has nothing to do with it.

I can only assume you are trolling because some of this stuff is obvious and I'd like to believe that you can't possibly be this dense.

 

[Fordi]

Whenever I hear about that thought experiment that goes like "If you were on a train going 80% the speed of light, and you shined a light in front of the train, would the light appear to only move 20% the speed of light to the person on the train?"

Well I understand the idea that time would actually slow down for the person on the train as the speed of light is constant and the distance is the same, so time has to change. But can't light be slowed down if it passes through a medium (refraction)?

Actually, distance would change; at 80% C, your view of distance along the axis of your travel, and your perception of the passing of time would be:

<i>
</i>Given: dL = l' / l; dT = t'/t; v/c = 0.8
l' = a length observed by the moving frame
l = the same length observed by the static frame
t' = a time observed by the moving frame
t = a time observed by the static frame 

Find dL and dT

Lorenz time and length dilation equations:
l' = l*sqrt(1-pow(v/c, 2))
t' = t/sqrt(1-pow(v/c, 2))

dL = l*sqrt(1-pow(v/c, 2))/l
dL = sqrt(1-pow(v/c, 2))
(t' = t/dL)
dL = sqrt(1-pow(0.8, 2))
dL = sqrt(1-0.64)
dL = sqrt(0.36)
dL = 0.6
dT = (t/dL)/t
dT = 1/dL
dT = 1.667_

Time would pass, for you, 1+2/3 times the rate it would for the point you're moving at 80%C relative to, and length would be 3/5 what it is for that point along your axis of travel.

Mind you, I may have this backwards. Would someone check my work?