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why does space time not contract uniformly in every direction around a fast moving object?
I don't buy this at all. The electric field is a vector, but under a Lorentz boost, its component perpendicular to the boost can certainly change.The simplest answer to your question is that velocity is a vector quantity. Any contraction due to velocity couldn't very well be perpendicular to the velocity because there is no velocity in that direction.
IMO this is logically backwards, since Einstein's 1905 axiomatization of SR is clearly a mistake, with the benefit of 107 years of historical hindsight. We see SR now as a theory of space, time, and causality, in which light plays no central role. More appropriate axiomatizations have been known since 1911; see our FAQ: https://www.physicsforums.com/showthread.php?t=534862 [Broken]The reason length contraction occurs in the first place is to preserve a constant speed of light for all inertial frames of reference. If an observer says that you're moving in only the x direction, then lengths only need to contract along that direction for you to preserve the speed of light. Since you have no motion in the y or z direction, no length contraction is needed in the perpendicular directions.
Thanks! I wish I could say that I came up with it myself. I related it from memory (i.e. I understand the argument, so I can recount it myself), but it was something I read in Introduction to Electrodynamics by David J. Griffiths (and he explains it far less verbosely). He, in turn, says in the book that he adapted it from Spacetime Physics by Taylor and Wheeler.I like cepheid's argument, because it's rigorous and also conceptually simple.
Interesting, I hadn't thought about that. What do you mean by "space is isotropic?" In this case it sounds like you are saying that, "the laws of physics are the same regardless of what direction you're moving in." Is that basically it?My only minor criticism is that it depends on a symmetry principle that wasn't invoked explicitly in #4. A's velocity relative to B and B's velocity relative to A point in opposite directions. It's possible that one of these directions produces contraction, and one expansion. To rule this out, we need to assume that space is isotropic.
I think that might be the same idea, yeah.I would have to look more carefully, but cepheid's argument may be the same as the "nails on rulers" argument given here: https://www.physicsforums.com/showthread.php?p=2108296#post2108296
That's a cool link! I read the section that you were referring to, and I like the way they just used reasoning from the five postulates to arrive at the necessary geometric properties of the transformation. (EDIT: "They" being you, I gather).Another argument is the following. In 1+1 dimensions, one can prove straightforwardly that Lorentz transformations must preserve area. (For a proof, see http://www.lightandmatter.com/html_books/0sn/ch07/ch07.html#Section7.2 [Broken] , caption to figure j.) By a similar argument, Lorentz transformations in 2+1 dimensions must preserve volume. The only way that both of these can be true is if lengths in the transverse direction are preserved.
IMO this is logically backwards, since Einstein's 1905 axiomatization of SR is clearly a mistake, with the benefit of 107 years of historical hindsight. We see SR now as a theory of space, time, and causality, in which light plays no central role. More appropriate axiomatizations have been known since 1911; see our FAQ: https://www.physicsforums.com/showthread.php?t=534862 [Broken]
Eh, misconception. The electric field is not really a vector. Its transformation follows from the full transformation of [itex]F_{\mu \nu}[/itex]--i.e., from the transformations of the tx, ty, and tz planes. The electric field is a field of planes, and those planes' transformations are entirely in agreement with what you expect by boosting the individual vectors that span them.I don't buy this at all. The electric field is a vector, but under a Lorentz boost, its component perpendicular to the boost can certainly change.
You mean then the EM field is not really a vector. Not the electric field.Eh, misconception. The electric field is not really a vector. Its transformation follows from the full transformation of [itex]F_{\mu \nu}[/itex]--i.e., from the transformations of the tx, ty, and tz planes. The electric field is a field of planes, and those planes' transformations are entirely in agreement with what you expect by boosting the individual vectors that span them.
Everything you say is true, depending on one's notion of a vector. There are really two definitions of a vector that are commonly used: (A) the definition of a 3-vector from freshman mechanics, and (B) the definition of a 4-vector from SR. The electric field fits definition A but not definition B. However, the argument given in #2 doesn't make use of any specific properties of the B definition as opposed to the A definition, and the electric field is a counterexample under the A definition, so the argument can't be correct.Eh, misconception. The electric field is not really a vector. Its transformation follows from the full transformation of [itex]F_{\mu \nu}[/itex]--i.e., from the transformations of the tx, ty, and tz planes. The electric field is a field of planes, and those planes' transformations are entirely in agreement with what you expect by boosting the individual vectors that span them.
I asked about this symmetry assumption some time ago and at the end I was convinced that it is principle of relativity and nothing else.Interesting, I hadn't thought about that. What do you mean by "space is isotropic?" In this case it sounds like you are saying that, "the laws of physics are the same regardless of what direction you're moving in." Is that basically it?
I would say that it's the principle that the laws of physics don't distinguish any direction in space from any other. As a special case, you can apply it to a velocity vector.Interesting, I hadn't thought about that. What do you mean by "space is isotropic?" In this case it sounds like you are saying that, "the laws of physics are the same regardless of what direction you're moving in." Is that basically it?
Makes sense to me. Thanks (also to Muphrid and zonde) for the clarification.I would say that it's the principle that the laws of physics don't distinguish any direction in space from any other. As a special case, you can apply it to a velocity vector.
1. Motion extends the distance photons move between em interactions because light speed is constant.why does space time not contract uniformly in every direction around a fast moving object?
Yes but it's insufficient: the Lorentz transformations state that there is no vertical contraction, so that is what you want to prove (or make plausible). You demonstrated that based on the starting assumptions (equal speed of light etc), the vertical contraction factor must differ from the horizontal one. However, you could assume, for example, that the vertical contraction is gamma and the horizontal contraction gamma square. Then with zero time dilation your calculation will also work.Ok so thankyou all for the help, I think I'm nearly there. I think I may have a clear understanding, is this a correct explination.....
If I have a light clock on a fast moving spacecraft being observed from earth, with a vertical set of mirrors (perpendicular to the motion of the overall clock) and a horizontal set of mirrors. The mirrors time the pulses of light, eminating from the same source. I then apply the equations for calculating the time it takes for the light pulses to bounce between each set of mirrors using the values of c = 10, v = 6 and l = 4.
I find initially that the horizontal bounces take 1.25 seconds and the vertical bounces take only 1 second. It's only when I apply the lorenz transformation to the length in the horizontal clock to give me new decreased value for l of 3.2, that I discover my time calculations for both mirrors agree on 1 second. I then conclude that the length must contract around the moving pulse of light to preserve its consistancy for all frames of reference.
Is this correct?
I can't make sense of your setup. You haven't said what c, v and l are and you haven't said what their units are. Usually, we reserve the letter "c" to be the speed of light and "v" is a velocity. It's a little unusual for someone to set the speed of light to be 10, we usually make c = 1 to make the equations simpler. And you haven't said what equations you are using nor what l applies to.Ok so thankyou all for the help, I think I'm nearly there. I think I may have a clear understanding, is this a correct explination.....
If I have a light clock on a fast moving spacecraft being observed from earth, with a vertical set of mirrors (perpendicular to the motion of the overall clock) and a horizontal set of mirrors. The mirrors time the pulses of light, eminating from the same source. I then apply the equations for calculating the time it takes for the light pulses to bounce between each set of mirrors using the values of c = 10, v = 6 and l = 4.
I find initially that the horizontal bounces take 1.25 seconds and the vertical bounces take only 1 second. It's only when I apply the lorenz transformation to the length in the horizontal clock to give me new decreased value for l of 3.2, that I discover my time calculations for both mirrors agree on 1 second. I then conclude that the length must contract around the moving pulse of light to preserve its consistancy for all frames of reference.
Is this correct?
1. Your question is "Why does length contraction only occur parallel to the direction of motion?". Although you now suggest the contrary, I thought that you did not intend to discover what the Lorentz transformations state (contrary to valentin). As a matter of fact, they state that y=y' and z=z', so if that was your question and you did not want to prove what you assumed, then that was the answer and the end of this topic. :tongue2:How will my calculation show length contraction with, zero time dillation? My calculation shows that time on the ship (ts) would be 0.8 and time from say earth (te) would be 1. Also why would I want to make vertical contraction possible? The vertical clock dosent contract, the path the photon takes is extended, as per a little pythagoras, hence the time dilation.
Why is my above calculation insufficient to explain length contraction? I dont follow the reasoning here, please could someone explain (to a lamen) if the above quote really does apply to my above calculation.Yes but it's insufficient: the Lorentz transformations state that there is no vertical contraction, so that is what you want to prove (or make plausible). You demonstrated that based on the starting assumptions (equal speed of light etc), the vertical contraction factor must differ from the horizontal one. However, you could assume, for example, that the vertical contraction is gamma and the horizontal contraction gamma square. Then with zero time dilation your calculation will also work.