- #1
peterspencers
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why does space time not contract uniformly in every direction around a fast moving object?
HallsofIvy said: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.
Mark M said: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.
bcrowell said:I like cepheid's argument, because it's rigorous and also conceptually simple.
bcrowell said: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.
bcrowell said: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
bcrowell said: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 , 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.
Hmmm, interesting. I don't think I have any problem with Einstein's original axiomatization, but even with his original axiomatization, it seems that MarkM's argument is backwards as you suggest (no offence intended), because the constancy of the speed of light is assumed, and then length contraction is derived as a consequence of it, not the other way around.bcrowell said: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
bcrowell said: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.Muphrid said: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.
Muphrid said: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.cepheid said: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?
cepheid said: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?
bcrowell said: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.
peterspencers said: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.peterspencers said: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.peterspencers said: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.peterspencers said: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.
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.
The Lorentz transformations tell you directly that there is no length contraction parallel to the direction of motion; to find that out you don't need to make such a calculation. However, your question was why length contraction only occurs parallel to the direction of motion.peterspencers said:Why is my above calculation insufficient to explain length contraction? I don't follow the reasoning here, please could someone explain (to a lamen) if the above quote really does apply to my above calculation.
peterspencers said:why does space time not contract uniformly in every direction around a fast moving object?
harrylin said:- Your calculation doesn't show why that is the only feasible possibility based on the postulates.
Once more: if you assume that there is no time dilation but all distances contract by an additional factor γ (so that the length contracts by γ^{2} and the width by a factor γ), then your scenario will also work (the 'light distance' in both directions as measured with a clock is equal and the same in the rest frame and the moving frame).
I agree with that; however, based on what fact or assumption do you make that claim?peterspencers said:In my scenario I have a rest observation and a moving one. Where the clock is being observed in motion, velocity is an obvious consideration. As soon as velocity is acting upon the clock the equations for calculating the time change and time dilation becomes an inevitable and unavoidable factor. [..]
Then I may have misunderstood your scenario, as I think that you describe two systems in which clocks are observed that are in rest in each system. Please check.peterspencers said:In my scenario 'assuming no time dilation' is not an option! My scenario is one where we are making observations of a moving clock, therefore time dilation is an intrinsic part.
Yes, I will, as I promised, after you reply my repeated question to you so as to be sure that we are "tuned to the same frequency". So, for the third time: please clarify if you agree with the part that you did not cite, here it is again:Please can you show me your mathematical workings step by step using my initial values for l, c and v. Also an explination of how 'assuming zero time dilation' is possible in a situation where we are observing a moving clock. [..]
Then I may have misunderstood your scenario, as I think that you describe two systems in which clocks are observed that are in rest in each system. Please check.
It's sufficient to understand how the Lorentz transformations work. It's not sufficient to determine that for relativity the Lorentz transformations are the only solution. And apart of the relativity principle there is also a physical reason for length contraction (yes we could discuss that later!).peterspencers said:[..] I am fascinated at the thought of there being other ways to mathematically and intuitively describe and explain the reasons for length contraction. Before I begin along that line of questioning however I must first clarify if my current understanding (based upon my scenario) is sufficient. As you have stated that it is not... [...]
I did not think that you describe 2 clocks that are in rest, so probably I did understand your scenario which looks to me the "standard" one.No my scenario does not describe 2 clocks that are at rest, why would I have included v (velocity) in my equations if that were the case?
Yes that's sufficient to get a basic understanding of how length contraction and time dilation work. And here's your calculation redone for an alternative solution* (I simply copy-pasted from you with a few modifications) :I hope I have answered you questions sufficiently, I must ask again, in light of my attempt at clarification... if my scenario and calculations are sufficient to explain length contraction and time dilation?
There's been a mistake here. The formula I found for [itex]te[/itex] is [itex]te[/itex] = [itex]\frac{2l}{\sqrt{c^2-v^2}}[/itex]. It gives [itex]te[/itex] = 1 second for this case.harrylin said:Then for the horizontal clock:
[itex]te[/itex] = [itex]\frac{2lc}{c^2-v^2}[/itex]
[itex]te[/itex] = 1.25 seconds
That can hardly be right, even when correcting for a typo in your equation: MMX would not have been performed with equal round times for equal lengths. Peterspencer's equation (which I copied from his post #24) is easy to derive, see https://en.wikisource.org/wiki/On_the_Relative_Motion_of_the_Earth_and_the_Luminiferous_Ether, page 336:vin300 said:There's been a mistake here. The formula I found for [itex]te[/itex] is [itex]te[/itex] = [itex]\frac{2l}{\sqrt{c^2-v^2}}[/itex]. It gives [itex]te[/itex] = 1 second for this case.