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Question RE: Susskind Entanglement Lecture 2

  1. Aug 23, 2013 #1

    meBigGuy

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    In lecture 2 of the Entnglement lecture series at theoreticalminimum.com, Susskind is explaining a classical interpretation of Measureable and Observable that left me confused. I'll watch it again tonight, but thought I might get a good clarification from the excellent teachers here.

    In his example he assumed 6 classical states, using a six sided die as an example. He defined the observable mapping as a 1 if the die state was 6, and 0 otherwise. This is were I became somewhat confused. He didn't address, at all, the operation that sorta converts the state to the observable. Or even, how the state is determined. I understand that his choice of mapping values is arbitrary (that is he could have chosen any mapping).

    So I thought, maybe this could be likened to a die with all sides 0 except 1, which is a 1. But, in this case you don't know what state you are in. You have the answer, but not how it came to be.

    It seems that you need to know the state in order to apply the mapping.

    So, I'm not entirely clear how all this fits observable and measureable, and I know I'm going to need to be rock solid on the classical analogy of this for lecture 3.

    I know the answer to this is simple, it is just evading me. It feels fuzzy.

    Thanks
     
  2. jcsd
  3. Aug 24, 2013 #2
    If only it were 'simple'!!!
    This has been a subject of discussion and debate since QM was first formulated. [And in these forums, too.] Check out, for example, 'measurement problem' and 'measurement in quantum mechanics' anywhere, like Wikipedia... and read a few paragraphs from each....or search these forums.

    From this post I suggest you remember: " linearity, superposition, and complex numbers". You will find over time that those words serve a a good reminder and introduction to quantum mechanics.


    From another discussion in these forums:

    The following quote is from Roger Penrose celebrating Stephen Hawking’s 60th birthday in 1993 at Cambridge England:

    [I like it because it was given in front a room full of world famous physicists, so even those who disagree can't refute it.]


     
  4. Aug 24, 2013 #3

    meBigGuy

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    I'm just trying to apply the quantum measurement process to a classical system, kind of an analogy. But there may be fundamental problems that cause the analogy to break down. I'm trying to understand the breakdown.

    First, I have a 6 state system whose values are 1,0,0,0,0,0. Is that a problem right there? Do I need a linear system where all 6 states are unique? I wonder why Susskind threw in the 1,0,0,0,0,0 mapping of the classical system.

    So, can I apply a measurement matrix to such a system? Or do I need to go to 0,1,2,3,4,5 mapping or simpler yet 1,0 (to keep it simple).
     
  5. Aug 25, 2013 #4
    At 1 hour and about 15 minutes of this lecture Susskind describes STATES.....

    So it seems to me you are viewing a more advanced set of lectures....
    I haven't studied those yet....saving them for this winter!!

    Spend 20 minutes minutes around here and see what Susskind says about states:

    Susskind Quantum Physics…Lecture 1

    Lecture 1 | Modern Physics: Quantum Mechanics (Stanford) - YouTube

    From my notes of Susskind's explanations:

    At one hour 25+ minutes:


    depends what you mean by 'problem'. For example, QM does not declare whether or not those state exist before measurement. Nor are these each necessarily exact values, which is a classical concept, nor are such states restricted to real numbers....
     
  6. Aug 25, 2013 #5
    By sheer coincidence I happened across this post of mine from another current discussion:
    It relates to a possible 'problem'. Instead of the words 'particle' or 'spin' in the following, just think "state". Because all we know about a 'particle' or 'spin'are its various 'states'...measurement results.


    Tom Stoer:
    What it means to me: 'particles' normally exist in a superposition of wavelike states....reread my comments on 'orbitals' earlier in this post. This means trying to visualize electron spin via classical analogies has many pitfalls.

    A related description from another forum expert:

    Marcus:
    What it means to me: So we can't observe such a wave, but an atomic nucleus with orbiting electrons knows exactly the spin characteristic of every particle...and force carriers as well!! That is mind boggling!!
     
  7. Aug 25, 2013 #6

    meBigGuy

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    "First, I have a 6 state system whose values are 1,0,0,0,0,0. Is that a problem right there?"

    By that i meant that possibly the concept of 1,0,0,0,0,0, is not a valid state vector. Is it legal to have 6 states but only two values? Is this actually a two state system (1,0) with different probabilities? (1/6 and 5/6). What I don't understand is why he brought that up at all.

    He discusses applying a function to the state to determine the observable, but doesn't talk much about the function. In order to apply the function, you need to know the state.

    For the classical states of 1,2,3,4,5,6 with measurables of 1,0,0,0,0,0, and probabilities of 1/6 for all states, What is the measurement matrix, eigenvectors and eigenvalues. Or, is this a problematic classical example.

    It is at 1:15 in lecture 2.
     
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