Ask me any one question about space, please!

[How2FoldSoup]

These kind of go together. What I described is a 1-particle exchange. Two particles pass each other, one of them emits a photon/gluon/graviton, the other absorbs it, and they part ways. Again, which does emitting, and which does absorbing doesn't matter. What matters is that one particle got exchanged. But that's not what really happens. Or more specifically, that's not all that happens. There can be exchanges of 2, 3, 4, and any number of force-carrying particles. And they need not be absorbed in the same order that they are emitted. Worse yet, there can be particle-antiparticle pairs that form from vacuum, absorb one of these force-carrying particles, and then emit another one. There is an infinite number of categories of infinite number of possibilities to how two particles can exchange energy and momentum. And they all take place.

This is for the same reasons within vector fields where you can integrate across any path inside the bounds(In a confined area or volume) yet the answer will always be same, correct? Just trying to connect recent things I'm learning to life. I'm taking vector calculus currently.

Lets forget about interaction for a moment. Picture just one particle propagating through space. Since this is a quantum particle, it will have uncertainty in momentum and position. And so you can describe propagation of the particle as probability amplitude that changes in time. But alternatively, you can describe it as particle with precise location and precise momentum following one of precise trajectories. What you are uncertain of is which trajectory it follows. So instead of looking at it as particle being in many places at once, you look at it as particle following many paths at once. This is the Path Integral Formulation of quantum mechanics. While it tends to be fairly impractical in classical QM, it turns out to be indispensable in RQFT. Part of the reason is that it lets you describe interactions in terms of Lagrangian directly, and that looks after all the symmetries out of the box. Since all interactions are understood to be consequences of local symmetries, this is clearly useful.

Same idea applies to many-particle systems. Not only can particles take all possible paths, but the interaction can follow all possible combinations of particles being emitted and absorbed. The main requirement is that all conserved quantities are conserved. Momentum is one of these. So it's often useful to go from coordinate representation of the dynamics to a momentum representation. Mathematically, what that means is that we take Fourier Transform of the Green's Functions, so that they become functions of momentum instead of functions of coordinate. As a result, each particle path we consider has a very specific momentum associated with it. And for every possible trajectory of all the particles, the momentum is conserved. So I can still carry out all of the operations in the previous post as if we are dealing with classical particles that have definite momentum.

That makes sense actually makes some sense to me thanks! What you're saying is that because we're thinking of a particle that follows any number of paths, but all of these paths conserve momentum because of the principle quoted on up above correct?

You've given me a lot of wiki pages to read and I don't have the time but I will catch up on the specifics soonâ„¢

Thanks!

[rtxoff]

Here's another one:

I need the answer to the Ultimate Question of Life, the Universe, and Everything.

;-)

[KASASpace]

Why someone had the bright idea of mounting a fuel tank, a liquid hydrogen fuel tank right next to a crew compartment (the Space Shuttle)

[K^2]

This is for the same reasons within vector fields where you can integrate across any path inside the bounds(In a confined area or volume) yet the answer will always be same, correct? Just trying to connect recent things I'm learning to life. I'm taking vector calculus currently.

No, you actually get different phase following different trajectories, and these add up either constructively or destructively.

A much more familiar example is propagation of light. You can think of light as being absorbed and re-emitted as a spherical wave along each point in space. This is absolutely equivalent to light taking every possible path. But because the electric field in the source is oscillating, the strength and direction of electric field contribution from a particular path will depend on the path. At a given random point, the contributions from all possible paths are most likely to be random, and all of the contributions are going to cancel out. In contrast, there are special paths along which the phases match almost perfectly, so you could detect light there. Specifically, the phase depends on the length of time it took like to follow a path. If we consider the "shortest" path between two points, calculus of variations tells us that any tiny deviation from the path will not change its length. That means all of the paths in the neighborhood will have matching phases, allowing constructive interference. That means that in vacuum, light appears to propagate in the straight line. If you throw in some obstacles, or have materials with different optical densities, you end up with more interesting trajectories.

[Rowsdower]

Guys, I think it's time you give Maximus the floor and let him do what he set out to do at the top of the thread. Keep the questions coming. If you have an answer to the question and/or a rebuttal to a video, please leave that for until after it gets posted. Thanks.