Recent content by DopplerDog

Also, try Wald's "Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics", chapter 7.

Penrose points out in "Road to Reality" how this presents a bit of a puzzle for cosmologists. On the one hand, the big bang must have occurred in a "thermalized" state, because the background cosmic radiation is more or less uniform. This means that the radiation must have been in thermal...

If you look at the comms thought experiment I mentioned, you'll see that both participants can take measurements of spin within seconds of each other and have their results consistent - in spite of the fact that they are separated by a distance that light could not cover in that time. The...

That's a normal objection to make when first faced with QM. After all, take two "classical" electrons with opposite spins, mix them up, and take them far apart - and surprise, surprise, they'll also point in different directions. That, in itself, is not a quantum effect. The quantum nature...

That should be "the victim... feels nothing strange". I placed the observer far away from the horizon, and the victim traveling towards it.

No. There is a relativistic effect on emitted radiation which is known as the relativistic Doppler shift, but it doesn't have anything to do with the mass of the object doing the emitting (ignoring gravitation).

Keep in mind that the distant observer cannot see inside the black hole. The observer sees no light coming out from inside the horizon. As the victim falls closer to the horizon, light coming from him is increasingly red-shifted to the observer, and the victim's clock appears to run slower and...

I always thought it had to be infinite dimensional - Wolfram Mathworld says it can be finite dimensional. Looks like you're right.

A Hilbert space is an infinite dimensional vector space, where an inner product is defined, and the space is complete (i.e. if an infinite sequence approaches a limit, then the limit is in the space). As an example, think of the space of functions where an inner product is defined (e.g. as an...

That's right. Imagine an entangled pair of electrons, with opposite spins. Your friend takes one to point B, and you take one to point A. They are entangled, so you don't know if yours points up or down, they are both in a state of superposition. You take yours, it could point up or down...

Well, the Lorentz Transformation assumes uniform motion in inertial frames (Special Relativity), and with gravity the issue is a little more complicated (requires an understanding of General Relativity). However, I think what you're getting at is that gravity must somehow have a bearing in...

There should be a qualification here that this rule only applies to Fermions, i.e. particles with spin 1/2, 3/2, etc. Particles with spin 0, 1, etc are Bosons, and do not obey Pauli's exclusion principle. As an example, protons and neutrons are Fermions, photos are Bosons.

You could think of entanglement as "spooky action at a distance", but it can't be used to transmit information. Quantum entanglement is a real phenomenon, but it won't let you transmit a message faster than light.

Ok, I think I see the source of your confusion. It doesn't help to think of time as having a "speed". You could say a clock slows down relative to another, but the "speed of time" is not clearly defined. Time is a coordinate, used to mark events. Think of your cartesian coordinates to...

What do you mean by "time naturally progresses"? Did you notice that the situation is symmetrical between A and B? A sees B's clock slow down, but B sees A's clock slow down. B doesn't experience anything substantially different from A, because there are no preferred frames: A's frame and...