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Guest Message © 2012 DevFuse

ajb's Profile User Rating: *****

ajb's Photo
Reputation: 466 Beacon of Hope
Group:
Resident Experts
Active Posts:
4,508 (2.06 per day)
Most Active In:
Speculations (791 posts)
Joined:
04-June 06
Profile Views:
13,568
Last Active:
User is offline Today, 06:47 PM
Currently:
Offline

My Information

Member Title:
Physics Expert
Age:
34 years old
Birthday:
November 23, 1977
Gender:
Male Male
Location:
Back in South Wales
Interests:
angling and astronomy
College Major/Degree:
PhD pure mathematics, the University of Manchester
Favorite Area of Science:
Mathematical/Theoretical Physics. Modern differential geometry and applications in physics.
Biography:
Born in Newport South Wales. Studied at Swansea, Cardiff, Sussex , Manchester, now back in South Wales.
Occupation:
Somewhere in between physics and mathematics, a little closer to mathematics I think.

Contact Information

E-mail:
Click here to e-mail me
Website URL:
Website URL  http://www.angelfire.com/geek/susy/index.html
  1. Recent Status Updates
  2. About Me
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  4. Posts

Posts I've Made

  1. In Topic: Definition of "Classical Mechanics"

    19 May 2012 - 09:14 AM

    View Postpmb, on 18 May 2012 - 09:47 AM, said:

    Note: I will say one last thing before I sign off this thread. When I started this thread it to get an idea of how many people use/interpret the term Classical Mechanics to include relativistic mechanics as Goldstein uses/defines it.


    I would say that just about every theoretical and mathematical physicists would.

  2. In Topic: Definition of "Classical Mechanics"

    18 May 2012 - 08:23 AM

    View Postjuanrga, on 18 May 2012 - 07:41 AM, said:

    Yes. Precisely the classical limit of a quantum theory is the limit when \hbar \rightarrow 0.


    But one should take care to note that not all quantum theories have unique classical limits. It is possible for a quantum theory to arise from the quantisation of two or more distinct classical actions.

  3. In Topic: Definition of "Classical Mechanics"

    18 May 2012 - 07:25 AM

    View Postpmb, on 17 May 2012 - 10:48 PM, said:

    Classical Mechanics is a system which is based on Newton's laws. If the Galilean transformation is employed to transformed between inertial frames then we have what I refer to as Classical Newtonian Mechanics (for lack of another term) and when we use Lorentz transformations we have SR. When we add to this like equivalence principle etc the we have GR.



    Okay, so what are the corresponding transformations for non-relativistic quantum mechanics?

    Well for the free Schrödinger equation we have the Schrödinger group. This group is the Galilean group with a central extension.

    The Lorentz transformations play a very important role in quantum field theory on Minkowski space-time, so I cannot see that we can necessarily separate classical and quantum here.

    View Postpmb, on 17 May 2012 - 10:48 PM, said:

    ajb - What does this hand waving thing you mentioned have to do with anything? Take a look at Goldstein et al's text and notice how everything they've derived is rooted on Newton's three laws which have a very small explicit mathematical content it them. Lagrangian and Hamiltonian mechanics can be deduced from those laws as can the rest of classical mechanics.



    It is more the other way round and one can certainly write down mechanical systems that do not obey Newton's laws.

    In essence, by picking just about the simplest Hamiltonian or Lagrangian for a point particle (these will be non-degenerate and so equivalent) you can "re-derive" Newtonian mechanics. However, the formalism works much more generally than that.

  4. In Topic: Definition of "Classical Mechanics"

    17 May 2012 - 10:23 PM

    View Postpmb, on 17 May 2012 - 10:12 PM, said:

    It's just so much easier to say that Classical Mechanics is physcs which is outside of quantum mchanics?


    Okay, that we can agree on, but...

    View Postpmb, on 17 May 2012 - 10:12 PM, said:

    Did you interpret "precise" to mean that I was asking about something more complicted than


    I interpreted the question as looking for a fairly robust definition of classical and quantum. To my mind, the best distinction is the commutative verses the noncommutative world.

    View Postpmb, on 17 May 2012 - 10:12 PM, said:

    Perhaps I didn't state the question so as I'd get the type of response I was looking for. I was looking for a non-mathematical definition of "classical mechanics".


    This is going to be difficult as classical mechanics is really a mathematical construct in which to model phenomena. Very hand waving, classical mechanics works well for anything that is not too small, i.e. quantum effects are negligible.

  5. In Topic: Definition of "Classical Mechanics"

    17 May 2012 - 09:23 PM

    View Postmississippichem, on 17 May 2012 - 09:06 PM, said:

    So you are saying that there are other non-classical frameworks in physics where planck's constant (or reduced plancks constant) is not seen in the important commutators?


    In the context of quantising spaces themselves, say via a deformation or quantising the coordinate ring (a la Manin) you usually want a parameter that plays the role of Planck's constant, though the units may be different.

    I am thinking that in the path integral formulation it is probably not immediate that Planck's constant measures the noncommutativity of something. Here it is the parameter that controls the contribution of the paths to the amplitude. The configuration space of all paths is a classical space, so noncommutativity here is harder to see.

    View Postpmb, on 17 May 2012 - 09:06 PM, said:

    I wish I knew what you were talking about. :D You're describing this in some way that I don' recognize. It seems that what you wrote could also be interpreted as quantum mechanics. Can you restate it so that it makes moe sense to me? I.e. please dumb it down for me.:P


    In classical physics any two observables (fundamentally functions of position and momentum) commute. That is

    A(x,p)B(x,p) = B(x,p) A(x,p).

    (Just think about multiplication of real numbers)

    In quantum theory any two observables will in general not commute. To distinguish the quantum position and momentum I will put a hat on them. In particular we have

    \hat{x}\hat{p} - \hat{p}\hat{x} = i \hbar \hat{1},

    which is really the root of all quantum mechanics. Non-relativistic quantum mechanics is then all about the representation theory of the above.

Comments

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    Amr Morsi 

    16 Apr 2012 - 12:06
    Missed you Andrew. How is your wife? She is better than you no wander, just obvious as she can look into your deep eyes.
    Don't kill ladies with innocence, but with the reason of innocence. I killed a cat before. :)~~~~~
    Just kidding man. She gonna be okay, after God's Will.
    You seem gettng higher in field, professor. Keep on and leave if IT REALLY GOT PR...
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    ajb 

    28 Feb 2012 - 09:25
    I do not know very much. I often surprise myself with my ignorance. But this is a good state of mind to be in.
  3. Photo

    Xittenn 

    27 Feb 2012 - 04:06
    How do you know so much dammit! **super jealous**
  4. Photo

    URAIN 

    21 Feb 2012 - 10:56
    Dear friend, I hope again you took a look on my paper. http://spaceandconsensus.wordpress.com
    Presently discussing on thread "matter occupy space" in main forum and "space and consensus" in speculation.
    Previously I had left "universe smallest existence is neutral existence" and my hypothesis is it is "neutron" Till I have left one thing.
  5. Photo

    Amr Morsi 

    01 Sep 2011 - 04:13
    Andrew ..... admire. You are a magnificent physicist/mathematician.
  6. Photo

    ajb 

    01 May 2011 - 13:20
    I quite like Nakahara's book, thought it is not the most complete book mathematically speaking. It does however introduce you to many of the basic ideas of topology and geometry.
    Isham's Modern di®erential geometry for physicists is also quite good, but again lacks some rigour. Tohru Eguchi, Peter B. Gilkey, and Andrew J. Hanson. Phys. Rept.,66 is also good.
    K...
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    A Tripolation 

    01 May 2011 - 03:49
    Can you recommend any good introductory books on differentiable geometry? Preferably one with a lot of hand-holding, and in-depth explanations of the various concepts?
  8. Photo

    ajb 

    09 Feb 2011 - 09:54
    In physics differential geometry probably is advanced mathematics used "day to day". The reason for this is that physics, or for sure classical physics is usually smooth, i.e. you can take derivatives and does not depend on exactly how you decide to present it. Both these are fundamental ideas in differential geometry.
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    A Tripolation 

    08 Feb 2011 - 19:56
    It seems to me that most advanced math is a form of, or heavily relies upon, differentiable geometry. Is this the case, or am I mistaken?
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    ajb 

    11 Nov 2010 - 08:13
    Odd variables appear in quantum field theory when looking for semi-classical descriptions of fermions, like the electron and also are needed in gauge theories like Yang-Mills. Supersymmetric theories uses them, including superstring theory. They also can be very useful linear algebra and differential geometry as a neat description of alternating forms.
    So, Ok maybe I could include ...
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    ydoaPs 

    11 Nov 2010 - 06:19
    How about an entry on application of odd variables? Why would we use them other than for pure mathematical enjoyment?
  12. Photo

    needimprovement 

    14 Sep 2010 - 05:36
    My personal thanks to ajb for all his help.
  13. Photo

    swaha 

    10 Feb 2010 - 10:05
    what is this resident expert u have under ur name?
  14. Photo

    DJBruce 

    20 Nov 2009 - 01:47
    Hey, could you by chance recommend any good introductory number theory books.
  15. Photo

    swaha 

    12 Nov 2009 - 10:56
    sir i didnt understand the calculation on ur on black hole entropy. could u pls explain me that?
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