Severian

I honestly don't understand why this is such a big deal for gay folks. I mean to be openly gay, out of the closet so to speak, must take a great deal of courage. They must be willing to risk social condemnation and adverse reactions, so I had always thought of such open people as being strong personalities. But to need acknowledgement and official recognition of their relationships from the state seems very much at odds with my previous view. (And it isn't for the extra rights given with marriage - these can be done with a visit to a lawyer.)

I found a very cool one the other day but it was too big Does anyone know how to compress these animated ones?

Well spotted' date=' but that and the p[sup']2[/sup] were just typos though. And Aeschylus's H is really just notation. (I'll correct them.) I was really meaning that I switched from operators to normal quantities without a by-your-leave. It isn't a big problem - we could just consider ourselves continually collapsing the wavefunction into four-momentum eigenstates, ie making lots of observations, watching the motion, but to be rigorous we should really solve the differential equation for a superposition of plane wave states.... The time dependence is also a little bit of a fudge (as has been pointed out) but since I made V(x) explicitly time independent, it is fair enough I think). It would be for a fermion, but I was thinking of the Klein-Gordon Equation (for bosons), which is more relevent in this case. (Edit: Aeschylus and I cross-posted here)

Don't worry - no-one will laugh.... well, not to your face at least...

The Schrodinger Equation is: [math]i \hbar \frac{\partial \Psi}{\partial t} = -\frac{\hbar^2}{2 m} \frac{\partial^2 \Psi}{\partial x^2} + V(x) \Psi[/math] Now, since the momentum operator is [math]\hat p = -i \hbar \frac{\partial}{\partial x}[/math] and the energy operator is similarly [math]\hat E = i \hbar \frac{\partial}{\partial t}[/math], the Schrodinger equation is just: [math]\hat E \Psi = \frac{\hat p^2}{2m} \Psi +V(x) \Psi[/math] This is just conservation of energy. [math]p=mv[/math] (remember Shrodinger Eq is non-relativistic), so we have [math]E=\frac{1}{2}mv^2+V(x)[/math] Carry on as usual.... (Can anyone see where I fudged slightly...) Extra credit for anyone who can write down the relativistic version!

That is not quite true. The two accelarations work on the baloons in the same way. Once you have the vector you don't in principle yet know in which direction the balloons move (with the combined acceleration or against). However' date=' the fact that the He balloon moves upwards when there is no horizontal acceleration tells you that it will have the same response to the horizontal acceleration and will move forwards. 0.5/10 (I give you the half mark since I bothered to respond to the troll )

Excuse me? As I already stated' date=' I think [b']my[/b] 'little bit of math' before your post was a lot more elegant explanation than yours. No I didn't. It was Swansont who (implicitly) used that (reasonable) assumption. I pointed out to you that your objection to his argument (of the air filled baloon) was not a reasonable objection. My explanation requires no assumption. Well, since I set the question, I don't really need to give myself points now do I?

I quite liked it. It had nothing to do with the book though (which would be interesting to see made into a movie).

I think you have beautifully demonstrated the difference between a physicist and an engineer. I still like my relativity explanation better.

Yes - that is right. But since the circular orbit is a single configuration in an infitire space of psossible orbits, its probability of occurring is (practically) zero. If you throw a pencil in the air, it is as likely to land on its tip (and balance there) as a planet would be of forming a circular orbit in 1/r3 !

No I didn't. I was answering the question of why does the balloon rise. Any motion tangentional to the direction the frame is being accelerated is unaffected by that accelaration. Your question is rather unfair since we have previously been applying the assumption that the weight of the baloon itself (ie the rubber, or whatever it is) is negligable compared to the weight difference between air and the gas inside. Clearly this is not true for a baloon filled with air, but if it were (ie in the limit of the baloon mass approaching zero) the ballon would not move. The way to think of this problem is in my opinion to use relativity. Do not think of the car as accelerating as x ms-2 (I forget my original figure) but realize that it has the same affect as if there were an additional gravitational force in the (backwards) horizontal direction. So if the accelaration due to gravity is y ms-2, then we have to add the two 'gravitational forces' together and find that rreluting force (seen from inside the car) is [math]\sqrt{x^2+y^2} \: {\rm ms}^{-2}[/math] at an angle [math]\sin^{-1} \frac{y}{x}[/math] to the horizontal. Therefore it is natural that the He filled ballon moves forward, since in a 'gravitational sense', this is 'up'.

No, they couldn't - that's what I was meaning. It is quite surprising I think, but we need the inverse square law in order to form planets. If we had Gmm/r or Gmm/r3 we would be screwed because there would be no stable orbits whatsoever.

I have always found it interesting that gravity is a 1/r2. If you sit down and work out the orbit equations 1/r2 is the only law which has stable orbits. 1/r or 1/r3 and no planets would form....they would either fall into the sun or float away into space.... Is this a coincidence or an anthropic principle?

No - what you are seeing when you look at something is light from some external source reflecting off the body. Otherwise you would see it in the dark. (Actually, light is being constantly emitted in the infra-red, since the objects are warm, but not at a wavelength you can see.)

I get the impression that people on this site have an over-inflated notion of what string theory has achieved. While string theory is a great idea and hopefully will yeild great dividends in the future, it is nowhere near the level of development of our other lower energy theories. Our low(er) energy theory - The Standard Model - is also based on quantum field theory and explains all the forces except gravity (though not in a unified way). It is now the best tested theory ever. Despite almost 30 years of testing in big colliders, there has been no deviation from the Standard Model observed (unless you count nuetrino masses, but that was really just an ansatz). This is a remarkable acheivement. As fuhrerbeebs has pointed out, string theory has made no testable predictions. In order to test string theory directly we need to investigate energy regimes approximately 10,000,000,000,000,000 times those we currently probe at colliders. And until we do that, we cannot test string theory at all. (Martin recently pointed out to me some new ideas for testing some aspect of (admitedly 'non-standard') string theories, but in my opinion these are a long-shot.) In principle we should be able to test string theory indirectly by working out what happpens at low energies. First of all, there is a factorisation of energy scales present in the Standard Model, so that the tests of the Standard model are independent of the physics at the string scale (this property is called 'renomalisability') so the low energy tests are not testing string theory at all. One can on the other hand ask if string theory reproduces the Standard Model at low energies (an indirect test) and indeed one finds that some string theories can (although the rigour of the maths leaves a little to be desired), but this is really just a consistancy test.

Gravity (or if you want to be pedantic' date=' it is really gravity which makes the air pressure below the baloon larger than that above and it is the diferential in air pressure which puches the baloon up....) Is it just me, or do a large proportion of the statements made on this site not make any sense whatsoever? (I am not meaning I am being dazzled by science.)

Which explains why homosexuality was more tolerated in Victorian England than in ancient Greece..... erm.... hang on a minute.....

Well done. I was expecting people to say they both mover backwards. You have reafirmed my faith in humanity

Good! It is a step towards annuling the other 50,000,000 (or whatever) marriages in the US. (I felt I had better add a wink smilie just in case...)

A baryon is a particle made of 3 quarks (like the proton and neutron). Photons are in no way baryons. In the Standard Model, matter is defined as being quarks and leptons (and obviously anything made out of them). The force mediating particles (like the photon) are not matter.

No-one knows. It is one of the many unanswered questions. Each particle has a value which is the charge (it could be zero) but our theories don't say why. (Actually, each particle has a hypercharge, which combined with isospin gives it its charge, but that is just a technicality.)

So what's the answer then?

They are neither. They have energy, but they are not energy itself. They are not matter (although this is just from the definition of 'matter').

Photons are electrically neutral, so they do not bind with one another. Therefore you could not make any substance which is entirely made of photons and bonds. Since a solid is defined by its bonding, you cannot have solid light.

If you are thinking of wormholes like in Stargate, then no, you can't. A wormhole is only any good for moving to a destination faster if there is fortuitously a shorter route to the destination by using an extra dimension. In other words they are only any use when the topology of space-time is such that two 'distant' points in the universe are actually almost touching in another dimension. For example, if we lived on the surface of a sheet of paper, we could get to a the point exactly on the opposite side by either going the long way round (converntional travel) or by punching a hole throught the paper and travelling through the extra dimension (a wormhole). Unless we can fold space at will, the possible positions for useful wormholes are fixed. Even if we could fold space at will, we couldn't fold it faster than the speed of light, so the first folding would take quite a while. So the physics of Stargate doesn't hold water.