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      Further discussion on the double slit experiment

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      Double slit experiment; Particle interference; Superposition state.

            Author Summary


            In a double slit experiment, a screen position x could be endowed with two probabilities: the probability of finding particles which passed through slit A and arrived in x, c1; and the probability of finding particles which passed through slit B and arrived in x, c2.
            If the probability of finding particles in x when the two slits opened simultaneously was p12, then, p12 = c1 + c2 held. This meant that when the two slits opened simultaneously, the probability of ”finding particles in x” would increase rapidly.
             For example, if c1 = 0.45 and c2 = 0.5, then when only one slit opened, the event of ”finding particles in x” would be uncertain. However, when the two slits opened simultaneously, p12 = 0.95 would hold meaning that the event of ”finding particles in x” would be almost certain. 
            Thus, in a double slit experiment,  as long as the time that the two slits opened simultaneously was long enough, the particle interference phenomenon in x would occur with certainty.


            Author and article information

            13 February 2019
            [1 ] College of Information Engineering, Zhejiang A&F University, Lin’an, China

            This work has been published open access under Creative Commons Attribution License CC BY 4.0 , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Conditions, terms of use and publishing policy can be found at www.scienceopen.com .

            Double slit experiment; Particle interference; Superposition state.



            My opinion:  the author’s interpretation could not explain the observed data in double silt experiment and he made several conceptual errors.

            To explain the interference with only probabilities, the author provided the condition for occurrence of the particle interference phenomenon as:

            N12 > N                                                                                             (3)


            t > (c1t1 + c2t2)/p12                                                                             (4)

            This is his first error: the observed interference pattern not just has enhanced places like in Eq. (3), but also the destructive places where: N12 < N.

            Then he assumed that: “Because in almost all experiments, t1 and t2 had very small values with t having a large value. These would cause t > (c1t1 + c2t2)/p12 to hold”.

            This is his second error. In double split experiments, the time durations (t1, t2 and t) corresponding to three different experimental settings, without any logical relation. We can use the following counterexample: first open slit A for 1000 minutes, then open slit B for another 1000 minutes, finally open both slits for 10 minute, so:

             t = 10 << 1000(c1 + c2)/p12 = 1000   (p12 = c1 + c2 as the author claims)

            The inequality (4) now is totally violated, but, in the experiment, we can see very clear interference pattern with both constructive and destructive strips, no matter if any slit was closed earlier.

            Later, in his Discussion, the author argues: “If ψA represented the wave function of particles which passed through slit A, then, | ψA |2 should depend on c1, n, and t1”, that is:

            |ψA |2 = c1n t1                                                                                     (5)

            This is his third error: How can |ψA |2 be proportional to time? In quantum mechanics, |ψA |2 is a probability by nature and almost time-independent for this experiment.   His Eq. (6) has the same trouble. 

            Finally, the author suggested that:  p12 n t − (c1 n t1 + c2 n t2) = |ψA + ψB |2

            This is his fourth error, not only because |ψA + ψB |2 should not proportional to time, but also because it must be nonnegative. Nevertheless, by using our counterexample again, the above suggestion would lead to negative value of |ψA + ψB |2

            Bottom line: An acceptable new interpretation of double slit experiment must, at least, explain both the constructive and destructive interference pattern with two slits open, no matter how long one slit is closed earlier or later.

            2019-08-31 04:43 UTC
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