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hijack from Minkowski space and geometric intuition


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2 hours ago, Lorentz Jr said:

I'm interested in why less time passes on the spaceship than on Earth in the twins paradox of special relativity, and the only explanation I've ever seen is that the spaceship takes a "shorter path through spacetime". By "explanation", I mean a proposal for a physical mechanism that would slow down the time evolution of the spaceship's wave function, or some other theory that provides a framework for understanding the phenomenon.

The twins paradox still includes a time dilation as a part of the explanation. The other part is travel through space and then how to combine the two.

Einstein said gravity and acceleration are equivalent. We can ignore gravity for the twin in space but the twin in space has to deal with acceleration.

As you probably know, gravity is defined as curved spacetime and acceleration is likewise curved spacetime. It is hard to visualize how either space or time can curve so I prefer to think of gravity as shorter space and slower time.

The space traveling twin experiences a greater acceleration than his Earthbound brother so, just as a greater gravitational field slows time, greater acceleration slows time by an equal amount. So the space traveling twin’s clock ticks slower and he ages less than his brother.

Acceleration is the physical mechanism that slows time.

If the space traveler is traveling to a destination a light year away, averaging 80% the speed of light, he will reach his destination in half the estimated time by his clock because he is either accelerated by speeding up or slowing to a stop. And it will be the same as he returns to Earth.

If he measures his travel distance by time, he will say he made the trip to his destination and back in one year instead of the expected two years and he will have aged by one year while gone. His twin will have aged by two years if he was away form Earth’s gravity.

But by any observation, if he traveled by train and measured the distance by the number of ties in the track, all observers would say he traveled the same distance in ties crossed. But he covered the distance in half the expected time so he took a shortcut through spacetime.

I like to think if the little squares on a Minkowski or Epstein diagram as little time zones. Each square you pass in any direction is essentially a trip to an earlier time zone. Travel through space is simultaneously travel through both space and time as Minkowski said. Each time zone you cross whether coming or going subtracts a little time from your clock.

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