There must be something that you have fundamentally misunderstood. I will try to clear up some aspects that I think may cause this confusion.
First of all, the scattering processes presented in the paper are very generic to demonstrate the range of possible processes. The blog contains a specific realization which you may find closer to known physical processes.
Let me explain in detail again what this section is about, maybe this will help to overcome our misunderstanding. A photon scatters on a single qubit. The photon and the qubit each bring in a two dimensional state space and the scattering process is unitary and agrees with conservation laws. The state of the qubit before the interaction is known, the state of the photon is external to the observer’s system and therefore entirely unknown, and it is independent of the state of the qubit.
The result of the scattering process is traced over the external outgoing photon states to get a local objective state operator. You then write I apply the Born rule, but that’s really exactly what I don’t do. I use the earlier derived fact that a local observer can only reconstruct the eigenstate with the greatest eigenvalue. This will result in getting either the qubit’s |0> or |1> state.
In order to get the exact probability distribution of these outcomes you have to assume exactly nothing about the state of the photon, because it is entirely unknown. If you assume nothing then all polarizations are equally likely, and you get an SU(2) invariant distribution of the coefficients. That’s all. There are no assumptions whatsoever about the generation of the photons, them being thermal or anything. Just that all polarizations are equally likely. This is a very natural assumption and hard to argue against. The result in then not only the Born rule but also an orthogonal basis which the outcomes belong to.
So if you accept the derivation that the dominant eigensubspace is the relevant state description for a local internal observer and you accept that the state of the incoming photons is not known, then the Born rule follows for certain scattering processes. If you use precisely the process described in my blog is up to you. It merely stands for a class of processes that all result in the Born rule.
You don’t need any modification of quantum mechanics for that. Why do you think you would? Also, this is not just a random combination of algebraic conditions and random distributions. Th assumption about the state distribution of the photon is the only valid assumption if you don’t want to single out a specific photon polarization basis. And all the results are consequences of local observation and unitary interactions.
Have you worked through my blog posts from the beginning in the meantime? I ask because I was hoping that they describe all this very clearly. Please let me know if you disagree with how the internal observer reconstructs the quantum state, because I think that’s the problem here.
I understand that you have an algebraic derivation of Born probabilities, but what I’m saying is that I don’t see how to make that derivation physically meaningful. I don’t see how it applies to an actual experiment.
Consider a Stern-Gerlach experiment. A state is prepared, sent through the apparatus, and the electron is observed coming out one way or the other. Repeat the procedure with identical state preparation, and you can get a different outcome.
For Copenhagen, this is just a routine application of the Born rule.
Suppose we try to explain this outcome using decoherence. Well, now we are writing a wavefunction for the overall system, measuring device as well as measured object, and we can show that the joint wavefunction splits into two parts which are entirely decohered for all practical purposes, corresponding to the two different outcomes. But you still have to apply the Born rule to “obtain” a specific outcome.
Now how does your idea explain the facts? I really don’t see it. At the level of wavefunctions, each run of the experiment is the same, whether you look at just the wavefunction of the individual electron, or at the joint wavefunction of electron plus apparatus. How do we get physically different outcomes? Apparently it requires these random scattering events, that do not feature at all in the usual analysis of the experiment.
Are you saying that the electron that has passed through the Stern-Gerlach apparatus is really in a superposition, but for some reason I only see it as being located in one place, because that’s the “dominant eigenstate”? Does this apply to the whole apparatus as well—really in a superposition, but experienced as being in a definite state, not because of decoherence, but because of scattering + my epistemic limitations??
This would be a lot simpler if you weren’t avoiding my questions. I have asked you whether you have understood and accept the derivation of the dominant eigenstate as the best possible description of the state of a system that the observer is part of. I have also asked if you have read my blog from the beginning, because I need to know where your confusion about what I am saying comes from.
The Stern Gerlach experiment goes like this in my theory: The superposition of the spins of the silver atoms must be collapsed already at the moment the beam splits up, because a much later collapse would create a continuous position distribution. That also means a Copenhagen-like act of observation cannot happen any later, specifically not at a screen. This is a good indication that not observation itself forces the silver atoms to localize but something else, that relates to observation but is not the act of looking at it.
In the system that contains the experiment and the observer, the observer would always “see” a state that belongs to the dominant eigenstate of the objective state operator of that system. It doesn’t really matter if in that system the observer is entangled with the spin state or not. As soon as you apply the field to separate the silver atoms you also create an energy difference (which is also flight time dependent and scans through a rather large range of possible resonant frequencies). The photons in the environment that are out of the observer’s direct observation and unknown to him begin to interact with the two spin states, and some do in a way that creates spin flips, with absorption and stimulated emission, or just shake the atom a little bit. The sum of these interactions can create a total unitary evolution that creates two possible eigenvectors of the state operator, one containing each spin z-eigenstate and a probability for each to be the dominant eigenstate that goes conform with the Born rule. That includes the assumption that the photon states from the environment are entirely unknown. The scattering process I give in my blog shows that such a process is possible and has the right outcome. The dominant eigenstate of the system containing the observer is then the best description of reality that this observer can come up with. Or in other words, he sees either spin up or down and their trajectories.
If you accept the fact that an internal observer can only ever know the dominant eigenstate then state jumps with unknown/random outcome are a necessary consequence. That the statistics of those jumps is the Born rule for events that involve unknown photons is also a direct consequence. And all that follows just from unitary evolution of the global state and the constraints by locality and unitarity on the observer. So please tell me which of the derived steps you do not accept, so that we can focus on it. And please point me to exactly where in the blog the offending statement is.
Earlier, I should have referred to the calculation as being in part IV, not part V. I’ve read part V only now—including the stuff about “branch switching” and how “The observer can switch between realities without even noticing, because all records will agree with the newly formed reality.” When I said these ideas led towards “stochastic, piecewise-linear Bohmian mechanics”, I was more right than I knew!
Bohmian mechanics is rightly criticised for supposedly being just a single-world theory, yet having all those other world-branches in the pilot wave. If your account of reality includes wavefunctions with seriously macroscopic superpositions, then you either need to revise the theory so it doesn’t contain such wavefunctions, or you need to embrace some form of many-world-ism. Supposing that “hidden reality branches” exist, but don’t get experienced until your personal stream-of-consciousness switches into them, is juvenile solipsism.
If that is where your theory leads, then I have little interest in continuing this discussion. I was suspicious from the beginning about the role that the “subjectively reconstructed state of the universe” was playing in your theory, but I didn’t know exactly what was going on. I had hoped that by discussing a particular physical setup (Stern-Gerlach), we would get to see your ideas in action, and learn how they work by demonstration. But now it seems that your outlook boils down to quantum dualism in a virtual multiverse. There is a subjective history which is a series of these “dominant eigenstates”, plucked from a superposition whose other branches are there in the wavefunction, but which aren’t considered fully real unless the subjective history happens to jump to them.
There is some slim possibility that your basic idea could play a role in the local microscopic dynamics of a new theory, distinct from quantum mechanics but which produces quantum mechanics in a certain limit. Or maybe it could be the basis of a new type of many-worlds theory. But branch-switching observers is ridiculous and it’s a reductio ad absurdum of what you currently offer.
ETA: I would really like to know what motivates the downvote on this comment. Is there someone out there who thinks that a theory of physics in which “the observer” can “switch”, from one history, to another in which all memories and records have been modified to imply a different past, is actually worth considering as an explanation of quantum mechanics? I’m not exaggerating; see page 11 here, the final paragraph of part V, section A.
You keep ignoring the fact that the dominant eigenstate is derived from nothing but the unitary evolution and the limitations of the observer. This is not a “new theory” or an interpretation of any kind. Since you are not willing to discuss that part your comments regarding the validity of my approach are entirely meaningless. You criticize my work based on the results which are not to your liking, and not with respect to the methods used to obtain these results. So I beg you one last time, let us rationally discuss my arguments, and not what you believe is a valid result or not. If you can show my arguments to be false beyond any doubt, based on the arguments that I use in my blog, or alternatively, if you can point out any assumptions that are arbitrary or not well founded I will accept your statement. But not like this. If you claim to be a rationalist then this is the way to go.
Any other takers out there who are willing to really discuss the matter without dismissing it first?
Edit :
And just for the record, this has absolutely nothing to do with Bohmian mechanics. There is no extra structure that contains the real outcomes before measurement or any such thing. The only common point is the single reality.
Furthermore, your quote of page 11 leaves out an important fact. Namely that the switching occurs only for the very short time history where the dominant eigenstates interact and stabilizes for the long term, meaning within a few scattering events of which you probably experience billions every second. There is absolutely no way for you to switch between dominant eigenstates with different memories regarding actual macroscopic events.
There must be something that you have fundamentally misunderstood. I will try to clear up some aspects that I think may cause this confusion.
First of all, the scattering processes presented in the paper are very generic to demonstrate the range of possible processes. The blog contains a specific realization which you may find closer to known physical processes.
Let me explain in detail again what this section is about, maybe this will help to overcome our misunderstanding. A photon scatters on a single qubit. The photon and the qubit each bring in a two dimensional state space and the scattering process is unitary and agrees with conservation laws. The state of the qubit before the interaction is known, the state of the photon is external to the observer’s system and therefore entirely unknown, and it is independent of the state of the qubit.
The result of the scattering process is traced over the external outgoing photon states to get a local objective state operator. You then write I apply the Born rule, but that’s really exactly what I don’t do. I use the earlier derived fact that a local observer can only reconstruct the eigenstate with the greatest eigenvalue. This will result in getting either the qubit’s |0> or |1> state.
In order to get the exact probability distribution of these outcomes you have to assume exactly nothing about the state of the photon, because it is entirely unknown. If you assume nothing then all polarizations are equally likely, and you get an SU(2) invariant distribution of the coefficients. That’s all. There are no assumptions whatsoever about the generation of the photons, them being thermal or anything. Just that all polarizations are equally likely. This is a very natural assumption and hard to argue against. The result in then not only the Born rule but also an orthogonal basis which the outcomes belong to.
So if you accept the derivation that the dominant eigensubspace is the relevant state description for a local internal observer and you accept that the state of the incoming photons is not known, then the Born rule follows for certain scattering processes. If you use precisely the process described in my blog is up to you. It merely stands for a class of processes that all result in the Born rule.
You don’t need any modification of quantum mechanics for that. Why do you think you would? Also, this is not just a random combination of algebraic conditions and random distributions. Th assumption about the state distribution of the photon is the only valid assumption if you don’t want to single out a specific photon polarization basis. And all the results are consequences of local observation and unitary interactions.
Have you worked through my blog posts from the beginning in the meantime? I ask because I was hoping that they describe all this very clearly. Please let me know if you disagree with how the internal observer reconstructs the quantum state, because I think that’s the problem here.
I understand that you have an algebraic derivation of Born probabilities, but what I’m saying is that I don’t see how to make that derivation physically meaningful. I don’t see how it applies to an actual experiment.
Consider a Stern-Gerlach experiment. A state is prepared, sent through the apparatus, and the electron is observed coming out one way or the other. Repeat the procedure with identical state preparation, and you can get a different outcome.
For Copenhagen, this is just a routine application of the Born rule.
Suppose we try to explain this outcome using decoherence. Well, now we are writing a wavefunction for the overall system, measuring device as well as measured object, and we can show that the joint wavefunction splits into two parts which are entirely decohered for all practical purposes, corresponding to the two different outcomes. But you still have to apply the Born rule to “obtain” a specific outcome.
Now how does your idea explain the facts? I really don’t see it. At the level of wavefunctions, each run of the experiment is the same, whether you look at just the wavefunction of the individual electron, or at the joint wavefunction of electron plus apparatus. How do we get physically different outcomes? Apparently it requires these random scattering events, that do not feature at all in the usual analysis of the experiment.
Are you saying that the electron that has passed through the Stern-Gerlach apparatus is really in a superposition, but for some reason I only see it as being located in one place, because that’s the “dominant eigenstate”? Does this apply to the whole apparatus as well—really in a superposition, but experienced as being in a definite state, not because of decoherence, but because of scattering + my epistemic limitations??
This would be a lot simpler if you weren’t avoiding my questions. I have asked you whether you have understood and accept the derivation of the dominant eigenstate as the best possible description of the state of a system that the observer is part of. I have also asked if you have read my blog from the beginning, because I need to know where your confusion about what I am saying comes from.
The Stern Gerlach experiment goes like this in my theory: The superposition of the spins of the silver atoms must be collapsed already at the moment the beam splits up, because a much later collapse would create a continuous position distribution. That also means a Copenhagen-like act of observation cannot happen any later, specifically not at a screen. This is a good indication that not observation itself forces the silver atoms to localize but something else, that relates to observation but is not the act of looking at it. In the system that contains the experiment and the observer, the observer would always “see” a state that belongs to the dominant eigenstate of the objective state operator of that system. It doesn’t really matter if in that system the observer is entangled with the spin state or not. As soon as you apply the field to separate the silver atoms you also create an energy difference (which is also flight time dependent and scans through a rather large range of possible resonant frequencies). The photons in the environment that are out of the observer’s direct observation and unknown to him begin to interact with the two spin states, and some do in a way that creates spin flips, with absorption and stimulated emission, or just shake the atom a little bit. The sum of these interactions can create a total unitary evolution that creates two possible eigenvectors of the state operator, one containing each spin z-eigenstate and a probability for each to be the dominant eigenstate that goes conform with the Born rule. That includes the assumption that the photon states from the environment are entirely unknown. The scattering process I give in my blog shows that such a process is possible and has the right outcome. The dominant eigenstate of the system containing the observer is then the best description of reality that this observer can come up with. Or in other words, he sees either spin up or down and their trajectories.
If you accept the fact that an internal observer can only ever know the dominant eigenstate then state jumps with unknown/random outcome are a necessary consequence. That the statistics of those jumps is the Born rule for events that involve unknown photons is also a direct consequence. And all that follows just from unitary evolution of the global state and the constraints by locality and unitarity on the observer. So please tell me which of the derived steps you do not accept, so that we can focus on it. And please point me to exactly where in the blog the offending statement is.
Earlier, I should have referred to the calculation as being in part IV, not part V. I’ve read part V only now—including the stuff about “branch switching” and how “The observer can switch between realities without even noticing, because all records will agree with the newly formed reality.” When I said these ideas led towards “stochastic, piecewise-linear Bohmian mechanics”, I was more right than I knew!
Bohmian mechanics is rightly criticised for supposedly being just a single-world theory, yet having all those other world-branches in the pilot wave. If your account of reality includes wavefunctions with seriously macroscopic superpositions, then you either need to revise the theory so it doesn’t contain such wavefunctions, or you need to embrace some form of many-world-ism. Supposing that “hidden reality branches” exist, but don’t get experienced until your personal stream-of-consciousness switches into them, is juvenile solipsism.
If that is where your theory leads, then I have little interest in continuing this discussion. I was suspicious from the beginning about the role that the “subjectively reconstructed state of the universe” was playing in your theory, but I didn’t know exactly what was going on. I had hoped that by discussing a particular physical setup (Stern-Gerlach), we would get to see your ideas in action, and learn how they work by demonstration. But now it seems that your outlook boils down to quantum dualism in a virtual multiverse. There is a subjective history which is a series of these “dominant eigenstates”, plucked from a superposition whose other branches are there in the wavefunction, but which aren’t considered fully real unless the subjective history happens to jump to them.
There is some slim possibility that your basic idea could play a role in the local microscopic dynamics of a new theory, distinct from quantum mechanics but which produces quantum mechanics in a certain limit. Or maybe it could be the basis of a new type of many-worlds theory. But branch-switching observers is ridiculous and it’s a reductio ad absurdum of what you currently offer.
ETA: I would really like to know what motivates the downvote on this comment. Is there someone out there who thinks that a theory of physics in which “the observer” can “switch”, from one history, to another in which all memories and records have been modified to imply a different past, is actually worth considering as an explanation of quantum mechanics? I’m not exaggerating; see page 11 here, the final paragraph of part V, section A.
You keep ignoring the fact that the dominant eigenstate is derived from nothing but the unitary evolution and the limitations of the observer. This is not a “new theory” or an interpretation of any kind. Since you are not willing to discuss that part your comments regarding the validity of my approach are entirely meaningless. You criticize my work based on the results which are not to your liking, and not with respect to the methods used to obtain these results. So I beg you one last time, let us rationally discuss my arguments, and not what you believe is a valid result or not. If you can show my arguments to be false beyond any doubt, based on the arguments that I use in my blog, or alternatively, if you can point out any assumptions that are arbitrary or not well founded I will accept your statement. But not like this. If you claim to be a rationalist then this is the way to go.
Any other takers out there who are willing to really discuss the matter without dismissing it first?
Edit : And just for the record, this has absolutely nothing to do with Bohmian mechanics. There is no extra structure that contains the real outcomes before measurement or any such thing. The only common point is the single reality. Furthermore, your quote of page 11 leaves out an important fact. Namely that the switching occurs only for the very short time history where the dominant eigenstates interact and stabilizes for the long term, meaning within a few scattering events of which you probably experience billions every second. There is absolutely no way for you to switch between dominant eigenstates with different memories regarding actual macroscopic events.