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    (Original post by generalebriety)
    Never mind, that was probably the way they wanted me to do it.

    Another question. "In an inertial frame S a photon with energy E moves in the xy-plane at an angle theta relative to the x-axis. Show that in a second frame S' whose relative speed is u directed in the x-direction, the energy and angle are given by E' = gamma E(1 - (u/c) cos theta), cos theta' = (cos theta - (u/c)) / (1 - (u/c) cos theta)."

    I don't have a clue where to start on this. I know E = gamma mc^2, where gamma = (1 - v^2/c^2)^-1/2, but I don't know what v is. Anyway, aren't photons massless?!
    This is the question that came up on the exam this year. Just in case you're still confused, 4-momentum of a massless particle is p4 = E/c (1, n) where n is the unit 3-vector in the direction of motion.
    Standard Lorentz transformation with n = (cos, sin, 0) should sort you out.
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    (Original post by yusufu)
    This is the question that came up on the exam this year. Just in case you're still confused, 4-momentum of a massless particle is p4 = E/c (1, n) where n is the unit 3-vector in the direction of motion.
    Standard Lorentz transformation with n = (cos, sin, 0) should sort you out.
    Yep. Had my supervision today and he said the same thing, but thanks. I can never get my head round dynamics questions and similar topics - they all seem to be "here's an innocuous situation, can you derive this horrible equation? No, of course you can't, you lose"-style questions. How depressing.

    Back to RichE's post above: no, I do actually understand it. I think I'll have to wait for Analysis II to understand a lot of this, but it should click at some point. Thanks for the replies, and thanks to Dave too.
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    (Original post by RichE)
    I think the answer is yes. Take the point as (0,0) and the trees as open discs in R^2. Then each disc blocks out a range of angles/arguments/views from the origin - we can think of this as blocking out an open subset of the unit circle S^1. So these blocked ranges form an open cover for S^1, and as S^1 is compact it is possible to find a finite subcover of S^1 corresponding to finite set of trees that block out all views.
    Hmm... I have to admit, I was thinking that a tree was closed ball, not an open one.
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    (Original post by generalebriety)
    Yep. Had my supervision today and he said the same thing...
    You had a supervision after your exams had finished? Jesus. Are you at Christ's or something?
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    (Original post by DFranklin)
    Hmm... I have to admit, I was thinking that a tree was closed ball, not an open one.
    I think that's an entirely reasonable starting point given that the question says nothing on the matter. But, there again, with open trees the problem does seem to have a topological aspect to it.
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    (Original post by Cexy)
    You had a supervision after your exams had finished? Jesus. Are you at Christ's or something?
    Selwyn. :p: They're technically optional, but I'm not leaving work to build up that I could be doing now when I have nothing else to do - I don't want twice the stress next year. Anyway, all my work has now officially finished. Thanks for all your help, everyone - though I expect I won't stop working entirely over the summer, so I may well be back.
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    (Original post by generalebriety)
    Selwyn. :p: They're technically optional, but I'm not leaving work to build up that I could be doing now when I have nothing else to do - I don't want twice the stress next year. Anyway, all my work has now officially finished. Thanks for all your help, everyone - though I expect I won't stop working entirely over the summer, so I may well be back.
    That's what I thought last year!
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    (Original post by yusufu)
    That's what I thought last year!
    I won't, though - I'll get bored and have to do something. :p:
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    (Original post by generalebriety)
    I won't, though - I'll get bored and have to do something. :p:
    You might as well try and get CATAM out of the way. It can become quite a headache later but I suppose that depends how interested you are in it. I wasn't in the mood to learn any programming until the Christmas holidays came round.
 
 
 

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