How does many-worlds interpretation explain Interference of the wave function and interaction free measurement? According to the many-worlds interpretation there inst any superposition. But for example  in the Elitzur–Vaidman bomb  experience the photon is Interfering with itself.
If the universes have no effect on each other how can the photon Interference with itself. And how can the fact that the bomb was real or not effect the universe  where the photon didn't took the path of the bomb.
I was using these two sources
https://en.wikipedia.org/wiki/Elitzur%E2%80%93Vaidman_bomb_tester
https://en.wikipedia.org/wiki/Many-worlds_interpretation
 A: In the original Everett Interpretation, there are no parallel universes, only pure superposition. When Bryce DeWitt - an early populariser of the theory - was trying to explain to a lay audience back in the 1970s how it worked, he described the superpositions as being as if each possibility existed in a separate world, and the description stuck - hence the alternative name of 'Many Worlds Interpretation'. While the image has successfully propelled the idea into the public consciousness, it has posed endless problems for its acceptance among physicists. All the questions previously raised about wavefunction collapse, which the Everett Interpretation had answered, simply got raised again with regard to the creation or splitting or interaction of new universes.
The Everett Interpretation does not need to invent any new metaphysical machinery like extra universes to work. It just takes the unitary evolution of quantum mechanics that physicists following Bohr's Copenhagen Interpretation already agreed happened on the microscopic level and pointed out that if you took it seriously and extended it to the macroscopic level, it already predicted that quantum observers would experience classical, one-possibility-at-a-time observations. When a quantum observer interacted with a quantum system, the observer would evolve into a superposition of orthogonal states, in each of which the observer saw a different outcome, and which (being orthogonal) didn't interact. They only affect each other by interference, the only observable consequence of which is to change various probabilities.
This is no different to the way an electron passing through one slit does not see itself simultaneously passing through the other slit (for example, they do not repel one another electrostatically). An electron cloud surrounding an atom does not see the rest of the cloud: it does not have any contribution to energy from self-repulsion, as a classical cloud of negative electrical charge in such a confined space would. Quantum mechanics is linear. If two solutions are added, the sum is also a solution. It means there can be no interaction terms between the superposed components.
In short, there is no measurement problem. Unitary quantum mechanics already provides an explanation for why we see what we do. It was only sloppy thinking that led us to believe that in a macroscopic quantum universe we would see fuzzy clouds of possibilities overlapping; ghostly cats leaping out of boxes containing their own semi-transparent corpses, and so on. The Everett Interpretation requires no additional physics, no new assumptions - it is a subset of the Copenhagen Interpretation.
So as far as the unitary evolution of interfering waves goes (Elitzur-Vaidman bomb tests, EPR experiments, double slit, etc.), MWI is identical to the Copenhagen Interpretation. It simply re-iterates it. They only differ in what they say about the observation process. In MWI, unitary evolution leads to a superposition of mutually-invisible observers, each seeing exactly one outcome. In the Copenhagen Interpretation, all but one of these alternatives simply vanishes. The surviving alternative is selected completely at random, with a probability distribution given by a rule that has to be simply asserted as an axiom. The mechanism by which this happens is unexplained - proposals range from the unknown physics of quantum gravity, the possibility of as-yet undetected higher order non-linearities, to more mystical explanations involving the role of consciousness, intelligence, and vitalism. Their vanishing also has awkward metaphysical implications for faster-than-light, backwards-in-time (e.g. the quantum eraser experiment) effects.
Since the interpretations only differ in their claims about things that can never be observed, even in principle, there is no way to distinguish them experimentally. (At least, if quantum mechanics is correct. If it's not, the new observations might be more compatible with modifications to one alternative than another.) The only grounds on which to select between them are aesthetic - which of them is more mathematically elegant, simple, parsimonious, easy to calculate with, etc.
A: According to the many worlds interpretation (MWI) each system exists in multiple versions. Those versions can interfere with one another under some circumstances. But if information is copied out of the system while it is undergoing interference this may prevent interference by a process called decoherence. When a system decoheres its different versions won't interfere with one another and can be regarded as being in different universes because they don't affect one another. Universes are an approximate, emergent consequence of quantum mechanics and the parallel universe approximation isn't always correct. In this case, it's wrong during the Elitzur-Vaidman bomb experiment.
"The Fabric of Reality" and "The Beginning of Infinity" by David Deutsch have some pop science explanations of the MWI.
The following papers explain aspects of the MWI:
https://arxiv.org/abs/quant-ph/0103092
https://arxiv.org/abs/0707.2832
https://arxiv.org/abs/quant-ph/0104033
A: My humble thoughts:
According to MWI (Many-Worlds Interpretation), when the photon passes the first glass, the universe splits into 2. In one the photon goes up, and in the other down.
If there's no bomb in the bottom path, in both universes the photon reaches the second glass.
Now, MWI clarifies that the universes are never 100% split, in rare circumstances (like here) they can interact again.
The photons in each universe interact with each other (they are at the same place at the same time, and they are from 'compatible universes', whatever that means), causing both of them to go always to the same detector, C.
Now both universes are identical again. Are they recombined into a single universe? I don't know.
Note that only universes that have a lot in common, like those 2, can interact like that. Which is why we only see it in very specific quantum experiments.
If your experiment is open to external disturbances, they can make each universe 'less compatible', in which case the 'inter-universe interaction' will be diminished: the 'weird quantum effects' will be less visible.
If there's a bomb in the bottom path, the photon in the second universe never reaches the last glass. So the photon in the first universe feels no foreign interaction and, again, splits the first universe into 2: in one the photon goes to detector C, and in the other, D. Here you have 3 universes.
