beefpatty

Electric fields and magnetic fields are not independent phenomena; you can only fully describe them by combining them into what is known as the electromagnetic field. A moving electric field induces a magnetic field, and vice versa. Even if you have just a static electric field, this is merely the special case where you are at rest with respect to the electric field. You could easily "boost" into a different frame where the E-field is moving with respect to you, and thus it would also have a magnetic field. Thus, there is no quanta for electric fields or magnetic fields. There are only quanta for electromagnetic fields.

There are other independent lines of evidence for the existence of dark matter. For example, according to standard cosmology we require a dark matter component in order to observe the Universe we see today. This is completely independent of any observations of galaxy rotation rates. Also, you need dark matter to explain pictures like this: This is known as the Bullet cluster and shows two colliding clusters of galaxies. The (false color) pink regions denote the visible matter. The interesting thing is that, using the visible matter alone, this cluster cannot look like this. For the visible matter to have this distribution, you need "extra" matter to contribute to the gravitational potential, which many people interpret to be dark matter.

You can always find a reference frame in which the two particles are moving directly away from each other. That is, in your case where they separate both with an "x" and "y" velocity, there is a reference frame in which they only have an "x" or "y" velocity. Since physics must be valid in all reference frames, the fact that it does not conserve momentum in the "directly away" reference frame forbids it in all other frames as well. I posted a couple pictures to help illustrate. What you are talking about would be this frame: However, if I moved "up" with the electron and positron, it would look like this: which obviously does not conserve momentum.

I see you are quite passionate then. I myself am a second year grad student doing research in inflation, so I find all of these topics interesting. Thanks for the other papers!

No problem! After looking more carefully it seems the second paper (by Jegerlehner) is rather interesting and probably what you are looking for. I should probably study it more . I think it is rather interesting because it only requires SM physics to account for inflation and a small cosmological constant both from the Higgs. Do you mind if I ask if you are a graduate student in Physics, an amateur, or perhaps even a full-blown researcher? Edit: He also appears to have some talks related to this on this website: http://www-com.physik.hu-berlin.de/~fjeger/

1) B-E should be correct; have you read otherwise or are you just making sure? 2)The scalar field eq. of state would be appropriate, which I write here for convenience (in the perfect fluid approximation): [math]w = \frac{\frac{1}{2}\dot{\phi}^2 - V(\phi)}{\frac{1}{2}\dot{\phi}^2 + V(\phi)} .[/math] You can see that for [math]w = -1[/math] you need a vanishingly small kinetic term for the region you are interested in. For the Higgs field this can be achieved either through a non-minimal coupling of the Higgs field to gravity http://arxiv.org/abs/0710.3755 or with a non-minimal coupling in its kinetic term http://arxiv.org/abs/1006.2801. The previous two papers work to identify the Higgs field as the inflaton, however. Why do you need B-E statistics, though? The Higgs field may contribute to dark energy, but its VEV is much too large and would either have to elegantly cancel with other VEV's or should be finely tuned. Lawrence Krauss wrote a paper trying to connect the Higgs and dark energy (unfortunately it is behind a paywall but you can read the abstract here.) Here is also another paper, which I admittedly did not read as it is rather lengthy at 39 pages.

We should be careful to distinguish between the vacuum energy during inflation and that caused by dark energy today. While inflation occurs from a vacuum energy, the inflaton is a scalar particle and should have some underlying particle physics. The cosmological constant is just a measure of the energy density of free space. It could be a process left over from inflation, or similarly a field decaying to it's vacuum expectation value like the inflaton, but in general we separate the two from each other.

Is that the letter "o" or a zero?

You can only predict the probability that it will be in a given state, not deterministically as swansont pointed out.

Yes, add the two equations together and you'll see where the derivation comes from.

A universe made entirely of anti-matter would behave exactly the same way as our universe. That is, our universe and the anti-matter universe would be virtually indistinguishable. So in theory, anything you can build out of matter you can also build out of anti-matter. But to do so would be patently absurd because it would turn into pure energy as soon as it made contact with any type of matter i.e. the atmosphere. Currently, laboratories that create anti-matter store it with a very strong magnetic field because even putting it in a conventional container would cause an explosion of energy.

By "biggest" do you mean strongest, or size-wise biggest? The biggest known gravitationally-bound structure in the universe is a mind-boggling 4 billion light years across! In terms of strength, though, black holes are probably the "strongest", simply because you can get very, very, very close to their center of gravity.

I can't really imagine what the author means by "mass-like properties." I think they misinterpreted the equation, as it simply tells you how much mass is equivalent to a given amount of energy, and not that light has "mass-like properties."

Not quite. In QM, observables are promoted to operators. Since momentum is an observable, in QM it becomes the operator, [math]\hat{p}[/math] so inserting it into the expression for kinetic energy we easily find that [math]\hat{T} = \frac{\hat{p}^2}{2m} = -\frac{\hbar^2}{2m}\bigtriangledown^2[/math] which you could then operate on a state to get an eigenvalue corresponding to the kinetic energy. You can also find the expectation value rather than a single eigenvalue by taking [math]\langle\psi|\hat{T}|\psi\rangle[/math] where [math]\psi[/math] is some wavefunction that describes your system.

Light is not both a particle and a wave, but is instead something completely different that exhibits properties of waves and particles.

I think I see where you're going with this. What makes the 4th spatial dimension special i.e., why is only an overlap in our three dimensions enough to cause annihilation? What happens if they overlap in all four dimensions? What determines a scattering event isn't the overlap in some the dimensions but the overlap in all of them, which is easily generalized to any number of spatial dimensions you want. If there were a fourth spatial dimension, then we would expect there to be collisions where a scattering event should have happened in our three dimensions but didn't because the particles missed each other in the fourth dimension. What I'm getting at is we should see cross sections that deviate from theory (namely that are lower than what theory predicts), which we don't.

My gut reaction is that if the photon is entirely (or partially) polarized in the 4th space dimension we would notice some energy missing in our 3 dimensions. I'm not sure what your equation is supposed to represent, could you explain it further?

I'm pretty sure you're correct, although I haven't studied that area of particle physics too in depth yet. The link says the branching ratio for [math]H \rightarrow \gamma\gamma[/math] is less than 0.3%, which means only that many are produced on average from a Higgs decay (depending on the mass of the Higgs).

Do you possibly mean 4 spatial dimensions and one time dimension?

Yes but you can get around that by say, two photons interacting and creating massive bosons (or fermions) which then interact to form a Higgs. The reverse process (Higgs -> bosons/fermions -> photons) I believe is one of the main channels they investigated to discover the Higgs. Here's a helpful link: http://www.hep.lu.se/atlas/thesis/egede/thesis-node17.html

Galaxies are hardly solids, and thus don't have a constant resonant frequency that would break the entire galaxy apart. Besides, the expansion of space is not periodic to begin with. I don't mean to sound condescending, but the fact that forces are additive is one of the most elementary topics in physics. The net force determines the dynamics of the system. If I push a block with constant force to the left, and a smaller force is applied to the right, the block will continue to accelerate to the left at a constant rate. It's only when the force applied to the right overcomes the opposing force that the block will accelerate in the opposite direction.

Sorry, by "opposite effect" I thought you meant 2 down and 1 up quark.

The electron is fundamental, i.e. it is not made of quarks.

Fundamental particles do not have to touch to interact, but the intrinsic spin of the interacting particles (more importantly their helicity) can determine what kind of angle dependence, if any, the final particles have.

Without time the only separation between events is spatial. By talking about snap shots in different frames you are invoking a time dimension.