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Where do I find the Quantum Mechanics notes by Prof. Richard Littlejohn from Berkeley?
There is a relatively simple intuitive approach to this that I have developed many years ago as a student. I believe it is equivalent to the “many worlds” interpretation, however I am not a philosopher, so I don’t know. Bear with me. Take the (thought) experiment of an electron passing through a double-slit. The (single) electron is a quantum wave passing through both splits of the double-split and interfering behind, creating the well-known interference pattern. Now imagine two scenarios. (1) the distance between the two splits is increased to a high mulitple of the wavelength. Result. no significant interference remains, the two splits behave as two single splits instead of a double split. Coherence between the splits may still exist but is of no physical significance since there is no effect resulting from it. (2) You place an observer at the double split, determining which split the electron is passing through. As you probably know, this has the same effect as (1). the interference pattern vanishes, and we are left with two single-slit pictures that are simply added on top of each other. In the Copenhagen interpretation, (1) and (2) are two different things, because only in case (2), the wave function is “collapsing”. Observation makes it “collapse”, and because of the collapse, only the “observed” part of the wave function influences the future of the “observer”, i.e. creates a single-slit picture behind that slit the electron chose to pass through. I understand (1) and (2) as two very similar things, and this is my intuitive approach. If you take the observer (with his many degrees of freedom) as part of the system, the whole system including the observer has to be modeled by a wave function. In this multidimensional wavefunction space (because of the many degrees of freedom), the two different possibilities of the electron passing through the left or right slit are actually quite “distant” from each other, because t differ not only in the path of the electron but also in the paths of the oberver’s degrees of freedom. So to say, adding the observer is the same thing as vastly increasing the distance of the two slits. And because of that, coherence and interference are lost. Short answer to your question. an “observation” of a system A in the Copenhagen interpretation is another system B (with a vast number of degrees of freedom) that couples differently to the various possible states of system A. Because of that, the various states of system A will not interfere after this coupling has happened.
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When the two systems are not coupled, there exist other systems that behave completely differently than system A does. When a coupling has occurred, all the degrees of freedom associated with the different systems of A will interact and influence each other, and therefore interfere to the extent a single slit does. When coupled, that process does not occur, and the influence of each system does not interfere with that of the other. Question: Is it true that a wave function in quantum mechanics collapses when there are no coherent states? The answer is yes. If there are no coherent states, no change in the momentum equation and zero change in the Higgs field. A photon going in one slit, and then going through the other, does not enter either slit differently, except due to the measurement applied at each slit. If the wave function collapses, no change occurs in a change in momentum.
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