Because tau = sqrt(1-(v^2/c^2))
The difference between 1-(30^2/300,000^2) and 1 is very very small. So small that the tau difference between 30 km/sec and zero km/sec can only be measured by ultra-precise atomic clocks.
If this is the reverse of the Twin Paradox why doesn’t the twin come back the same age for the same reason you just described?
OK, let’s hope I explain this correctly.
A scenario where you “slow down” and let Earth scoot along at nearly light speed and then rejoin it, is exactly the same as a scenario where you zoom away from Earth at nearly light speed and then rejoin it. Exactly the same, because there’s no privileged reference frame.
It’s fairly easy for people to grasp the idea of a spaceship zooming away and having time dilation and coming back to find your girlfriend in the nursing home.
The reason it’s called a “paradox” is just because, since there is no privileged reference frame, why are we saying that you zoomed away from Earth Nearly As Fast As Light, and not Earth that zoomed away from you NAFAL?
The resolution of the apparent paradox only comes when both twins are brought back into the same reference frame. And which twin ages faster depends on how that happens.
Bear with me if I am missing something.
I understand the resolution of the Twin Paradox. When the twins are reunited they are different ages.
But in the reverse, which we agree is essentially the same thing, you said the 20 years I spent coming up with a cure for my girlfriend will be erased when I return. All the time I “gained” will be lost coming back to earth which is different from the Twin Paradox.
No, that’s still exactly the same Twin Paradox, just viewed in a different reference frame. But that’s OK, because every reference frame must agree on which twin is older once they reunite.
Ok, here’s a question that always bugged me about the twin paradox. Which twin is actually accelerating and returning? There’s nothing special about earth’s position, so why can’t we say that it’s earth that is accelerating away from space twin and then accelerates back toward space twin? Why do we say that earth twin is stationary? Relative to space twin he’s not.
Acceleration has physical effects, like being abruptly pushed into (or pulled out of) the drivers seat, and only one twin experiences those effects. He’s the one that’s switching reference frames, so he’s the one that ages least, while the twin on earth, who experiences no discontinuous effects, ages the most.
Because the end scenario is that the twin returns to the Earth reference frame. That establishes the asynhronicity, so they are no longer the same. If you instead speed up the Earth to match the ship, then it reverses.
At least, that’s want I remember from a book I got back in seventh grade that mentioned this question.
The key to understanding the Twin Paradox is to realize that there aren’t two frames of reference involved; there are three. We can’t speak of “the traveling twin’s reference frame”, because he’s in two different reference frames: One for the outgoing trip, and a different one for the return.
Velocity is relative, acceleration isn’t.
Yep. One way to think about this issue that eliminates the need to discuss acceleration is to have “twin b1” be a spaceship that passes very close to Earth (at its constant speed) at the moment “twin a” is born, so that clocks can be synchronized then. Some time later the “twin b1” spacecraft passes very close to a spacecraft headed towards earth, and this “twin b2” spacecraft’s clocks are set equal to “twin” b1’s clocks at the moment of closest approach. When twin b2 passes Earth, its clock shows an earlier time than twin a’s clock (the one that stayed on Earth the whole time) - but it doesn’t seem so surprising now. With only two twins there’s the temptation to think there are only two reference frames, but the acceleration that only the traveling twin experiences is when the reference frame switch (that makes this the story of three frames, not two) occurs.
I’m curious how you draw a line to differentiate the two.
In a discussion about this long ago on the SDMB I asked about the rocket twin taking a big loop to return to the earth as opposed to an out, stop, turn around, return scenario. I was assured they are the same thing.
So if you are in a big loop can you specify where the break from one to the other frame occurs?
In the loop, the traveling twin is constantly changing reference frames (and constantly accelerating) - at every point in time, you can create an inertial frame that he will be (momentarily) a part of, but he never stays in it.
To expand a bit on the loop proposed on Andy L… Isn’t the universe thought to be finite with a wrap around like the old Asteroids game? Can’t I just go in one direction and eventually circumnavigate the entire universe? Would this plan work?
In Chronos’ version there is either an instantaneous change of velocity (180 degrees) or two twins (in Andy L’s slightly more real world example). You draw the line at the changeover point.
And as already explained by Andy L, in the big loop there’s an infinite number of “the travelling twin’s rest frame”.
The universe wrapping around is a hypothesis with no real empirical support. I have no idea if the proposed wrappings warp our dimensions or not though.
I read a short story once in which a heroic astronaut from the first American mission to travel close to the speed of light was nominated to run for President. Biologically he was still under 35 and thus ineligible under Art. II of the Constitution; going by how time had passed on Earth while he was gone, he was well over a hundred.
I read a science fiction detective story that involved a scientist who invented a way to speed up or slow down entropy inside a force field. The police discovered a murder victim (I think it was the inventor himself) inside a field, with the corpse appearing to be several months dead. They noticed that the hour hand on the victim’s watch was spinning very fast and the minute hand was an invisible blur. They couldn’t determine the time of death. A minute to the outside world translated to roughly a week inside the field. That might be easier than building a spaceship anyway.
There is a way that the spaceship could be useful, indirectly. If you can create a wormhole and carry one end of it in a spaceship at a high velocity, you could make one end of the wormhole older than the other end, forming a time tunnel a few seconds into the future or past depending on which way you go. Then make another wormhole and carry one end of it through the first wormhole multiple times to create a wormhole that goes minutes or hours. Then build a third wormhole and pass one end of it through the second one several times to create a days or weeks wormhole. Now you can do research for a month, then go back in time one month and do more research for another month, repeat as needed. The only limitation would be competing with copies of yourself to find available office space. Oh, and current theories about making an artificial wormhole require a quantity of mass which is negative, something that we have never yet observed to happen. So good luck with that.
Larry Niven - the story is called “ARM”