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By beginning we need some notion of 'after' and so time is explicitly involved. Classically we can 'rewind' our models to 't=0', but at this point the physics breaks down. It is quite possible that, because of quantum effects, that 'before' and 'after' are not really workable concepts when we get close to the 'beginning' of the Universe.

See what I just posted!

You can have a speed greater than the global speed of light, but not the local speed. For example, warp drives and wormholes make use of this fact. The general problem then seems to be the actual implementation of these methods - they require exotic matter (negative energy etc) to support them. Along side that, as soon as you can beat a light signal you can create time machines. Causality may also be a problem!

Space, or space-time? This is not what one would usually mean by aether, though space-time and fields would be the modern equivalent to what the 19th century physicists were looking for. However, there are some subtle differences. The basic idea of a aether is some mechanical or quasi-mechanics material that is responsible for electromagnetic waves. This idea became more and more abstract and Maxwell, Poincare and Lorentz all worked with more and more looser concepts. The exact mechanical properties are not properly explained in these old works - if I am not mistaken just about the only thing that Lorentz needed was the immobility of this medium. Lorentz used more ad hoc ideas such as length contraction to make his theory fit. The trouble is that the aether is now undetectable, and so the theory is not fully testable. The question for philosophers need to think about is in what sense does this medium exist if we cannot really see it? Now, if you have some medium that fills all of space then you can think about a preferred rest frame - in this case the one in which the speed of light is always c. Your idea that 'Lorentz aether = choice of rest frame' is not really correct. The point is that there should be some canonical choice of rest frame. (There are such frames in cosmology, but these arise due to special solutions to general relativity rather than being written into general relativity from the start) So, at some level the aether should be some 'material' in that it is a localised notion - think about waves in a pond, you have particles of water going up an down. Results like the MM-experiment and so on, together with Einstein's special relativity and field theory show that the 'aether' (space + time + metric + other fields) are not really 'rigid things' in the sense that we have a universally defined rest frame. Classically we should think of 'fields' as the 'aether' or quantum mechanically one may like to think about vacuum states (but forget the idea of a universal frame).

I am not sure how this is really any different to other physical theories. The only thing to be careful with is that most of our intuition is based on Newtonian ideas - some of which do survive passing to special relativity. Anyway, can you tell me what is understood by 'aether' in Lorentz-Poincare theory?

I have not read any of these old papers carefully - I have looked quickly at modern historical accounts - but my general impression is that people quickly became loose, and a careful description of the aether and its nature was missing. Maxwell passed to a more abstract notion and this I think that this heavily influenced Lorentz. One had to remember that this was all formulated before the modern formulation of fields.

This is my understanding - so there is in Lorentz-Poincare models some aether, but the idea is that we can chose a frame for which this can be considered at rest. If this is possible, then there would be a preferred inertial frame. So, Lorentz's theory does not sit well with special relativity at all. Tim88... I don't quite agree with this. The point is that when we pass to special relativity the mathematics is really based on the symmetries of Minkowski space-time. We have a clear geometric understanding of what is going on, and furthermore this leads to general relativity. There is no notion of absolute rest in Newtonian mechanics - but absolute time does make sense. Of course I am think of Minkowski space-time... the total number of dimensions is 4, or as common we think of 3 space and one time dimension. Einstein and almost all of the other names at the time thought about how Maxwell's theory and related things could be understood in terms of some aether theory - whatever they meant by 'aether'. As the aether seems not to be required due to the work of Einstein and others, physics took another direction.

As the others have said, biophysics is the application of the ideas from, and the philosophy of physics to biology.

1911-ish seems to be about the time that everyone in physics accepted special relativity over aether models - though the idea has never gone completely. From what I can gather, Maxwell first sort a mechanical aether to explain his electromagnetic theory. He then changed to a more abstract notion of an 'electromagnetic aether' - I am not sure how 'non-mechanical' this really is. Lorentz took this more abstract idea and made modifications, as did Poincare. The theory is more a theory of electrons and how they interact, this is not quite written into Maxwell's equations. Today, special relativity and field theory (both classical and quantum) form the basis of our understanding. My understanding is that the rather ad-hoc theory of Lorentz and Poincare can be better and easier explained using special relativity. Also, the mathematical elegance of special relativity should not be overlooked. Still, the 3+1 dimensional notion of Minkowski space-time has little bearing on the aether - or really it shows that the idea of using Galilean/Newtonian notion of space and time together with some other 'medium' is probably wrong. By passing to Minkowski space-time we really get to grips with the Poincare invariants of Maxwell's theory and remove auxiliary notions.

The model was thrown out in 1911 - you have to forgive me if I am not familiar with details. I am not sure if the nature of he aether is really explained in this and related models. But for sure if you have a aether then you must be implying that the Universe is filled with 'something'. The moden understanding would be in terms of fields, and we now know about the electromagnetic field. As you are an expert, what do the old paper say about the nature of the Lorentz(-Poincare) aether? If you are talking about understanding the Universe as 3+1 dimensonal then you are right, this has nothing to do with a aether.

Cleaning staff will be employed by the university or work via a contract with an outside company, rather than be part of the mathematics department itself. You could cheak the website of the department. Why is that interesting? I am actually British - and soon will no longer be in Poland (in fact I am not there right now!)

Sure, for now I assume we are really speaking of classical notions. At some level one may wish to have some more complete quantum theory of 'space-time' and then show how the classical notions follow. But right now we don't have much of a clue on this. Mechanical here refers to the classical notion of space-time being filled by some very rigid fluid that we canot for various reasons detect. For example in the Lorentz theory length contraction is used to explain why we cannot see this aether. I am - like the others - not really sure what you mean by this and so what answer you are looking for. Well, this is a philosophy thread so maybe there is no clear answer anyway!

I don't know if standard undergraduate study has been dumbed down, but for sure students have an expectation to pass based on he fact that they are paying for this. This, together with the numbers of graduates, means that a masters or similar is the best way to - as you put it - filter out students. I see this kind of thing all the time.

StringJunky, there has for sure been a general increase in science graduates to the point that a degree is not enough anymore.

Why not? No one knows why nature 'uses' Minkowski space-time (locally at least), we just know that our models fit well. I think you will not get a good answer to your question.

So you really mean a kind of mechanical aether theory? (Which of course should still be a mathematical model) This is deep philosophical question that I fear cannot have a decent answer. If the mathematical model works well, then it works well. I don't see that one can say much more.

Exactly, the vast majority of science graduates have to move into other things and a tiny tiny minority make it to professor (and similar). Each person has reach their own conclusion on this.

And there are lots of people who do have a reasonable understanding of special relativity. What do you think a physical model is? The standard formulation of special relativity - in terms of Minkowski space-time and its isometries - is a physical theory. That is we have a mathematical framework in which to make predictions that can be tested against nature. The aether is now not thought to be needed - either using such a notion leads to predictions that do not agree with nature, or the aether is unobservable and so not needed.

It turns out that people in science are not usually bothered by their IQ. Generally, no-one is sure that IQ means much other than you are good at IQ tests. I have never had anyone in a professional capacity ever say that their IQ is XYZ and that they are a member of Mensa. If someone did say that, they would come across as a bit self-centred and even obnoxious.

Scientist covers a lot of things - generally science is about understanding our world, where engineering is about using this understanding. (This is a bit of a vulgar separation, but generally the case) Engineering covers a lot of things and a lot of professional levels. But generically I would say that there is more money in engineering than pure science. Depends who you ask. At a university a PhD would be expected, but in industry this is not necessarily the case. I would say that there are more opportunities in the engineering sector than pure science. Careers are very hard to forge in academia whatever the subject. What was your actual title? In academia research associate has some specific meaning (which can be a little different country to country). To my mind calling yourself a research associate would be a stretch - but this may depend on who you are addressing.

Depending on the subject, people do work for, say, pharmaceutical, chemical and energy sectors in a research role. Many people with physics and mathematics degrees work in engineering (across all areas) as well as finance and banking - some of this can be research.

Like Strange, I am not sure what you mean by 'pierce space'. If you can explain a little better what you mean by this, we maybe able to say more.

Well, neutrinos are very hard to detect, they move through space, and as they are nearly massless they can have relative velocities close to the speed of light. Not that I think that any religious book predicts neutrinos, my point is that with hindsight we can match many things to medieval writings. In truth, there is not much to debunk. What you have quoted is not enough to really match with the modern understanding of black holes.

Linear independence of vectors (in a metric space) need not imply orthogonality. However, one can always use the GS-procedure to construct an orthogonal basis given any basis. In the other direction, as long as we don't include the zero vector, any set of orthogonal vectors constitutes a linearly independent set of vectors.

I think your analogy is okay - the thing to keep in mind is the number of numbers needed to describe any point of the space in question. Dimensions are not orthogonal as such. Orthogonality is to do with the local coordinates you chose and then you need orthogonality to be with respect to some metric. In Minkowski space-time of any dimension we have a canonical class of coordinates which are rectangular in the obvious sense. Yes, in the sense that we have a metric of the right signature ie., (1,1,...,1, -1) or the other way round depending on conventions. The notion of orthogonal requires metric and then refers to vectors or local coordinate systems. You can pick coordinate systems that are not rectangular. https://en.wikipedia.org/wiki/Orthogonality Generally orthogonal gives us a notion of two vector being 'at right angles' with respect to each other.