Severian

The most recent development in cosmology has been the studies on the cosmic microwave background radiation done by WMAP. I suggest you take a look at their website: http://map.gsfc.nasa.gov/ they discovered lots of interesting new stuff: for example, it looks like the universe is open.

They couldn't be used for efficiently transfering power because most of the neutrinos would escape, running away with your power. However, they do interact, so you could send signals with them, and their unreactivity could be very useful - you could send a beam straight through the planet for example. Unfortunately their interactions are very weak (as Swansont already pointed out) so you would have to send a hell of a lot of them to make sure you got a good signal. I suspect there will be other techs which are better by the time this would become feasible.

If you lived in Scotland like me, you would never suggest this. brrrrr

High heels and stockings. .... or did you mean in public?

To answer the original question, yes it is possible. To travel at a speed less than c, the photon needs to have a non-zero mass. Current limits on the photon mass are that it is < 2x10^{-16} eV. That is extremely small (by contrast, the electron is 511,000 eV). For the photon to have such a small mass would be very difficult to explain in a physics theory. Indeed, our current theory of QED requires that the photon be completely masses (and thus travel at c). Therefore there is a lot of circumstantial evidence that its mass is zero, but in principle this has not been proven (and never will be). Edit: incidentally, if you put in the upper bound for the mass and work out the velocity of a photon with energy 1GeV (quite a high energy, but not too high, easily achievable with current tech) you would find a velocity of 0.99999999999999999999999999999999999999999999999999c (with about 50 9's in it) so it is definitely close to c (and would get closer with higher energies).

I am a bit confused as to why Tom doesn't regard this problem as simple. It is (as far as I can tell) because there is a perfect symmetry in the problem. (So you don't need to work it our mathematically.) Johnny5 is almost right with his first post. Because there is a perfect symmetry you cannot tell the brothers apart, and therefore each will see the other brother's watch in exactly the same state - with less time on it than their own. But you must remember that they are making frame dependent measurements, so this is not a contradiction since the measurements are not directly corresponding to each other. For example, someone in a third frame travelling at half the speed of the travelling brother (and coincidentally meeting them at the same time that they coincide) would see the same time on both of their watches (which would be both slower than his). Alternatively, if one of the brothers now accelerates to the other's rest frame, he will find himself younger than his brother (it is not the acceleration with makes the time dilation, but the acceleration makes it observable by allowing them to make measurements in the same frame).

What do you mean by that statement? Theoretically at least I can measure the momentum of a particle to whatever precision I like. The uncertainty principle is only telling me that the position of the particle will be uncertain. Of course, one can't measure it infinitely accurately because one never has perfect equipment, but that is hardly a qunatum mechanical restriction.

Study physics.

I am dreadfully sorry, Mr Phi for All, Sir. I meant no disrespect and I promise to be a good boy in future. Please forgive me!

I had to chuckle at the possible 3 warning points for "Disrespect Towards Forum Leaders".

OK, in QM and QFT we have operators which tell us the value of an experimental quantity when we act on a physical state. So for example, in the Schroedinger equation the energy operator is i*hbar*d/dt (not sure if LaTeX is working again yet...): taking this operator and acting on the state tells us the energy of the state. Making this 'measurement' actually (usually) changes the state of the system, so you can imagine that if we make two different measurements we might get different answers depending on which order we make the measurements. The classic example of this is position and momentum: measuring a particle's position and then its momentum will give different answers from measuring its momentum and then its position. The momentum and position operators do not commute. Now, when you measure a position, you are in fact making 3 measurements (4 if you you are measuring its position in time as well as space) because you are measuring the x-coordinate, the y-coordinate and the z-coordinate. All of these measurements can be made 'at once' because measuring one has no effect on the others. The measurements commute. The extra 'fermionic' dimensions I mentioned in the previous post are not like this. They 'anticommute' with each other, so if I make the measurements in the opposite order I will find a relative minus sign. The link between fermions/bosons and anticommutation/commutation has already been described by Tom, so I won't go into that....

Did my rather too technical description kill this thread?

Virtual photons cannot be made real. They are virtual because they have a missmatched energy and momentum. That is, we do not have E2 = m2c4 + p2c2. In principle, one could make them real by adding enough momentum or energy to make the equation work, but in practice there is no way to do this. The reason is that the photon can only couple to charged objects and conservation of charge means that any interaction vertex with a photon must contain at least two charged particles. Therefore (since the interaction vertices usually involve three particles) any incoming photon is always destroyed. The particle which absorbes the photon can re-emit another photon though (since it is charged) and the new photon could be real, but there is no continuous link with the old virtual one.

Normally, when one thinks of the usual dimensions of space-time (like 'up-down', 'left-right' etc) one takes for granted that they are bosonic. By that I mean that the operators for the position co-ordinate in a particular direction commute with one another. So that if I ask 'what is the x-coordinate of the particles position?' followed by 'what is the y-coordinate of the particles position?' I will get the same answers as if I had asked for the y-coordinate first and then the x-coordinate. However, quantum mechanics has shown us that assumptions like this are dangerous and some operators do not commute, but anti-commute (they are fermionic), so that if you ask the questions in the opposite order you will get a relative minus sign. Supersymmetry postulates that there are extra dimensions in space time which anti-commute. This sounds silly, but in fact it is a very natural idea. In the '70s Colman and Mandula 'proved' that the maximum symmetry that space-time could have is the Poincarre symmetry of relativity (boosts and translations). It was only the advent of supersymmtry that showed us a flaw in their argument - they had forgotten the possibility of anti-commuting operators (or to be more technical, graded Lie algebras). Now we have 'proven' (until someone else finds something that we have missed) that the maximal symmetry of space-time is the superPioncarre group which consists of the boosts and translations of the Poincarre algebra but also supersymmerty transformations which is basically a rotation in the enlarged space (bosonic + fermionic directions). So what does this mean for particles? Well, if we have extra fermionic directions, a field (in position space) will be not just a function of x and t, but also of this extra direction z (it is normally denoted theta but to save typing I will call it z). This field is called a 'superfield'. The weird thing about z is that it is anti-commuting so the anti-commutator of two such directions z1z2 = -z2z1 and thus the anti-commutator of z with itself must vanish: zz = -zz = 0. Now, you are all familiar with taylor series where we expand a function f(x) as a power series in x and if x<1 the higher order terms are small because a high power of x is small. If we do the same with a fermionic number z, the expansion of f(z) will only have two terms: f(z)=a+zb since terms like z2 (and higher) will vanish. Therefore this expansion is always true (even if z were large). Also notice that since the object f(z) is a bosonic object, then 'a' must be bosonic and 'zb' must be bosonic; but since z is fermionic, b must also be fermionic (add two objects of half-integer spin and you get one with integer spin). Now, a superfield can also be expanded in this way (although it is quite a bit more complicated) and similarly the series will be truncated at a certain order by the anti-commuting of the fermionic direction. One will find that each superfield in 'superspace' can be written as two fields in normal space: one bosonic and one fermionic exactly like 'a' and 'b' earlier. Supersymmetry postulates that every particle we have seen is coming from the expansion of a superfield and is either the bosonic part or the fermionic part. For example, the electron is the fermionic part of the electron-superfield and should have a bosonic partner (usually called the selectron). We are currently looking for these particles in colliders. So when people say that supersymmetry has twice as many particles, this is not true. The different 'particle' (fermionic and bosonic) are just different projections of the same particle in different directions. There are a lot more reasons for believing why supersymmetry is true, but I will leave these for another post.

QM is a description of one particle states. To allow particle pair production you need QFT.

Why were they denouncing it? Do you have a link?

You can't turn a neutron into a proton by hitting it with a photon. You can do it by hitting it with an positron though. The positron could emit a virtual W-boson (and turn into a neutrino) which is absorbed by a down-quark in the nuetron turning it into an up-quark. Since the neutron is udd and the proton is uud, this turns the neutron into a proton.

This is just a semantic issue. The 'universe' is defined as everything there is, so if there is something beyond what we currently the call 'the universe' we would have to relable this as the universe instead.

It is interesting that various people on this thread categarically state that there are 11 dimensions as if it is fact, and no-one objects. But when Johnny5 says there are 4 (well 3 spacial) everyone jumps down his throat. Since we have no experimental evidence at all suggesting that there are more than 4 dimensions (in fact the experimental evidence means that introducing extra dimensions is difficult to do without mucking things up), both points of view are equally valid. My second point is about compactification. It is not strictly necessary to 'roll-up' the extra dimensions tightly. Randall-Sundrum models for example have extra dimesnions which are not compactified, but restrict Standard Model particles and surfaces to lie on a surface in the extended space (a brane). So Standard Model physics would appear 4-dimensional (as it should to match experiment). However, gravity is allowed to flow through the entire space (the bulk): this dilutes it and makes gravity weak, as observed. (More technically, there is a SM brane and a Planck brane, and it is the exponential decay of the strength of gravity in the bulk between the two branes which makes gravity weak on the SM brane.)

One should think of space-time as simply a rule which allows you to define a distance between two events. Whether or not you choose to regard that as something physical, existing separately from the events themselves, is up to you but is once again an unscientific question since it is untestable.

That is not really what I was saying, but yes that is correct. (I was going a step further and saying that there is really nothing 'unreal' about complex numbers in the first place.)

That is not a good analogy, because the data implies that you will not come back to the same place if you travel in a straight line across the universe for long enough. Actually, whether or not the universe is infinite is another unscientific question (this site seems to like these) since it is untestable. the best you can ever do it say that it is bigger than the the size probed so far. This isn't just pedantry; since there was probably a period of inflation at some point, our past light-cone is not the whole universe, so there are part of the universe with which we can never come back into causal contact with. Ergo, we can never see the whole universe to know how big it is (even if it were finite).