Severian

I have often thought "Quantum Mechanics" is actually a rather bad name. Most of the time, when a quantity becomes "quantized" (in the sense that it comes in discrete chunks) it is because of boundary conditions imposed on the wave-nature of particles. For example, in the hydrogen atom, the electrons obey the Schroedinger equation, whose solutions for the radial part are called Laguerre functions. There are infinitely many Laguerre functions, usually quantified by an index [math]\nu[/math]. All Laguerre functions were [math]\nu[/math] is non-integer diverge as we move infinitely far from the nucleus, so imposing boundary conditions that there is no electron field infinitly far away from the nucleus insists that the only acceptable solutions are those with integer [math]\nu[/math]. Since the energy of the state depends on [math]\nu[/math], the energy is quantised (only allowed to take certain values). It is exactly the same for the harmonic oscillator, where one must restrict the Hermite functions to integer indices, thereby quantising the energy. So quantisation of energy is really a consequence of 'quantum' mechanics representing particles as waves, rather than a postulate. Indeed, the vocabulary has switched a bit to reflect this. When we say "first quantisation" we really mean that we change observables into operators. A much better term would have been 'operatorisation' (a bit of a mouthful) but I suppose the word 'quantisation' was already too deeply engrained.

Could you explain the philosophy behind linking nominations to inclusion in the poll? Particularly considering this post:http://www.scienceforums.net/forum/showpost.php?p=337512&postcount=14 Not that I particularly care, just wondering...

It is actually a bit worse than that. The Standard Model predicts a non-zero value of lambda (coming from the vev of the Higgs field), but unfortunately it is 120 orders of magnitude. You then have to put in a very large opposite sign contribution by hand, but of course, that is a fine tuning problem, known as the cosmological constant problem.

http://en.wikipedia.org/wiki/Gustav_III_of_Sweden

That is the proper definition. To be more exact, it is the time component of the conserved 4-current under translation symmetries.

To say an energy density is a little difficult, since it is a little bit ill defined. For example, would you consider particles which don't collide as part of the collision? probably not. If you just consider the particles which do collide (the gluons usually), then they are point particles. However, gluons do sort of have a spacial extent due to their wave like properties. If you work it out, their wavelength at the LHC comes to about 10-16m, into which radius we are squeezing 1TeV. If you want to compare to with the big bang though (which I suspect is your motivation), it is best to compare the LHC's 1TeV energy with the Planck scale at 1019 GeV. So we would need an extra 16 orders of magnitude in energy. Here are some extra statistics for the LHC: Nominal energy, protons: 7 TeV Minimum distance between bunches: ~7 m Design luminosity: 1034 cm-2s-1 Number of bunches per proton beam: 2808 Number of protons per bunch (at start): 1.1x1011 Number of turns per second: 11 245 Number of collisions per second: 600 million

It was horrible because it made so many wrong statements. For example, the very first thing they said is that the LHC may create a black hole which would swallow the Earth! It was horrible because it gave a wrong impression of what we are trying to acheive. It focussed on the big bang and astrophysics ("The Hubble telescope of inner space"!) and not on what we are really trying to find out. It was horrible because it mangled up interviews into tiny pieces which they could manipulate to make say what they wanted to say rather than what the interviewee wanted to say. It was horrible because it was the usual attempt to sensationalize everything, and pander to the cult of personality. Should we be surprised that the physicist who was interviewed (Brian Cox) was chosen not for his physics knowledge, but for the fact that he used to be in a boy band? Martin, as a matter of interest, which of de Rujula's statements did you disagree with?

It is a really horrible documentary.

The problem with this, that makes the question unanswerable on a scientific level, is that it is not something we can ever test. We cannot ever make an observation without "conscious observation" (since we are conscious entities). The only way around this is to introduce some other property of a state that collapses the wavefunction. For example, several people have suggested that it is the size or complexity of an object that collapses the wavefunction. So we collapse the wavefunction because we are made up of lots and lots of particles. This also has problems: what size is the relevant size and who decides; by what mechanism does this work. I think we could speculate on this forever... and probably will.

There is no country on Earth (that I am aware of) which is a true democracy. In most countries you elect someone to represent you in government. If the person elected to represent you does not reflect the wishes of the people who elect him (as a whole) then you have grounds for complaint. But you cannot expect to impose your minority view on the majority of your constituency.

I did a summer studentship at CERN long long ago. At the time the programme was twinned with an ESA programme, so the identity card they gave me had the ESA logo on it. All summer, when I met girls in bars, I used to tell them I was a trainee astronaut; they didn't believe me, but then I would show them my card, and they were mine...

If they were the same, either neutral objects wouldn't feel any gravity, or massive objects would have a huge electric charge. They are clearly not the the same thing.

Let's be honest, even if you raised the voting age to 80, there would still be a large proportion of the population not fit to vote. Here in Scotland we have had a lot of outrage recently about the number of spoiled ballots in last week's election. Apparently the system was too confusing. However, I think we should be making it more confusing. If they are too stupid to figure out where to put their cross (or whether it should be a cross of a '1') then they are probably too stupid to make a rational decision on whom they are voting for.

This is really a aesthetic question as to the definition of 'simplest'. The electron is perhaps the most 'obvious' particle in the world, but I am not sure I would call it the simplest. We have never seen a particle with zero spin, but if the Higgs boson exists, I think it is a much simpler particle than the electron. Indeed, any spin zero particle is simpler than the electron, in agreement with Dirac's original prejudice.

Yes, they seem fairly reasonable. Most of them (especially the first two) are not really science though, since they can't be tested.

I would like to clarify that the graviton is not part of the Standard Model. I don't think you were claiming it was, but your phrasology may be unclear to our other members. I am interested why you think this. I actually agree, but I think we may have different reasons for thinking this. My reasoning would be that the form of the Higgs couplings and any possible solution to the hierarchy problem that plagues it would give us hints of new physics beyond the Standard Model. Any new physics would presumably help point us towards the correct formulation of gravity, even if as just an effective theory. However, no matter what we discover, gravity is still undeniably a force, under any reasonable definition of the word 'force'.

Do you mean renormalizability and Fermi? Long before the W and Z bosons were discoverd we knew about weak interactions. They cause things like beta decay and influenced the interactions of particles we saw in our colliders at the time (various mesons mainly). We had a quantum field theory for electrodynamics, QED, and we wanted a similar idea for the weak interaction. One formulates QED in terms of a Lagrangian where the fields (particles) couple to one another with an arbitrary coupling (the electric charge in QED's case). So Fermi, by analogy, wrote down all the terms he could think of containing the currently known fields, hoping that one of these extra terms in the equation could describe the weak interaction. One such term involved 4 fermions. However, since the Largangian has mass dimension 4 (since there are 4 space-time dimensions) but fermion fields are dimension 3/2 each, a term with 4-fermion fields in it has dimension 6, so he had to divide the term by some arbitrary energy squared (in other words, his coupling constant GF in front of the term had dimension 1/mass2). Surprisingly this theory worked quite well, and with this simple addition of one term to the Lagrangian he could explain lots of physics. Unfortunatetly, when one does quantum corrections with this model, infinities crop up all over the place. You basically can't make any accurate predictions; you have to stop at tree-level (the semi-clasical level) and be happy with getting your predictions almost right. The reason for this is the mass dimension of the extra term. Later, when Pati, Salam and Weinberg came up with the SU(2) theory, they had W and Z bosons in them and all the terms in the Lagrangian, which contain these new fields and the fermions have mass dimension 4. The theory behaves itself under quantum corrections and can make precise predictions. (It is renormalizable.) However, if you intergrate out these new particles (the W and Z) from the Lagrangian (you are normally integrating over it anyway, so basically this is just saying that you should keep the W and Z bosons away from the initial and final states) and take the low energy limit (where Fermi's theory was useful) you reproduce Fermi's 4-fermion theory. In fact the GF turns out to be [math]\sqrt{2}g^2/8M_W^2[/math] where MW is the W mass and g is a coupling constant. The reason Fermi's theory gave infinities, is that when you include quantum corrections you must include particles in loops at arbitrarily high energies. So even the heavy W and Z become important. He was missing their contributions and his calculation didn't work. Similarly today we have a theory of gravity which is non-renormalizable. It does fine at the semi-classical level but screws up the quantum corrections. However, I am fairly sure that we are simply missing some dynamics at high energies (just like we were missing the W and Z). If we include the right stuff, I am sure the theory will become well behaved. The question is, what is the 'right stuff'....?

Why is that line interesting? it sounds pretty ordinary to me.

Its fundamental origin is the desire to have a local U(1) symmetry for the universe. This U(1) is the symmetry you see in quantum mechanics, where you have a wavefunction [math]\psi(x)[/math] and the probability of finding the particle at a point [math]x[/math] is [math]|\psi(x)|^2[/math]. If I multiply the wavefuntion by a complex phase, i.e. [math]\psi \to e^{i \theta} \psi[/math], no observations change because [math]|e^{i \theta} \psi(x)|^2 = |\psi(x)|^2[/math]. In other words, there is a symmetry in the theory. It is the desire to make [math]\theta[/math] in the above vary with [math]x[/math] while still keeping the symmetry which directly insists that you introduce a new particle. And low and behold, it has exactly the properties of the photon. So the photon (and electromagnetism) are a direct consequence of a local U(1) symmetry.

That isn't true. They have run where they have had a net output of energy for a short time. It is just that they have not yet managed to sustain the reaction for very long. I am 100% sure that if we had pumped as much money into fusion research as we have into oil exploration, we would have had working fusion reactors by now. (This would probably be true with just 0.001% of that investment.)

It really depends on what you mean by 'something'. Is a mathematical equation 'something'? Is the colour green 'something'? Space-time is intimately linked to the notion of events, and is in some sense a property of these events. The metric (space-time if you like) tells us how to define a 'distance' between two events (in both space and time). And this distance is important for physical law. As such, the metric is a property of the events itself, so it doesn't really exist on its own (or rather, its independent existence would be meaningless). Warping space-time is in effect, warping the rule by which we measure distance. So if you regard a rule as 'something' then spacetime is 'something'.

Ah, but I don't feel the need for acknowledgement of my scientist status from a bunch of web nerds. I make my own classifications.

I am a superbeing... and don't you forget it!

I had forgotten about that.

I really don't see the point. I didn't win anything last year...