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PeterDonis
#30
Feb18-12, 07:09 PM
Physics
Sci Advisor
PF Gold
P: 6,039
Quote Quote by nitsuj View Post
1.b.)You asked me what I meant by slice in 3D, that is what I mean; the path of a photon. Im leaving it at that.
Well, that's not a very clear place to leave it, IMO. :-) If by "path" you mean "path in a 3-D space", that is *not* the same thing as "path" meaning "worldline in 4-D spacetime". The latter is the concept that is used in SR, and all the things I've said, and you apparently agree with, about a photon not having a standard frame of reference, having zero Lorentz interval, etc., only apply to the photon's "path" as a worldline in 4-D spacetime, *not* as a line in 3-D space. The "path" in 3-D space can, in special cases, be thought of as a projection into a 3-D spatial slice of the 4-D worldline, but only in special cases; and in any case the 4-D worldline is what you have to use to do the physics.

Quote Quote by nitsuj View Post
You can't fool me, you know exactly what I mean with "time & length perpendicular to each other." especially after, oddly as it is, you describe what I meant in the very next sentence.
I conjectured that that was what you meant, but I'm glad to have confirmation.

Quote Quote by nitsuj View Post
3.) Im not talking about EM from the perspective of an observer, I'm talking about em from the perspective of em.
I don't know what "em from the perspective of em" means. To write down any equations for Em at all, you have to define what the symbols in the equations mean. I know how to do that from the perspective of an observer; I don't know how to do that "from the perspective of em". Can you please clarify?

Quote Quote by nitsuj View Post
4.) actually peter it is fundamentally different perspectives of the same thing.
No, it isn't. "Spatial" is not just a different perspective of "null". They are physically different and distinct. Spatial curves have a nonzero Lorentz interval (a negative squared interval if we are using a timelike sign convention). Null curves have a zero Lorentz interval. Nonzero is physically different and distinct from zero.

Quote Quote by nitsuj View Post
So Peter if EM is not purely spatial from it's perspective, can you catch up to a beam of light? Probably not enough time in the interval for that. How else can a meter be defined by EM but by this kinda of reasoning.
I still don't understand what you're getting at here. I understand the Wiki definition of a meter that you quote next, but I don't understand how you're interpreting it.

The path of a photon, meaning its worldline, is a null line; in the case given in the Wiki definition, it goes between two events in spacetime with coordinates (in a suitably defined inertial frame) (0, 0) and (1/299,792,458, 1), where the (t, x) coordinates are given in (seconds, meters). The "length" you are talking about would be a *spacelike* line going from (0, 0) to (0, 1); the "proper time" you are talking about would be a timelike line going from (0, 0) to (1/299,792,458, 0). Neither of those lines is the worldline of the photon. The spacelike line could be thought of as the "spatial path" of the photon, since it is a projection into the (t = 0) spacelike slice of the photon's worldline; but that spacelike line is *not* the line you have to use if you want to figure out the photon's physics. You have to use its worldline.

If the above was in fact how you were interpreting things, then good; but it wasn't clear from what you wrote before. It the above was not how you were interpreting things, then please clarify further.

Quote Quote by nitsuj View Post
Comprehension question for two points and a smiley face: Is there a difference in position of axis between measuring time with EM and measuring length with em? If so what is it, Peter?
Again, I'm not sure I understand what question you are posing.

Take the Wiki scenario above again. Suppose there is a mirror at x coordinate 1 in the given inertial frame. I emit a photon at event (0, 0), and I want to verify that the mirror is exactly 1 meter away. I measure the round-trip light travel time to be 2/299,792,458 seconds, which verifies it.

Conversely, suppose I want to verify that my clock is calibrated correctly, and I know for sure that the mirror is exactly 1 meter away. Again, I bounce a photon off the mirror and verify that my clock measures the round-trip travel time to be 2/299,792,458 seconds, which shows that it is properly calibrated.

It seems to me that these experiments count as "measuring length with EM" and "measuring time with EM". But I did the same thing both times; the only difference was which parameter I took to be known and which one I took myself to be measuring. So I don't see how there's any difference in "position of the axis" between the two measurements. But I'm not sure if that's the question you were asking.