In special relativity, this becomes a problem. In a way of thinking that mostly relies on everything being relative and the speed of light being constant in a relativistic fashion, you have to suddenly drag in some concepts that aren't relative.
The fundamentals of special relativity can be easily summed up: There is no universal frame of reference. If you were in a vacuum and there was nothing around except a wrench that was lazily riding its way past you, there would be no way to tell whether you were the one moving or if the wrench was the one moving.
This changes, however, when you introduce acceleration into the picture. When you're acceleration there is a force acting on you, which you can feel. This is what makes general relativity different from special relativity.
I'm now gonna have a tiny look at this "paradox":
If we imagine there are three planets; Earth, Rigel and Jeff (Name's not important, don't mind it). Rigel is right smackdab between Earth and Jeff, with there being 200 lighyears to both other planets. If some rocketman decides to travel from earth to Rigel at 99% of the speed of light it would take, according to people still on the planet, 202 years for him to reach Rigel. However, it would only take 28.5 years for him. This is all fine and dandy so far, no laws of reality broken yet (or so I've been told). Time dilation is a thing.
Now, if we let the rocketman come back at the same speed,0.99c, we can find that the total trip took for him 57 years, while it took 404 years for people on planet earth. Since this is relativity, we can switch this around, and find out that during the 28.5 years it took to travel from Earth to Rigel only 4 years had passed on Earth. "But we already calculated that it had taken 202 years, not 4!", well buckle up, kiddo, cause this actually makes sense in relativity! It's when we calculate the return trip and get 8 years versus 404 years that shit gets fucked. This is because timespace between two events remain constant, and when the space-section of timespace gets changed, the time-section of timespace has to compensate.
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Anyways, it's time for the dramatic entry of general relativity! tahdaaa!
General relativity is just like special relativity, but generalised. It also accounts for acceleration! See, relativity is built on the concept of everything being relative, and when you're just dealing with constant velocities, that's all fine and dandy, but when acceleration comes into the picture, things aren't as relative anymore. When you are being accelerated, you can actually feel a force, and therefore it is not relative. This means that we can't just calculate the time difference using special relavitity both ways, because there is a very very very very very big acceleration when Rocketman hits Rigel, and this acceleration slows the time down by, like, a lot. (fun fact, because acceleration slows down time, if you drop something into a black hole, the gravity is so fucking large at the event horizon that whatever you dropped just starts hovering there, forever remaining until the end of time). This adds a lot of time to the travel, and if you calculate the total time for travelling from Earth to Rigel and turning, when observed from Earth the total comes out as *drum roll please* 400 years! That's like all the time that's missing! (400 for the trip there + 4 for the trip back again = 404 (not found), which is how much time we expected to have passed for the non-accelerating planet that still follow special relativity!)
booyah!
For those who are curious about the calculation from of 28.5 years from 200 years, I will explain the use of the Lorentz factor, because you're worth it:
When things move, they bend space. It's not just when things move very fast, it's just that when things don't move very fast we don't really have to account for the time distortion. Anyways, the distortion is dependent on how fast something moves, and this can be accounted for with the Lorentz factor (cue badass and epic bass noises of awesomeness).
\(\gamma = \frac{1}{\sqrt{1-(\frac{v}{c})^2}}\)
This is the little devil. Quite a strong fella for being so small. The c is the speed of light, as it tends to be, btw. He comes from a place called spacetime invariance. This is a concept that talks about a place made up of both space and time, and that is always constant: \(\Delta S^2 = \Delta t^2 - \Delta x^2\), where S is the movement through spacetime, t is the movement through time and x is the movement through space. Spacetime is always the same for all observing, so if one person observes one \(\Delta t\) and \(\Delta x\) for an event, and another person observes another \(\Delta t'\) and \(\Delta x'\), then the spacetime differences for those observations have to be the same:
\(\Delta S^2 = \Delta t^2 - \Delta x^2\)
\((\Delta S')^2 = (\Delta t')^2 - (\Delta x')^2\)
\(\Delta S^2 = (\Delta S')^2\)
\(\Delta t^2 - \Delta x^2 = (\Delta t')^2 - (\Delta x')^2\)
Here, we assume that we are observing from the referance system without the ', because why would we observe from anywhere else? Then we aren't moving, so \(\Delta x = 0\). We can also describe \(\Delta x' = v\Delta t'\), because that's how movement works.
then we get
\(\Delta t^2 = (\Delta t')^2 - (v\Delta t')^2\)
If we isolate the \(\Delta t'\) we get that
\(\Delta t' = \frac{1}{\sqrt{1-v^2}}\Delta t\)
which might look familiar to you! This is the Lorentz factor where v is given as a fraction of c, like we did earlier by saying the rocketman had a speed of 99% the speed of light, or v = 0.99c! Fascinating!
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