Originally Posted by johanfprins
JFP: Then why are there experiments that can trace the charge-density of the matter-waves and find that this density correlates with the calculated intensity of these waves? Why is chemical bonding successfully modelled by assuming that the charge-densities of wave-orbitals correlate with the intensities of these orbitals?
RC: Because the wave function determines the probability of electrons being measured at a position. Duh !
You should then only measure spots: Not the uniform intensity of the electron-wave!
Even in most non-Cophenhagen interpretaions, it is the wave function that determines the measurement.
It plays a role but not the primary role: When you make a measurement, you usually (not always) change the boundary conditions of the wave, and when this happens, it forces the wave to morph. Thus the boundary conditions caused by your measurement are primarily responsible for what you measure. Obviously the shape and size of the wave, before it encounters the new boundary conditions also play a role but not the primary role.
Originally Posted by johanfprins
JFP: Suffice to state at this point that my model for the Elitzur-Vaidman bomb tester does not explode all the live bombs 100% of the time
RC: Suffice to say that this is yet another a unsupported assertion.
If you have actual physical waves (as you imply since what you have is nothing to qo with QM wave functions) and they go along both paths, all of the bombs will explode.
If you have actual physical waves (as you imply) and only one path is taken the 50% of the bombs will explode. Repeat the experiment and 50% of the remainder will explode. Continue repeating and all of the bombs will explode.
If you have some magical 'resonance' then the 'wave' or bomb can always be selected to explode 100% or 50% of the time.
The Elitzur–Vaidman bomb tester experimental results are that you can determine whether 25% of the usable bombs are usable without being consumed in a single run, going to 33% by repeating the experiment.
There is a theoretical proposal (made in 1996 so it may be experimentally veified by now) that allows up to 100% of the bombs to be identified as usable.
I did post that I would prefer to return to this topic after we have concluded our discussion on superconduction: However, in view of your childish intransigence I will post the explanation for the Elitzur-Vaidman bomb-tester in terms of waves only:
I will use the diagram in the thread:
http://thisquantumworld.com/wp?page.id=153
Assume that the splitter S1 and the bomb are both absent from the interferometer set-up: A single photon is injected along either one of the two possible paths (say the path with the mirror M1) to reach the splitter S2. When using a non-paranormal interpretation of quantum mechanics, according to which all interactions at the quantum-level are purely determined by actual waves and the causal interactions between waves, the photon must be an actual wave and not a “particle”. Therefore, when the photon-wave reaches the splitter S2, it splits into two actual wave-fragments which stay in instantaneous contact with each other: The latter must be so since the photon is a holistic wave-entity which is “self-entangled”. “Entanglement” and “instant communication” is an experimentally, well-established property of quantum-waves. The ½-fragment of the photon-wave generated by transmission through the splitter S2 moves into the detector D1, and the reflected ½-fragment generated by reflection within the splitter S2 moves into the detector D2.
After Max Planck discovered the quantum of light energy, it has been established that a detector cannot detect a fragment of a photon: Thus, also in this case, neither one of these detectors can detect a fragment of a photon’s energy. In order to detect the injected photon within one of the detectors D1 or D2, the two ½-fragments must in some manner come together in order to reconstitute a complete photon-wave. In order to detect the photon within (say) detector D1 mandates that the ½-fragment at D2 must first collapse and merge with the ½-fragment at D1. “Collapsing” is also an experimentally, well-established property of quantum-waves: So that this explanation is not paranormal. Similarly, for detector D2 to detect the photon, the ½-fragment at D1 must collapse into the ½-fragment at detector D2. Each of the ½-fragments has a fifty-fifty probability to collapse into the other ½-fragment: This, in turn, means that the photon has a 50/50 probability to be detected by either one of the detectors D1 or D2.
Let us remove detector D2: When the reflected ½-fragment now reaches D1, the transmitted ½-fragment, which is then at the position where D2 would have been, if this detector were there, will have to collapse into the ½-fragment at D1 in order for D1 to detect the photon. But since there is a 50/50 probability that either fragment can collapse, it is equally possible that when the ½-fragment which transmitted through S1, reaches D1, this causes the latter ½-fragment to collapse into the ½-fragment, which is at the position that D2 would have been if it were there. When this happens, the detector D1 does not detect the photon: In other words, although the arrival of its reflected ½-fragment at D1
causes the collapse of this ½-fragment into the transmitted ½-fragment, the detector D1 does not detect the photon-wave.
Let us place both S2 and D2 back into the spectrometer arrangement. When now injecting a single photon-wave into the interferometer, S1 splits it into two ½-fragments. The reflected ½-fragment now follows the path with mirror M1, and the transmitted ½-fragment follows the path with the mirror M2. These two ½-fragments will thus reach the splitter S2 simultaneously. Both of these ½-fragments must now each split again within S2, into two ¼-fragments; so that there are now four ¼-fragments. The ¼-fragment, of the ½-fragment which followed path M1 and which formed by transmission within the splitter S2, will overlap with the ¼-fragment of the ½-fragment which followed path M2 and formed by reflection within S2: The latter two overlapping ¼-fragments are thus moving into detector D1.
Both the latter two ¼-fragments have undergone two reflections in order to be generated. The ¼-fragment which transmitted within S2 after it has followed path M1, had reflected at S1 and at M1; while the ¼-fragment which reflected within S2 after it has followed path M2, had reflected at M2 and at S2. Thus the accumulated phase angles (caused by reflection) of these two ¼-fragmented waves moving into D1, are exactly the same. Consequently, these two ¼-fragments will overlap constructively to contribute a ½-fragment that impinges into the detector D1.
In contrast, the ¼-fragment generated along path M1 and reflected within S2, so that it impinges into detector D2, has been formed by three reflections at S1, M1 and S2; whereas the ¼-fragment generated along path M2 and transmitted within S2 so that it also moves into detector D2, has only been reflected once at M2. Thus, these two ¼-fragments, on their way to detector D2, are totally out of phase and will thus overlap and cancel each other totally. There will thus not be any light-energy, whatsoever, moving towards detector D2. But energy cannot be destroyed, and therefore these two ¼-fragments can thus not form at all within S2. This mandates that the ½-fragment that followed path M1 must totally transmit through S2, and the ½-fragment that followed the path M2 must totally reflect within S2. Accordingly, the light-energy leaving S2 and impinging into D1 is the whole reconstituted photon-wave that has initially been injected into the spectrometer at S1; even though its two ½-fragments followed different paths to get to S2. Thus, all photons initially injected into the splitter S1 will, under these conditions, end up within the detector D1.
Now let’s add the bomb. When the bomb is a dud, the ½-fragment of light following path M1 does not encounter a functioning detector at the bomb and will thus move on as if there is no bomb. The injected photon is then reconstituted within S2 and detected by detector D1. When the bomb is not a dud, the ½-fragment of light along path M1 arrives at the detector, and if it’s opposite fragment following path M2 collapses into the fragment following path M1, the bomb will detect the photon and explode: However, if the ½-fragment following path M1 collapses into the ½-fragment that follows path M2, the bomb cannot detect the photon and will thus not explode, even though it is not a dud. The fully reconstituted photon will now be following the path M2 on its way to the splitter S2.
When this fully reconstructed photon-wave reaches the splitter S2, it is split into two ½-fragments which then move into the detectors D1 and D2: And as already shown above, there is a 50/50 probability that either one of these detectors will detect the reconstituted photon after one of these ½-fragments has collapsed into the other ½-fragment. According to the paranormal, wave-particle interpretation of this experiment, the bomb is a dud when the photon is detected by D1, while it is not a dud when detected by D2. But according to the present causal interpretation, each live bomb which do not explode will generate a photon which will, with a 50% probability, be detected by detector D2 (and thus be correctly classified as live) but also with a 50% probability be detected by detector D1 (and thus incorrectly rejected as a dud). A very dangerous situation indeed!
It is now also clear why Wheeler’s interpretation of his experiment that “what we do at present affects the past”, is nothing else but paranormal metaphysics. In Wheeler's experiment, the photon is
always split in two ½-fragaments which follow the two paths. When after they have started following the two paths, the experimenter decides to measure which path a photon is following, the two ½-fragments collapse into each other to follow a single path. A not too intelligent experimenter (Anton Zeilinger where are you?) will then conclude that this photon has followed this path from the start; and it has thus anticipated in a paranormal manner which measurement Anton is going to make! If Anton, however, does not make this measurement, the two ½-fragments actually do follow both paths and will thus interfere with each other before being detected. The results obtained for both possible measurements are thus totally causal and has nothing to do with metaphysics that involves "knowing the future"..