how can a measurement go without collapse and though producing a response that can be copied as many times as we wish? Don't you know the "no-cloning theorem"?

@lionelbrits : no, Lionel, it was another reason that I objected about cloning. He says "A measurement is an interaction that produces information about a system that can be copied to multiple other systems." This is cloning, i.e. creating other systems with the same wave-function. I disagree! The measurement (α|0⟩+β|1⟩)|0⟩→α|00⟩+β|11⟩, I mean, even repeating the measurement many times, will never tell us what are α and β, only what are |α|^2 and |β|^2. We have to change the apparatus in different ways and do measurements, for being able to infer α and β.

@lionelbrits : I have to postpone everything to tomorrow. It will be a very difficult day, very bad weather was announced and I have to travel. So, I have to make preparations. "See" you tomorrow in the afternoon or so.

@lionelbrits , I see your point but due to your explanation. From alanf's words "information about a system that can be copied to multiple other systems" I understood that he wants to copy the whole state of the examined system, which is impossible. Though, there are some things that don't arrange well, but, see you tomorrow.

No. Saying that there is information about one system that can be copied to others does not imply that all the information about that system is copied and in fact it is not all copied. The information that is copied is the information instantiated in a particular set of orthogonal projectors.

@alanf : won't you be so kind to insert this explanation into your answer? Thus, whatever misunderstanding would be avoided.

I deleted my post about many words because I am sick with this. We can know only what happens in our world. If someone believes that the unitarity can be rescued by inventing worlds where we cannot get in, I wish him to enjoy that. The collapse cannot be rescued by many worlds, but it's of no use to hold this, because who believes in it would invent more and more ad-hoc arguments, like kids that want smth. that the parents disagree.

@Hipnosifl I don't know who is obsessed by the MI. I deleted my answer because I am sick with this. The collapse cannot be solved by many worlds, because it is not known what causes it. It is not sure that the decoherence at the contact with the macroscopic apparatus, produces the collapse - see entanglements where we have more than 1 apparatus, and we can't even say at which time are the worlds generated. But it won't help, because who wants those worlds at any price would argue endlessly, and invent new and new ad-hoc arguments. So, pleasant journey in other worlds.

@Sofia: What's ad hoc about applying the equations of motion of quantum systems to everything and working out their consequences? We can make precise predictions about the expectation values of observables, and about what systems will exhibit interference and entanglement. The "worlds" are a distant and unimportant consequence of all that stuff. They are necessarily vague since some interference is always happening, e.g. - electrons in atoms. Also, since nobody has never seen a dinosaur, only dinosaur skeletons, do you reject the existence of dinosaurs?

@alanf did you see the skeletons of those many worlds? An ad-hoc assumptions, is an assumption supported by no evidence, and only made for explaining your theory. A plausible assumption is one that also explains other experiments.

@sofia: The existence of the multiverse is entailed by the only known explanation for single particle interference, entanglement and so on, just as the existence of dinosaurs is entailed by the only known explanation of their skeletons. The MWI does not introduce ad hoc qualifications of quantum mechanics. Also support does not make sense. Any given evidence is compatible with an infinite set of theories, so it can't support any particular theory in that set. But it can refute a theory, see "Logic of Scientific Discovery" and "Realism and the Aim of Science" by Karl Popper.

@alanf I apologize but there in so "pope" in physics. So, what Popper said is equal in rights to what any other scientist said. The skeletons of the dinosaurs were seen, they coincide in the geological époque with the époque of other huge reptiles, with other evidences of the flora and fauna of that époque, so, it's not as you say. This is why MWI is ad hoc, while the dinosaurs is not. Moreover the MWI is at odds with entanglements. So, what will we do, deny entanglements, which are an experimental fact, and retain worlds that nobody perceived by any apparatuses?

@sofia: You haven't answered the argument against support. Do you have an answer? I was referring you to Popper to get more details than I could fit in a comment. Ad hoc means that an idea has been made up to solve a particular problem and has no other implications. The MWI is an explanation of how the world works, not a made up solution to a single problem, unlike collapse. The MWI is not at odds with entanglement, it helps to explain entanglement, see arxiv.org/abs/quant-ph/9906007 arxiv.org/abs/1109.6223.

@alanf I don't need to see what different people said about MWI. This idea falls in front of the entanglements, and in front of the conservation of matter. Creating universes means creating more matter in amounts needed to fill universes. Our universe was produced by a big bang. How are produced those universes? By an electron falling on a photographic plate? Also, how can universes become entangled? Now, I regret but I won't read 24 pages, we can discuss it in the chat room where you can tell me what the article told you. I am willing to answer you not the authors of the article.

@alanf I am here, but where are you?

I am currently writing replies to your questions.

@alanf can't you reply in this room?

I will post the replies in this room once I have finished writing them in a text editor. The character limits make it difficult to compose a sustained argument in the chat itself.

@alanf Aaaaa! Then can you tell me where to look? I.e. to which site?

I will post the replies directly in the chat. They are not currently on any site.

@Sofia: The MWI doesn't start with universes, it starts with the wave function or observables as a correct description of how the world works. The universes are structures within the multiverse. They have to understood in that context.

@sofia: A system starts in a particular state and that state differentiates over time into two or more distinguishable states |a> -> alpha|a>+beta|b>. One way of describing this is that there is a continuous infinity of instances of the system before and after the differentiation, so the number doesn't change.

@Sofia: A more precise way to put it would be that there is a set of instances of a particular system that has a measure on it and that measure does not change over time. This position has been around since David Deutsch's 1985 paper "Quantum mechanics as a universal physical theory".

@Sofia: Since the measure doesn't change over time, it is not the case that whole universes worth of matter are being created. Rather, instances of that matter that were initially the same become different over time.

@Sofia: A universe is a structure within the multiverse in which information flows. So I am in the same universe as the instance of the keyboard on which I am typing this because it can receive information from me via key presses and vice versa.

@Sofia: Energy and matter conservation in a single universe mean that the systems between which information flows have records in which the amount of energy enither increases nor decreases.

@sofia: Now, about entanglement. Each system contains some information about which versions of other systems it can exchange information with: entanglement information. The universes are patterns in that entanglement information.

@sofia: For example, entanglement information results in me seeing on the screen what this version of me is typing rather than what some other version of me is typing.

@alanf next time, please, tell me the issues one by one. It's more effective, it economizes your time and mine. O.K.?

OK.

@alanf You say Since the measure doesn't change over time, it is not the case that whole universes worth of matter are being created. Rather, instances of that matter that were initially the same become different over time. Can you tell me, how many universes exist, right now?

I can put rough bounds on how many distinguishable versions of me there could be and likewise for any particular system you care to name.

For well controlled and understood experimental systems it may be possible to do a lot better.

@alanf yes, and what are those bonds?

Roughly the relevant bound would be that the entropy of the system is the log of the number of distinguishable states. For calculations of bounds on the entropy under various circumstances see Bekenstein Universal upper bound on the entropy-to-energy ratio for bounded systems Phys. Rev. D 23, 287.

@alanf universes necessary to explain experiments done in other labs are additional universes?

To explain experiments in lab A, you generally need multiple versions of lab A, likewise for lab B. Unless there is some entanglement between the two labs, the number of universes as a result of the experiments will be something like the product of the number of versions of each lab.

@alanf Aaaaaa! So, with each new lab, new universes!!! If a new lab is built, new universes should appear?!

@Sofia: If you had not built the new lab, then something would have been happening in the region where you built the lab, and there would be multiple versions of whatever is happening. So whether the new lab results in more or fewer universes is unclear.

@alanf What would have been happening? Does someone, or something, guess my intention to build a lab? Or, putting otherwise, I (or we) don't have free will? I build a new lab because so I am predetermined?

@Sofia: If you want to build a lab, you buy or lease some land. If you don't buy or lease the land, something else will happen there. Maybe weeds will grow, or cats will fight, or somebody will put up a shop. Exactly what would happen is not predictable in general.

@sofia: It is not predictable because the growth of knowledge is unpredictable: you can't know today what you will know tomorrow. There may be some set of initial conditions from which you could in principle predict the quantum state of the region if you had large enough computer.

@alanf we talk about universes, which seem, by what you say, to be already available when we build a new lab. How so?

@alanf isn't it reasonable to think that all these universes were created simultaneously with our one?

@Sofia: If you consider a particular version of some system, like me, then that version of me can be described by a measured set, like the set of real numbers. That set becomes differentiated into two distinct versions over time, as you could distinguish two halves of a line by drawing a mark half way across the line.

Those distinguishable versions are distinct universes. Before the differentiation the two versions of me can still undergo interference and that sort of thing in principle, although in practice this doesn't happen as a result of decoherence.

@alanf how much matter is necessary to differentiate two versions of you? And when does the additional version appear?

@alanf are you aware that you are two-fold?

@alanf I'd like to answer some question.

@Sofia: No additional matter is necessary. What happens is that two versions of me that were initially identical become different.

@Sofia: The two different versions of me can't exchange information, so I can't know what's happening to him, except that it won't break energy conservation and that sort of thing.

@Sofia: If you have further questions you can e-mail me at the address on my profile page physics.stackexchange.com/users/28512/alanf

@alanf no need, I am here!

@Danu please see, can you come here?

@Danu so, the problem is which charges are on the internal sides of the two metal plates.

@Danu, but do you see my words?

Okay, got it!

@Sofia it makes no sense to me that you're in this room, but okay :P

@Sofia it is of no use to ping me (or anyone else) if I haven't been in the room before

Only when I've talked in a room at some point during the past 48 hours or so will the system 'ping' me

This is signified by the fact that my name will pop up when you type part of "@Danu"

if it doesn't it means I won't be pinged

:)

Secret chat?