Recent content by Nugatory

When @geordief wrote that he was still under the misunderstanding that “I think parallel transport relies on these tangent planes [that is, planes in the 3D space]” from the original post.

Does that force us to deal with clock synchronization? Start with a source of light signals and a mirror, move the mirror around until the reflected signal is back at the source in 2/299792458 seconds and we have a one-clock standard meter. I’m thinking that we need clock synchronization for a...

They aren't "on" the sphere anywhere. There is a mapping from each point on the surface of the sphere to a two-dimensional vector space specific to that point, which we call the "tangent space" at that point. But the elements of that vector space are neither vectors in the embedding...

The tangent space at a point is not a plane in the 3D embedding space (although that is a natural way of visualizing it, continuing our general tendency to think of the 2D surface of a sphere as embedded in the 3D euclidean space containing the sphere) and can be defined without reference to...

You have been victimized by pop-sci misdescriptions. The entire notion of “wave-particle duality” was abandoned as a false start almost a century ago and is not part of the modern understanding of quantum mechanics. There’s no substitute for a real textbook with its non-trivial mathematical...

You might want to, as it makes it possible to prove that a message came from you. Say you want to make a public proclamation that is unquestionably from you instead of an imposter…. You would encrypt it using your private key, then release that to the world. As long as your public key is...

You are starting from the premise that there is such a thing as a "multiverse". Maybe there is, maybe there isn't, but nothing in our current understanding of physics would be affected either way. Thus, speculation about the possibility is out of scope for this forum. You may be confusing...

thank you, yes.

By proposing a further explanation. Until this happens there is no explanation, just as a book does not exist until someone writes it.

You have not thought through the implications of the question in post #16 of your other thread. Say that we set this random number generator to work. How will observing its output permit us to distinguish between “probability zero” and “probability very small but not zero”?

The way to get a levitating table is through classical physics: just by random chance a substantial fraction of the air molecules under the table just happen to moving upwards. Depending on various back of the envelope assumptions you might calculate that such an event has a probability of...

Take ##\psi(x)## to be an arbitrary function and expand the commutator. You will end up with a term proportional to ##\frac{dV}{dx}##, which works just fine when ##V## is continuous and is in general non-zero (but is zero where ##V## is constant, which creates the "at first glance" illusion in...

Does it? We have ##[H,P]=[P^2/2m,P]+[V(x),P]##; the first term is trivially zero but there’s no reason to expect the second one to be. You can calculate the in general non-zero second term by applying it to an arbitrary test function: what is ##[V(x),P]\psi(x)## when you expand the commutator?

There's no sensible answer to your question until you have defined what you mean by the word "time". This being a physics forum where we discuss measurable quantities and the math that describes their behavior, it might be best to go with Einstein's definition: "Time is what a clock measures"...

No. There is no way of distinguishing a so-called collapsed state from an uncollapsed state (the “so-called” is there because even trying to make that distinction betrays a fundamental misunderstanding of the theory). All we know is the time that we made our measurement, and with our result we...