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Simultaneous Measurements

  1. Apr 28, 2006 #1

    eep

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    Suppose you have a particle which is not in a momentum eigenstate. You then measure the momentum (say, in the x-direction) by two seperate apperati simultaneously. Do the results have to agree? I asked my professor about this and he said that quantum mechanics will tell you that you can't perform such an experiment, as one of your measurements is going to have to occur before the other one. He also said that this isn't a very satisfying answer, which is isn't. Can anyone elaborate further or is this just one of the things you have to accept about QM.
     
  2. jcsd
  3. Apr 28, 2006 #2
    According to what i think is the most common belief, the very act of doing a measurement collapses the wave function to an eigenstate of what you measure. So as soon as you have a measurement, the second measurement is forced to yield the same result. As far as trying to measure twice at the same time, i think that is a bit non-sensical. Measuring once you collapse the wavefunction, therefore there is no way to make a second measurement. No such thing as "exact" same time, as i'm sure you are aware, because of the uncertainty principle. You could hope to "clone" your particle and make many copies and then measure each of them, but it is a theorem of quantum mechanics that you can not make a clone without collapsing the wave function. (Making the clone is a sort of measurement by itself)
     
  4. Apr 28, 2006 #3

    eep

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    Ah, of course. We hardly ever talk about energy/time uncertainty so I hadn't considered it. That fixes everything!
     
  5. Apr 29, 2006 #4

    vanesch

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    Yes, and now comes the big joke. Of course you cannot perform a simultaneous measurement twice at the same moment on the same particle. In fact, if it is the same measurement, at the same time, on the same particle, then it is just one single measurement !

    But, but, people tried to find a way around it. They set up systems of 2 particles, of which they KNEW that the measurement on one fixed also the outcome of the other. For instance, take conservation of angular momentum. If you start from a state with angular momentum zero, and you produce 2 particles that way, you know that they have OPPOSITE angular momentum.
    And now the trick was to find out of this still works, because now we can do a simultaneous measurement on BOTH particles, which comes down to 'the same measurement' because we know that if we have one measurement, the other is fixed.

    Well, lo and behold, THIS WORKS. These are called EPR experiments, for Einstein Podolsky and Rosen, who first thought up this kind of experiment (in fact, to show that it couldn't work! But it does...)
     
  6. May 12, 2006 #5
    is that so?



    How exactly do the so-improperly-called energy/time uncertainty fix THIS?
     
  7. May 12, 2006 #6


    Oh, can we?. Simultaneous measurement with respect to which reference frame?
     
  8. May 15, 2006 #7

    DrChinese

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    EPR tests can be performed in the same reference frame in many ways, up to and including performing the measurement at very nearly the same location. All you need is some fiber cabling and you can pretty well place the entangled photons anywhere (and therefore "anywhen" since you can control the length of the fiber) you want. At that point you are left with defining what you mean by "simultaneous". I.e. to what level of precision is it considered simultaneous.
     
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