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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?

ralfcis
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3 Answers3

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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.

Professor Sushing
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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.

ralfcis
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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...

Cryo
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