Hi Guys,
New post this time. It's late and I'm tired, so I thought I'd give all the relativists among you a conundrum to enjoy.
This is one that's based on the theory of special relativity, and also one that I posted long ago on Philosophy Forums before it went away. You may still be able to find it under my nom-de-net of Psychotick.
This is based on the commonly known twins paradox. Most of you will be familiar with the basics of it. In essence special relativity says that if you have two twins and you stick one on a rocket ship and he flies away at high speed and comes back, because he's been traveling at a significant fraction of the speed of light, he will have experienced less time. So when he comes back to Earth and meets his twin brother, he'll actually be younger than him.
Now about three or four years ago it occurred to me that this scenario is self defeating. (From a philosophical / logical point of view. Those of you who've watched The Good Place - which is brilliant by the way - will have heard the oft repeated complaint that "this is why everybody hates moral philosophers". Here I'm going to expand that to "this is why everybody hates philosophers!")
Okay, so lets get back to the paradox - and try and place it within the frame of special relativity. Now the first tenet of relativity is that there is no absolute inertial frame of reference. A complicated way of saying that you can't look at an inertial problem from the outside. You can only examine it from the perspectives of the - usually two - inertial frames of reference concerned. Call them A and B - or in this case the rocket ship and Earth.
Immediately you do this, you run into a basic problem of definitions - and no I don't mean that semantically. In short if we have no absolute inertial frame of reference, then it becomes impossible to say that a rocket ship leaves Earth. You can only say that if you have an external perspective on the situation such that you can see that the Earth is stationary or alternatively moving at a standard rate with no accelerative force acting on it, while the rocket ship is traveling away from it. Since you don't have this by definition of the theory of special relativity, you can't make this statement.
Instead the statement you have to make is that the earth and the rocket ship are moving apart.
I know, that sounds screwy. But within the confines of special relativity, it's correct. And you can understand it from a practical perspective too. If you're on the rocket ship and you stare out of the port hole at the retreating Earth, who are you to say that you're the one who's leaving the Earth and it's not leaving you? If you're not accelerating, you won't feel any motion. So the only thing that tells you you're leaving the Earth is your understanding that the Earth is huge and you blasted off from it. Likewise if you're on the Earth staring at the rocket ship, the sensation of gravity makes you think that you're standing still and it's leaving you, but that is no part of special relativity.
Alright, now lets hook this new definition into the twins paradox. Now according to the original paradox the rocket ship was leaving Earth. Now we can say instead that the rocket ship and the Earth are leaving each other. If that's the case than our two twins are both in the same situation. Each sees the other leaving him at whatever speed, and according to special relativity that means they're both in the position of claiming that because the other is traveling away from them at a significant fraction of the speed of light, and therefore both will expect the other to have experienced less time. Which means that when they come back together, there should be no real difference in elapsed time. Time slowed down equally for both of them.
So now we find ourselves in a conundrum - I think I'll call it a Psychotickian Conundrum! There are two options. Either the paradox doesn't hold, and we don't expect the twins to come back together having experienced different amounts of time - despite what we are constantly being told has been observed. Or the basic tenet of relativity, that there is no absolute inertial frame of reference, does not hold.
Now of course those who believe in relativity, are going to argue that it's due to mass, gravity and acceleration, none of which I would point out are a part of special relativity.
Okay, so enough of this. I'll leave you to your head scratching, and just finish with this most basic of all understandings. This is why everybody hates philosophers! We love to poke holes in things!
Cheers, Greg (aka Psychotick).
