Recent content by mikeu

If three-dimensional space were quantized then you would still need three numbers to describe a location in it. Essentially you would be changing your space from \mathbb{R}^3 (triplets of real numbers) to \mathbb{Z}^3 (triplets of integers). In some sense you are right that there are fewer...

I have a question that I sort of feel should be easy to answer, but I haven't figured out how yet... Hopefully someone can either show me the easy answer or tell me that it's a little more subtle :) Consider a system of two particles, distinguishable by some continuous parameter, which can...

Yes, the energy in a photon does curve spacetime, although really not very much :). The http://en.wikipedia.org/wiki/Stress-energy_tensor" on the right-hand side of Einstein's equation G_{\mu\nu}=8\pi T_{\mu\nu} describes how the existence and flow of both matter and energy curve spacetime. I...

I have restated a more specific version of the problem in post #10... Does it make the problem I little more clear? I'm a bit confused by this - don't the paths of photons in a flat spacetime have to be straight lines (in the Euclidean sense) in both 3 and 4 dimensions? This is the...

That's the original reason for my post - I first thought it would be easy, then impossible, then wasn't sure so came here :) . That is essentially what I want to do. Parametrizing a curve in 4D isn't a problem, but requiring the arbitrary curve to be a geodesic is the part at which I got a...

It does appear to be a proof by contradiction, at least for observables. If A is not Hermitean then \langle a|A=(A^\dagger|a\rangle)^\dagger\neq (A|a\rangle)^\dagger, so acting A to the left in the term \langle a|AB|a\rangle doesn't yield a\langle a|B|a\rangle, as required to obtain the...

Pervect I agree with you in general, but what is bothering Hurkyl was what was also bothering me as I posted :smile: . My original idea was to find a way to say, for example, that light was to follow a parabola. I would then have a curve in 3D like \gamma(\lambda)=(\lambda^2,0,0) and want to...

Hi all, I would like to write down the arc-length parametrization of a curve in 3-dimensional Euclidean space, \gamma(\lambda), then specify that in a certain spacetime this path is a null geodesic z^\mu and solve for the metric of that spacetime. My first question is, does this even make...

Except you can always find such A and B, so you can always find 0=1... :) It's just the definition of the commutator and linearity of the inner product: \langle a | [A,B] | a\rangle = \langle a | (AB-BA) | a \rangle = \langle a | AB | a \rangle - \langle a | BA | a \rangle. Physics...

George, do you know of any good reference books (or articles or websites) on this topic that would be accessible at the early graduate level? I'm interested in learning about Gelfand triples in general from a mathematical point of view, and specifically how they allow us to use delta...

I'm trying to gain a better understanding of how the electric field operator is used and what it can do. I know that calculating its expectation value tells you that a coherent state is the 'most classical' quantum state of light, and the number states have zero average electric field. The...

These basically apply to three different possibilities for the spacetime distance between two events: positive, negative or zero. Lightlike (or null separated) events have zero distance between them; how timelike and spacelike match up with positive and negative depends on the signature of your...

However, the point of a postulate is that it must be true by assumption (at least so long as you are working within the system it is helping to define). If you take it as true, then it turns out (as you'll learn in your course) that what isn't true is you're assumption that the speed of the...

Yes, time dilation causes the satellites' clocks to lose about 7us per day, and gravitational redshift causes them to gain about 45us. The net effect is a gain of 38us per day which, as Russ said, is accounted for by adjusting the frequency of the clocks when they are on the ground. Check...

In case anyone's still interested in this... I tracked down the two papers above in the campus library and will attempt a quick summary here. If there's interest I could post more complete derivations or possibly scan the papers... Takeno uses a group-theoretic approach based on a few...