# How does relativity...work?

I understand the principles of relativity. I understand why we need relativity if we are to have the laws of physics be the same in all inertial frames. But physically speaking, how does relativity actually work? In particular, I was thinking about length contradiction, and I don't understand how moving objects shrink. I understand why they need to, just not how. Is the fabric of spacetime bending in some weird way around a speeding object in order to shrink the object? (Presumably, this might make sense, since massive objects warp spacetime, and fast moving objects have a large relativistic mass). Is this explainable using general relativity?

Edit: To elaborate, my question is more about the mechanics of what is happening to make the object appear shorter. For example, consider a straw in a glass of water, and a straw not in a glass of water. In both cases, the straw is the same. However, it looks weirdly disjointed when in the glass of water; from a new perspective, it looks different. However, there is a good explanation for why this is; the light refracts when changing mediums, and this thus changes your perception. I'm looking for a similar explanation as to "how" the perception that something has changed length actually comes about in S.R. –

• Magnetism is possible because of relativity... I'm talking about an electromagnet. Dec 4 '19 at 8:07
• NOTHING shrinks, really. To fully understand this you need to learn special relativity, and avoid pop science explanations. No shortcuts. Dec 4 '19 at 10:38

## 4 Answers

The object does not physically shrink. Its length appears to change when viewed from a moving reference frame. You must remember that the effects of relativity are symmetrical. If a fast moving spaceship, and all the people in it, seem to have contracted in length from your perspective, from their's it is you who is fast moving and contracted.

The effect comes about in a way that is precisely analogous to a rotation of spatial coordinates. If you have a 3D coordinate system that is rotated relative to mine so that your axes point in different directions to mine. We will now disagree about the coordinates of any point in that space. Moreover, if we consider two points in space, we will disagree about the horizontal and vertical distances between them, for example. The same effect occurs in spacetime. Observers that are stationary relative to each other each have a time axis pointing in a common direction, but if they start to move their time axes diverge so they are no longer pointing in the same direction in 4D space, which causes them to disagree about positions and separations in time.

• My question is more about the mechanics of what is happening to make the object appear shorter. For example, consider a straw in a glass of water, and a straw not in a glass of water. In both cases, the straw is the same. However, it looks weirdly disjointed when in the glass of water; from a new perspective, it looks different. However, there is a good explanation for why this is; the light refracts when changing mediums, and this thus changes your perception. I'm looking for a similar explanation as to "how" the perception that something has changed length actually comes about in S.R. Dec 4 '19 at 20:02
• @MarcelMazur First think about how one measures the length of something that is moving relative to them. Then think about how your measurement would appear to someone who is at rest relative to the object whose length you are measuring. Dec 4 '19 at 20:22
• I disagree that the object doesn't physically shrink. Consider the Ladder Paradox, where it's possible to close both the front and back doors of a 10-foot deep barn as a person carrying a 20-foot ladder runs through it (at near-light speed). The ladder doesn't just look shorter from the barn's frame, it actually is shorter (you can close both doors). Of course, from the ladder's perspective, the barn has shrunk, so there is no absolute definition of what's shrinking. But in neither case does the barn or ladder only appear shorter, it is actually, in reality, shorter than when at rest. Dec 4 '19 at 20:24
• That isn't quite right- you are shutting the doors simultaneously in your reference frame, but in the ladder's frame the exit door re-opens before the entry door closes, so the leading end of the ladder has already left the barn. Obviously the shrinking can't be real- think of it this way, if the ladder is observed by three observers each moving at different speeds they each think it is shrunk by a different amount- it cannot actually shrink by three different amounts simultaneously. Dec 4 '19 at 20:36
• @NuclearWang Seems like a bit of a philosophical problem. What is reality? If every test that I perform in my frame suggests that the the ladder has shrunken, then perhaps in my reality it has actually shrunken. But I think this is why the notion of proper length is needed; this gives a length that everyone can agree upon, that is, the length in the rest frame of the object. Dec 4 '19 at 22:14

It shrinks for simultaneous (according to your own clock) readings of a your meter stick at both ends. Given that the object is in a different frame, the measurement cannot be simultaneous to it's clock, and will furthermore be of a not contracted length. So you have a "shorter" time displacement and you should have as a consequence a shorter spatial displacement, because the overall space-time difference must be agreed between you and the thing.

So, simultanous in our frame means $$\Delta t = 0$$. But $$-c^2\Delta t^2+\Delta x^2 = \Delta x^2 = -c^2\Delta t'^2+\Delta x'^2$$. So it must be that

$$\Delta x'^2 > \Delta x^2$$

Suppose you're in Chicago, facing New York, which is 800 miles straight ahead.

Now turn ninety degrees to the right. All of a sudden, New York is 800 miles to your left!

How did New York manage to shift its position so dramatically all of a sudden?

The answer, of course, is that it didn't. What changed is your description of New York's location, which switched from one perfectly valid description ("800 miles straight ahead when I face east") to another ("800 miles to my left when I face south").

That's just what happens in relativity. There is no one correct answer to "how long is the meter stick?" any more than there's one correct answer to "which direction is New York?". The direction of New York depends on which way you're facing. The length of the meter stick depends on how fast you're traveling with respect to that stick. Neither New York nor the stick needs to know anything about this, or to adjust itself in any way just because you changed from one description to another.

• I understand this. As another example, you could consider a straw in a glass of water, and a straw not in a glass of water. Your description of the straw is different in the two cases, but the straw itself is the same physically. However, there is a physical explanation for what is going on here; in the case of straw in glass, the light refracts as it moves between mediums, changing your view of it. I am looking for some sort of analogous explanation for relativistic effects. Dec 4 '19 at 19:56

It's just a math model, it's not necessarily literally describing reality. You can interprete it that way in some instances if you want to. I don't think that any of the special relativity effects have been observed directly and explicitly..

• "I don't think that any of the special relativity effects have been observed directly and explicitly.." - Muons literally live longer when they go faster. That's why we're able to see them on the ground when they're produced at the top of the atmosphere. This is a direct and explicit observation of time dilation. Dec 4 '19 at 9:26
• Saying "I don't think" isn't a great way to answer a question, especially when you are wrong. Did you even try to look it up? en.wikipedia.org/wiki/Tests_of_special_relativity Dec 4 '19 at 10:41
• Full ACK on the previous comments: Special Relativity is one of the best tested theories, and every test to date has only yielded the result that its predictions are both measurable and correct. Similar story with General Relativity (though we don't have as much opportunity to test this as in the Special Relativity case) and Quantum Mechanics (the weirdest and probably most well-tested of the three, it's just so easy and cool to do). This site is driven by people who know this, so no answer denying this will be well received around here. Dec 4 '19 at 22:30
• Are all of you crazy? Show me when was lenght contraction ever shown explicitly, do you know what that word means? From muons perspective they live exactly as long as regardless of speed, and have any of you geniuses gone close to c to see what is actually happening with lenght. No. SR and GR are just math models that apply to a very specific set of systems. Dec 5 '19 at 17:43
• Also even if the theory was 100 percent right the objects would never shrink but rotate instead. Obviously people answering this question never attended a single university physics class.. Dec 5 '19 at 18:01