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EPR paradox

  1. May 12, 2009 #1
    Hi,
    I am little bit lost in what is so called EPR paradox (see also http://en.wikipedia.org/wiki/EPR_paradox). It takes into account two particles A and B that have some "same" characteristics (states) and by messuring some of this characteristics of particle A implies that the same characteristic particle B has. Quantum physics says that there exist some complementary characteristics (as e.g. position and velocity) - let's call them C1 and C2 - that cannot be messured together with arbitrary precision (so called uncertainity principle). (With this come also another question - what does mean "to be measured together"?) EPR paradox operates with measuring characteristics only on one particle (say A) which I don't quite understand - when measuring C1 on A than I in fact can not meassure C2 on A with arbitrary precision (or is it false?). But I think that it would make sense to measure C1 for A and C2 for B - both with arbitrary precision. And because A and B have C1 and C2 same, that can break uncertainity principle - or not?

    Thank you for answering my questions and also for explaining (or sending link) the thought of EPR paradox.

    Honzik
     
    Last edited: May 12, 2009
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  3. May 12, 2009 #2

    JesseM

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    You can measure C1 for A and C2 for B, but you can't actually assume that A and B have the "same" value for all their unmeasured properties (i.e. that A had the same value as B did for C2 even though you didn't measure C2 for A), and that this is the explanation for why they always have the same value when you do measure the same properties for both (if you measure C2 for both A and B, you are guaranteed to get the same measured value). This idea would be a "local hidden variables" explanation for why they always give the same results when you measure the same properties, but it implies certain conclusions about the expected statistics when you measure different properties--conclusions that can be written as a "Bell inequality" of some type--and it turns out that these conclusions are falsified by the actual statistics predicted (and experimentally verified) in QM. Here's an analogy I came up with a while ago that illustrates this:
    And you can modify this example to show some different Bell inequalities, see post #8 of this thread if you're interested.
     
  4. May 12, 2009 #3

    DrChinese

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    Welcome to PhysicsForums, Honzik!

    The answer is YES - you can measure to arbitrary precision Alice for C1 and Bob for C2; and NO - this does not violate the HUP. The explanation is: a measurement of C2 on Bob after a measurement of C1 on Alice doesn't tell you anything about C1 on Bob or C2 on Alice. This is in violation of common sense, and is also in violation of what EPR assumed. But nonetheless, this has been experimentally confirmed many times.

    It will help you to read about Bell's Theorem along with EPR as they go together and are almost never considered separately anymore.
     
  5. May 22, 2009 #4
    Thanks for answering - Bell's Theorem is really very fascinating result.


    I have some more questions about measurement and characteristics discussed above. Please tell me whether my questions (answers on them) are right or wrong:

    1) first measurement - i.e. C1 on Alice - tells me that the same value of C1 has also Bob (because Alice and Bob are entangled)

    2) important question: are Alice and Bob still entangled after arbitrary number (especially the first) of measurements on them or will they at some point in time loose this property of "being entangled"?

    3) after second measurement (suppose it was done just after the first measurement in ponit 1)) - i.e. C2 on Bob - has still Alice "retained" its measured value of C1 (from point 1) or will this measure of C2 on Bob somehow destroy the value of C1 on Alice? And another question connected to the second measurement (in case Alice and Bob are still entangled): will Alice have the same value of C2 as Bob after this second measurement (of C2 on Bob)?

    4) One common question: It is commonly known that measurement causes collapse of wave function, but: what in fact is the "measurement" from the physic's point of view? What kind of physic's interaction is it? And after we answer this question can we admit that the same physic's interaction spontaneously taking place in the nature can also cause collapse of the wave function? (and are we able to detect it?...)


    Thank you in answering this questions, they will help me to understand many nuances of quantum physics.

    Honzik
     
  6. May 22, 2009 #5

    DrChinese

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    1. Yes, that is correct.

    2. No, they are no longer entangled after the first measurement. Note that the order of the measurements of Alice and Bob does not affect the observed outcome.

    3. Yes, repeated measurement of C1 on Alice will yield the same results. But no, Alice will not have the same C2 as Bob (except by coincidence) as a result of his measurement.

    4. We don't really know what a measurement is, or what physically happens with collapse. This leads to what is called the "measurement problem", which some feel is a deficiency in the standard interpretation of quantum mechanics.
     
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