Irrelvancy of motion in C perspective

[JJRittenhouse]

If time dilation and lorentz contraction from a C perspective (a photon) eliminates both time and one dimension of space from that perspective, then from that perspective, can motion actually be said to have occurred?

If not, then how does one resolve the paradox of a subluminal perspective observing motion, and the luminal perspective not?

Since C is precisely known, does the uncertainty principle resolve this paradox, since there is no way at all to know the position of a photon if we know its exact velocity, indicating that it may have no position at all until it is observed?

 

[JesseM]

Light doesn't have its own inertial rest frame in SR, so it isn't too meaningful to talk about what things are like from the "perspective" of something moving at c. This is a question that comes up a lot and has been discussed on a lot of previous threads, see this one for example:

https://www.physicsforums.com/showthread.php?t=398812

 

[JJRittenhouse]

Okay, I saw a few different stances on this matter, all of them to me seem to agree, however, that any description of motion at C is irrelevant.

What I don't understand, though, is why time dilation and lorentz contraction can't answer this simply.

Most of what I caught was that there is no inertial frame, which is not really an argument if there is no actual motion.

Also, if there is no inertial frame for light, then how can we say anything (theoretically) about the movement of light in OUR inertial frame, if light has no frame itself? Observation gives us the answer, but we don't have an answer in our theory?

I did like your approach, where there was a non-inertial frame, however it was meaningless to any inertial frame ( I think that is what you were getting at).

I do wonder, though, how we can say we can measure C from an inertial frame, and then say that anything said about a C frame has no meaning to the frame from which we measured it.

Something obviously happens @ C that we can observe from any inertial frame. Arguments about division by 0 seem counterproductive, because they don't cut the validity of the question nearly as deeply as they cut into a paradox about light itself. If light travels at C, and the theory produces a division by zero result at C...doesn't that imply directly that light traveling at C is a paradox, and therefore C can't be true? We have observations that seem to contradict this. Does this point to a conceptual problem in the theory? Does it point to a misinterpretation of our measurement of the speed of light? Saying that the question has no meaning still doesn't resolve the division by zero problem. We know that C is an actual velocity. We may as well say that the speed of light is undefined, and has no relevance to any intertial frame. Perhaps this is why it is always constant, because there is no relevance to either frame?

Sorry if this is long. I took a long time to read over the posts, I didn't understand all of them, but I kind of got the gist of it.

I just don't see the problem in expressing the question in a form that arrives at the same answer. Motion at C is irrelevant.

 

[bcrowell]

FAQ: What does the world look like in a frame of reference moving at the speed of light?

This question has a long and honorable history. As a young student, Einstein tried to imagine what an electromagnetic wave would look like from the point of view of a motorcyclist riding alongside it. But we now know, thanks to Einstein himself, that it really doesn't make sense to talk about such observers.

The most straightforward argument is based on the positivist idea that concepts only mean something if you can define how to measure them operationally. If we accept this philosophical stance (which is by no means compatible with every concept we ever discuss in physics), then we need to be able to physically realize this frame in terms of an observer and measuring devices. But we can't. It would take an infinite amount of energy to accelerate Einstein and his motorcycle to the speed of light.

Since arguments from positivism can often kill off perfectly interesting and reasonable concepts, we might ask whether there are other reasons not to allow such frames. There are. One of the most basic geometrical ideas is intersection. In relativity, we expect that even if different observers disagree about many things, they agree about intersections of world-lines. Either the particles collided or they didn't. The arrow either hit the bull's-eye or it didn't. So although general relativity is far more permissive than Newtonian mechanics about changes of coordinates, there is a restriction that they should be smooth, one-to-one functions. If there was something like a Lorentz transformation for v=c, it wouldn't be one-to-one, so it wouldn't be mathematically compatible with the structure of relativity. (An easy way to see that it can't be one-to-one is that the length contraction would reduce a finite distance to a point.)

What if a system of interacting, massless particles was conscious, and could make observations? The argument given in the preceding paragraph proves that this isn't possible, but let's be more explicit. There are two possibilities. The velocity V of the system's center of mass either moves at c, or it doesn't. If V=c, then all the particles are moving along parallel lines, and therefore they aren't interacting, can't perform computations, and can't be conscious. (This is also consistent with the fact that the proper time s of a particle moving at c is constant, ds=0.) If V is less than c, then the observer's frame of reference isn't moving at c. Either way, we don't get an observer moving at c.

 

[JesseM]

Also, if there is no inertial frame for light, then how can we say anything (theoretically) about the movement of light in OUR inertial frame, if light has no frame itself? Observation gives us the answer, but we don't have an answer in our theory?

Different frames are just different ways of analyzing the exact same physical situation, there is never a need to use frames where various objects are at rest in order to predict their behavior, you could analyze an arbitrary huge collection of objects moving at different velocities from the perspective of a single frame without ever making use of any others.

 

[Dale]

If light travels at C, and the theory produces a division by zero result at C...doesn't that imply directly that light traveling at C is a paradox, and therefore C can't be true?

How is there a paradox? The theory starts with the postulate that the speed of light is c in any inertial frame, therefore by definition a frame where the speed of light is 0 is non-inertial. The undefined result is a necessary consequence of the postulate, so how is that in any way paradoxical, it should be completely obvious.

 

[JJRittenhouse]

How is there a paradox? The theory starts with the postulate that the speed of light is c

It was in the link that was given to me earlier.

The argument was that trying to take the reference frame of C caused a division by zero in a calculation they were making.

My question is this...

We know light travels at C

If we try to use a reference frame @ C you have an unsolvable equation.

...light STILL travels at C, whether the equation allows for it or not.

I know that the equations aren't supposed to handle this, from what they said, but, where is the one that is? How can every frame be equal, but one in C be truly indescribable? How can it not make sense to ask...what is happening at C? If the equation isn't able to handle it, that doesn't stop the fact that light has some state. So using an equation that can't handle the question to say that the question is meaningless isn't logical at all.

Is there another field that can handle this question? I can ask them. I know that the uncertainty principle makes it seem as if you couldn't say anything about a photon's position at all, since you know it's speed accurately...should I be asking this on the Quantum physics forum?

 

[JJRittenhouse]

How is there a paradox? The theory starts with the postulate that the speed of light is c in any inertial frame, therefore by definition a frame where the speed of light is 0 is non-inertial. The undefined result is a necessary consequence of the postulate, so how is that in any way paradoxical, it should be completely obvious.

ahh, wait I reread again, and I see what you are saying.Okay, so...a postulate...really?

...and because the postulate turns the question in such a way as to make it unanswerable, then it is truly unanswerable? I remember some questionable postulates, such as parallel lines never intersect...

I understand what is being said. I understand that it seems obvious to you, but it isn't obvious to me how a postulate can turn the question we should be asking into something that can't be answered...and have people assume the question is the problem.

Just because a postulate turns the solution meaningless, it doesn't mean that nothing meaningful happens at C.

What if C isn't the speed of light? What if C is something completely different, and we can detect it because it makes light appear to move at a certain rate. Just because we measure something doesn't mean we understood it. So if assuming light has a speed (as I understand it, any speed you put to C won't change the answer to the question, so..maybe the assumption we have about C is missing something.

 

[Dale]

I remember some questionable postulates, such as parallel lines never intersect...

I understand what is being said. I understand that it seems obvious to you, but it isn't obvious to me how a postulate can turn the question we should be asking into something that can't be answered.

I like the analogy that you bring up. If you were to ask the question: "In Euclidean geometry what happens at the intersection of two parallel lines" the answer would be "Parallel lines do not intersect". It is not so much that the question is unanswerable as that the correct answer is simply to point out the logical self-contradiction buried in the question. Similarly here. If the question is: "In Relativity what happens in the inertial rest frame of a photon" the answer is simply to point out the logical self-contradiction in the question by saying "A photon does not have an inertial rest frame".

Your statement that there is a paradox in relativity because of this question is logically on the same footing as claiming that there is a paradox in Euclidean geometry because the equation for the intersection of two lines doesn't have a solution for 2 different parallel lines. "No solution" or "the null set" are perfectly valid answers despite your objections.

You can continue to wave your hands and try to make yourself feel better about your valuable and incisive line of questioning, or instead you could listen to the answers, learn a little about relativity and logic, and accomplish something valuable.

...light STILL travels at C, whether the equation allows for it or not.

Obviously the equation allows light to travel at c. In fact, the equation requires light to travel at c, as you would expect from the second postulate. What it does not allow is for it to travel at 0, which is what you are asking and what is strictly contrary to the second postulate.

 

[JJRittenhouse]

Obviously the equation allows light to travel at c. In fact, the equation requires light to travel at c, as you would expect from the second postulate. What it does not allow is for it to travel at 0, which is what you are asking and what is strictly contrary to the second postulate.

soo...then why do we need to assume light is at rest in order to know what happens there?which was the original question, I didn't ask "what happens if light had a speed of 0" You guys asked that question.

 

[JJRittenhouse]

"In Euclidean geometry what happens at the intersection of two parallel lines" the answer would be "Parallel lines do not intersect".

I'm also willing to find an answer outside of relativity, sooo..it isn't like I'm restricting anyone to relativity to answer the question if there is another answer. I'm not sure why everyone keeps hiding from the question...if the question is about parallel lines intersecting, then you aren't using euclidean geometry...right? not "Parallel lines do not intersect" You required euclidean geometry, not me.

No matter what you say, something happens at C. If you can't get the answer by assuming light has 0 speed, then why assume it has 0 speed to solve the question? Why assume the paradox to find the answer. I didn't ask what happens if light didn't move.

 

[Dale]

I didn't ask "what happens if light had a speed of 0"

Yes, you did:

If time dilation and lorentz contraction from a C perspective (a photon) eliminates both time and one dimension of space from that perspective, then from that perspective, can motion actually be said to have occurred?

If not, then how does one resolve the paradox of a subluminal perspective observing motion, and the luminal perspective not?

In relativity the phrase "from X's perspective" is shorthand for "from the inertial frame where X is at rest".

 

[JJRittenhouse]

Yes, you did:

In relativity the phrase "from X's perspective" is shorthand for "from the inertial frame where X is at rest".

well, maybe then the question needs to be rephrased.

What happens to time and space for particles traveling at C?

if that is the same question, then you still are left with no description for something that has to have some kind of answer. What happens at C? How can the question be a paradox when light exists?

Maybe I should ask what can SR say about light?

 

[Dale]

Maybe I should ask what can SR say about light?

That it always travels at c in any inertial frame.

 

[JJRittenhouse]

That it always travels at c in any inertial frame.

so then what happens with lorentz contraction and time dilation?

 

[Dale]

The amount of length contraction and time dilation between any given pair of inertial frames is given by the Lorentz transform.

 

[JJRittenhouse]

The amount of length contraction and time dilation between any given pair of inertial frames is given by the Lorentz transform.

...and at C?

 

[Dale]

There is no inertial frame which moves at c wrt any other inertial frame.

 

[JJRittenhouse]

That is the problem I have.

Why can't you say anything about time or space at C? It has to be something. The question is only irrelevant in the theory, and leaves the question unanswered.

Unless you can translate what the answer means. If the answer is meaningless, does that mean time and space @ C is meaningless? what does that mean?

 

[Nisse]

Asking what things look like from a photon's point of view is like asking what the world looks like to a Mexican wave as it travels through the crowd in a stadium.

 

[Dale]

That is the problem I have.

I don't know why you have a problem with that. Lots of problems have empty solutions. Like, "what is the minimum of x³", or "which point in S2 is the center", or your excellent example "where is the intersection of two parallel lines". Why should this particular empty set bother you?

Look JJ, this conversation has become boring and repetitive. There is no inertial frame which moves at c wrt any other inertial frame. If it bothers you that much then become a musician or something. Now, if on the other hand you are actually interested in learning physics then go ahead and ask another question. This current one has been fully answered and your dissatisfaction with it is not going to change the answer.

 

[JesseM]

That is the problem I have.

Why can't you say anything about time or space at C? It has to be something. The question is only irrelevant in the theory, and leaves the question unanswered.

You don't seem to understand that even for an observer A moving slower than light, when we say that objects moving relative to him are length-contracted and clocks moving relative to him are time-dilated, that isn't any sort of objective claim about what "time and space" are like for that observer A, it's just a statement about coordinate distances and times in a particular choice of coordinate system, namely the inertial frame in which A is at rest. So no claims about what lengths and times are like for any object or observer have objective coordinate-independent answers, they always depend on some appropriate choice of coordinate system.

Also, nothing's stopping you from coming up with a coordinate system where a given photon is at rest and asking how lengths and times look in that coordinate system, it's just that it won't satisfy the necessary requirements to qualify as an inertial frame. And there are many different types of non-inertial coordinate systems you could come up with where a photon is at rest which would give different answers about lengths and times, with no compelling physical reason to prefer any of them (whereas inertial frames are 'special' in some sense because the equations for the laws of physics in one inertial frame look exactly the same as the equations for the laws of physics in any other inertial frame). Earlier I pointed you to this thread on whether light can have its own frame, and you indicated you had looked at, but perhaps you didn't see the discussion on the later pages about the possibility of creating a non-inertial rest frame for a photon, for example take a look at these comments of mine from post #75:

If you aren't talking about a rest frame, then what do you mean by "frame for a photon"? Usually talking about a frame "for" any object suggests you're talking about its rest frame. And if you are talking about a frame where the photon is at rest (i.e. one where its coordinate position doesn't vary with coordinate time), then it can't be an inertial frame, and there are an infinite number of different ways to construct a non-inertial coordinate system where this is true. For example, suppose in a sublight inertial frame F a photon is released at t=0 from x=0, and travels in the positive x direction of F, so its position as a function of time is given by x(t) = ct. Then here are two different coordinate transformations from F which yield non-inertial frames where the photon is at rest:

x' = x - ct
t' = t

and

x' = 52*(x - ct)
t' = 1.25*(t - 0.6x/c)

In both these coordinate systems the x' coordinate of the photon will always be 0 (this is guaranteed by that factor of x - ct that appears in the formula for x' in both cases). But the two frames define simultaneity differently--the first has a definition of simultaneity that agrees with F, the second would have a definition of simultaneity that agreed with a second sublight inertial frame moving at 0.6c relative to F (since it has the same formula for t' as that sublight frame). And these two non-inertial coordinate systems would also disagree about distance and time intervals.

 

[JJRittenhouse]

isn't any sort of objective claim about what "time and space" are like for that observer A, it's just a statement about coordinate distances and times in a particular choice of coordinate system, namely the inertial frame in which A is at rest. So no claims about what lengths and times are like for any object or observer have objective coordinate-independent answers, they always depend on some appropriate choice of coordinate system.

coordinate systems, equations and inertial frames are not real, they are symbols we use to describe reality.

 

[Fredrik]

Asking what things look like from a photon's point of view is like asking what the world looks like to a Mexican wave as it travels through the crowd in a stadium.

Actually it's not. To ask what stuff "looks like" from the point of view of an object X is to ask how the inertial coordinate that the standard synchronization procedure associates with X's motion would assign coordinates to events. That procedure can be applied to a (specific peak of) a Mexican wave, and the result is an inertial coordinate system in which that peak is stationary at the spatial origin. The procedure doesn't work for massless particles, or electromagnetic waves, and there is no inertial coordinate system in which such things are at rest.

Why can't you say anything about time or space at C? It has to be something.

What it "is" is completely independent of what coordinate systems we're using. A coordinate system is just a function that assigns a 4-tuple of real numbers to each event.

The question is only irrelevant in the theory, and leaves the question unanswered.

The only thing that can answer a question about reality is a theory. What theory do you want us to use if we're not allowed to use SR? If we use SR, then to ask what the world looks like to an object moving at the invariant speed is to ask how coordinates are assigned to events by a coordinate system that doesn't exist. There is no other answer than that the question doesn't make sense.

If the answer is meaningless, does that mean time and space @ C is meaningless? what does that mean?

It just means that there's no inertial coordinate system in which a massless particle is at rest. It's actually pretty obvious that this has to be the case if you consider the fact that a massless particle has speed c≠0 in all inertial coordinate systems.

See also this post.

 

[JesseM]

coordinate systems, equations and inertial frames are not real, they are symbols we use to describe reality.

That may be so, but then you should also agree that "lengths" and "clock rates" are not real, since they can only be defined in terms of some coordinate system. Therefore there is no "real" truth about what "time or space" are like for a given observer/object, so your question "Why can't you say anything about time or space at C? It has to be something" doesn't really make any sense if you are asking about the "real" truth as opposed to just what's true in some arbitrary choice of coordinate system where a photon is at rest.

 

[Dale]

coordinate systems, equations and inertial frames are not real, they are symbols we use to describe reality.

So why should it surprise you that we have to be careful with those symbols and carefully use the right values if we want them to accurately describe reality?

 

[JJRittenhouse]

wait a minute, yes they do.

For one, at the very least, time dilation is real, not an illusion. For another, when something moves, space and time slow and compress for the rest of the universe outside of him. Is this not really happening? I know that it doens't change for the rest of those in the universe, however, when the twin paradox is explained, both of these effects have a real impact, which is seen even after the twin stops.

So what is the translation for there not to be a reference with respect to C? What does that mean for light? what is the difference between that and saying that motion is meaningless with regard to light?

 

[JJRittenhouse]

So why should it surprise you that we have to be careful with those symbols and carefully use the right values if we want them to accurately describe reality?

it doesn't. what surprises me is that you don't have a translation for your answer. You can translate the results of your other answers, yet for this one you act like it just isn't real. Okay, fine, if it isn't real, then what does that mean, because that doesn't make sense to me. It doesn't have anything about being "Dissatisfied" with the answer, it has everything to do with there not being an answer at all.

What can your answer say about light? It travels at C, but through what? Through space in our frame? How does this even explain how light can move at the same speed regardless of the observer? Oh, wait I forgot, it's a postulate. I guess I expected there to be an answer in there somewhere, but if there is no reference for C wrt any other frame, then my question changes.

How can C be constant regardless of the observer?

And I am taking physics, we just aren't studying relativity yet.

 

[Fredrik]

For one, at the very least, time dilation is real, not an illusion.

It's certainly not an "illusion", but it's derived from the assumption that we use the standard procedure to associate an inertial frame with the observer's motion.

For another, when something moves, space and time slow and compress for the rest of the universe outside of him. Is this not really happening?

The events would only be described that way in that particular coordinate system. (I'm not answering with "yes" or "no", because to do that I would have to define what "really" means in this context).

So what is the translation for there not to be a reference with respect to C? What does that mean for light?

It just means that we can't associate an inertial frame with its motion, as we can with massive particles.

what is the difference between that and saying that motion is meaningless with regard to light?

"Motion is meaningless" is a vague and imprecise statement. "Velocity relative to a massless particle is undefined because the method we use to to associate a coordinate system with an object's motion doesn't work for massless particles" is more accurate.

 

[JJRittenhouse]

Look JJ, this conversation has become boring and repetitive.

Then don't answer. If you are getting weary from the question, none of you are required to answer. None of you have any reason to be frustrated that I don't get it when there is no requirement for you to answer, explain it, whatever. You HAVE your answers, I'm the one who doesn't understand it.

 

[JJRittenhouse]

Okay, so...

How is the speed of light a constant regardless of the observer.

SR doesn't explain it, it's simply a postulate. What does explain it?

 

[Fredrik]

How can C be constant regardless of the observer?

It's not that hard to see that it is, if we already know that the functions that change coordinates from one inertial frame to another are Poincaré transformations. Motion is represented by curves in spacetime. Coordinate systems map those curves to points in \mathbb R^4. Take any two points on a straight line \mathbb R^4 with velocity c and apply any Poincaré transformation to them. You will find that the line that connects the transformed points is also a line with velocity c.

So why are Poincaré transformations the functions we use to change coordinates between inertial frames?. In the context of SR, this is either an axiom or a statement that follows almost immediately from the axioms. However, you can also ask if there's a theory that uses \mathbb R^4 as the mathematical representation of space and time, in which the coordinate change functions satisfy a few reasonable requirements, like if f and g are coordinate change functions, then so is f\circ g. If we include preservation of simultaneity in the "reasonable requirements", then there's exactly one set of coordinate change functions that work: Galilei transformations. If we drop that specific requirement, there is exactly one more: Poincaré transformations.

The details are pretty complicated, unfortunately.

By the way, the word is "regardless", not "irregardless".

SR doesn't explain it, it's simply a postulate. What does explain it?

As I mentioned above, the only thing that can answer a question about reality is a theory. There is no theory that really answers this question, and even if there was, you could still ask why the axioms of that theory holds. To answer that question, we need another theory, and so on, ad infinitum.

 

[Dale]

it doesn't. what surprises me is that you don't have a translation for your answer.

I can translate it into math or into spanish if you like.

It doesn't have anything about being "Dissatisfied" with the answer, it has everything to do with there not being an answer at all.

Yes, there is an answer. The answer is that there is no inertial frame which moves at c wrt any other inertial frame.

What can your answer say about light? It travels at C, but through what? Through space in our frame?

Through vacuum in any inertial frame.

How does this even explain how light can move at the same speed regardless of the observer? Oh, wait I forgot, it's a postulate.

Exactly. Now you are getting it. You don't explain the postulates of a theory, you use the postulates to explain and predict other things. Then you test those predictions and if they hold then you have a scientific reason to accept the postulates, as weird as they may seem.

And I am taking physics, we just aren't studying relativity yet.

Have you studied Maxwell's equations yet?

 

[JesseM]

For one, at the very least, time dilation is real, not an illusion.

There is no coordinate-independent way to define the rate a clock is ticking. If two clocks meet, compare times at a single point in space and time, then move apart, then come back together and compare times at a second single point in space and time, then there is a coordinate-independent truth about how much time each clock has elapsed between the two meetings. But there is no coordinate-independent way to answer questions like which clock was ticking faster at some point midway between the two meetings.

For another, when something moves, space and time slow and compress for the rest of the universe outside of him. Is this not really happening?

Not in any coordinate-independent sense, so if you define coordinate-dependent statements as "not real", then no, it's not "really" happening. It is true that in the object's inertial rest frame, the coordinate length of moving objects is compressed and the rate moving clocks are ticking relative to coordinate time slows down.

So what is the translation for there not to be a reference with respect to C?

There is not an inertial rest frame for light. As I said you can certainly define a non-inertial coordinate system where the light is at rest (an infinite variety of them, in fact).

 

[JJRittenhouse]

As I mentioned above, the only thing that can answer a question about reality is a theory. There is no theory that really answers this question, and even if there was, you could still ask why the axioms of that theory holds. To answer that question, we need another theory, and so on, ad infinitum.

Allright, well, thanks for the time.