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That is the application I am talking about - I have never used it before. It does not look anything like as advanced as Mathematica, but I expect it will do some donkey work with solving algebraic and differential equations, linear algebra and basic plotting.

Not at all... anyway we all feel like shouting at editors and referees. This is normal, but don't do it lol!

I have just installed Maxima on my laptop running Ubuntu. I will have a play with it over the coming weeks. I was wondering of anyone else here has used Maxima? Are there any annoying features, bugs or other problems you would like to share? Is there anything you particularly like about the system? (The price is one great feature!)

You should not read too much into letters of this kind from editors - just move on and submit to another journal, that is what we usually do. Once I bothered to send an email back saying that one of the editorial reviewers was wrong, just for my own sanity. Of course, that did nothing to change the mind of the editorial team. It sucks, but you get over it and get on with the job.

Anyway... the problem here is that one should avoid trying to think of [math]\infty - \infty = \: ?[/math] Remember that infinity is not a real number and so one has to be very careful here and try to make sense of such thing using limits. Well, for the case at hand there is no real trouble as others have pointed out, x-x =0 and the limit of this as x gets large is clearly zero.

The usual thing is find a conference you want to attend, when you register they usually ask (assuming slots are available) for you to submit a title and abstract of a talk. The organising committee will look at your title and abstract and see if they think is is okay for the conference. Also be aware that not all conferences and meetings publish proceedings, and if they do you should check on the peer-review policy. Generally, conference papers are not seen as being on par with proper journal papers, but then I do know important works published that way. Anyway, good luck.

Invariant under the Poincare group to be a little more careful - anyway all the strange and wonderful effects we have in special relativity really come down to the space-time interval being invariant when changing between inertial frames. This really is the key thing to keep in mind.

In short yes, the Lorentz, or more properly the Poicare group (and its Lie algebra) are the cornerstone of special relativity and also general relativity where we have such transformations locally. Nothing seems to come close to special and general relativity in modelling nature. It is not at all understood why the Poincare group plays such a vital role in physics: for example representations theory is related to the 'species' of fundamental particles we see. All the basic notions are indeed tied to Riemannian geometry. The earliest hint is in Maxwell's equations which are invariant under Lorentz transformations and not the ones found in classical mechanics. Why geometry, I am not sure, but geometry really does seem to be 99% plus of all classical physics. We get invariance of the speed of light in all inertial frames - not all frames in general. And yes, this was a puzzle and seemingly written into Maxwell's equations. Lorentz, Minkowski and others were thinking along the same lines as Einstein. But he was the first to bring special relativity together.

Even before we get to KK theories, differential geometry is the basic language of the classical description of forces. Connections and curvature are central to this description. In short, the answer to your question is yes, but it is not the curvature of space-time, but something built over space-time. You should look up fibre bundles, connection and curvature.

You question if the rock had any purpose and that part of this purpose was to trap this guy? I don't think there is any great purpose to anything, we make our own purpose as we are able to. The rock is just a rock.

I know people who did electronic engineering for their first degree and then went into physics later - for example Brian Cox. I also know a string theorist who started in electronic engineering. So it is possible and electronic engineering is vital in experimental physics.

Everybody knowns that fields are sections, but this does not seem to be really used in standard physics treatments. One okay treatment is G.Sardanashvily's Five Lectures on the Jet Methods in Field Theory - you can find it on the arXiv.

In the context of physics, the base manifold is 4D space-time. But in general we need not have this.

A fibre is some specific manifold - all the fibres are the 'same'. A line bundle maybe the easiest to think of - here you attach the real line understood as a manifold to each point. You have to do this in a right way, but usually there are many ways you can do this - like adding twists like the Mobius band.

No, you attatch a fibre to every point.

No - the fibres are not small. They may be non-compact as in the case of a vector bundle where the fibres are R^n for some n.

Maybe your local priest has an opinion on that - physics cannot really answer your question.

I think mathematics is the only way. Every experiment or observation made today is interpreted in terms of a physical theory. You need this mathematical background to make any sense of what you are looking at - well if you want some deeper understanding that is. One can make observations of the Moon and planets and doing so can be wonderful, but it is not really science until the maths hits in.

I disagree with this. Much of our modern technology is founded on physics, which itself requires mathematics and sometimes quite advanced mathematics.

This is rather a metaphysical question. Pragmatically, the best we can do is match our models to what we can measure/observe. Space-time 'exists' and is 'real'in the sense that we can use the mathematical structure to make predictions that match nature very well. One can ask the same of the electromagnetic field or any other concept in physics.

I have no idea - all I do know is that the mathematical notions here are very useful in our understanding of the Universe.

Not so much metaphorically, but mathematically.

Space-time is a manifold and you add extra geometry to this in terms of fibre bundles 'build on top' - you attach more manifolds to each point of space-time. The 'reality' of these fibre bundles is another philosophical question - fibre bundles are used because their sections give us the right objects for physics. All tensors and tensor-like objects can be seen as sections of particular fibre bundles. Does he explain that a bit more?

To some extent this all depends on what you mean by deterministic. Standard non-relativistic quantum mechanics of a single particle is deterministic - give me the state at time t = 0 and I can give you the state at any other time. It is just that the results of measuremants are now stated using probability theory. Non-determinstic really means that stochastics plays a role - the dynamics itself involves randomness and probability. We usually see this when we make approximations when dealing with large numbers of objects. For example, the whole subject of statistical phsyics is just that - using 'averages' to get at bulk properties. Another thing, as Strange speaks of, is chaos theory. Here the system is determanistic (usually) but very sensative to initial conditions - even if you start at two near by initial conditions after finite time you may end up at states that are very different. Models of the climate are like this and so people run many computer similations with similar initial conditions and then average over all this to make statistical predictions. So, is the Universe deterministic - I think so, in the sense I have given above. The problem is that we can mathematically deal with only a few interacting objects at a time and are forced to use statistical methods rather quickly.