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Everything posted by ajb

  1. Been busy... I may return one day.

    1. Show previous comments  7 more
    2. MigL


      Good to hear from you AJB.

      Hope you're back soon.

    3. zapatos


      Hope you return when you get the chance. You are one of my favorite posters.

    4. Raider5678


      I want the ajb poster......

  2. Okay, so correct me! Looking at the syllabus of a few universities it does not seem that a typical student leaving with an undergrad education will have been exposed to any high brow mathematics - the same is true of typical physics educations. After that things will depend a lot more on the tastes and interests of the individuals - chemistry research covers a lot of things including things boarding with theoretical physics.
  3. Can you point to some results to back up what you are supporting?
  4. I guess the only thing that can be done is to learn the mathematics and mathematical language needed. One may only need a working knowledge rather than a deep understanding.
  5. Can you expand on that with some nice examples that really are beyond arithmetic, basic calculus, linear algebra and integral transforms? One thing that has been touched upon is 'mathematical chemistry', which does use some graph theory, combinatorics and topology. There is also quantum chemistry, but I think as dealing with more than a few interacting particles explicitly is impossible one resorts to numerical methods - I am not sure that many people in this field really need deep results from topological algebra, operator theory and spaces. Chemical engineering - as suggested in this
  6. Chemistry is far from my interests - however I am sure you can find MSc programmes on mathematics and chemistry. You have have to leave Kosovo though.
  7. So you are thinking of an MSc or PhD in `mathematical chemistry'? I accept that.
  8. At what level? Generally, I would say that there is almost no mathematics in chemistry apart from basic numeracy. There are exceptions like quantum chemistry, molecular dynamics and similar. And even then, the level of mathematics will depend on personal preferences to a large extent.
  9. Great suggestion - you really can picture what is going on.
  10. Some of these questions you should be able to find reasonable answers to via wikipedia... But as to the point of calculus, well there are two at first seemingly different topics in calculus i) Differentiation ii) Integration The first as you say deals with the instantaneous rates of change of functions (and similar objects). For example, a straight line can be described by y(x) = mx +c. Taking the derivative gives dy/dx = m. This is like the `velocity'. Taking the derivative (w.r.t. x) gives zero - the rate of change of the gradient or slope of a straight line is zero, thus it
  11. I think that could have been a possibility. For sure special relativity via the Poincare transformations is `written into' Maxwell's equations, as are other important things in modern physics like conformal invariance, gauge invariance and electromagnetic duality (in vacuum). Maxwell's work really was the starting place of a lot of modern physics - so like Einstein and Lorentz's work on time dilation the philosophy of physics was changed by the understanding of the mathematics.
  12. What time dilation tells us is that the old notion of time ticking away in the 'background' is not really the right way to view the Universe. A global time for everyone works okay for Newtonian physics - well this is actually written into the maths - but this is only an approximation and relativity gives us a deeper view of time. Still, lots of things we don't really understand about time and its direction...
  13. In the words of Patrick Smash - It was the best day of my life... ever

    1. StringJunky


      Care to share?

    2. ajb


      First day at work, met my masters student... all seems good.

  14. I think that you understand this well, but Tim88 I am not so sure... Just for future reference, the Poincare group (Lorentz + translations) is a Lie group - that is both a smooth manifold and a group. Minkowski space-time can be considered as a homogeneous space of the Poincare group. In fact this approach is more used with the supersymmetric extensions or spaces like ADS and DS, but it is worth knowing.
  15. Just to clarify something, one does not think of the manifold of space-time as a field - this is just nonsense - but the metric is a field. Classical fields are sections of various fibre bundles over a manifold. In slightly less technical language, fields are well defined mathematical objects that you attach to space-time.
  16. The biggest problem is that in our standard canonical formulation of quantum theory time plays a special role and one that is different to space. The ethos of Einsteinian relativity is that we should treat space and time equally, but in a canonical quantum theory this is not easy. If you apply the ADM formulation of general relativity (which used a space-time cut) you see that one does not really have dynamics, but rather a Hamiltonian constraint.
  17. As this thread is in the philosophy section we should discuss some philosophy... When people discovered that Maxwell's equations give the speed of electromagnetic radiation as being c, this was interpreted as meaning that Maxwell's equations really only hold in the rest frame of the aether. There was then a lot of theoretical work to understand this, which leads to a more and more 'magical' aether with less and less reasonable properties. The whole idea was to make sense of this canonical inertial frame - the philosophy was that one should have some quasi-mechanical aether and that one mu
  18. The rules of this forum say that you should not simply link to pdf files - you should present some of the theory here and use pdfs and so on as additional supporting information. So, with that in mind, could you sketch the theory and make it clear what you want to discuss?
  19. We call this a Wick rotation... it is often used in quantum field theory as analysis works better with a positive definite metric. One then uses what is called analytic continuation - loosely it means that we can rotate between 't' and 'it' (c=1 as ever!). This is generally not okay, but in physics the kinds of functions encountered in quantum field theory are okay for this to make sense.
  20. One should use ct as this is what appears in the metric and is essential in the Poincare transformations which mix x and ct.
  21. I like the way you mathematical physics researchers that they are almost right! Lorentz for sure tried to understand the mathematics in terms of a aether. Einstein also worked with this idea, but I think he did abandon the idea as it was once understood. I know that Einstein tried to introduce the idea that space-time is the 'aether', but this language did not catch on. For one, we do not think of space-time as being material, so the language is not really correct. I disagree. Field theory, both classical and quantum is the bedrock of modern physics. Field theory gives u
  22. Right, so the modern understanding of the Lorentz, or really the Poncare transformations are as isometries of Minkowski space-time. As for any older and no longer used understandings, I know less about. Lorentz and others who were working with the aether hypothesis tried to understand the invariance of Maxwell's equations in terms of the rest frame of the aether and so on... If there is some notion of the rest frame of the aether - whatever that aether is - then we have a canonical inertial frame to work with (at least ignoring gravity). One could then formulate everything in terms of thi
  23. You are hinting at space-time cuts. That is making a meaningful cut of space-time into space and time. While this is not a problem locally, doing in globally in a nice way is problematic, unless your space-time has some nice properties - in particular the space-time is globally hyperbolic. In a loose sense this means that you can cut you space-time into Cauchy surfaces that evolve in time. In particular, all the information about the theory is contained on each surface and you can evolve this. This is needed in the standard formulation of quantum field theory on curved backgrounds (there
  24. Special relativity is a model itself - you may be thinking of interpretations or analogies. The model of special relativity is not very deep once you start to think geometrically, but for sure some of the results are not so intuitive from our everyday Newtonian perspective.
  25. ajb

    FTL Travel

    Well, particles with negative mass might exist, but we don't have any evidence of such thing - they would break the various energy conditions imposed on general relativity. Interestingly, negative energy densities are common in quantum field theories on curved backgrounds, one may be able to exploit quantum effects and manufacture the necessary conditions. However, it is not at all clear that this is possible as subtle effect in quantum theory may render wormholes and so on unphysical. That could avoid free will issues, but causality is a problem whatever you send through
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