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How Should We Think About Quantum Mechanics?

  1. Jun 5, 2013 #1
    Greetings people of Physics,

    How should we think about quantum mechanics? For example, what is meant by a "measurement" in quantum mechanics? Does "wavefunction collapse" actually happen as a physical process? If so, how, and under what conditions? If not, what happens instead?

    Kind Regards,
    AlfieD
     
  2. jcsd
  3. Jun 5, 2013 #2

    Simon Bridge

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    Those are interesting questions which have been covered copiously here and elsewhere - besides asking in this thread, what have you done to try to answer them?

    If we know this, then we can better tailor the answers to you.
    Thank you.
     
  4. Jun 5, 2013 #3
    Simon, if you've read my other reply to your comment (link is at the bottom of the page) then you will know that I have not done much in terms of answering these questions. However, unlike my endeavours in finding out the answer to my other question, I have performed a Google search on this:

    https://www.google.co.uk/search?q=What+is+a+measurement+in+quantum+mechanics&rlz=1C1CHFX_enGB500GB500&oq=What+is+a+measurement+in+quantum+mechanics&aqs=chrome.0.57.11695j0&sourceid=chrome&ie=UTF-8#rlz=1C1CHFX_enGB500GB500&sclient=psy-ab&q=what+is+a+measurement+in+quantum+mechanics&oq=What's+a+measurement+in+quantum+&gs_l=serp.1.0.0i22i30l3.10811.21281.0.25033.46.31.7.8.11.0.91.1875.31.31.0...0.0.0..1c.1.15.psy-ab.byGs_5jHtVo&pbx=1&bav=on.2,or.r_qf.&bvm=bv.47380653,d.d2k&fp=9a303c08cdeb5d94&biw=1920&bih=971

    and taken information accordingly; I know do not need to know what a measurement is in Quantum Mechanics. However, I still don't understand whether or not "wavefunction collapse" happens as a physical process and, if it does, under what conditions, and, if not, what happens then?

    https://www.physicsforums.com/showthread.php?t=695536

    Kind Regards,
    AlfieD
     
  5. Jun 5, 2013 #4

    stevendaryl

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    ...and never answered to everyone's satisfaction.
     
  6. Jun 5, 2013 #5
    Here's an extremely boiled-down version of an answer to your question ("What is the measurement process?"). Though your question is a very big question that you should be more specific on, I think this explanation is the best way to get started thinking about these ideas.


    The measurement process involves two objects: the object being measured and the measurement device. The object being measured is arbitrary; let's call it "the sample." The measurement device can be thought of as the kind you see in everyday experience (a multimeter, oscilloscope, photomultiplier tube, etc.)--a macroscopic object which has different "pointer" states; i.e. a macroscopic device which takes on a state corresponding to the result of the measurement performed on the sample, such that a human looking at the device can tell what state it's in. In the spirit of quantum mechanics, we could write the measurement device's state as a quantum state, just like any other quantum system.

    Now let's focus on a specific example to make everything concrete. Let's say that the subject is an electron, and suppose we have a measurement device which measures the electron's spin. We will write the electron's state [itex]\left |\psi \right \rangle_e[/itex] as a linear combination of up and down states (with respect to the z-axis): [itex]\left |\psi \right \rangle_e = a\left |\uparrow \right \rangle_e+b\left |\downarrow \right \rangle_e[/itex].

    Now the measurement device, described by a state [itex]\left |\phi \right \rangle_m [/itex] is one that starts out in some neutral state [itex]\left |\phi \right \rangle_m = \left |0 \right \rangle_m [/itex]and then changes its state indicating whether the electron was spin up or spin down--if it sees the electron as spin up, the measurement device's state becomes [itex]\left |\phi \right \rangle_m = \left |\uparrow \right \rangle_m [/itex], whereas if it sees the electron as spin down, the measurement device's state becomes [itex]\left |\phi \right \rangle_m = \left |\downarrow \right \rangle_m [/itex]


    As an example, let's write down how the measurement device would measure an electron which happens to be in the spin up state: Before the measurement, the electron-measurement device system is in the state
    [itex]\left |\psi \right \rangle_e\left |\phi \right \rangle_m = \left |\uparrow \right \rangle_e\left |0 \right \rangle_m[/itex]
    After the measurement is made, the measurement device reflects the electron's state.
    [itex]\left |\psi \right \rangle_e\left |\phi \right \rangle_m = \left |\uparrow \right \rangle_e\left |\uparrow \right \rangle_m[/itex]

    This particular measurement process can be written in summary as:
    [itex]\left |\uparrow \right \rangle_e\left |0 \right \rangle_m \rightarrow \left |\uparrow \right \rangle_e\left |\uparrow \right \rangle_m[/itex]




    Now suppose we can prepare the electron in a state such that it is in a superposition made of equal parts up spin and down spin (relative to the z axis. This can be prepared by measuring the spin along the x-axis first.)

    [itex]\left |\psi \right \rangle_e = \frac{1}{\sqrt{2}}\left (\left |\uparrow \right \rangle_e+\left |\downarrow \right \rangle_e \right )[/itex]

    What happens when the measurement device tries to measure this state?

    According to Schrodinger evolution (forgetting about collapse for the moment), and moreover the principle of superposition, we could easily see the following evolution should happen (absent collapse):

    [itex]
    \left |\psi \right \rangle_e \left |\phi \right \rangle_m = \frac{1}{\sqrt{2}}\left (\left |\uparrow \right \rangle_e+\left |\downarrow \right \rangle_e \right )\left |0 \right \rangle_m\rightarrow\frac{1}{\sqrt{2}}\left (\left |\uparrow \right \rangle_e\left |\uparrow \right \rangle_m+\left |\downarrow \right \rangle_e\left |\downarrow \right \rangle_m \right )[/itex]

    However, in subjective experience, when we look at a measuring device, we never see it in the superposition of states above. All we see is either [itex]\left |\uparrow \right \rangle_e\left |\uparrow \right \rangle_m[/itex] or [itex]\left |\downarrow \right \rangle_e\left |\downarrow \right \rangle_m[/itex]. Somewhere along the lines, one part of the quantum state gets thrown out.

    This modeling of the measurement process and the apparent contradiction is due to Von Neumann. Though this argument at first appears to support the objective reality of wavefunction collapse, some deeper reflection on it shows that it's just the same as what would happen in the many-worlds interpretation (no collapse). For that argument, watch Sidney Coleman's lecture "Quantum Physics In Your Face" which is available on the Harvard website.
     
    Last edited: Jun 5, 2013
  7. Jun 5, 2013 #6

    Simon Bridge

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    It's a good idea to use the resources you have at hand before asking questions of others - that way you can be more specific.
    The questions you have asked are central questions in whole physics courses at college level and aspects of them form active areas of research. From your reply in another thread, you are at A-level, so any answer you get here that you can understand at that level is going to be unsatisfactory. Don't sweat it - it takes time to learn these things.

    Ah well done: what did you discover? Can you explain it to someone else?

    The "collapse" of the wavefunction is probably easiest to understand as a kind-of narrative fiction that helps us talk about systems involving wavefunctions. It is certainly not considered a physical process.

    Richard Feynman describes it as similar to the way ancient astronomers used to predict eclipses by moving stones or nuts between bowls.

    You will probably benefit from his lectures series on QED:
    http://vega.org.uk/video/subseries/8
     
  8. Jun 6, 2013 #7
    A measurement in quantum mechanics is any interaction of any kind that conveys information as a form of detection, best described as anything that gives you information. And information is what allows you to narrow your choices, or at least refine your probabilities.

    I'm currently on Part 2. Thanks for the link!
     
  9. Jun 6, 2013 #8

    Fredrik

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    Those Feynman lectures are also available as a book titled "QED: The strange theory of light and mattter".
     
  10. Jun 6, 2013 #9
    Thanks, I'll check it out!
     
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