beefpatty

What level of maths are you at? The QM book titled "Principles of Quantum Mechanics" by R. Shankar commits the entire first chapter to the mathematical machinery necessary to understand QM. It's a graduate level text, but the maths is easy enough to understand, as long as you don't skip any steps. In my opinion, when working through a textbook you need to be very methodical. Don't skip problems, and if the author makes a derivation and skips some steps (which they almost always do), fill those in yourself. You cannot learn from a text just by reading, you have to work alongside it with pencil and paper.

You are correct, that is not true. What makes them so strong is that you can get very, very, very close to the center of gravity. Since the strength of gravity is proportional to 1/r^2, where r is the distance from the center of gravity, you can see as the distance gets close to zero the strength blows up to infinity. If the Sun were to suddenly turn into a black hole, we'd still rotate around it all the same.

You have to be careful with the distinction between the meaning of "disorder" in thermodynamic processes and the meaning in everyday language. "Disorder" in thermodynamics is a measure of how close a system is to some equilibrium energy. Entropy tells us that the energy of a system will tend toward this equilibrium. The closer to equilibrium, the higher the amount of disorder.

Entropy is basically a measure of the heat transfer between two systems. In a completely reversible process, one could return all the heat transferred from a system back to its source, and thus the change in entropy would be zero. In reality, though, no process is completely reversible as heat will be lost one way or another, thus causing a net increase in entropy. It doesn't apply to anything outside of this, such as laws or forces.

Did you possibly mean entropy?

At the Big Bang antimatter would not have necessarily been separated far away from it's matter counterparts. Antimatter behaves physically identical to its matter counterpart. If we had a universe made entirely of antimatter the laws of physics would essentially be the same.

There is no increase in distance since gravity is overpowering the expansion. If the expansion could overcome the force of gravity, then you would see an increase in distance and therefore the effects of gravity would become weaker as it expanded. Photons are quite different, in that they are both massless and fundamental, meaning there is no internal structure binding them together, such as quarks bound via the strong force to create protons, neutrons, etc.

All I could think while reading this was "Poor Jim..."

Hi khj512, Chemistry is not exactly my area of specialty so take what I say with a grain of salt. I think just about every chemical reaction involves only the outer electrons on an atom and doesn't actually affect the nucleus itself. When you say "fuse" and then "diffuse" I think you mean bond as opposed to the actual nuclei fusing together, as is the case in say the Sun. I can't definitively tell you because, as I said, I'm not a chemist but when two elements bond it's because the bound state is usually a lower energy state and is more stable. You wouldn't expect them to rapidly break that bond without an external source of energy.

They are not exotic since they obey the known laws of physics. That would imply positrons are exotic, which they are not.

Ah, I didn't realize that was what you meant with your question. Hmm, that does seem like an interesting idea, but my initial thoughts are that, detecting a negative energy electron going backward in time would be the same as a positron forming out of your detector which, as swansont pointed out, would decrease entropy. So in that sense, for a particle running backward in time entropy should decrease so an increase would violate entropy, while to us running forward in time the opposite is true.

In order for their to be a collision they would have to meet at the same location in space and time, regardless of the direction they are traveling in time.

AFAIK, Einstein-Rosen bridges and Alcubierre drives require negative mass propagating forward in time, although I don't know much about them to really say. The two processes are entirely equivalent and give the same answer. Consider the following process in QED. At interaction 1 the electron can be scattered back in time by a potential, propagate to interaction 2, and then be scattered forward in time. Equivalently, before the electron reaches point 1 pair production can occur at point 2 due to the potential. This creates both a positron and electron propagating forward in time, and the positron annihilates with the incoming electron at point 1. The two interpretations are equivalent.

The positron is not negative energy, but rather the electron traveling backward in time has negative energy. You have to take into account the negative proper time. Here is Feynman's original paper on the subject: http://authors.library.caltech.edu/3520/1/FEYpr49b.pdf The second paragraph in the abstract is where he states: and in the final paragraph on the left on page 753:

It depends on the situation. If the wavefunction goes to zero as you go to infinity on either side, or as [math]|x|\to\infty[/math], then the integral will be finite and you can normalize it so it's equal to 1.

You could give a shot at David Tong's lectures online. They closely follow the book by Peskin and Schroeder, although I don't believe he goes into gauge symmetries in depth. You can also try an online text by Robert Klauber, in which he does go into gauge symmetries.

I was just confused by what you meant by 2pi . I think I see where the confusion is. By rotating the spin you can indeed return back to the original state, so in that sense it is modal. But in terms of a spin 3/2, 4, etc. particle it just arises from their spin states lining up. Thanks for the clarification, although as far as I understand it spin can be represented in physical space as a vector, for example when talking about helicity, or in spinor space as a spinor, which exhibits the properties you mentioned.

It would be the future electron, but phantom image isn't really the right word. They are two possible interpretations for the same object, although most people would just say it is a positron moving forward in time. The possibility that it can be interpreted as a negative energy electron moving backward in time is, as far as I can tell, just a product of the math. Whether that has any real physical meaning, I don't know. 2 pi in the denominator? There are in fact an infinite number of solutions that correspond to different spin and momentum states of the particle, but they can all be expressed in terms of the two unique solutions. As far as I know the graviton could have a spin of 2. Atoms can have spins of any integer multiple of 1/2 or 1, for example 3/2, 4, etc. Spin is just the intrinsic angular momentum of a particle. If you have a particle completely at rest, that is it has zero momentum, then you still measure a discrete angular momentum. It also behaves like a vector, in that it can have a direction and magnitude and points in the same direction as the orbital angular momentum.

I'm not sure what axis you are referring two, but by two solutions I mean the following. Given the Dirac equation (which applies to fermions), there are two unique solutions that when you plug them into psi the equation is satisfied. When we quantize the Dirac field we interpret these two solutions as separate particles, and when you calculate some observable such as charge we find they are opposite each other. I'm afraid I don't understand what you mean by a modular system of 1. Could you explain in more detail?

Experimentally we observe this to be true. In theory, say for example spin-1/2 particles, there are two solutions to Dirac's equation. Each corresponds to a different particle of identical mass but opposite charge, and we interpret these as particles and antiparticles. As for turning matter into anti-matter, one could take the example of electron-positron annihilation into a muon and antimuon pair. In this case, I suppose you could say that the energy of the electron went into the creation of the antimuon, but really there's no way to distinguish this. If you are instead thinking of something like an electron turning into a positron, this would violate charge conservation.

We consider it anti because it's basically a mirror image in properties of its matter counterpart. Every antiparticle has the same mass as its particle, but opposite charge (if it has any) and anticolor (if it's a quark). That, and it also annihilates with matter.

If I turn on a beam of light, and then turn on another beam perpendicular to it, does the universe simultaneous move in perpendicular directions to give the illusion that both beams are traveling at c? Actually, we can measure our motion on earth against the CMB, or Cosmic Microwave Background radiation, since our relative motion creates a doppler shift. In that case you would have to say that the entire universe is moving to fit our Earth and we are somehow special.

In terms of math what immediately comes to mind are bra-ket notation, integrals, contour integrals, and dirac delta functions. You can get pretty far with integrals, since when it comes down to it cross sections are just integrals of a square amplitude over all spacetime. The more pertinent question, though, is what sort of background do you have in physics? Do you feel comfortable with Lagrangian mechanics? Special Relativity? QM? I'm just a lowly master's student so I don't have experience with Ryder yet, although I am currently working through the book by Peskin and Schroeder and don't have major complaints. Although with just a sample size of 1 it's hard to truly recommend!

It's actually matter, not anti matter that is going backward in time. A negative energy particle going backward in time can also be interpreted as a positive energy antiparticle going forward in time.

Hello Mike Smith, I think you make a fair point, no personal offense taken. But I also can't, for example, give an every day analogy to the fact that the photon can act like a wave in some cases and a particle in other cases. Observing a water wave does not give this effect, and neither does leaving a tennis ball to its own devices. In this sense it directly counters our intuition and I cannot give someone a satisfactory reason for why it acts that way. The non-mathematical explanation would be it just does, as far as we can tell. Mathematically, however, you can see how it acts the way it does, and that is what I meant.