Recent content by kochanskij

Yes, there is a preferred at-rest frame. A person in that frame will experience the most proper time compared to a person who circumnavigates the universe at any relativistic speed and returns to their start point. So the moving person must measure a smaller universe circumference, right? The...

Yes, there is a preferred at-rest reference frame in a closed universe. But special relativity still applies locally, doesn't it? In such a universe, if a ship goes to a star 10 ly away at .99C, relative to earth, it will take less than 10 years of proper time for the astronaut, (1.42 yrs) won't...

In this thought experiment, I am assuming a finite but unbounded flat space with a 3-torus topology. There is no concern about curvature. This problem is completely special relativity. No GR needed. When the spacecraft travels very near C, the universe contracts, relative to the craft's frame...

Thank you for pointing that out. You are correct. The fact that one twin changes from one inertial frame to another is the important event. (Outbound constant velocity frame to inbound constant velocity frame) This is usually done thru acceleration, but it doesn't have to involve acceleration...

Yes, absolutely right. Inertia force of acceleration can be regarded as a gravitational force. Just like fictitious centrifugal and Corriolis forces can allow us to consider a rotating frame to be inertial, the gravitational force allows us to consider an accelerated frame to be inertial. As you...

When the astronaut is moving at a constant speed, he is in an inertial frame, so he can consider himself to be at rest. But during his turnaround, he is accelerating. He feels the force but the earth twin doesn't. He can not consider himself to be at rest during his acceleration.

Yes, there is another part to the scenario. I was just explaining why Twin A isn't going on a 10 lightyear trip, from his point of view. You are correct that he considers himself to be at rest (except during his turnaround) and the earth/star system is moving past him at almost C. Thank you for...

Yes, I got the same result. You gave an excellent complete solution.

I think I understand your question. The traveling twin A is NOT making a 10 lightyear trip at almost C. He is making a much shorter trip at almost C, so it takes him less time. Remember length contraction! Relative to twin A, he is at rest (except during turnaround) and everything else is moving...

An N dimensional manifold can be tied into a knot only in N+2 dimensional space. So a 2D surface, like a plane or surface of a sphere, can be tied in a knot in 4 dimensional space. A 1D string can only form a knot in 3D space. In 2D space, a string can not pass over itself. In 4D space, a knot...

Fascinating! I like your generalization of Collatz. It is a perfect analogy of Collatz for different a values. I would like to point out a few interesting things I noticed. In your table of occurrences that do not lead to 1, your value of the starting number n is not unique, because any number...

Mathematically, a flat 2D surface folded down over the edge of a desk has no curvature, so a Flatlander could not detect the fold. Same for us in space if our 3D space was folded down in a 4 dimensional sense. Suppose 3D space was folded down in two different perpendicular directions, both...

Thank you for your correction. I feel silly that I forgot that you don't find an average velocity by adding the two velocities and dividing by 2. A very basic error on my part.

From what I've read, it is not possible to measure the one way speed of light. We must reflect it off a mirror and then divide its travel time by 2, giving us its round trip average speed. Time dilation makes synchronizing two separated clocks impossible. We just assume light goes at C in all...

Thank you for explaining this misunderstanding I had of gravity inside a black hole. So what would I see and feel while inside? I would be weightless in my free fall? I will feel increasing tidal forces no matter how I orient my body? I can't see or point to the singularity? Am I in a self...