Recent content by Nugatory

This is wrong, and we can try one more time to explain why Using the frame in which A is at rest, events E1 and E2 are simultaneous - that's what A means when they say that B is running slowly. But when we use the frame in which B is at rest, we find that E1 and E2 are not simultaneous...

Not directly because the operation is symmetric: it provides the same result for 0^1 and 1^0 (where the caret is the xor operator). However, you can construct a more complicated expression that does what (I think) you're looking for. Try A&(A^B), which will be one or zero according to whether...

Because of that phrase "at the same moment". They are different "same moments", because if A and B are moving relative to one another they have different definitions of "same moment". That's relativity of simultaneity. And how can this be? Well, let's go back to a more intuitive situation...

That's similar to saying that two bullets moving relative to one another will have different kinetic energies in different frames (which also can be described in terms of non-parallel four-momenta). They're different, but not in a way that we would generally consider to be "intrinisically"...

She will only arrive at this incorrect result if she forgets to allow for the relativity of simultaneity, as you are in your calculation. There really is no substitute for doing the general calculation based on the Lorentz transformations as I described in post #2 above, and until you at least...

This may be the root of your misunderstanding -until you get over it relativity will continue to confuse you. It is equally valid to analyze the problem using the frame in which rocket is at rest and earth is moving, or the frame in which the sun is at rest so both are moving (the earth is...

And a comment about the thread title: this is not a twin paradox variation, the age difference seen in the twin paradox has nothing to do with the time dilation between observers moving relative to one another. The crucial element in the twin paradox is the travelers are at the same place when...

You have overlooked the relativity of simultaneity here. What did the ship clock read at the same time using the frame in which the ship is at rest that the radio signal was emitted? What did the earth clock read at the same time using the frame in which the earth is at rest that the radio...

That one confused me for a moment, and then I realized why it had to be specifically a "train" wheel - the flange extends below the bearing surface and the top the rail.

Depends on what you mean by “sure”? The best current theory we have is General Relativity, and it says that a black hole of mass M has exactly the same gravitational field as the same amount of ordinary matter, and that it affects everything the same way. But are we sure that GR is correct? It...

Not quite. We need to consider the resolution of our position-measuring apparatus. That resolution is not infinite, so the result of a position measurement does not leave the particle in an "eigenstate" of the position operator (scare-quotes because as others have pointed out, those position...

There isn’t any single “the concept” of infinity in math. There are multiple concepts, all of which have rigorous definitions that don’t create any logical difficulties. The problems that you’re seeing (infinite monkeys and Shakespeare, the zeta function and -1/12, infinite possibilities imply...

”All branches exist” isn’t quite right, it’s better to say that there is a branch for every possible outcome, but violating the laws of physics is not a possible outcome. There will be a branch in which a subatomic particle has randomly decayed and there will be a branch in which the particle...

I think a clock and a speedometer (or tachometer, which as a one-time autocrosser is more what I was thinking about) are fundamentally different. Reading a clock, especially at one-minute granularity is for all practical purposes a static observation; it changes, but at rate that is long...

Having read the article, I think it’s suggesting that specifically cursive is being lost, not pen and paper in general.