Is Faster than Light travel impossible?

[james_mcgrath]

Or is it just that it can't be observed? This is a question that has been on my mind for some time, so i thought it worth asking here.

Imagine the following scenario: Two spacecraft travel towards each other. Each travels at 0.6C relative to their point of origin (the points of origin being stationary relative to each other). Now as they both approach each other at 0.6, observers at the points of origin will be able to observe the distance between the two craft closing at a rate of 1.2C, breaking the rule of not traveling at a speed greater than 1C.

What am I missing here?

Thanks.

 

[Pengwuino]

Objects CAN recede and approach each other at a speed greater than the speed of light from a different rest frame (namely,the origin you speak of). However, SR tells us that in each of the spaceships frame, the other spacecraft is not moving at a speed greater than the speed of light towards it.

 

[mgb_phys]

The rule is that information (eg. matter, a signal) cannot travel faster than light.
It's possible for mathematical points to travel faster than light.
The distance between the spaceships doesn't transfer any data, there are a couple of other examples such as a projected laser spot moving across the moon (lighthouse paradox) or even in theory the closing point of a pair of scissors.

 

[cfrogue]

Or is it just that it can't be observed? This is a question that has been on my mind for some time, so i thought it worth asking here.

Imagine the following scenario: Two spacecraft travel towards each other. Each travels at 0.6C relative to their point of origin (the points of origin being stationary relative to each other). Now as they both approach each other at 0.6, observers at the points of origin will be able to observe the distance between the two craft closing at a rate of 1.2C, breaking the rule of not traveling at a speed greater than 1C.

What am I missing here?

Thanks.

SR's velocity addition equation solves this.

 

[JesseM]

SR's velocity addition equation solves this.

SR velocity addition deals with what one ship's velocity will be in the other ship's inertial rest frame; in this case the answer is always less than c. However, the question was about how fast a third inertial observer who sees both ships moving at 0.6c would measure the distance between them to be shrinking, something known as the "closing velocity". Here the distance measured by the third observer would indeed be shrinking at 1.2c.

 

[james_mcgrath]

Thanks for the replies. I find it fascinating that even though an outside observer would witness the two ships approaching at 1.2C, any observers on-board those vessels would be observing the other object approach at something less than 1C. I'm thinking that this must be explained by time running differently on the moving craft relative to the "stationary" observer.

Can anyone point me to a good book / site that describes the theory of SR in laymen friendly language (I'm thinking something like "The Selfish Gene", but for SR). I'm not really interested in the mathematics of it yet, so something lite on the formulas would be good.

Cheers.
__________________
Jimmy McGrath
http://www.zizee.com"

 

[Demystifier]

Can anyone point me to a good book / site that describes the theory of SR in laymen friendly language (I'm thinking something like "The Selfish Gene", but for SR).

Try
http://xxx.lanl.gov/abs/physics/0411219

 

[bcrowell]

Can anyone point me to a good book / site that describes the theory of SR in laymen friendly language (I'm thinking something like "The Selfish Gene", but for SR). I'm not really interested in the mathematics of it yet, so something lite on the formulas would be good.

I like Martin Gardner's Relativity Simply Explained. Just be aware that it's a little out of date in some spots.

 

[martix]

So I watch some Discovery sci-flick and where they yap about the usual stuff - aliens and wormholes and stuff. But then it occurred to me that for all the science and relativity theoretical mumbo-jumbo I know I can't answer a very simple question. Then I come here and - lo and behold, there's already such a topic among the first ones in the forum.

So - having in mind this post:

The rule is that information (eg. matter, a signal) cannot travel faster than light.
It's possible for mathematical points to travel faster than light.
The distance between the spaceships doesn't transfer any data, there are a couple of other examples such as a projected laser spot moving across the moon (lighthouse paradox) or even in theory the closing point of a pair of scissors.

I'll paraphrase it a bit: Is it possible for one and the same piece of information that is in one place to come to be in another place faster than it would take the speed of light to cover the distance between these 2 places?

 

[diazona]

hmmm... well, to give a straight answer: as far as I know, it is not possible for any piece of information that is in one place to come to be in another place in less time than the shortest possible time in which light in the one place could come to be in the other place. (I say "shortest possible" because there are sometimes different paths that light can take to get from point A to point B, and they may take different amounts of time)

 

[fando1234]

Was just wondering (and I think this links on to what 'matrix' was saying). What happens if you were to hypothetically have a rod, which is so long that each end of it is separated by say, the distance it would take light to travel in an hour.
Now if you had two people on either end of the rod you could set up a system whereby one guy could prod the other guy in order to send some sort of message, Say they had a code that told them two prods = send me a light pulse, one prod = don't.
Using this system is there any physical reason why you could not send a message (via prods) to the other person. The rod would only be moved a few feet at a time so no part of it would be exceeding the speed of light, however the message would surely reach the receiver before a beam of light. I know this would defy causality, but is there any physical reason why this would be impossible.

-That was a lot longer than I hoped it'd be. Anyway, if anyone can be bothered to read all that (and if it makes sense), could you explain why it wouldn't work.

 

[russ_watters]

Using this system is there any physical reason why you could not send a message (via prods) to the other person. The rod would only be moved a few feet at a time so no part of it would be exceeding the speed of light, however the message would surely reach the receiver before a beam of light. I know this would defy causality, but is there any physical reason why this would be impossible.

The "prods" travel through the rod at the speed of sound in the rod, so the messages are transmitted far slower than the speed of light.

 

[mgb_phys]

Is it possible for one and the same piece of information that is in one place to come to be in another place faster than it would take the speed of light to cover the distance between these 2 places?

No - that's the whole point of SR
(except - there is some experimental evidence that's it's possible to transfer information a very short distance in some special quantum situations)

if you were to hypothetically have a rod, which is so long that each end of it is separated by say, the distance it would take light to travel in an hour.

That comes up regularly.
The 'push' travels through the rod at the speed of sound (in the rod), which unless you have an infinitely stiff rod is a lot less than the speed of light.
It feels instant because the speed of sound in a metal is a few km/s

 

[fando1234]

Ah right. Cheers, that makes a lot of sense. The questions been annoying me all day. I knew something had to be wrong with it, i just couldn't figure out what.

 

[Al68]

Was just wondering (and I think this links on to what 'matrix' was saying). What happens if you were to hypothetically have a rod, which is so long that each end of it is separated by say, the distance it would take light to travel in an hour.
Now if you had two people on either end of the rod you could set up a system whereby one guy could prod the other guy in order to send some sort of message, Say they had a code that told them two prods = send me a light pulse, one prod = don't.
Using this system is there any physical reason why you could not send a message (via prods) to the other person. The rod would only be moved a few feet at a time so no part of it would be exceeding the speed of light, however the message would surely reach the receiver before a beam of light. I know this would defy causality, but is there any physical reason why this would be impossible.

-That was a lot longer than I hoped it'd be. Anyway, if anyone can be bothered to read all that (and if it makes sense), could you explain why it wouldn't work.

Sure. Simply put, when the rod is "prodded" at one end, the other end doesn't instantaneously move. There is no perfectly rigid rod. The propagation speed of the prod from one end of the rod to the other is limited to the speed of sound in the rod.

A perfectly rigid rod would be one that the speed of sound in the rod equals the speed of light, and all rods are less than perfectly rigid.

 

[JesseM]

Can anyone point me to a good book / site that describes the theory of SR in laymen friendly language (I'm thinking something like "The Selfish Gene", but for SR). I'm not really interested in the mathematics of it yet, so something lite on the formulas would be good.

Here's a nice formula-lite online book written in a Q&A format:

www.oberlin.edu/physics/dstyer/Einstein/SRBook.pdf[/URL]

 

[cfrogue]

SR velocity addition deals with what one ship's velocity will be in the other ship's inertial rest frame; in this case the answer is always less than c. However, the question was about how fast a third inertial observer who sees both ships moving at 0.6c would measure the distance between them to be shrinking, something known as the "closing velocity". Here the distance measured by the third observer would indeed be shrinking at 1.2c.

This is not true.
The SR velocity add equations deals with a third observer observering 2 relative moving frames limitied by the speed of light.

SR velocity addition deals with what one ship's velocity will be in the other ship's inertial rest frame;
This is LT.

 

[jmallett]

I am not sure that I fully understand this correctly but the theory of Special Relativity is derived from the Mitchelson Morley and similar experiments. An inherent assumption in the experiment is that light traveling within the apparatus can travel faster then light. Check out Einstei8n's 1905 paper. The experiment assumes that light moving towards the observer is traveling at (c + v) where c = the speed of light and v = the speed of the apparatus, and therefore the observer on the apparatus sees light traveling faster than the speed of light.

Later, of course, it is concluded, from special Relativity, that nothing travels faster than the speed of light.

How does an experiment which is based on the theory (and math) that light traveling faster than the speed of light can end up concluding nothing travels faster than light ?

It makes no senese to me.

 

[mgb_phys]

Not quite, Special Relativity is based on simply assuming that the principle of relativity and Maxwell are both right. The michelson-morely experiment is used in some books because it's an easy way to derive the lorentz-fitzgerald contraction ( ie. the famous sqrt(1-v^2/c^2) )

The experiment was trying to determine if you could measure absolute motion, which would disprove relativity - Special relativity and length contraction explains the experiment but came 20years later

 

[jmallett]

Thanks for the reply, however I am still stuck at the earlier point - is faster than light travel possible. Doesn't (c + v) represent something faster than c ?
If Special Relativity explains the experiment then Special Relativity must justify a situation in which a speed of (c + v) can exist.

Does it matter whether the experiment explains SR or whether SR explains the experiment ? If either is the case then they should agree v - but they don't. In the experiment there is a velocity of light relative to the apparatus of greater than c.

 

[mgb_phys]

Thanks for the reply, however I am still stuck at the earlier point - is faster than light travel possible.

In the sense of information/matter going faster than light no

Doesn't (c + v) represent something faster than c ?

Before relativity yes - after relativity we know that velocities don't ad like that and it's impossible to reach.
M+M didn't know this when they did the experiment but that doesn't matter.

Their experiment was to try and detect the medium that light traveled in - which doesn't exist.
One of the consequences of it existing is that we would be able to know if our laboratory is moving - which means the older principle of relativity is wrong. Einstein's special relativity assumes that the principle is correct an we can't know if the lab is moving.

The solution is that velocities don't add as (v+c) they add with sqrt(1-v^2/c^2)
You can also interprete this as the experiment shrinking in the direction of movement.

 

[martix]

In the sense of information/matter going faster than light no

So no wormhole travel, no stargates, no starships, no interstellar travel, no aliens, no nothing?!

Now I'm just really, really sad.

So all that is left is to hope that when they come up with GUT, it won't even in the slightest resemble any ideas in SR.

 

[jmallett]

Well that's not what Einstein says.
Forget the ether and all that junk, that's just a confusion.

Einstein says that the speed of light in the apparatus is (c - v) in the forward direction and (c + v) in the inbound direction. The formula sqrt(1-v^2/c^2) is derived by making the error of assuming (c + v), then comparing it with a perpendicular ray of light (which is what leads to Loentz's transformation) and then finding that the math doesn't work, in which case Einstein makes a leap to - then one leg must be getting shorter somehow.

 

[jmallett]

Martix,

Unfortunately that is true. All of those things come from mathematical contortions that result from a fundamental error. We are lucky that the math has a beauty to it - even if it is just skin deep.

 

[vociferous]

My understanding is that information can travel faster than light in certain instances. The prime example would be the quantum effects that Einstein called, "spooky action at an instant," and it seems to me that constitutes information traveling faster than light. Assuming I am not missing anything here, perhaps it is better to say that information that could potentially be used to communicate cannot travel faster than light, at least if the Copenhagen interpretation of quantum mechanics holds?

 

[Integral]

.. Check out Einstei8n's 1905 paper. The experiment assumes that light moving towards the observer is traveling at (c + v) where c = the speed of light and v = the speed of the apparatus, and therefore the observer on the apparatus sees light traveling faster than the speed of light.

...

No, No, No, a million times no. No where does AE claim anything moves at the rate of c+v, he uses that quantity to (IIRC) compute the time it takes a light pulse to travel the length of a moving rod. In one case the light pulse is traveling in the same direction of the rod so it takes:

t = \frac l {c+v} to reach the end of the rod.

The pulse is reflected back from the far end and is now moving in the opposite direction of the rod so it takes:

t = \frac l {c-v} to reach the end of the rod.

The c+v and c-v account for the fact that the rod has moved while the light pulse is in transit.

Perhaps you need to dwell on the opening pages of that paper a bit more. You cannot just look at the equations and understand what he is doing. You need to read his words carefully as well.

 

[jmallett]

Those are the equations Einstein uses in his paper, yes, we are all familiar with that. However take the case of a photon leaving the leading end of the rod and traveling towards the trailing end.
Are the photon and the rod in the same inertial frame of reference ? Let's assume no ether, right ?

The photon is traveling at the speed of light (of course) but the trailing end is moving towards the photon as well.
Now the question is - what is the relative speed of the trailing end of the rod compared with the photon. Is it the speed of light or is is something different ? what do you think Einstein is saying it is ?

Explaining it as the movement of the rod breaks the principles of relativity and is the same issue introduced in the speeding train thought experiment.

 

[Integral]

...

Now the question is - what is the relative speed of the trailing end of the rod compared with the photon. Is it the speed of light or is is something different ? what do you think Einstein is saying it is ?

As is clearly stated in the paper the velocity of the rod as measured from the fixed reference frame is v. The light pulse has velocity c and is not a useful frame of reference, it is not meaningful to talk of the speed of anything compared to light, As an aside, in the 1905 paper Einstein makes no mention of a photon.

Explaining it as the movement of the rod breaks the principles of relativity and is the same issue introduced in the speeding train thought experiment.

Explain to me just how the movement of the rod "breaks relativity"

Again I ask you to actually READ the words of AE. When doing so drop all of your preconceived notions and try to understand what he is saying.

 

[jmallett]

Let's assume the rod exists in free space. A light is fixed to one end which emits flashes. We are taught that within this frame of reference the time taken for the flash (i.e. a photon) to travel the length of the rod cannot exceed the speed of light c.

You are trying to tell me that if I now turn around and see that stars are passing me by then I can decide to measure this movement, suddenly shift the rod relative to the light photon, and watch the photon travel faster than light.

This is an argument that needs the ether in order to work because it demands that the speed of light is relative to the cosmos and you can move a rod around freely and just add that vector to the speed of light.

It's not possible to argue that the speed of light can exceeded by the end of the rod without breaking the laws of relativity. If everything is relative, then c must at least be relative to the inertial frame in which it is travelling.

 

[heldervelez]

In a closed loop path(A-B-A) light speed is 'c' .
Unidirectional (A-B) is undetermined.
I do not know any theory nor experiment that derules Einstein.

 

[Doc Al]

This is not true.
The SR velocity add equations deals with a third observer observering 2 relative moving frames limitied by the speed of light.

Once you specify the speed of two ships (A & B) with respect to a third frame (C), the velocity addition formula is used to find the speed of B as measured in the frame of A. But that's not what's being discussed here. Here we're talking about the rate at which A and B approach each other as measured in frame C. That approach speed--the closing speed--can certainly be greater than the speed of light.

 

[jmallett]

I don't get it at all then. If the speed of light in one direction can be undetermined then it's speed can be either

- faster than the speed of light (which is not possible)

- slower than the speed of light in which case the return trip must now be faster than the speed of light (again not possible).

Surely there is only one case in which the closed loop path speed is c and that case is when it is c in both directions.

What is it relative to in this case ? Well in the case of the rod we assume the light and rod are a closed frame of reference. This means that the speed of the rod relative to the cosmos doesn't enter the picture as that would then represent classical physics and requires a fixed medium - the old ether concept - and the speed of light is no longer relative to the rod.

 

[A.T.]

If everything is relative, then c must at least be relative

Who said that everything is relative? The speed of light is actually frame invariant therefore not relative. Einstein actually wanted to call his theory "The Theory of Invariants", the name "Relativity" wasn't his idea.

Also try not to confuse two different meaning of "relative":
- frame of reference dependent
- coordinate system dependent
A coordinate system in not exactly the same as a frame of reference, because you can have many different coordinate systems in the same frame of reference.

 

[jmallett]

Once you specify the speed of two ships (A & B) with respect to a third frame (C), the velocity addition formula is used to find the speed of B as measured in the frame of A. But that's not what's being discussed here. Here we're talking about the rate at which A and B approach each other as measured in frame C. That approach speed--the closing speed--can certainly be greater than the speed of light.

Are you proposing that Faster than Light travel is possible then ?

Are A and B both in the C Frame of reference ?

 

[jmallett]

Who said that everything is relative? The speed of light is actually frame invariant therefore not relative. Einstein actually wanted to call his theory "The Theory of Invariants", the name "Relativity" wasn't his idea.

Also try not to confuse two different meaning of "relative":
- frame of reference dependent
- coordinate system dependent
A coordinate system in not exactly the same as a frame of reference, because you can have many different coordinate systems in the same frame of reference.

Ok, you got me really confused then, just when I thought I was beginning to get it.
In Einstein's original paper he talks about a rod moving in space. In his paper what specifically is he considering to be in that "frame". I assumed the Rod and the light traveling along it.

Am I understanding that first step correctly ?

 

[Doc Al]

Are you proposing that Faster than Light travel is possible then ?

I'm saying that the rate at which ships A and B approach each other as measured by frame C can be greater than the speed of light. That has nothing to do with any object or information traveling faster than light.

Are A and B both in the C Frame of reference ?

A and B are two ships traveling with different velocities with respect to frame C.

 

[A.T.]

Are you proposing that Faster than Light travel is possible then ?

Nothing is traveling faster than light here. Velocity is defined as change of space coordinate per time change. Change of distance to another moving object per time change is not velocity, and can be greater than c.

Ok, you got me really confused then, just when I thought I was beginning to get it.

Then forget what I wrote. I just wanted to point out what 'relative' means, and that not everything is relative in Relativity.

 

[jmallett]

Nothing is traveling faster than light here. Velocity is defined as change of space coordinate per time change. Change of distance to another moving object per time change is not velocity, and can be greater than c.

Then forget what I wrote. I just wanted to point out what 'relative' means, and that not everything is relative in Relativity.

Can I try my question then in a different way ?
I am in free space in my own frame of reference inside a box, sitting on a rod that has a light source mounted at one end of it. The light flashes and releases a photon. Am I correct in believing that I will see that photon traveling at the speed of light ? because that's what I was expecting.
I now open a door in the box and see that there are stars passing me by. Why do I now have to add the speed of the rod relative to the stars into my equation ? and if the speed is positive and opposed to the direction of the photon then doesn't that mean that the end of the rod is now closing in on the photon at the speed of the rod relative to the stars plus the speed of the photon (light).

Why does observing the stars make any difference ? Isn't that an argument that derives from the proposition of an ether ?

HELP !

 

[Doc Al]

Can I try my question then in a different way ?
I am in free space in my own frame of reference inside a box, sitting on a rod that has a light source mounted at one end of it. The light flashes and releases a photon. Am I correct in believing that I will see that photon traveling at the speed of light ? because that's what I was expecting.

You are correct.

I now open a door in the box and see that there are stars passing me by. Why do I now have to add the speed of the rod relative to the stars into my equation ? and if the speed is positive and opposed to the direction of the photon then doesn't that mean that the end of the rod is now closing in on the photon at the speed of the rod relative to the stars plus the speed of the photon (light).

You will measure the speed of any photon as traveling at the same speed with respect to you, regardless of your motion with respect to anything else. Only if the rod is moving with respect to you do you need to add or subtract its motion to find the closing speed of the photon and rod as seen by you.

If you are observing a rod that is moving with respect to you and there's a photon traveling along that rod, then the rate at which the photon and rod approach each other as seen by you can certainly be greater than the speed of light. (This is what Integral was explaining in post #26.)

 

[jmallett]

You are correct.

You will measure the speed of any photon as traveling at the same speed with respect to you, regardless of your motion with respect to anything else. Only if the rod is moving with respect to you do you need to add or subtract its motion to find the closing speed of the photon and rod as seen by you.

If you are observing a rod that is moving with respect to you and there's a photon traveling along that rod, then the rate at which the photon and rod approach each other as seen by you can certainly be greater than the speed of light. (This is what Integral was explaining in post #26.)

OK, great, thanks, I get that, and I am still with you, for the moment.
Now I go back to Einstein's 1905 paper and look at the last part of Para 2 of Section 1. Here he says that there are 2 clocks, one at each end of the rod and there is an observer at each clock, at least that's what I understand. These observers are not moving with respect to the rod, right ?

Next in about 2 very cryptic sentences he concludes that light will travel faster in one direction than in the other. In fact he does add/subtract the rod's motion even when the observer and the rod are not moving relative to each other by suddenly introducing the cosmos.

 

[Doc Al]

Now I go back to Einstein's 1905 paper and look at the last part of Para 2 of Section 1. Here he says that there are 2 clocks, one at each end of the rod and there is an observer at each clock, at least that's what I understand. These observers are not moving with respect to the rod, right ?

I think I'm looking at the passage that you are referring to. (It's not paragraph 2 of Section 1 in my version of "On the Electrodynamics of Moving Bodies"; more like the middle of Section 2.)

There are two sets of observers. The 'stationary' observers (who see the rod moving) and the 'moving' observers (who travel along with the rod).

Next in about 2 very cryptic sentences he concludes that light will travel faster in one direction than in the other. In fact he does add/subtract the rod's motion even when the observer and the rod are not moving relative to each other by suddenly introducing the cosmos.

I don't see any introduction of the cosmos, just some basic kinematics as viewed from the 'stationary' frame. (I wonder if we are looking at the same thing? )

 

[jmallett]

I think I'm looking at the passage that you are referring to. (It's not paragraph 2 of Section 1 in my version of "On the Electrodynamics of Moving Bodies"; more like the middle of Section 2.)

There are two sets of observers. The 'stationary' observers (who see the rod moving) and the 'moving' observers (who travel along with the rod).

I don't see any introduction of the cosmos, just some basic kinematics as viewed from the 'stationary' frame. (I wonder if we are looking at the same thing? )

Yes, we are looking at the same place in the paper. Yes, there are observers moving with the rod, then there are the stationary observers.

What are the stationary observers stationary relative to ? They are not stationary relative to the rod, they are stationary relative to an external frame of reference which I am equating to the cosmos in a general sense.

 

[Doc Al]

Yes, we are looking at the same place in the paper. Yes, there are observers moving with the rod, then there are the stationary observers.

OK.

What are the stationary observers stationary relative to ? They are not stationary relative to the rod, they are stationary relative to an external frame of reference which I am equating to the cosmos in a general sense.

Nothing quite so dramatic. Just imagine that some observers are in a space station floating in space and they are observing a long rod which is moving past them. All that matters is the relative motion between the space station and the rod. In order to specify who is who, we arbitrarily call the space station observers the 'stationary' frame, but this does not mean stationary in any absolute sense.

 

[jmallett]

OK.

Nothing quite so dramatic. Just imagine that some observers are in a space station floating in space and they are observing a long rod which is moving past them. All that matters is the relative motion between the space station and the rod. In order to specify who is who, we arbitrarily call the space station observers the 'stationary' frame, but this does not mean stationary in any absolute sense.

By the way, thanks very much for your help - it is really and truly appreciated.

So do these observers see what is happening on the rod instantaneously ? I think Einstein is saying that all of their clocks are synchronised, right ? so that would imply that they see the same thing at the same time, or else are at least easily able to make a correction based on time and distance, right ?

 

[Doc Al]

So do these observers see what is happening on the rod instantaneously ? I think Einstein is saying that all of their clocks are synchronised, right ? so that would imply that they see the same thing at the same time, or else are at least easily able to make a correction based on time and distance, right ?

I don't know what you mean by seeing things happen 'instantaneously'. The 'moving' clocks are synchronized in their own frame, as are the 'stationary' clocks. One point of Einstein's paper is to show that clock synchronization is frame dependent--the 'stationary' observers will see the 'moving' clocks as unsynchronized.

 

[heldervelez]

Light speed is independent of the movement of the source.
It means that the medium only (vacuum, aether, field, space, glass) determines the speed of propagation of light.
We measure the light speed as 'c', in our local referential, and the same occurs to the measures made in others referentials.
But the limiting value 'c' is a two way (closed loop) measure.
The one way light speed has an undefined value (AFAIK unmeasured), maybe/maybe_Not greater than 'c'.
May be is my answer to the OP question (ONE WAY speed, only)

 

[Doc Al]

Light speed is independent of the movement of the source.
It means that the medium only (vacuum, aether, field, space, glass) determines the speed of propagation of light.
We measure the light speed as 'c', in our local referential, and the same occurs to the measures made in others referentials.

Just a clarification: The speed of light in vacuum will be measured as 'c' in any local inertial frame. Since the speed of light slows in some media--such as glass--we'd need to add (relativistically, of course) the speed of the medium plus the speed of the light with respect to the medium to find its measured speed in some frame. (See Fizeau's experiments.)

But the limiting value 'c' is a two way (closed loop) measure.
The one way light speed has an undefined value (AFAIK unmeasured), maybe/maybe_Not greater than 'c'.
May be is my answer to the OP question (ONE WAY speed, only)

I don't think issues about one-way speed of light have anything to do with the OP's question, which has to do with understanding how a 'closing speed' > c does not violate relativity.

 

[jmallett]

I don't know what you mean by seeing things happen 'instantaneously'. The 'moving' clocks are synchronized in their own frame, as are the 'stationary' clocks. One point of Einstein's paper is to show that clock synchronization is frame dependent--the 'stationary' observers will see the 'moving' clocks as unsynchronized.

I had understood from the paper that all of the clocks were synchronized.

Why don't the stationary observers see the error that the moving observers made in the measurement of the length of the rod ?

 

[Doc Al]

I had understood from the paper that all of the clocks were synchronized.

You can't synchronize clocks that move with respect to each other. The moving clocks are synchronized with each other (in the moving frame) and the stationary clocks are also synchronized with each other (in the stationary frame).

Why don't the stationary observers see the error that the moving observers made in the measurement of the length of the rod ?

I wouldn't call it an error. The moving observers used standard methods to measure the length of the rod. The stationary observers see that the moving observers' clocks are unsynchronized and their measuring rods are shortened according to the stationary frame. The moving observers, in turn, see the 'stationary' observers' clocks as being unsynchronized. (From the viewpoint of what we are calling the 'moving' frame, it is the 'stationary' frame that is moving.)

 

[jmallett]

You can't synchronize clocks that move with respect to each other. The moving clocks are synchronized with each other (in the moving frame) and the stationary clocks are also synchronized with each other (in the stationary frame).


I wouldn't call it an error. The moving observers used standard methods to measure the length of the rod. The stationary observers see that the moving observers' clocks are unsynchronized and their measuring rods are shortened according to the stationary frame. The moving observers, in turn, see the 'stationary' observers' clocks as being unsynchronized. (From the viewpoint of what we are calling the 'moving' frame, it is the 'stationary' frame that is moving.)

OK, so I am going wrong somewhere, this is how I saw it as an error:

What the stationary observer sees is that the moving observers did not measure the actual length of the rod. Suppose there is a backdrop on the other side of the rod from the stationary observers (think of the rod going down a tunnel). The stationary observers see the photon emitted at the front of the rod against the backdrop, watch the rod move forward and the photon move "backward" until it reaches a coordinate where the end of the rod is going to be when it meets the photon. From the stationary observers point of view they definitely did not measure the rod's length, did they ? They measured a distance between two points that they observed and, if they had quick enough eyesight would see the front of the rod has already passed the reference point for the start of the measurement.

Now a stationary observer who knows the value of c and v can use simple math to determine the error in the measurement made my the moving observers.

The moving observers, because they don't recognize the stationary frame of reference, simply assume that the photon traveled the length of the rod. It didn't because by the time the photon reached the back end the back end had moved (they just didn't know it because they were completely absorbed by their own frame of reference).

What worries me is how does the photon and the end of the road move relative to each other at faster than the speed of light ? because when we think of either of those points being the "fixed" point and the other the moving one they are now seeing the other travel faster than the speed of light.