elfmotat

Any imbalance will tend to cancel out over time. Think about it: if some large positive charge builds up on Earth, then what happens? Positively charged cosmic rays will be repelled very strongly, and negatively charged rays will be attracted very strongly. So Earth will start accumulating more negative charges until the planet is electrically neutral again.

No, don't do that. That makes no sense.

I think he gets it. He just doesn't like Beckham.

In regards to the Green's function comment, a table of common Green's functions can be found here: http://en.wikipedia.org/wiki/Green%27s_function#Table_of_Green.27s_functions. (Yours is on there.) Additionally, at a glance it should be easy to see that it looks very much like a wave equation. In fact, it looks nearly identical to the Schrodinger equation, except that's it's real everywhere. Should you have no knowledge of Green's functions you could try to solve it by analogy with wave equations.

Test: [math]\frac{d^n}{dz^n} \left [f(z) \right ]= \frac{n!}{2 \pi i} \oint \frac{f(s) \, ds}{(s-z)^n}[/math] Awesome. Now I don't need to worry about double spaces .

We weren't talking about changing volume.

I'm assuming you're working with ideal gasses? The relationship between pressure, volume and temperature can be found with the ideal gas law: [math]PV=mRT[/math] where R is a constant and m is the mass of the gas. So if we hold V and m constant, we get: [math]\frac{P}{T}=const.[/math] Or, in a perhaps more useful form: [math]\frac{P_1}{T_1} = \frac{P_2}{T_2}[/math] This does indeed say that increasing temperature results in increased pressure. However, you seem to be confusing volume and pressure as indicated by the equation you posted. Pressure and volume are not the same thing. Also, these equations don't say what "causes" what, as you have phrased it, they simply state a correlation between different properties of a gas. In other words, they don't say that "adding pressure" will cause increase temperature, they say that there is a correlation between the pressure of a gas and its temperature. Heating a gas up causes its pressure to go up. I'm not sure what it means to "add pressure" without adding more gas or adding heat.

I'm a bit surprised that this even got past the arxiv screeners. Pure pseudoscientific nonsense is what it is.

It would be helpful if you mentioned what literature you've been reading. You appear to have set a bra vector equal to a ket vector, which doesn't make much sense.

The lowest order scattering process where γ+γ → γ+γ is the following Feynman diagram: Physically, what the diagram actually means is that a photon will fluctuate into a virtual electron-positron pair, one of them will absorb a nearby photon, the other one will emit a photon, and then they will annihilate to form another photon. This diagram has four vertices, which means the probability for the process to occur is [math]P \propto \alpha^4 \approx 10^{-9}[/math]. I would calculate the full amplitude for the process, but it involves integrating over d4p for each internal line, which doesn't sound like too much fun. But without even calculating the full amplitude, it's still easy to see from the vertex factors above that the probability for the process to occur is going to be very very tiny. Of course, there are even higher order diagrams which contribute, but each vertex will contribute a factor [math]\alpha \approx \frac{1}{137}[/math] to the probability of that process occurring.

I'm not sure I understand the question.

Sorry, but I don't see what any of that has to do with anything.

The event would have to take place at some sort of interaction vertex. A high energy photon could scatter off something (an electron, another photon, etc.) with one of the products being a black hole. A free photon won't spontaneously collapse, for the reason you mention.

I'm not sure I understand. What do photons having rest frames have to do with them turning into a black hole?

http://en.wikipedia.org/wiki/Planck_scale#Theoretical_ideas

I think you're excusing the crackpots too readily, implying it's not really their fault that they think/say the nonsense that they do. There is nothing elitist about demanding that people actually learn physics before they try to discuss the cutting-edge of physics. It's not as if this is top-secret information that only a select few have access to! Anyone with internet or library access can learn this stuff. I am not a physicist. Physics is not even my major, yet I know a great deal of physics. I spent a fair amount of time learning it because it's interesting to me. It's frankly a bit insulting to suggest that our conversations should be dumbed-down to placate people who haven't put in any time or effort. If you want to play ball then you need to learn how to play ball. Crackpots are like children who like to pretend they're Derek Jeter. Sure it's imaginative, but in the real world that doesn't count for much.

An eigenvalue is some number, call it [math]\lambda[/math], that satisfies the following equation: [math]\hat{O} \psi = \lambda \psi[/math] where [math]\hat{O}[/math] is some operator. If [math]\psi[/math] is a function, we call it an eigenfunction. In quantum mechanics all observables are associated with a hermitian operator (position, momentum, energy, etc.). The function [math]\psi[/math] itself satisfies the Schrodinger equation. Eigenvalues of each observable operator represent the possible values you might get if you were to take a measurement. For example, if we have solved the Schrodinger equation for a particular scenario and we're interested in the spectrum of possible momentum values we might measure for an electron, we simply find all numbers [math]p[/math] which satisfy the equation: [math]\hat{P} \psi = p \psi[/math]

The only cutoff I can think of would be at the Planck energy scale, where it would likely turn into a black hole.

I suppose you could use matrices: [math]\begin{matrix} \alpha & \beta & \gamma & \delta\\ \epsilon & \zeta & \eta & \theta\\ \iota & \kappa & \lambda & \mu\\ \nu & \xi & \pi & \rho \end{matrix}[/math]

Hey, it looks like somebody is finally figuring out what physics is! It generally goes like this: step 1) guess model, step 2) compare model predictions to experiment. Physics cannot and does not give you anything more than a testable model, and nobody has ever claimed otherwise. It's your misconception if you think that science answers meaningless metaphysical questions. It's your problem if you can't wrap your brain around the idea of there being no absolute velocity. So then what the hell are you arguing about?! If you can't even define the thing you're so adamant must exist, then why in the world should I be wasting my time with this nonsense? I don't know how to argue with such a non-argument. Just stop with the metaphysical bunk already. This is a science forum. If you're not interested in science then you can move to the philosophy section. Nobody cares if you disagree with the scientific method. That's the way science works. If you want to propose an alternative to the scientific method then go propose it in the philosophy section. Because that's what "absolute velocity" means, by any standard definition of the word! In the example with aether, Maxwell's equations were expected to be different depending on your speed through the aether. But no laws of physics are changed depending on your velocity, as discovered by experiment. If some preferred frame existed then we should be able to see it, because it means by definition that some laws are velocity-dependent. These are just meaningless metaphysical assertions. Strange said it already, but this is basically the definition of a religious view. You have some preconceived notion of how the world should behave, and you ignore all evidence to the contrary. Since you've demonstrated a lack of willingness to argue in an intellectually honest manner, I don't think I'll be participating in these shenanigans any longer. Your attitude and style of debate are incredibly tiresome. In regard to any further posts: ditto.

99.87% the speed of light,

http://science.howstuffworks.com/induction-info.htm :

You aren't listening. Try to come up with your own definition of "absolute velocity." $20 says the way you'll do it is by referencing something you claim has a preferred frame. Except we know for sure (we've done a buttload of tests) that such a preferred frame does not exist. Before relativity and after Maxwell, physicists thought that light propagated through a medium called "aether." The aether's rest frame was taken to be a preferred frame, i.e. absolute velocity would be measured relative to it. If you ever want to know how fast you're moving relative to the aether, all you need to do is measure the speed of light and compare it to what it would be if you were at rest. That's exactly what Michelson & Morley tried to do. So what went wrong? They figured out that no matter how they tried to do the experiment, it would always give a velocity of zero. In other words, it didn't matter how they oriented the experiment or moved it around, it seemed like we always remain stationary relative to the aether. Special relativity was proposed as a solution to this puzzle. Einstein started with the principle, "there is no test an inertial observer can perform to determine whether or not he is moving or stationary." Another way to say this is, "the laws of physics are the same for all inertial observers." This was not a new idea (called the principle of relativity), and was actually widely accepted up until Maxwell's equations, which implied that the speed of light should be independent of reference frame. That's when people tried to abandon it in favor of aether. Einstein said, "no, forget about aether, it doesn't exist. Let's keep the principle of relativity and Maxwell's equations and see what happens." And what happens is we get a theory that agrees wonderfully with experiment. So, how do we know there are no preferred frames? We've done tests! You keep trying to drag this into the metaphysical, but it's really as simple as that. We're talking about physics after all - comparison with experiment is the end game. It would be very easy to spot if a preferred frame existed. Particle accelerators, for example, should work differently depending on the time of the day or year due to Earth's rotation and motion around the Sun. But so far the laws of physics look identical for all inertial observers. Why do you assume physicists would be interested in such things? If it can't be detected then it can't be corroborated, and so it belongs on the philosophy scrap pile. Can you prove that pink goblins don't inhabit the core of the Moon? Of course not, but to believe in such things when there is no evidence is ludicrous. However the coordinates you use to describe it are completely arbitrary. The universe doesn't care whether you call a particular point "A" or "B." It continues doing what it does regardless of your choice of coordinates. Fixed in which reference frame?

I think it would help if you try to define exactly what you mean when you say "a velocity that isn't relative." What would that mean? Come back to me with a definition and I'll tell you why it fails.

Are you asking what physics would be like if it wasn't the way it is? We can't use physics to describe situations which violate physics. This is the same question you've been repeating. It's equivalent to asking what the absolute velocity of something is. There is no such thing - I thought I was pretty clear on that.