Severian

That's Special Relativity. It is really a statement that the length of a four-vector is invariant under a Lorentz transformation. This is exactly the same principle that the length of a space vector is invariant under a rotation. Take a piece of string, hold it horizontally and measure its length - now hold it vertically and measure its length again. The two lengths are the same - can you tell me why? (I am neglecting gravity here.)

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oops, I misread the question. My bad

I would have thought that the modern evolutionary trend would be towards smaller brains. It is definitely true that people who are successful academically (who you would suppose have larger brains) have fewer offspring than their small brained (McDonald's serving) neighbours. Of course, this was not true 60,000 years ago....

Use symmetry first: [math] \int_{-a}^{a} |x| e^{-|x|} dx = 2 \int_0^a x e^{-x} dx [/math] Now [math] \int_0^a x e^{-x} dx = \left[- e^{-x} (1+x) \right]_0^a = 1- (1+a)e^{-a}[/math] (integration by parts to see this) So [math]\int_{-a}^{a} |x| e^{-|x|} dx = 2 \left( 1- (1+a)e^{-a} \right)[/math] Finally, taking [math] a \to \infty[/math], [math] \int_{-\infty}^{\infty} |x| e^{-|x|} dx = \lim_{a \to \infty} 2 \left( 1- (1+a)e^{-a} \right) = 2[/math]

It doesn't matter whether they are terrorists or not. Torture is never acceptable. If you torture your enemy, then you become the bad guy.

Quantum entanglement is just the interference between different quantum states. The calculations of corrections to g-2 do include all such interference effects (even though I didn't go inot the calculations in general). Note that you have to use Quantum Feild Theory of course, since QM really only describes one particle moving in a potential.

Your brain?

What was their motivation for voting against? I can see no political gain for them.

I had a friend (well, actually a friend of my mother) who was shot dead in Florida while on vacation there. He hired a car and then got totally lost and ended up in white picket fence suburbia. It seemed like a nice area, so he just stopped the car to ask for directions from someone standing in their garden. Before he could speak, the guy pulled out a gun and shot him. Apparently it was a case of mistaken identity - the guy waiting in the garden was waiting for the owner of the house to come home in order to shoot him.

Well, there is no way I am going to Florida any more....

Are you implying that the situation in New Orleans wasn't a complete shambles and utter disgrace? Or are you just surprised that an ice-cream salesman doesn't know much about how political budgets work?

Yes, that is why I pointed out that the quantum case was a bit different - you don't get bremstrahlung in the quantum situation because there is no lower energy state to occupy. Interestingly, a gravitational mass must presumably emit real gravitons too, so even if there were no frictional/dissipative forces all planetary orbits will eventually decay...

Even if the atom were perfectly classical, the electron would orbit the nucleus. This would just be analagous to the way the Earth orbits the Sun. The Earth is attracted to the Sun by gravity, but the Earth has enough angular momentum to counterbalance the attraction and orbit (it is falling toward the Sun but is going so fast that it keeps missing). classically the elctron is attracted to the nucleus by electromagnetism in almost exactly the same way. In QM it is slightly different since there is a quantization of energy. Particle-wave duality tells us that the electron is also a wave, so it has a associated wavelength. Only certain wavelengths of the electron can fit around the nucleus, so it cannot just fall in.

All the force carriers are bosons, but bosons don't have to be force carriers. Even in the SM this is true because the Higgs boson isn't a force carrier. Of course, exchaning a boson (of any kind) between two particles will transmit momentum from one to another, so it really depends on your definition of 'force carrier'. Usually the expression is meant in technical terms:a "force carrier" is the gauge boson which makes the symmetry of the force local. You can add as many photons into the box as you like, but the pressure on the sides of the box will get larger because you are reflecting more and more phtons off the sides.

You should shave it all off. I have heard that it grows in much more managably if you shave it all off. PS: YT may not be the best person to ask for hair advice (though I may not be either).

It is interesting that most problems in physics can be answered by simple symmetry arguments....

Imagine a matter particle and an anti-matter particle colliding. The matter particle has an amount of matter equal to +1 (ie. it is one matter particle) while the antiparticle has matter -1. So before they collide, the total matter of the system is (+1)+(-1)=0. then they collide and annihilate each other, turning into a photon with all their combined energy (which is conserved). The photon has matter 0 (since it is not matter by definition of 'matter'), so the amount of matter after the collision is 0, just as it was before. Therefore matter (in this interaction) is conserved. (As Swansont pointed out, this matter conservation can be violated in certain other processes.)

I like sci-fi and fanstasy best I think, but they have to be well written and have well developed characters in them. There is so much trash written these days (especially in fantasy) that it is sometimes hard to find the good ones. In the fantasy genre, one of my favourites was Transformation by Carol Berg. It has great, believable characters in it. As for sci-fi, I have just finished reading Illium by Dan Simmons which, as the name suggests, is a retelling of the seige of Troy, but from a sci-fi perspective....

That doesn't mean that it is wrong of course - just that it is not useful from a scientific perspective.

Presumably ST is 'string theory'. Again, this is holding onto the SM - no string theorists are suggesting that the SM is wrong. They hope to demonstrate that the SM is a low energy limit of string theory. That way, you keep the nice predictive features of the SM, while explaining some of the 'why's with string theory. This is not really any different from (a). I disgree. There are plenty of new physics theories out there which build on the SM and will be testable soon. A lot of these are actually inspired by string theory's low energy limit in fact. If you have something to be peer reviewed then that is great! My post was not to discourage this, but to encourage people to think through their ideas before making a fool of themselves? So before you put yourself up for public ridicule (which is what all new theories are subjected to (Einstein's included)) you have to ask if it makes reasonable predictions for things that have already been tested. For example, if it is a quantum theory, does it describe the motion of electrons correctly? Does it describe electromagnetism? Does it get the correct value for the magnetic moment? (I was being a little tongue in cheek with my first post - I don't expect you to have it calculated to 10 significant figures, but it should agree with 2 to a reasonable approximation.) If it is a theory of gravity, does if have newtonian gravity as its low energy limit? Does it predict the correct perhelion of Mercury? If you have a theory which passes these sort of tests, then we will be very happy to hear aboiut it. If it doesn't pass these tests then surely it is already wrong, and a lot more 'wrong' than the SM. Putting up a theory for peer review which you already know is wrong is asking for public humiliation.

I know Andre Linde. Nice guy, and very smart, but certainly not a young physicist anymore...