Would it Feel as if Time Stopped If I Became Light?

[atyy]

In this sense these two things are consistent with each other: if all of space contracts to a single point, then through an analogy of ds = vdt we get 0 = 0 which is consistent with finite distances contracting to points and also the fact that time doesn't pass for the photon.

I'm not very fond of "space contracting to a point" language. But your equation is close to dss=dtt-dxx=0. I'm only giving a very, very abbreviated explanation here, try looking up Minkowski metric, the spacetime interval, and null geodesics.

 

[phyti]

What clock? There is no physically possible "clock" moving at the speed of light. You can't use the Lorentz transformation to conclude that a "clock stops" at the speed of light any more than you can use it to conclude that a clock's ticking rate becomes imaginary when it moves faster than light.

-The poster is a biological clock. At c, he or any device obviously would cease to qualify as a clock. We could accelerate the person to within a fraction of c, to make it more 'real', and at least make him comatose.
How does anyone determine that a device has stopped, or are they wrong?

Equations in physics often have some restricted domain of physically meaningful applicability, this is just another such case.

- Like when the observer is measuring the length of an approching rod along the x-axis, and as he records it, the rod hits him between the eyes?

Some people are just curious and don't have the time or inclination to do detailed studies of certain subjects. If their question is simple then give a simple answer in terms they can understand. To know your subject is one thing. To impart understanding about the subject is another. The first does not imply the second.
If someone asks for the time of day, no need to instruct them on how a clock works!

 

[Dale]

And if somebody asks what 5/0 it is not our fault if he doesn't like the answer that the question is bad.

 

[JesseM]

-The poster is a biological clock. At c, he or any device obviously would cease to qualify as a clock.

It's not that he would cease to qualify as a clock "at c", it's that it's physically impossible to get him moving at c in the first place, since he is made out of particles with nonzero rest mass. If you are arguing that his clock would stop at c, I would say this is just as incorrect according to known laws of physics as saying he would become a bowl of petunias at c.

We could accelerate the person to within a fraction of c, to make it more 'real', and at least make him comatose.

Sure, but the question was about what happens at c, not at a fraction of c. Again, any question about how time passes for someone moving at c just isn't physically meaningful according to the current understanding of physics.

Equations in physics often have some restricted domain of physically meaningful applicability, this is just another such case.

- Like when the observer is measuring the length of an approching rod along the x-axis, and as he records it, the rod hits him between the eyes?

Perhaps you are being facetious, but no, the fact that the rod hits him in the eyes doesn't change the fact that the length contraction equation correctly gives the rod's length in his frame (regardless of whether he is able to measure that length or not).

If their question is simple then give a simple answer in terms they can understand.

And the simple answer in this case is that there is no well-defined notion of light's "perspective" in SR. Anyone who tries to give any definite answer to this question, like your answer that "the clock stops" at c, is probably just confused about the physics.

 

[mordechai9]

My area of study lately has been plasma physics, and I find it very interesting to ask myself "What would it be like to be one of the electrons (or ions) zooming around in the field?"

For a photon, at the speed of c, I don't know a lot about special or general relativity, but you can at least say a few things, can't you? Basically the intuition is that you would be moving through space very rapidly. I can't think of a lot else to say. Obviously your motion might terminate or change depending on your surroundings, like light in a rainbow being diffracted around in a big circle, and scattering off at different frequencies. You find yourself moving along gravitational geodesics, I think, but I'm not entirely sure how that's interpreted.

 

[Dav333]

Just a noob question. Can you speak about the reference frame of a fast moving electron at 99.9999999999 c?

Would the universe from its view in the forward direction be extremely short?

 

[Phrak]

The specter of inertial frames has been raised a dozen times in this thread despite complete irrelevance. Carry on.

 

[matheinste]

Just a noob question. Can you speak about the reference frame of a fast moving electron at 99.9999999999 c?

Yes we can, and in fact we are possibly moving at very very high speeds withe respect to other objects in the universe. The transformation equations apply to any subluminal speed is inserted into them.

I must plead ignorance of what does or does not happen phyically when we plug c into the equations. The usual answer is that we cannot theroretically achieve a relative speed of c. This is true. However if the result of the mathematics gave a definite answer in the limit as we approached c then perhaps we would have no qualms in venturing an opinion. But in this case the result is indeterminate and so we cannot extrapolate although we can get as close as we like.

It is of course tempting and, to me, not unreasonable to assume that the trend continues towards time "standing still" for the "stationary" observer and length in the direction of motion becoming zero for the "travelling" observer, and vice versa.

Although I am aware of the problem, or non problem, I have no definite answer but I do not worry about it as it is a scenario that is not going to happen.

Matheinste.

 

[JesseM]

The specter of inertial frames has been raised a dozen times in this thread despite complete irrelevance. Carry on.

So what do you think is relevant to defining a photon's perspective? Do you agree that there are an infinite number of distinct possible non-inertial frames in which a photon is at rest (with different definitions of simultaneity, distance, and time intervals) and none are preferred over any other by the laws of physics? If "perspective" isn't interpreted in terms of a coordinate system, how is it to be interpreted?

 

[phyti]

Anyone who tries to give any definite answer to this question, like your answer that "the clock stops" at c, is probably just confused about the physics.

What's the probability?

Light mediates all energy transfer, therefore processes slow down for moving objects,
which includes clocks. This is also the reason objects can't be accelerated to light speed.
By reason without LT, the processes must stop, a consequence of a constant and independent light speed.

'No well-defined notion of light's "perspective"' doesn't answer his question in the context he's asking, and allows him freedom to imagine anything.

The poster got a hypothetical answer to his hypothetical question, which shows that nothing physically meaningful happens.

Of the many posts I've read (including other forums), some in broken english, there are only a few that were not easily understood. I think some answers have more complexity than the question merits.

Can you give an answer in laymans terms without all the techno-babble of theory?

 

[Fredrik]

Light mediates all energy transfer,

This isn't true in the real world.

therefore processes slow down for moving objects,

This isn't true even in electrodynamics.

which includes clocks.

Clocks don't "slow down" in special relativity. They just keep doing what they're supposed to, which is to measure the proper times of the curves in spacetime that represent their motion.

This is also the reason objects can't be accelerated to light speed.

This calculation of the energy required to accelerate a mass m to speed v doesn't involve light at all. (It does of course involve the invariant speed).

'No well-defined notion of light's "perspective"' doesn't answer his question in the context he's asking, and allows him freedom to imagine anything.

How would you answer a question that asks you to assume that the theory you're supposed to use to answer the question is logically inconsistent? It clearly doesn't make sense to allow "the freedom to imagine anything".

Can you give an answer in laymans terms without all the techno-babble of theory?

You want to know what the theory says, but we're not allowed to use the theory? You don't see a conflict there? Anyway, the bottom line is that there's a specific reason why we think of inertial frames as massive particles' points of view, and that reason isn't there when we consider massless particles. The synchronization procedure we'd like to use just wouldn't work.

 

[ZirkMan]

...since a photon can't have an inertial rest frame (and there's no physical reason to prefer any of the infinite number of non-inertial rest frames you could invent), nor does a photon have any internal processes that could be used to mark the time on different events on its worldline.

Einstein already did this exercise in imagination when he was child. The answer to "what it would be to ride a beam of light?" was if I remember correctly that you would see nothing but a pulsating electric and magnetic field changing one into the other. Couldn't this pulsation serve as your hypothetical clock? Could you start to count these pulses and measure your internal time this way?

I also think that the depiction of a "rest frame" of a photon is as far from frame of an observer moving with a limit approaching c as is velocity of c to this observer. These frames are totally different even they seem to be very close to each other.

 

[JesseM]

Einstein already did this exercise in imagination when he was child. The answer to "what it would be to ride a beam of light?" was if I remember correctly that you would see nothing but a pulsating electric and magnetic field changing one into the other.

But he was considering what would have been true in pre-relativistic theories of light...some discussion of what he may have been thinking about here. At best the thought-experiment shows some internal problems with non-relativistic theories of light, but it doesn't make sense as a thought-experiment in the context of relativity itself.

Couldn't this pulsation serve as your hypothetical clock? Could you start to count these pulses and measure your internal time this way?

You can use those to define a time coordinate in a non-inertial frame if you want, but there's no unique way to decide how many pulses should be equivalent to one second in a sublight inertial frame (since such a clock cannot be constructed in these frames), you could define the time between pulsations as 1 nanosecond or 12 trillion years. So, this doesn't give you a basis for any kind of time dilation equation relating the rate time is passing for an observer moving at c to the rate time is passing for an inertial observer. Likewise this doesn't give you any physical basis for deciding how simultaneity and distance "should be" defined in a non-inertial frame moving at c, there are many different ways you could do this.

I also think that the depiction of a "rest frame" of a photon is as far from frame of an observer moving with a limit approaching c as is velocity of c to this observer. These frames are totally different even they seem to be very close to each other.

The concept of the "rest frame" of a photon is not even well-defined (it can't be an inertial frame, and there are an infinite number of different ways to construct a non-inertial rest frame for an object with different judgments about simultaneity and so forth, none preferred over any other by the laws of physics). I agree that it doesn't make sense to view the limit as you approach c as equivalent to the perspective of someone actually moving at c.

 

[jtbell]

Einstein already did this exercise in imagination when he was child. The answer to "what it would be to ride a beam of light?" was if I remember correctly that you would see nothing but a pulsating electric and magnetic field changing one into the other.

From the Usenet Physics FAQ entry, http://www.phys.ncku.edu.tw/mirrors/physicsfaq/Relativity/SpeedOfLight/headlights.html

Einstein reported that in 1896 he thought,

``If I pursue a beam of light with the velocity c (velocity of light in a vacuum), I should observe such a beam of light as a spatially oscillatory electromagnetic field at rest. However, there seems to be no such thing, whether on the basis of experience or according to Maxwell's equations. [...]"

I added the emphasis, to point out that Einstein realized that such a configuration of E and B fields does not satisfy Maxwell's equations and is therefore impossible according to electromagnetic theory as it was understood then.

Instead of modifying electromagnetic theory to allow for such a situation, Einstein ended up modifying mechanics so as to prevent such a situation from ever happening!

 

[ZirkMan]

Thank you! That essentially closes the case (at least for me )

 

[ZirkMan]

You can use those to define a time coordinate in a non-inertial frame if you want, but there's no unique way to decide how many pulses should be equivalent to one second in a sublight inertial frame (since such a clock cannot be constructed in these frames), you could define the time between pulsations as 1 nanosecond or 12 trillion years. So, this doesn't give you a basis for any kind of time dilation equation relating the rate time is passing for an observer moving at c to the rate time is passing for an inertial observer. Likewise this doesn't give you any physical basis for deciding how simultaneity and distance "should be" defined in a non-inertial frame moving at c, there are many different ways you could do this.

Actually this is an interesting thought experiment. Imagine you would define 1 pulse as one second. That would be your definition of a second. Would you be able to count a finite number of "seconds" and determine a time interval between you started counting and something else happened e.x. you were absorbed or reflected by an atom (as a photon)?

 

[JesseM]

Actually this is an interesting thought experiment. Imagine you would define 1 pulse as one second. That would be your definition of a second. Would you be able to count a finite number of "seconds" and determine a time interval between you started counting and something else happened e.x. you were absorbed or reflected by an atom (as a photon)?

Sure, using this definition you could assign a value to the time between two events on a photon's worldline, though any such time/pulsation convention would be an arbitrary one since there's no physical reason to define the time between pulses as one second as opposed to ten seconds or whatever. And this wouldn't be sufficient to define the time between events not on the photon's worldline since we haven't picked a simultaneity convention.

 

[ZirkMan]

Sure, using this definition you could assign a value to the time between two events on a photon's worldline, though any such time/pulsation convention would be an arbitrary one since there's no physical reason to define the time between pulses as one second as opposed to ten seconds or whatever.

Yes, but it's the only convention you can make since nothing else changes until something happens.

And this wouldn't be sufficient to define the time between events not on the photon's worldline since we haven't picked a simultaneity convention.

I'm not sure what you mean by a simultaneity convention in this case. But the fact that a photon can theoretically have its own internal clock is an important one. At least we can say that time doesn't have to stop entirely for a photon from its own perspective (if there is such a thing).

The only "window" to the outside world would be by recording interference patterns of its own EM field with other pulsating EM fields that it happens to cross on its way (and those happen to be parts of images of the outside world). I'm not so good in EM theory so I do not know if you would be able to detect these interferences in its EM field and if they can transfer any information by changing frequency of the photon's EM field?

 

[JesseM]

Yes, but it's the only convention you can make since nothing else changes until something happens.

When you say "it's the only convention you can make", I assume you're talking about the general idea of defining time in terms of pulses, rather than the specific idea of defining the time between pulses to be 1 second rather than some other amount like 1 microsecond or 1 hour? The point is that even if you choose to say equal number of pulses = equal time interval, that still doesn't give a unique way for comparing how much time has passed for the observer moving at c between a given number of pulses and how much time has passed for slower-than-light observers between the same number of pulses, so it doesn't give any specific time dilation equation.

I'm not sure what you mean by a simultaneity convention in this case.

Are you familiar with the relativity of simultaneity for slower-than-light inertial frames? For these inertial frames there's a natural way of defining what "same time" means in different frames, but no obvious way to extend this to the type of non-inertial frame you're talking about...so if you know a particular event on the light beam's own worldline happens at T=23 seconds according to the time coordinate you've defined, how do you decide whether some other spatially separated event not on the light beam's worldline happened simultaneously with the first event (i.e. it should be assigned a time coordinate of T=23 seconds too) or at a different time?

But the fact that a photon can theoretically have its own internal clock is an important one.

Not a type of clock whose rate can be compared to identical clocks moving slower-than-light though, so there's no non-arbitrary basis for saying the photon elapses less or more time between two events on its worldline than the time between those events as judged in my frame according to my clocks.

At least we can say that time doesn't have to stop entirely for a photon from its own perspective (if there is such a thing).

Since there's no basis for assigning an amount of time in seconds between oscillations "for a photon", you could say the time was zero seconds (or an infinitesimal fraction of a second).

I'm not so good in EM theory so I do not know if you would be able to detect these interferences in its EM field

By "you" do you mean an ordinary slower than-light-observer or an FTL one? I don't know how to construct anything resembling an "observer" out of things moving at light speed, but certainly we should be able to detect changes in the EM field when two electromagnetic waves cross.

and if they can transfer any information by changing frequency of the photon's EM field?

Again, we can transfer information by changing the frequency of an electromagnetic wave, sure.

 

[ZirkMan]

When you say "it's the only convention you can make", I assume you're talking about the general idea of defining time in terms of pulses, rather than the specific idea of defining the time between pulses to be 1 second rather than some other amount like 1 microsecond or 1 hour?

Exactly. One pulse equals one unit of time and in terms of these units you would measure all observed events.

By "you" do you mean an ordinary slower than-light-observer or an FTL one?

By "you" I meant and further in discussion I will mean the observer at the photon's rest frame as I try to look from its perspective.

The point is that even if you choose to say equal number of pulses = equal time interval, that still doesn't give a unique way for comparing how much time has passed for the observer moving at c between a given number of pulses and how much time has passed for slower-than-light observers between the same number of pulses, so it doesn't give any specific time dilation equation.

Are you familiar with the relativity of simultaneity for slower-than-light inertial frames? For these inertial frames there's a natural way of defining what "same time" means in different frames, but no obvious way to extend this to the type of non-inertial frame you're talking about...so if you know a particular event on the light beam's own worldline happens at T=23 seconds according to the time coordinate you've defined, how do you decide whether some other spatially separated event not on the light beam's worldline happened simultaneously with the first event (i.e. it should be assigned a time coordinate of T=23 seconds too) or at a different time?

Thank you for an interesting read. It was one of the clearest explanations of series of thought experiments that lead to SR that I have ever seen.

But you somehow suppose that from the perspective of light the world would look exactly as from our perspective i.e. divided to the worlds of subluminal and luminal speeds. But so far nothing seems to give indications this would be the case. I think that from a perspective of a photon where luminal speed is your rest frame you cannot even learn subluminal or maybe any velocities exist at all. From the photon's point of view you would have no way of finding out velocities exist until you were absorbed by an atom. And even then it is a question if you could ever find out because you might not slow down at all. You might only acquire a spin that gives an illusion of subluminal speed because you no longer travel in straight line but we probably do not want to discuss this now

I don't know how to construct anything resembling an "observer" out of things moving at light speed, but certainly we should be able to detect changes in the EM field when two electromagnetic waves cross.

Again, we can transfer information by changing the frequency of an electromagnetic wave, sure.

So information from these changing frequencies of your own EM field resulting from interactions with other EM fields would be the only way you could find out something exists outside your refference frame.

What I'm thinking now is if we can use this limited but still potentially usable frame of reference to get some insight into relativity.

For example if we could count and compare nr. of pulzes from perspective of each photon from http://www.pitt.edu/~jdnorton/Goodies/rel_of_sim/index.html" in section 2 and see how and if they differ for different observers, if you would be able to detect existence of gravity in such a frame by measuring effects of gravitational red(blue) shift etc.

 

[Grimstone]

I think I already know the answer, but a friend of mine disagreed with me on this point:

If I were to become light, i.e. my consciousness was transferred to a photon moving with speed c, would it then seem to me as if I existed outside of time? I think it would because of the fact that moving clocks seem to travel slower. If you do a time dilation calculation you get the time interval in the moving system to be infinite compared to the proper time interval. It seems to me as if you would paradoxically experience two different things:

1. The universe would stand still (i.e. time would stop) for the rest of eternity.

2. All events in the future would happen instantly.

IF you could become a Photon.
you would not exist outside of time.
time is relative to the observer.
I would not see you go screaming by me at the speed of c. and I to you would look like a big blue blur, would you have human eyes.
your perception would be that of a photon and therefor i would be stationary to your perception.
Einstein says that two spaceships with headlights racing towards each other at the same speed. (unlike when two cars hit the speed does not stack to the measured force of impact.) would see each other at the same speed.
OK, he did not put it that way. but it is as I understand.

AND JEEZ can you guys not accept him becoming a Photon?

 

[LukeD]

Guys, I'm not convinced that there's no sense in asking "what would a photon 'see'", and here's why:

Even though everything "collapses to 1 point" if you'd try to transform smoothly to this frame from another, if we view the path of a photon in some other frame, it certainly exists. And we can talk about what events occur along the path. And in what order. And everyone agrees on those! Even the photon can agree on that.

And photons have wavelengths and frequencies. Everyone can agree on how much the phase has changed between 2 events on the photon's path. Even the photon can tell you that. (I'm not sure if this gets modified by QED)

But there are some things the photon doesn't seem to know.. For instance, it doesn't seem to know its own energy. Anyway, no one agrees on that number so who cares anyway.

 

[Phrak]

So what do you think is relevant to defining a photon's perspective?

The vectored quantity v=c is relevant.

Do you agree that there are an infinite number of distinct possible non-inertial frames in which a photon is at rest (with different definitions of simultaneity, distance, and time intervals) and none are preferred over any other by the laws of physics?

There are an infinite number of frames were v=c or the limit v-->c. But I don't think that's what you mean. Specifically there in one unique frame for a photon moving in the positive x direction for instance. Other than that, I don't know if "at rest" is a necessary condition or meaningful, but it would be another question to look at.

If "perspective" isn't interpreted in terms of a coordinate system, how is it to be interpreted?

I interpret one kind of "perspective" as the non-bijective map from the coordinate system where v=0 to coordinate system where v=c. Another perspective might involve time dilation and spatial contraction.

 

[Vanadium 50]

I couldn't stand it any more...I retitled the thread.

 

[JesseM]

There are an infinite number of frames were v=c or the limit v-->c.

There are no inertial frames where v=c...if you try to plug v=c into the Lorentz transformation you don't get a well-defined coordinate system, any point that had nonzero x and t coordinates in your original sublight inertial frame would have x' and t' of 1/0 when you put v=c in the Lorentz transformation, and any point with an x or t coordinate of 0 would transform to an x' or t' coordinate of 0/0.

Specifying that you want the limit as v approaches c doesn't pick out a well-defined coordinate system either. For one thing, since all sublight velocities are relative, "the limit as v approaches c" only makes sense if you're talking about v relative to some specific sublight inertial frame F. In that limit certain quantities might have a well-defined value, like the length of a rod at rest in F and parallel to its x axis, or the tick rate of a clock at rest in F (both would approach 0 in the limit). But other quantities don't seem to have a well-defined limit. For example, say you want to know what speed an object moving at c along F's axis would have in the limit as v approaches c. If you're considering a series of frames moving relative to F with velocities closer and closer to c, you could also consider a series of objects at rest in each of those frames, so in the limit as the velocities of the frames approached c, the object would remain at rest in each frame in the series but its velocity relative to F would approach c. So, this would suggest that "in the limit as v approaches c", the object moving at c in F would be at rest. But you could equally well consider an object which is always moving at exactly c in F, in which case each frame in the series will see it moving at c too, so this would suggest that "in the limit as v approaches c" the object moving at c in F would still be moving at c.

But I don't think that's what you mean. Specifically there in one unique frame for a photon moving in the positive x direction for instance. Other than that, I don't know if "at rest" is a necessary condition or meaningful, but it would be another question to look at.

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.

I interpret one kind of "perspective" as the non-bijective map from the coordinate system where v=0 to coordinate system where v=c.

What do you mean by "coordinate system where v=c"? Since there is no absolute velocity in relativity, v for anything can only be defined relative to some coordinate system. Obviously a coordinate system can't be moving at c in terms of its own coordinates, so presumably you are talking about the coordinate system's velocity relative to some sublight inertial frame F? (and when we talk about the velocity of one coordinate system F' as seen by another coordinate system F, I guess this means something like the velocity of the spatial origin of F' as seen in F, or the velocity in F of any object which is at rest in F')

Another perspective might involve time dilation and spatial contraction.

Both of these are entirely coordinate-dependent notions, so you can only talk about what time dilation and length contraction would be seen from the "perspective" of someone moving at c if you can specify what coordinate system is being used to define their "perspective".

 

[JesseM]

Exactly. One pulse equals one unit of time and in terms of these units you would measure all observed events.

So you agree there's no unique way to relate this unit of time to hour units of time, like saying whether one photon-unit is equal to one second or one hour? In that case there's no way to compare the two and say whether a photon's clock is running slower than ours or faster than ours.

By "you" I meant and further in discussion I will mean the observer at the photon's rest frame as I try to look from its perspective.

In relativity "frame" means a coordinate system for labeling the position and time coordinates of any event in spacetime. Is that what you mean? Your next comment might suggest otherwise...

But you somehow suppose that from the perspective of light the world would look exactly as from our perspective i.e. divided to the worlds of subluminal and luminal speeds. But so far nothing seems to give indications this would be the case. I think that from a perspective of a photon where luminal speed is your rest frame you cannot even learn subluminal or maybe any velocities exist at all. From the photon's point of view you would have no way of finding out velocities exist until you were absorbed by an atom.

Again, a frame is just a way of labeling space and time coordinates, it doesn't presuppose that you actually know what happened at each space and time coordinate. If you want to speak meaningfully about a photon's rest frame you need a coordinate transformation that can tell you, if an arbitrary event E happens at coordinates x and t in some sublight inertial frame, what coordinates x' and t' would be assigned to that event in the "photon's frame". Whether the specific x and t represent an point in spacetime you can actually see is irrelevant. And once you have a coordinate system for labeling events in spacetime, the definition of the "speed" of any object is very simple, it's just (change in coordinate position)/(change in coordinate time) between events on the object's worldline.

As an example, for two sublight inertial frames moving at v relative to one another (with one frame moving in the x direction of the other, and their spatial axes being parallel and the origins of their spatial axes lining up at a time of 0 in each frame), if one coordinate system uses coordinates x,y,z,t and the other uses coordinates x',y',z',t', the coordinate transformation would be:

x' = gamma*(x - vt)
y' = y
z' = z
t' = gamma*(t - vx/c^2)

where gamma = 1/squareroot(1 - v^2/c^2)

Note that this coordinate transformation works perfectly well for coordinates representing regions of spacetime I can't observe--for example, an event with a t-coordinate that lies 1 million years in my future. I might not know what is actually going to happen at coordinates x=1 light year, t=1 million years, but whatever event happens there I know what the corresponding x' and t' coordinates in the second frame would be.

You can have coordinate systems that only have a limited domain of applicability, covering only a "patch" of a larger spacetime, so that some x,t coordinates in an inertial frame covering all of spacetime might not have corresponding x',t' coordinates in your non-inertial frame, because they would represent events outside the patch of spacetime where the non-inertial frame is defined. Still in order to talk meaningfully about any non-inertial frame in SR, you need a clear definition of exactly how its coordinates relate to those of some inertial frame.

 

[mooneyes]

Okay. I've read this entire thread from start to finish, and maybe its just because I don't know that much relativity, but I get what yer man is saying, who posted the original question. Can someone just answer me this, in layman's terms. If I was traveling at 99.999% the speed of light time would be effectively still, yes? and would there be length contraction effects, too?

 

[JesseM]

Okay. I've read this entire thread from start to finish, and maybe its just because I don't know that much relativity, but I get what yer man is saying, who posted the original question. Can someone just answer me this, in layman's terms. If I was traveling at 99.999% the speed of light time would be effectively still, yes? and would there be length contraction effects, too?

Both speed and length contraction/time dilation are completely relative for inertial observers moving slower than light. If I was traveling at 99.999% the speed of light relative to you, in your frame my clock would be slowed down by a great amount (ticking at a rate only 0.00447 as fast as yours) and my length would be greatly shrunk in the direction of travel. However, in my frame it would be your clock that was slowed down by a great amount (your clock only ticking at 0.00447 the speed of mine) and it would be you who was greatly shrunk in length. Both frames are equally valid in relativity, and both of us would measure light to move at c relative to ourselves.

 

[Phrak]

There are no inertial frames where v=c...if you try to plug v=c into the Lorentz transformation you don't get a well-defined coordinate system, any point that had nonzero x and t coordinates in your original sublight inertial frame would have x' and t' of 1/0 when you put v=c in the Lorentz transformation, and any point with an x or t coordinate of 0 would transform to an x' or t' coordinate of 0/0.

Look up http://en.wikipedia.org/wiki/Indeterminate_form" 0/0 may, or may not have a well defined value but is dependent upon how one term is divided by another. x/y=1, for instance is well behaved at y=0.

Why you bring up this up, I don't know. The undefined values in this problem are usually a result of dividing a finite value by zero.

Specifying that you want the limit as v approaches c doesn't pick out a well-defined coordinate system either. For one thing, since all sublight velocities are relative, "the limit as v approaches c" only makes sense if you're talking about v relative to some specific sublight inertial frame F.

Of course we relate the limit c-->v for a given inerital frame. It's where the v comes from. This is implicit in the question.

In that limit certain quantities might have a well-defined value, ..

Finally. You realize that some things do make sense.

 

[JesseM]

Look up http://en.wikipedia.org/wiki/Indeterminate_form" 0/0 may, or may not have a well defined value but is dependent upon how one term is divided by another. x/y=1, for instance is well behaved at y=0.

Yes, in this case it is because the limit of x as y approaches 0 is well-defined. I think you have a point here in the sense that if we take some coordinates like x=2, t=2 and consider the limit of the Lorentz transformation as v approaches c, the limit will be x'=0 and t'=0 despite the fact that if we try to actually plug in v=c with these x and t coordinates we get x'=0/0 and t'=0/0. Still this isn't really a valid coordinate system, since it takes every event whose coordinates in the original sublight inertial frame satisfy x=ct (like x=2,t=2 and x=3,t=3) and assigns them all the same "limit coordinate" of x'=0, t'=0, whereas events whose coordinates in the sublight inertial frame don't satisfy x=ct will not have well-defined x' and t' coordinates even if we are talking about limits.

Why you bring up this up, I don't know. The undefined values in this problem are usually a result of dividing a finite value by zero.

Yes, that's why I said the part in bold:

if you try to plug v=c into the Lorentz transformation you don't get a well-defined coordinate system, any point that had nonzero x and t coordinates in your original sublight inertial frame would have x' and t' of 1/0 when you put v=c in the Lorentz transformation, and any point with an x or t coordinate of 0 would transform to an x' or t' coordinate of 0/0.

I actually made a mistake in that quote though, what matter is not whether x or t are zero on their own, but whether (x-ct) or (t-x/c) are equal to zero (i.e. whether x and t satisfy x=ct). If neither of these are zero, then when you try to do a Lorentz transformation on x and t with v=c, you'll get a nonzero number divided by zero like 1/0; if x=ct so both are zero, then when you try to do a Lorentz transformation with v=c, you'll get x'=t'=0/0, although as noted above x' and t' would both be equal to zero in the limit as v approaches c. Either way, you don't have a well-defined coordinate system where you can find a meaningful, distinct set of x' and t' coordinates to assign to every distinct event whose x and t coordinates are known in some sublight inertial frame.

Finally. You realize that some things do make sense.

I said all along that some things make sense in the limit. Look at post 21 where I wrote:

The closest you can come to answering this question in the context of relativity is thinking about what things look like in the limit as you approach the speed of light (relative to external landmarks like the galaxy), though not all quantities are well-defined in this limit. In such a limit, the traveler will see all the clocks at rest relative to the galaxy (or close to it) as approaching zero rate of ticking, and also sees the length of the galaxy in the direction of motion as squashed down to near zero.

(this post also seemed to somewhat satisfy the original poster, who wrote in post 23 'That's the kind of stuff I was looking for. Thank you JesseM. Perhaps I should have been discussing the limit as v approaches c.')

So I obviously wasn't disputing that some things make sense in the limit (though others don't, as I pointed out), I was disputing your claim that we can talk about a "frame" for the photon to define its "perspective". If you still stand by that claim, then please address the problems I pointed out for this, like the fact that the frame can't be an inertial one, and if you want to define a non-inertial frame where the photon is at rest, there are an infinite number of different possible non-inertial coordinate systems which have this property, which make different judgments about things like simultaneity and distances and times.