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

[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.