Severian

No they don't!! Go to the bottom of the class!

YT: In the first link, that is just a bad definition of 'mass'. This is something which is constantly taught badly in schools. What they are calling 'rest mass' is actually what scientists refer to as 'mass'. The other (link 1's) definition is frame dependent because it depends on the electron's velocity. In the second link, the electron mass ('rest mass' in the parlance of link 1) does indeed change with energy because of renormalisation in quantum mechanics. This is correct, even though most of the other stuff on that page is complete speculation! Its dependence on energy is logarithmic though, so it doesn't change very fast. I can explain this further if you like, but it gets quite complicated....

Changing the mass of the electron would not change the mass of the photon. The masslessness of the photon is protected by a symmetry (U(1)) so the quantum corrections to its mass are zero (for any electron mass). Otherwise one might imagine that it would change the photon's mass by exactly this process, so nice try ed. As YT said though, it has such a small mass anyway that I don't think it would make a big difference to anything fundamental.

Its funny that you show say that, because I gave a tutorial the other day where someone used exactly that formula. I took the opposite attitude to your books - I made him derive it. It is certainly not an equation that I remember, but it is so trivial to derive that you don't need to.

He/she was probably trying to find out the speed of an object, when he/she knew only the initial speed, the disctance travelled and the acceleration. In that instance, one would naturally use the expressions for distance and velocity in terms of time, which were derived above, and remove the dependence on time. One could in principle work out the time from the distance equation and stick it into the speed equation, but if you have multiple cases to do, this is very inefficient. It is better to substiture an equation for time in terms of distance into the equation for speed.

Yes and no. Yes, in the sense that that M-theory, if anyone could actually calculate things with it, has limiting cases which are string theories. No, in the sense that the string theories themselves are actually not linked: they are different limits of the M-theory. So before you can make predictions you have to know which limit you are in (if any at all). So they are not very predictive. If you are in a dark room with an elephant, can you predict which part of it you will touch if you stretch out your arm? We would also have to know the correct pattern of symmetry breaking down to our energy scales...

Yes, pretty much all of the LED predictions are basic phenomenology type stuff. No string theory at all. But (and this was Brian Greene's point) LED's imply that the Planck scale is much lower than we previously supposed, so you might expect that string theory would be probable. I haven't seen any phenomenology on this though, probably because the string theorists don't know much about expeiment and how to work out real phenomenology. Take a look at this paper. It is not the most recent or anything particularly groundbreaking but you can use their bibliography to browse the literature. (I know the authors, which is mainly why I know this paper.) This paper by Joe Lykken looks interesting too, and is surprisingly old. (Ironically enough, I think I was using his office during a visit to Fermilab round about the time he wrote this...)

String theory is not really predictive or falsifiable. It is too general a term to be predictive: there are a lot of different string theories out there which behave very differently. And it is probably not falsifiable become the required energy scalaes are too high. Large extra dimensions on the other hand are predictive and are falsifiable. They predict Kaluza-Klein states which would be visible at the LHC (at least to precision tests) and their phenomenology is rather constrained. They are definitely falsifiable because ther motivation for being at a low energy scale is to solve the hierarchy problem; if they don't do that there is no point in having them, and the theory goes away.

That's just the definition of a 'light second'.

I posted about this somewhere else on the forums. Let me summarize here. In order to have extra dimensions other than our usual 4 we have to hid them somehow, otherwise we would see them in every day life. Normally this is done by curling them up really small. Imagine a very long straw: if we move a long way away from it, it looks like a line (a one dimensional object) - we can't see that it is really a 2d surface with one dimension curled up. Similarly one proposal is that extra dimensions are curled up, so that we can't see them. It was realised recently (a few years ago) that the experimental limits on this are not as strong as was assumed. If they are curled up really tightly them we have no hope of seeing them in current experiments, but it may be that they are not so tightly curled up after all. It may be that we can see them at the Large Hadron Collider (LHC). This would be very exciting because it could mean that string theories were relevant at much much lower energies than previously thought, and may be able to be investigated experimentally in our lifetimes! Don't hold your breath though. The interest is because the experimental limits are in the ball park of the LHC experiment. (And secondly that the compactification could break electroweak symmetry, removing the need for the higgs boson.) Most likely the LHC will just say 'no extra dimensions here', and move on. There is still another 16 orders of magnitude in energy before the Planck scale - and they could be sitting anywhere in that.

Certainly! As I have explained elsewhere on this forum, the four forces of nature are probably all a consequence of symmetry in the universe. (I say 'probably' because gravity is still not understood, but will most likely be the same.) The laws of physics are symmetric under certain transformations, and as a result we have a force. For example, the strong nuclear force is described by Quantum Chromo-Dynamics (QCD), which is a consequence of an SU(3) symmetry. 'SU(3)' is just a technical description of a symmetry - but think of it as being like a rotation (in 'color-space') - we make the rotation and the laws don't change. Electromagnetism was found to be explained by Quantum Electro-Dynamics (QED) which is caused by a U(1) symmetry, which is just changing the wavefunction by a phase. Both of these forces are mediated by massless particles: QED has the photon, QCD has the gluon. The fact that they are massless is a consequence of the symmetry. Each of these forces have a number (a 'gauge coupling') which tells us how strong they are, ie. how strongly the photon or gluon interacts with matter. These numbers are parameters of the theory. The problem is the weak interaction. It is weak because the force mediators are heavy. To transfer momentum between particles via the weak interaction, we have to create one of these heavy particles and send it from one to the other. This is difficult to do, so the force is weak. It seems that since they are heavy they cannot be coming from a symmetry. This is where the Higgs boson comes in. It is postulated that without the Higgs mechanism, the weak interaction would be a consequnce of SU(2) symmetry, which is very similar to SU(3) of QCD. The symmetry would give massless particles which would mediate the weak interaction (which wouldn't be weak of course) and the strength of the interaction would be given by another gauge coupling. The Higgs mechanism 'breaks the symmetry' - it picks out a direction in SU(2) space so that the laws of physics do change under an SU(2) rotation. (Think of a table tennis or ping-pong ball: if I rotate it, it looks just the same, and you can't tell how much I have rotated it by. But if I draw a cross on at at one point, it will look different when I rotate it - the cross will move. The Higgs mechanism is like drawing a cross on a ping-pong ball.) This mechanism means that although the underlying laws of nature are SU(2) symmetric, their manifestation is not, and the weak mediating particles need not be massless. They become heavy and the force becomes weak. Now at the moment, this description has three forces in it. The forces are described by SU(3), SU(2) and U(1). However, it is not quite correct. The photon is not a result of the fundamental U(1) symmetry after all. This is because the particle resulting from the U(1), normally called 'B', and one of the particles coming from the SU(2), called W3, have the same quantum numbers. We cannot in principle tell one from the other, and when the Higgs mechanism breaks SU(2), it is not W3 which is given a mass, but some combination of W3 and B (which is then called the 'Z boson'). The orthogonal combination of W3 and B remains massless and is the photon. So the only link between the weak interaction and electromagnetism is that their force mediating particles mix with each other. This is not unification! If we want to unify the force, they must be explained by the same principle, and will have one common parameter which determines their strengths. In the Standard Model, we still have two separate strengths for the SU(2) interactions and U(1) interactions, so they are not unified. This is not to say that they won't be in the future. A Grand unified Theory (GUT) seeks to describe all three forces as a consequnce of a bigger symmetry group, eg. SU(5) or SO(10). Going back to our ping-pong ball, if I had drawn a circle rather than a cross and rotated the ball about the centre of the circle, keeping the circle at the north pole so to speak, you still wouldn't be able to see the rotation, so it still has a symmetry. It is thought that some large symmetry group may be broken down to SU(3)xSU(2)xU(1) giving us three forces. Before this breaking the three forces would all be described by one force, a consequnce of the bigger symmetry. But this is still speculation, and has definitely not been proven.

Seconded!

I disagree - there are lots of geniuses working on quite phenomenological physics. Did you know that Witten started off as a phenomenologist but turned to string theory because phenomenology was too hard? There will be renewed interest in 2007 when the LHC switches on, but still no-one will know all the details of theory and experiment. Consider the LHC... We don't even have a proper understanding of hadronization - the process by which quarks reform into hadrons like the proton. QCD is so bloody difficult that we can't solve it at low energies (at high energies we make an approximation which works reasonably well, and allows us to calculate things) and have to construct sophisticated models to describe it instead. This is on ongoing research topic of its own. Then there is the details of the beam - we don't just collide one particle, but collide bunches of particles, two of which hit head on. So we need to know all about the bunch of particles - their spread in energy etc. And the interaction of the particles after the collision with the detectors. It isn't bubble chambers anymore, with easy to undertand mechanisms. The workings of hardon calorimeters is extremely complicated, and I personally don't have a clue how they work. I have to rely on the experimentalist who builds it. Even the data read out will be a challenge. It is already acknowleged that the data will come in too fast to be processed, so a lot of it has to be thrown away. How do we know which data should be discarded and which should be kept (this is called the 'trigger')? It has been realised that we don't have enough processing power in any computer in the world to handle the data flow. A new field of research has developed around this, called the Grid Project, which aims to use a special high speed internet to connect different computers around the world to link them up as one huge supercomputer. (Often the grid is hyped as the new web.) I could go on and on... The challenges of the LHC are far too many for ne person to underatnd everything.

It always annoys me that this claim is made. They are not unified at all - just explained under the same framework. They are still quite distinct forces.

This is sort of already being done, at least on a small scale. Lattice gauge theory is an attempt to simulate physics by constructing a very fine mesh, or lattice, over space time, and simulating the values of quantum fields at the mesh-intersections. This is extremely difficult to do, and needs huge supercomputers, and so far the largest lattices are of the order of 64^4. They can calculate things like hadron spectra fairly well, but not much else.

A lot of things in undergraduate physics (including dark matter) are taught without (proper) evidence these days. This is mainly because the details of the experiement are too hard to describe to undergraduates, either in physics terms or just that the experiments are so complicated that there is insufficient time in the course. There ia usually some attempt to describe the evidence but it is very wishy-washy hand-wavy and wouldn't (shouldn't!) convince anyone. How can you calculate the relic density of a neutralino in class? You have to solve the Boltzmann equation numerically, making model assumptions for the mass and co-annihilation cross-sections. While this could concievably be done as a class project, not everyone can do it, and there are plenty of more things like this... This is true even for professional particle physicists these days. The community is now split into 'theory' and 'experiment'. The experimentalists have to believe what the theorists tell them without understanding all the background, while the theorists have to have faith that the experimentalists have taken all the backgrounds, errors, biases, triggers etc into account. There is just too much for one person to follow it all. I really can't stand Hawking's method of sensationalising physics, telling half-truths or making bogus statements just to sell his books....

There has been a resurgence of interest in KK theories lately as an alternative to the Higgs mechanism. People have realized that our experiments have not really ruled out KK theories with rather small compactification scales (ie. not curled up very tightly), so they would be a possible method for breaking electroweak symmetry. IIRC they have to have at least 2 extra dimensions to keep the compactification scale low enough to work though

I don't think there is a single correct statement in that entire post!

Supersymmetry introduces new 'fermionic' directions to space-time (our normal directions are 'bosonic') so if that turns out to be true then I suppose you could say there are more than 4 dimensions.

In fact, one usually lables time as dimension number '0' (or at least , I do).

The assumption is that the universe is uniform on a much much larger scale, so that galaxies are distributed more or less randomly etc. In fact the COBE and WMAP experiments showed that this is actually a much better assumption than anyone had previously thought. This is supporting evidence for inflation, since inflation would tend to smooth out any un-uniformity.

You are almost correct. If we imagine a big bang with matter moving apart slower than 'c', you are right to start with: the light will travel more quickly and pass the matter, so that the light from the big bang would already be gone. But actually it is not like that because you have to wait a little while for the matter in the universe to become transparent to light. Initially we have just one big soup, and the photons will be absorbed and re-emitted continuously. Eventually the 'soup' will clump into galaxies with space between and the universe will become 'transparent' allowing light to travel freely. You may have noticed that in previous posts I have been careful not to say that the photons from furthest away are coming from the Big Bang... After a little bit of time, these galaxies are far enough away that your problem does not occur. But eben if it did, many cosmolgists beleive the universe underwent a period of 'inflation' where the universe grew incredibly quickly (faster than 'c', but not violating special relativity since it is space-time itself stretching faster than 'c', so allowing no information flow). Then galaxies which are far away would move outside out light cone anyway... WMAP is not measuring the shape of the galaxy as such, but using physical measurements and laws to deduce it. For example, if there were a lot of mass, the gravitational attraction would pull space-time back in on itself, making the universe closed. They have measured the mass (locally, or in other words, measured the density), and found that there is not enough to do this, so they deduce that the universe is open, etc. What circumstance could possibly result in the universe being a cube? This should now be clear from my earlier comments.... As for your second post about light charging away from us anyway, that was the point I was trying to make (clearly unsuccessfully) earlier, when mumbling on about light cones.

Coincidentally, I went to a talk yesterday by Ulf Leonhardt (who is quoted in the New Scientist article) on this very subject. It was quite interesting. I particularly liked the idea of creating a 'fake' black hole: if light moves very slowly then your 'event horizon' would no longer be set at the place where something travelling at 'c' can't escape, but be set at a much lower speed, allowing 'black holes' to be constructed in the lab.

There is no centre of the universe. Why would there be? The only assumption which goes into the astrophysical experiments is that we are not in an exceptional part of the universe. That all the other bits of the universe that we can't see (because they are outside our lightcone) are much the same as the stuff we can see. This is completely akin to the assumption that the parts of the universe that we cannot see have the same physical laws as the bits we do see - an assumption which you seem happy with. So why do you have a problem with one assumtion but not the other?