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Light speed and time

by -=Red=-
Tags: light, speed, time
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JesseM
#19
Aug29-10, 04:10 PM
Sci Advisor
P: 8,470
Quote Quote by novop View Post
"The Lorentz transformations tell us that time stands still for an object moving at the speed of light. From the point of view of the photon, of course, it is everything else that is rushing past at the speed of light. And under such extreme conditions, the Lorentz-Fitzgerald contraction reduces the distances between all objects to zero. You can either say that time does not exists for an electromagnetic wave, so that it is everywhere along its path (everywhere in the Universe) at once; or you can say the distance does not exist for an electromagnetic wave, so that it "touches" everything in the Universe at once."
Who is the author of this quote? From a google books search it may be John Gribbin in the book 'Schroedinger's Kittens', a nontechnical book for a popular audience. Like I said, in some approximate sense you can talk about the "point of view of a photon" in terms of what would be seen in the limit as a slower-than-light inertial observer approached a speed of c relative to his surroundings, but this isn't really rigorous and I don't think you'll find any textbooks or scientific papers talking about the "point of view" of a photon.

edit: beaten to it by bcrowell!
-=Red=-
#20
Aug29-10, 04:23 PM
P: 19
Quote Quote by JesseM View Post
When you say "everything around those photons has stopped moving", are you imagining things in a "frame" where the photon is at rest?

Yeah
JesseM
#21
Aug29-10, 05:29 PM
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P: 8,470
Quote Quote by -=Red=- View Post
Yeah
So do you understand there can't be an inertial frame where this is the case, because one of the basic axioms of SR is that light must move at c in all inertial frames (the other says that all the fundamental laws of physics must look the same in all inertial frames)? Of course you can come up with a non-inertial coordinate system where light is at rest, but keep in mind that the usual equations of SR such as the time dilation equation only apply in inertial frames. And a bigger problem is that unlike with inertial frames, there isn't any single physically correct way to construct a non-inertial frame where a given object is at rest, you have an infinite number of choices. For example, if we have a light beam whose x-coordinate as a function of t-coordinate in some inertial frame is x(t) = c*t (so for example, at time t=4 seconds the light beam is at position x=4 light-seconds, and so on), then here is a coordinate transformation which gives a non-inertial frame with coordinates x' and t' where that light beam is at rest:

x' = x - c*t
t' = t

If you pick any event on the light beam's path with coordinates t and x=ct, then according to this coordinate transformation, in the non-inertial frame the event always has position coordinate x'=0, regardless of the t' coordinate, so the light beam must be at rest in this coordinate system. But since this coordinate transformation also says the t' coordinate of any event in the non-inertial frame is exactly the same as the t coordinate of the event in the inertial frame, there is no time dilation between the two frames! If a clock is ticking at a rate of 1 tick per second of coordinate time in the inertial frame, it's still ticking at a rate of 1 tick per second of coordinate time in the non-inertial frame. On the other hand, here's a different non-inertial frame where the light is still at rest, but now all clocks are slowed down by a factor of 1000 relative to the inertial frame:

x' = x - c*t
t' = 1000*t

And you could come up with plenty of weirder transformations which gave coordinate systems where the light was at rest, like this:

x' = 1.2*(9tc/x)*(x - c*t)
t' = 35*(t^2*c/8x + 19x/c)

The point is that there is a unique physical procedure for defining an inertial rest frame for a slower-than-light object moving inertially, but no such uniqueness for non-inertial frames.
-=Red=-
#22
Aug29-10, 07:03 PM
P: 19
Wow thats a mouthful. I am starting to understand the concept now. Let me just read this over a few times :)

Thanks for all the help on the subject. I appreciate your time.
-=Red=-
#23
Aug29-10, 07:22 PM
P: 19
Actually, do you know of any good books i can read on the topic? Relativity i mean.
novop
#24
Aug29-10, 07:55 PM
P: 125
Quote Quote by JesseM View Post
Who is the author of this quote? From a google books search it may be John Gribbin in the book 'Schroedinger's Kittens', a nontechnical book for a popular audience. Like I said, in some approximate sense you can talk about the "point of view of a photon" in terms of what would be seen in the limit as a slower-than-light inertial observer approached a speed of c relative to his surroundings, but this isn't really rigorous and I don't think you'll find any textbooks or scientific papers talking about the "point of view" of a photon.

edit: beaten to it by bcrowell!
Yep, its from Gribbin. And of course it's totally qualitative (and hardly rigorous). I just found it quite pertinent to the thread, that is all.

Quote Quote by -=Red=-
Actually, do you know of any good books i can read on the topic? Relativity i mean.
AP French's "Relativity" is one of the most succinct and intuitive intro texts to relativity... highly recommended:

http://www.amazon.com/Special-Relati...3130007&sr=8-1
JesseM
#25
Aug30-10, 01:09 PM
Sci Advisor
P: 8,470
Quote Quote by -=Red=- View Post
Actually, do you know of any good books i can read on the topic? Relativity i mean.
It depends on how technical of an intro. you want. If you want all the mathematical detail you'd get in an undergraduate course, the A.P. French book is a good recommendation as is Spacetime Physics by Taylor and Wheeler (which you can preview on google books here), but if you're just looking for more of a conceptual introduction these two online books are good:

Relativity for the Questioning Mind

wikibook on SR

Another good conceptual introduction is Geroch's General Relativity from A to B, which also has a lot on special relativity.
Naty1
#26
Aug30-10, 03:10 PM
P: 5,632
A convenient set of discussions on relativity:

http://www.mathpages.com/rr/rrtoc.htm

and Ben Crowell's:

http://www.lightandmatter.com/genrel/

and a shorter book by a student of Einstein's, easy/light math,inexpensive used via AMAZON

THE RIDDLE OF GRAVITATION, Peter Bergmann

also, don't let some of the stricter responses above deter you from thinking about moving along with a beam of light if that's what you like...or any other way you'd like...such thoughts can lead to legitimate insights.....after all it got Einstein started.....!!!! Thinking about things the way everyone else says they should be thought about might make new insights difficult....


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