-2
$\begingroup$

Most people believe length contraction is a real spatial phenomenon and if so there's nothing to contract in empty space and since matter contains mostly empty space then it is only the structure of matter that is physically contracting.

So now, if a mirror is mounted on a 45 degree plank coming out of the wall, only the plank and mirror will thin in the direction of motion when observed externally. The angle of the mirror won't change because there's nothing to contract irregularly behind the mirror. But if you mount the mirror on an L-bracket, the bottom of the bracket will contract more than the top and hence the angle of the mirror will now change solely because of the fact you've added matter to the bottom? Is this really how length contraction would work? Is this why pulses of light don't look contracted to us as they travel because they have no material structure to contract?

$\endgroup$
  • 1
    $\begingroup$ Congratulations for recognizing the importance of the the relativity of simultaneity;it is too often overlooked. However, you might take a close look at the Lorentz transformtion before proclaiming that relativistic phenomena are wholey attributable to changes in time-behavior. The transformation explicitly mixes time-and space coordinates between frames. $\endgroup$ – dmckee --- ex-moderator kitten Oct 10 '19 at 16:39
  • $\begingroup$ matter is made of empty space In mainstream physics, electrons and other elementary particles are not made of empty space. $\endgroup$ – G. Smith Oct 10 '19 at 16:41
  • $\begingroup$ edited OP to eliminate the misunderstanding $\endgroup$ – ralfcis Oct 10 '19 at 16:46
  • $\begingroup$ @dmckee yes space coordinates but in the pole and barn paradox, the "length" of the 15' pole is measured from the perspective of when the endpoint coordinates fit simultaneously within the 10' barn. The physical length of the pole does not correspond to those endpoints. In fact the front endpoint is way outside the barn. $\endgroup$ – ralfcis Oct 10 '19 at 16:53
  • 1
    $\begingroup$ See Bell's spaceship paradox (en.wikipedia.org/wiki/Bell%27s_spaceship_paradox) and the Lewis-Tolman lever paradox (en.wikipedia.org/wiki/…). $\endgroup$ – Dvij Mankad Oct 10 '19 at 23:02
1
$\begingroup$

This talk of physical contraction reflects a misunderstanding about the meaning of length contraction. The spatial distance between two points stationary in one reference frame will not equal the difference in another in which the points are moving. The disagreement is regardless of whether anything physical, such as a rod, spans the space between the two points. It arises purely because the coordinate systems of the two observers are rotated relative to each other. The effect is entirely reciprocal, so if you measure me as having shrunk in my direction of travel, I measure you as having shrunk by exactly the same amount. Neither of us has shrunk- our constituent parts remain the same shape and the same distance apart.

The effect is exactly analogous to the following familiar one. Suppose I hold a stick lengthwise in front of you. You see the full length of the stick. If I now rotate the stick so that one end moves toward you and one away the stick will appear foreshortened from your perspective, because its length is now projecting at an angle to your field of view. The stick has not compressed, it has just rotated so it is no longer fully aligned with the axis along which you assess its length, and so it appears shorter.

$\endgroup$
  • $\begingroup$ The question is not what is reciprocal length contraction. The question is if you believe length contraction physically happens in an observed moving frame, just like time dilation physically allows a muon to reach earth, will the mirror angle change if only space, as opposed to matter, is behind the moving mirror. Can empty space be length contracted. The answer I gave turned out to be yes. $\endgroup$ – ralfcis Oct 10 '19 at 23:24
  • $\begingroup$ From your perspective everything in the moving frame contracts in its direction of motion. If the mirror is at 45 degrees to its direction of motion its apparent orientation will change, so that it will appear to be more upright. This will happen regardless of whether the mirror is attached to anything or how it is mounted. $\endgroup$ – Marco Ocram Oct 11 '19 at 7:26
0
$\begingroup$

Ok, someone has explained this to me on another forum. When a frame jump occurs, time and space effects are no longer reciprocal. Only one participant ages less but the space imbalance is in the distance travelled, not in a permanent flattening of the returning ship. Hence if a non-time based odometer could be made, it would record the ship has travelled a contracted distance but you could not expect the return of a flattened ship because that would make the space effect reciprocal which it no longer is due to the frame jump.

So the answer to this particular question is the space must contract if your distance measured by your spaceship's "odometer" contracts. Matter is irrelevant to length contraction. So the angle of the mirror will move the same no matter what bracket you use.

However, I still can't answer why light pulses do not appear contracted from our perspective. So my question about femtosecond Raskar photography remains unanswered.

$\endgroup$
0
$\begingroup$

Fainberg (https://iopscience.iop.org/article/10.1070/PU1975v018n08ABEH004917/meta) asked a similar question - is length contraction a real phenomenon?

The answer he reached is yes, that it is, in the sense that as you accelerate the body you will have to supply real energy to achieve the length contraction, by pushing charges closer together.

The point here is that matter is held together by electromagnetic forces, so of course length contraction and all other relativistic effects will occur as you change the speed of an object. However, the only unambiguous way to test these effects is to start in the lab with a stationary object and then to accelerate it. This subtle point is lost when we start talking about jumping between reference frames.

Regarding the light-pulses not being contracted. Are you sure? The wavenumber and even the wavevector of a plane-wave will change depending on the observer (e.g. https://en.wikipedia.org/wiki/Relativistic_aberration), and a light pulse can be decomposed into plane-waves...

$\endgroup$
  • $\begingroup$ Length contraction like the light pulses would be viewed from a relative constant velocity, no acceleration involved. Even if you had to accelerate to speed, once at speed all the laws of physics work as if you were in a stationary frame. $\endgroup$ – ralfcis Oct 10 '19 at 21:39
  • $\begingroup$ Sorry, I don't understand which bit of my text you are commenting on. I also don't quite understand your point. $\endgroup$ – Cryo Oct 10 '19 at 21:43
  • $\begingroup$ The relativistic phenomenon of length contraction x'=Yx (Y is gamma, x is distance) is not caused by acceleration. You're talking of Newtonian F=ma. $\endgroup$ – ralfcis Oct 10 '19 at 21:51
  • $\begingroup$ I did not say that length contraction is caused by acceleration. What I said is that if you were to accelerate an object to the point where length contraction becomes measurable (by you, the stationary observer), then the extra energy to actually contract the object will have to be supplied by you (on top of the kinetic energy due to the speed you have accelerated the object to). $\endgroup$ – Cryo Oct 10 '19 at 22:12

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.