Layman Relativity

Factual Questions
1

I kind of get the gist of relativity… a little.

So I take off on a rocket from Earth and go .99 C for a while, come back and land, and I’m older than everyone.

Relative to Earth, I’m moving very fast.

But relative to me, Earth is also moving very fast.

How does the universe decide that I get older, and not the planet?

Is it based on mass?

I also get that acceleration factors in sometimes, as when close to a black hole.

Am I getting older faster or slower, relative to stuff that’s closer to it?

Does it make a difference if I’m going .99 C in a straight line or a tight orbit?
ETA: please ignore inertia, G forces, spaghettification as far as survivability goes and focus on time dilation for this if possible. Thanks

2

Heh I just realized, when I come back everyone else is older… time moved slower for me than on Earth

sorry brain fart

Questions are basically the same though. How does the universe decide that it only took me a year, and it took Earth a hundred?

3

The twin paradox is fun…but easily resolved, by noting which twin accelerated.

The relativity equations are wonderfully symmetric with regard to constant motion. To the guy at the train station, the train looks to be moving. To the guy in the train, the station looks to be moving. There isn’t any “right” frame of reference.

But when objects accelerate, the rules change, and the equations stop being so symmetrical.

In the scenario where one guy leaves earth on a rocket, goes really fast, then stops and turns around and comes back, he accelerates, and the earth doesn’t. It no longer works to say, “To him, it looks like the earth accelerated and reversed direction.” Because to the entire rest of the universe, no, it doesn’t.

(Also, anyone with high school math can do special relativity equations. They don’t involve much more than square roots. But general relativity equations are big and hairy and frightening and you need upper division college math classes to work with them.)

4

Thanks Trinopus! That makes a lot of sense.

Therefore we can’t ignore inertia in this scenario then, right? Because it’s a part of acceleration?

If I’m the one getting pushed back in my chair, then I’m the one accelerating.

Further, as I approach the event horizon of a black hole, I stop aging?

5

I think it’s because of light and the fact that in Einstein’s theory, the shape of space is orthogonal to the passage of speed (such that the sequence of individual space points is determined by how it behaves in accordance with light). For instance, when you’re on the rocket and you’re moving through space, if you were to reflect light from a mirror back onto itself, it’d have to travel 3 * 10^8 km/s. now, a second for your body could actually be defined by dividing the space crossed by the light by the speed of light. so when your body has aged 24 years, it still aged the same amount of seconds. so if you’re travelling really fast, by the time the light travelled from the pointer to the mirror once on your end it very well may have travelled doezens of times for the earthlings. its better understood by parameterizing tiem to lightseconds rather than revolution seconds

sorry for my incoherence

6

As I understand it from your viewpoint time passes at the same rate; from the viewpoint of the rest of the universe time stops for you when you reach the event horizon.

7

The way I like to explain it is that there aren’t two reference frames in the classic version of the Twin Paradox; there are three. It’s easiest to describe if we imagine the traveler as a hitchhiker, rather than in command of his own vehicle. That is, suppose that Larry stays home on Earth, while his twin Jerry hitches a ride with Xyzzy the alien, who happens to be passing by at 0.9 c. Later, as they’re passing alpha Centauri, Jerry gets homesick, and hitches another ride with Quux, who’s coming back the other way at 0.9c.

We now have three reference frames: Larry’s, Xyzzy’s, and Quux’s. Jerry doesn’t have his own reference frame, because he changes from one alien’s frame to the other’s. All three reference frames will agree that, when the twins meet up again, Jerry is younger than Larry, and by how much. They disagree about points in between, but that doesn’t actually matter.

From Larry’s point of view, Larry was always aging at the normal rate, and Jerry was always moving fast relative to him, and so Jerry was always aging slower.

From Xyzzy’s point of view, Xyzzy was always aging at the normal rate, and Larry was always moving fast relative to him, and so Larry was always aging slower than Xyzzy was. Meanwhile, for the first part of the trip, Jerry was at rest relative to Xyzzy, and so for that part of the trip, he was aging normally, too. But then when Jerry got homesick, he had to travel really, really fast to catch up to the already-fast-moving Larry. And during that time, he ages even slower than Larry does, so much so that by the time he does catch up, Larry is older.

Likewise, from Quux’s point of view, except that for him, Jerry’s time of aging really, really slowly is the first part of the trip, when he’s with Xyzzy.

8

If you look at a spacetime diagram, the asymmetry between the rocket-bound and Earth-bound observers is clear. The time experienced by an observer between two events is equivalent to the arc length of their worldline between those two events, the wordline being the curve in spacetime representing their path. The above diagram indicates that the arc length of the two observers differ, though due to the non-positive definite nature of the Minkowski metric it is actually the observer in the rocket who experiences the least time despite their worldline appearing to be longer on the spacetime diagram.

Gravitational time dilation such as seen in black holes is a bit more complicated because it involves the curvature of spacetime, but it is related to the fact that inn order to remain static in Schwarzschild coordinates an observer has to accelerate. The acceleration required to remain static diverges (goes to infinity) at the event horizon.

9

While we’re at it, here’s the best introductory relativity textbook I’ve ever seen. Yes, I know it’s a website, and yes, that website is primarily focused on aviation, which has nothing to do with relativity, and no, so far as I know, it’s never been published in dead-tree format. It’s still the best textbook I’ve ever seen on the topic.