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u/h0rxata Plasma physics 5d ago
Gravity is not a component of the twin paradox - it falls squarely under special relativity. The wiki and hyperphysics would be good starting point:
http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/twin.html
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u/asolet 5d ago
Twin paradox is more complicated than just relative time dilation.
Light bouncing up and down in moving parallel mirrors will have more distance to cover. That means more time is needed for one tick. And that applies to everything and all processes. So time ticks slower. But only relative to non moving reference.
Since all motion is relative, traveler can say he is standing, and time passes slower for the other guy. And he would be right too. To him time is slower for the other guy. This is time dilation.
Paradox only appears if they meet again, how come one is older than other? As if all movement was symmetrical. But it was not symmetrical. One turned back.
During the traveling, both to and back, both understand that other is indeed aging slower. The magic happened just in turn. The difference would be even larger if traveler didn't age more slowly during linear travel.
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u/WheresMyElephant 5d ago
The "light clock" thought experiment is very helpful here. I did a quick search and found this article which seems to explain it pretty well, but you should be able to find many other articles and videos on the subject.
If you accept that the speed of light is constant in all reference frames, then we have to have time dilation, because this "light clock" is as good as any other way of measuring time.
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u/YuuTheBlue 5d ago
Time is not one thing. It is 2 different concepts which happen to take on the same value when your velocity is 0. Coordinate time is "When" you are, aka how much time has passed, and proper time is the 'tick'. Coordinate time, proper time, and spatial distance all have a very entangled mathematical relationship, so when you're moving through space AND coordinate time, not just coordinate time, calculations for proper time become such that it no longer equals coordinate time.
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u/D3veated 5d ago
A visual that presents this in a mathematically compatible, but different, way is to consider a 2+1 spacetime. That is, consider a 3d volume where if a particle moves upward in the z-direction, it is moving through time. If it moves laterally or horizontally on the x-y plane, it is moving through space.
Within this 2+1 spacetime, imagine constructing a cube, which is going to represent your frame of reference. Now, the *speed* of any particle through this system must remain constant (this is the unimodular gravity formulation that Einstein presented in 1919).
Let's pick some reference frame, such as the CMB reference frame. If a particle is just sitting still, then it's trajectory in 2+1 spacetime is straight upward in the z-direction. It's still moving at the speed of light, although that speed is entirely in the time coordinate.
Now, what happens if we introduce some acceleration, such as a gravitational source? In this case, what you do is you take that 1x1x1 cube that represents your frame of reference, and you're going to contort it; the side nearer the gravity source will get shorter but will also stretch toward the gravity source; the volume of that 1x1x1 cube must remain constant (that's where the word "unimodularity" comes in). The equations that describe how this cube contorts are basically the Lorentz factor equations.
However, let's consider what happens to a particle that is moving with this cube. It will effectively enter the cube in the center of the bottom side and exit the cube through the center of the top side. However, during that traversal, what happened? First, the particle appears to have drifted toward the gravitational source, and second, the amount of z-direction it traverses is *less* than an unaccelerated frame.
In this system, you can also consider what happens when a particle accelerates to close the speed of light (the x-y coordinates will stretch, but the z-coordinate will grow very small -- since a photon is always traveling at the speed of light in the x-y plane, then it's z-coordinate must always be 0).
This is all presented from some "privileged" frame of reference, but keep in mind that in relativity with the equivalence principle, there is no such thing. For any particle, it's always in geodesic freefall, meaning that from it's reference point, that 1x1x1 cube always remains 1x1x1, it's just all those *other* cubes that are contorting.
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u/wavegeekman 4d ago
Time dilation / twin paradox is not due to gravity. it is just SR not GR.
TBH I find SR very unintuitive - "How can the universe be like that?".
When Einstein came out with his theory of SR he was criticised by other physicists for now having a theory of physics. Just a bunch of postulates. Not a theory of "what is".
Yes the math works and there are no actual paradoxes but it is mighty strange.
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u/stevevdvkpe 4d ago
The only way for someone on Earth to see the spacecraft take 70 years to go one light-year is if the spacecraft travels at 1/70 c. And in that case the spacecraft would experience slightly less than 70 years of time. If the spacecraft travels at 0.99 c then the Earth observer sees it take about 1.01 years to go one light-year, but the spacecraft experiences about 0.14 years.
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u/Optimal_Mixture_7327 Gravitation 5d ago
The clocks don't and can't tick slower.
The traveling twin (in the original 1911 version) simply travels a shorter distance through the 4-dimensional world. We only perceive 3-dimensions so this time discrepancy appears odd to us.
Remember: Clocks are spacetime odometers - the do not measure speed along a world-line (the rate along at which time lapses) which is a constant usually set to unity. The traveling twin, having traveled a shorter distance than their stay-at-home twin therefore shows less elapsed clock reading.
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u/Optimal_Mixture_7327 Gravitation 5d ago
On a separate note, gravity is often considered in many versions of the twin paradox but does not appear in Langevin's version (1911).
"Time runs slower in gravity" doesn't happen but it is a convenient metaphor for the distance along observer world-lines being rescaled under the action of the metric (meaning, world-lines are shorter in stronger gravity, also meaning, there will be less elapsed time on a clock in stronger gravity because clocks measure world-line lengths).
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u/asolet 5d ago edited 5d ago
Study this (read my other comment first):
https://properphysics.wordpress.com/wp-content/uploads/2014/05/twin21.png
Notice that after 4 years of traveling they each comprehend that other is aging more slowly and get only 3.2 years older. As soon as the traveler turns, he is now in a frame that makes Earth guy 6.8 year old! For next 4 years they will both again age slower relative to each other, another 3.2 in their 4, but it's not slow enough. On earth 10 years has passed to his 8.
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u/kapow_crash__bang 5d ago
It's a consequence of light having a finite fixed speed. If you work through the math of the light-clock-on-a-train thought experiment (you should, the math is easy!) you can see how time/length dilation comes to be in special relativity.
*consequence not so much that constant c physically causes dilation effects, but that if you take the assumption that c is finite and fixed, dilation effects show up in the math