Most “near the speed of light” travel questions involve getting in a spaceship, approaching the speed of light, and then returning to find that everyone that didn’t make the trip is now older or dead. In my scenario, I’ve found that I can run REALLY fast in circles in my backyard. When I get to a significant percentage of the SOL, will I experience the same time dilation as I would in a space ship?
I don’t see why not. (I assume we’re ignoring the unfortunately environmental side effects of a human-sized mass moving at relativistic speed…)
There isn’t anything special about space specifically, so from that perspective no, there wouldn’t be a difference between you running at a fraction of the speed of light or you flying off in a spaceship at the same speed. Of course, if you actually tried to run that fast on Earth, you’d end up vaporized when you slam into the particles that make up the atmosphere at enormous speeds.
However, since you noted that you are “running circles” specifically, I’ll note that a big factor in time dilation is your speed RELATIVE TO AN OBSERVER. If you’re running in circles, rather than in one direction, I’d think that you’d constantly be gaining and then losing speed relative to an observer. Exactly what impact this would have on your relative time dilation I will leave to someone more well-versed in physics than I to elaborate on.
Yes, we’re ignoring a lot of things in this scenario
As @Babale points out the fact that you are traveling in circles rather than straight out and straight back makes the calculations a bit tricky. One of the ways to deal with the twin paradox for the spaceship situation is to take into consideration the acceleration during the turn around and running in circles you are in constant acceleration so you have to include that as well as the oscillating velocity relative to Earth bound observers. Or possibly there’s a trick to be made to simplify the calculations. But you will definitely experience time dilation, and possible create a small black hole due to the forces required to maintain such a tight orbit.
Neat little experiment that validates time dilation in circular movement
The fact that there’s acceleration involved just means that we have to do a little bit of calculus to do the calculations, instead of just algebra. It doesn’t make the physics any more difficult. And for that matter, the out-and-back-again scenario involves acceleration, too.
Doesn’t matter; same effect either way.
I seem to recall Superman doing something similar after an earthquake.
If you’re running at a constant speed in a consistent circle, the easiest way to do the calculation might be by using the calculations for gravitational time dilation, with the “gravity” using in the calculation being the acceleration due to changing direction.
Don’t even go there.
Isn’t one of the points of relativity that the same effects result from the same causes anywhere and in any circumstances (taking into account gravity and friction and the other impedimenta of real life)? So time dilation will result from nearing the speed of light, period, no matter what or how you phrase the issue?
That sounds right but the paradox is usually phrased in the form of “moving away from you” instead of “moving around you” or even “moving towards you.” That’s what piqued my curiosity.
I put it in question form because IANAP and wanted to be sure that was right.
But I disagree about it usually being phrased as motion away. I normally see it as going and returning (as in the traveler is placed next to a now much older stay-at-home), and that’s basically a flat circle. It’s also talked about with satellite GPS and that’s certainly circular.
You still had a good question. I’m just confirming my understanding of the answers.
Sure, the same effect will result from the same causes. But the question here is whether traveling in a circle is the same cause as traveling in a straight line.
That’s true, it is usually expressed as going away and coming back so that the clocks can be compared.
For a real life example, GPS satellites are running in circles around the Earth and this slows down their clocks slightly, which has to be accounted for when using them (or setting them, I guess).
The circular motion doesn’t really make the claulatons more complicated, at least in the limited context of the OP. If you have a clock travelling in uniform circular motion in an inertial frame, the time dilation observed in the inertial frame depends upon the speed of the clock only. The formula to find is also the same one as if the moiton was linear.
Unofrom circular motion is well-studied in special relativity, though there’s a few connected apparent paradoxes to be aware of like the twin paradox, Sagnac effect and Ehrenfest paradox.
I think this is critical.
Acceleration is where it is at. If you are born on a spaceship moving 99% the speed of light and fly by earth you cannot say whether it is you or the earth that is moving.
The Twin Paradox happens because the spaceship with one twin turns around and comes back to earth so we know it was the spaceship that had an acceleration. The time dilation happens on the spaceship and not earth.
Running around in a circle is a constant acceleration so you would experience time dilation.
If the circular motion is due to gravity (as with the GPS satellites), then you have to use General Relativity, not Special Relativity. And it turns out that the net effect is actually opposite from the effect you’d get from just SR.
All of these effects that are due to acceleration use GR, not SR, right?
ETA: For example, the twin paradox doesn’t work using SR, since SR doesn’t account for acceleration. And, I think it’s the case that you can’t tell if you’re in gravity or in an elevator that’s accelerating. OK, that’s the limit of my relativity physics.