Author Mikalai Birukou replied on Apr. 27, 2013 @ 16:44 GMT
Thank you, this was a long effort. Chalk board is so much easier :).
Definitely, i should be on the W, cause when pair decoheres on W, quite particular info gets distilled into it. Normally, we miss this index, cause we abstract such details away. We think of environment like of a huge sink, right? But huge sinks do change their temperature, too.
What we refer of projection postulate, is definitely coming out of postulate 3, just like in Everett's thesis. But it shows from which postulate, which element of QM math is coming.
Yes, looking at the post, it is cut. All that I do not see now is a density matrix for pure state displayed, with saying that this should be used, but not mixed option (2) of your original post.
Jochen Szangolies replied on Apr. 27, 2013 @ 17:26 GMT
But then this highlights my troubles: if the index is there, you'll have to explain why in the end, we don't get the state
which the usual unitary quantum dynamics would produce. In the orthodox formulation, this is 'solved' by declaring that if there's been a measurement, the state collapses to either of the terms. This of course strikes most people as arbitrary: what counts as a measurement, and what doesn't?
Now you effectively want to get rid of that arbitrariness by stipulating that this in fact happens in every interaction, but that fact is 'hidden' to the outside world, which thus still needs to use the superposition in describing the system. Every interaction is a measurement, but not everybody gets told about it---only the interacting systems do.
The problem is, however, that if you declare that I should use the superposed state in calculating averages, then you're really in the same boat as the orthodox interpretation: the state the interacting systems see does not have any influence on the outcome of an interaction with a further system. That is, if lab and qubit 'see' each other in the state |L
0>|0>, then nevertheless, any external system interacting with them must have a 50% probability to measure the state |L
1>|1>, and thus, end up in the total state |W
1>|L
1>|1>. So, I mean, you haven't really won anything, have you?
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Author Mikalai Birukou replied on Apr. 28, 2013 @ 10:49 GMT
Stop, in W's perspective OR applies to W, but you replaced OR with +. This then must be a new perspective of a system that has no interactions with W, which was world, in a context of our discussion. You must pay attention to whose perspective it is, and put OR or + respectively.
Again, in the perspective with OR (classical OR), with all pronounced context, you just slipped an inch, replaced it with + (quantum OR), and start to claim that there is a problem again. You just cannot jump over this detail. Such jump is harmless in classical info flow, when vector multiplication is distibutative with respect to OR, but this is not how nature works at fundamental quantum level.
Author Mikalai Birukou replied on Apr. 28, 2013 @ 11:49 GMT
Since it is so easy for you to slip between OR and +, and accidentally switch a perspective, then, may be we should try to have an explicit indication of a perspective.So, when we write some expression, we assume a perspective, from which we make a statement. Let's try,
Indecies on brackets indicate in whose perspective expression in brackets is written in. Then the left side along can be seen as
meaning that it is one thing, seen from different perspectives.
Now perspective is explicit, and it is more difficult to accidentally switch.
Author Mikalai Birukou replied on Apr. 28, 2013 @ 12:04 GMT
Looking at this additional visual aid in equation, I find myself to like it. This highlights relative state concept soo much. And it is an easy rule, switching + to OR can be done only with proper switch of perspective index. And in brackets we may have density matrices, related to proper perspective. So, in identity above, with different perspective brackets, matrix inside W-bracket (W-perspective) shall be pure-state, but inside L-bracket, it will be mixed.
Yes. We should not be shy to find new ways of mathematical expressions. After all, it is man maid tool, for man's consumption.
Jochen Szangolies replied on Apr. 28, 2013 @ 12:22 GMT
I must confess that I'm pretty uncomfortable with your use of 'or'---typically, one would not speak about logical connectives regarding state vectors, but regarding properties represented using projection operators or closed linear subspaces of Hilbert space (which are of course one-to-one). Also, I presume when you say 'vector multiplication', you mean tensor multiplication.
But the issue...
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I must confess that I'm pretty uncomfortable with your use of 'or'---typically, one would not speak about logical connectives regarding state vectors, but regarding properties represented using projection operators or closed linear subspaces of Hilbert space (which are of course one-to-one). Also, I presume when you say 'vector multiplication', you mean tensor multiplication.
But the issue is quite simple: there's effectively two states to any given system, call this the internal and external states. The internal state is the one which according to your postulate 3 is always definite, and is the one the qubits see; the external state is the (in general, superposed) quantum state which the rest of the world assigns to the system.
First, we'll take the perspective of the rest of the world. If we measure a Bell inequality on the system, then, since things occur according to the external state, we will find it to be violated. This entails that, for instance, measuring both qubits in the {|0>,|1>}-basis, there is a 50% chance to get 0 for both, or 1 for both.
But now let's look at this from the internal perspective---say one qubit now plays the role of the lab. I, in my lab, have made a measurement on a qubit, and have received the value 0. Being 'confined' from the rest of the world means that the rest assigns to me, the lab, and the qubit the state
while I assign the state
But now, if I open my lab doors to the rest of the world, so to speak, there must be a 50% chance that it finds me and the qubit in the state
since previously it assigned the state (1), and this is the state that governs the dynamics from its point of view.
So either of two things must happen: 1) the state of my lab and the qubit changes to the state as perceived by the outside world in a bit of Orwellian revisionism ('we have always been at war with Eurasia'), or 2) I continue to ascribe the state (2) to myself and the qubit, while the rest of the world ascribes (3). Both cases, I think, aren't better off than standard collapse dynamics (and I'm not sure that the latter case is even consistent).
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Jochen Szangolies replied on Apr. 28, 2013 @ 13:07 GMT
OK, I think I can state the problem in your language now.
As you've given the rules, they are:
[equation]
where I've not distinguished between which qubit is the 'lab' and which is the measured one, since that distinction is immaterial, but have kept the index L to denote what I've called the 'internal' perspective. I also presume that the following...
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OK, I think I can state the problem in your language now.
As you've given the rules, they are:
where I've not distinguished between which qubit is the 'lab' and which is the measured one, since that distinction is immaterial, but have kept the index L to denote what I've called the 'internal' perspective. I also presume that the following holds:
since once both lab and world have interacted, their perspectives match.
Furthermore, we have:
where I've omitted the inessential normalization factor to de-clutter notation. (1) and (3) are supposed to say the same thing, just from different perspectives.
Now let's look again at (1), but write it in the {|+>,|->}-basis:
But now let's start from (3) and do the same thing:
This is clearly very different from the outcome in (4). But with (2), they should be the same! All I've done is a change of basis, which I can always do, and as you can see, the accounts (1) and (3) no longer agree. On (4), the account from the point of view of L, there will be no Bell violation; while on (5), the account from the point of view of W, there will (which is as it should be).
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Author Mikalai Birukou replied on Apr. 28, 2013 @ 13:43 GMT
I'll buy (3). You just put W'. I thought that W without mark, like initial one on the right will be more proper, and when you look deeper for W_i's, we shall have their own W_i's perspectives, expanding inside, under OR operator. In this expansion, of further and further interactions, we may construct a chain, but this might be a topic in itself, on how it will compare with Markov's chains (I am just dropping a possible avenue of exploration, without any deep thinking at this moment).
I do not yet buy (1), as W (external system) is drawn into L's (qubit's) perspective, but I just never thought about such thing. There must be symmetry, but do you care of qubit's perspective on world? This should be looked in details, as it is usual with newly introduced notations.
Have you just changed 0/1 to +/-, or have you actually changed basis? Since there is a non-distributivity of vector multiplication with respect to OR operator, change of bases should be shown to be proper under OR.
Yes, (5) is an interaction in the perspective of interacting system, and it is not unitary.
Author Mikalai Birukou replied on Apr. 28, 2013 @ 13:48 GMT
Yes, thinking about it further, (1) is correct, as L perspective, from a qubit on how world interacts with it.
Jochen Szangolies replied on Apr. 28, 2013 @ 15:30 GMT
Sorry for the confusion---the mark on the L and W is just a comma after the equation. And yes, I've performed the same change of basis in both cases (recall that in the {|+>,|->}-basis, |0> = |+> + |-> and |1> = |+> - |->, again leaving aside normalization).
As for the nondistributivity, I'm afraid the point is lost on me. If it's a proper or, how can there not be distributivity? (Yes, I know this---or something like it---is the case in quantum logic, but we're not reasoning about quantum properties here---in fact, your reconstruction can be seen as an attempt to interpret quantum properties classically.)
If, in one situation, you have the state |00> or |11>, and the world comes into contact with this state, then you have the state |W
0>|00> or |W
1>|11>, since in each individual case, you'd either have the state |W
0>|00> (if the prior state was |00>), or the state |W
1>|11> (if the prior state was |11>).
But if the issue is contentious, I can just as well perform the basis transformation after the world has come into contact with the system, the argument will go through regardless.
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Author Mikalai Birukou replied on Apr. 29, 2013 @ 20:59 GMT
I want to recall Schmidt's decomposition in light of our postulates.
We take a general case with lab (L) and two systems \psi and \phi. Let systems interact so that lab is not involved, i.e. have an internal interaction in a composite system that consists of \psi and \phi:
[equation]
each i-th outcome of internal interaction happens with probability p_i. Let's then update...
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I want to recall Schmidt's decomposition in light of our postulates.
We take a general case with lab (L) and two systems \psi and \phi. Let systems interact so that lab is not involved, i.e. have an internal interaction in a composite system that consists of \psi and \phi:
each i-th outcome of internal interaction happens with probability p_i. Let's then update coefficients on the right side under the OR operator
with definition
and due to sum of probabilities of all outcomes being equal to 1, have
So, looking at all of this from lab's (L) perspective, we have
Decomposition into i-th states with coefficients defined on probabilities, gives Schmidt's decomposition.
The right hand side can be seen as action of unitary U on initial state of a composite system
The right hand side of \psi and \phi perspectives can be seen as application of projective operators P's (capital letter, vs. small for probabilities), acting onto respective systems:
And this provides us, through the same coefficients, with a more rigorous relation between projection operators that systems see, and a unitary action that lab sees.
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Jochen Szangolies replied on Apr. 30, 2013 @ 05:43 GMT
Hm, how do you think (or do you think?) that helps with the problem? After all, {|0>,|1>} and {|+>,|->} *are* Schmidt bases for the state we've been considering (since it doesn't have full Schmidt rank, the decomposition is not unique)...
But even if that weren't the case, the problem persists if you now let an outside system come in: you can't oblige the outside world to measure only in the (particular) Schmidt basis you've selected as preferred, so one will always run into the inconsistency I pointed out.
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Jochen Szangolies replied on Apr. 30, 2013 @ 05:48 GMT
Ah sorry, I'm not quite awake yet: of curse the Schmidt rank of the state is maximal, it's its degeneracy (all coefficients equal to 1/\sqrt{2}) that makes the decomposition be non-unique...
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Author Mikalai Birukou replied on Apr. 30, 2013 @ 12:53 GMT
This description relates internal interaction to a particular form seen from outside, which happens to be Schmidt's mathematical decomposition. And with actual values for \lambda's it paves way of relating both internal and external perspective, using probabilities, the actual thing that physically matters. And since probabilities are used, the whole argument about relative perspectives gets more precise and digestible.
Jochen Szangolies replied on Apr. 30, 2013 @ 13:55 GMT
But this does not solve---or even address---the problem that (1) and (3) in my prior post, which should be always the same, or at least consistent with one another, in order for your account to work, disagree if something as simple as a change of basis is performed: on one account, you get entanglement, and on the other, you don't.
I mean, if you insist, I can rewrite the argument keeping the probabilities explicit, but I can give you the punchline: with a probability of 50%, if the view from the lab (the 'inside view' in my posts) is correct, the world will see a measurement outcome inconsistent with the state it assigns to the system (i.e. +- or -+ with the state being |++> + |-->).
Or am I missing your point?
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Author Mikalai Birukou replied on Apr. 30, 2013 @ 14:22 GMT
In (1) and (3), we had L, by inertia from another previous post, while L was switched to 1, making it a bit confusing (lab->to->qubit), especially, when you look at it two days after. Lets approach it in a clean and general manner, with \psi, \phi and Lab.
We get an entanglement, when we make an internal interaction between \psi and \phi, which can be viewed, from inside, as a measurement in a rotated basis. This basis is directly related with interaction setup. This is to say that entanglement arises out of physical setup, but not as a mere basis transformation. And, let's not forget, it is an external system (lab) that sees entanglement, which is why on experimentation we worry about spontaneous, unwanted decoherence, and on theorising we worry about perspectives, in which descriptions are done.
Jochen Szangolies replied on Apr. 30, 2013 @ 15:01 GMT
OK, I'll do it with psi, phi, the lab, and even keeping the Schmidt coefficients. The only thing, for simplicity, I'll continue to assume that psi and phi are qubits; this is only for notational convenience, and any generalization is straightforward. I'll denote the 'qubit frame' with Q, and the lab frame with L.
(1) Becomes:
[equation]
[equation]
This is essentially...
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OK, I'll do it with psi, phi, the lab, and even keeping the Schmidt coefficients. The only thing, for simplicity, I'll continue to assume that psi and phi are qubits; this is only for notational convenience, and any generalization is straightforward. I'll denote the 'qubit frame' with Q, and the lab frame with L.
(1) Becomes:
This is essentially the lab making a measurement on the qubits, which see themselves in the sate |00> or |11>, and receiving as a result either the values 00 or 11---things are as they should be.
The same as viewed from the lab frame is now:
The lab, assigning originally an entangled state to the qubits, performs a measurement, and ends up either having measured 00 or 11, and as part of the interacting system, now in a definite state. This far, all's well.
Now we make the basis change again. This amounts to nothing but the lab changing the measurement basis. To be perfectly clear here, let's write down how the states transform:
For the starting point in eq. (1), this means:
Nothing's been done here, no physical interaction occurred. Similarly, for the starting point in eq. (2):
And again, I've done nothing except for the basis transformation. But it's already completely clear what'll happen: measurement in (3) leads to each of ++, +-, -+, -- being observed with 25% probability, but in (4) it leads to only ++ or -- occurring, with 50% probability (which, needless to say, is the correct result if both qubits are entangled).
The bottom line is simply that you can't take the qubits as 'seeing each other' in the state at the beginning of (1); entanglement is not reference dependent. If you split apart the qubits by brute force, you break the entanglement, with observable consequences. If you want the lab to see the qubits as being entangled, they must actually be entangled.
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Author Mikalai Birukou replied on Apr. 30, 2013 @ 19:19 GMT
Let's repeat steps that brought us to (1). First we had two qubits, one |0>, another |+>, and they interact, so that lab is not involved. Qubit's perspective is the same for either qubit, so will put Q, but keep in mind that it is either 1st qubit's perspective, or the second's one:
[equation]
Qubits change their state, and they become only one or the other possibility. And I...
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Let's repeat steps that brought us to (1). First we had two qubits, one |0>, another |+>, and they interact, so that lab is not involved. Qubit's perspective is the same for either qubit, so will put Q, but keep in mind that it is either 1st qubit's perspective, or the second's one:
Qubits change their state, and they become only one or the other possibility. And I want stress that word "become" is applicable to a particular perspective, i.e. not globally.
Any further interaction, from qubits' perspective, should take into account that the first interaction have happened. But first interaction, by virtue of active change of systems, have split initial perspective into two. So, second interaction can be seen from zeroth qubit perspective as
the oneth qubit perspective will respectively be
but in lab's perspective we have
and, since lab has not been changing as a result of the 1st interaction, which is internal to qubits only, the L's perspective stays the same, and may be applied to the 2nd interaction, now involving the lab:
From this point, to describe anything further from lab's point of view, we should do it from either L0 or L1 perspectives.
So, let's make a clarification in a use of perspective brackets. Every perspective is good for predicting anything up to and including the first interaction. Interaction changes the system, and it forces a change in info perspective.
With this in mind, (4) in your ost is all fine, and in (1) Q's perspective is recycled second time, which we should not do. Its very nice that you fleshed this out, as it provides clarification to our formalism here.
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Author Mikalai Birukou replied on Apr. 30, 2013 @ 20:27 GMT
Let's take "measurement" #2 in +/-, while leaving internal "measurement" #1 as it was in 0/1. Now, in +/- second measurement, lab gets a terms ++ or --. Let's take ++. it may come from perspective Q0 or perspective Q1. But because it is indistinguishable from where ++ came, when we repeat experiments, ++ coming from Q0 or Q1 will add to the same term, producing statistics, which is different form the statistics where choice between Q0 and Q1 is fixed globally for all systems. This global fixing, is our classical OR at play in a chain of events. But, nature prefers locality of info (interaction confinement), which gives statistics of entangled pair in our case.
This, it seems to me, is the reason for OR in Q's perspective to be seen by external non-interacting system L as a plus, for which usual linear algebra's distibutivity works.
Jochen Szangolies replied on Apr. 30, 2013 @ 20:30 GMT
But in your second and third 'qubit perspective' equations, I can just make the change of basis, no? And then we're right back in the same muddle. After all, we must have a consistent description from all possible perspectives.
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Jochen Szangolies replied on May. 1, 2013 @ 07:54 GMT
Didn't see your second post yesterday, you posted almost at the same time as I did. You say:
"Now, in +/- second measurement, lab gets a terms ++ or --."
And then you assert that this is true from the Q-perspective. But according to the equations you wrote down, that doesn't seem to be the case: if I just rewrite your second and third equations as
and
I don't seem to be able to figure out why the +- and -+ results should be prohibited! Remember, after all's said and done, the qubits and the lab are 'one interacting system', so you should be able to describe their interaction from either perspective and come to the same result---but the way you write things, I can't see how that should be possible.
Perhaps you could just write how, from the qubit perspective, the lab's measurement in the +/- basis looks, if the qubits take themselves to be in the state |00> or |11>?
Furthermore, it's problematic, I think, for you to stipulate that one qubit sees the two qubits in the |00> state, while the other sees both in the |11> state. These will both evolve differently, and I'm not sure I can attach meaning to one qubit seeing the other evolve in a way that it does not see itself evolve in... Seems to me as confusing as the usual measurement troubles.
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Author Mikalai Birukou replied on May. 1, 2013 @ 14:14 GMT
And this cancelation of -+ and +- is a result of having unchanged L's perspective, while Q was broken into Q0 and Q1. As I said before, we do not have words/concepts in our common experience to express HOW results, that should not touch each other in Q(0/1) perspectives, can cancel each other in L's perspective. We just have to accept it from experiment, as we do with constant speed of light.
Author Mikalai Birukou replied on May. 1, 2013 @ 14:32 GMT
Notice, that taking only one of Q's perspectives is something normal for our classical world. And recalling double-slit experiment from essay, Q0 can be a perspective with choice of one slit, and Q1 can be with a choice of another slit. Adding additional counting at a slit, is like making an extra interaction with L in 0/1 basis, which is the same as internal intreaction's basis, before making final interaction on a screen, which is like a measurement in +/-, or rotate basis. And equation 5 in essay is what our classical logic tells us, having either Q0 or Q1, while equation 6 in essay says that 0to1 split does not matter, when seen from the outside.
Let's say that logical insistence that Q(0/1) perspectives must also correspond to L perspective, the way original Q perspective did, is ruled out by experiment. It is a mathematical reasoning branch, which is physically not applicable.
What was special about Q perspective, in comparison to Q(0/1)'s? At the very beginning, before the very first interaction, Q and L were the same and indistinguishable. The exactly one internal interaction happened, after which there is a departure from Q for "internal systems". This is relative state. But, again, with our cognitive experience of homo-sapience, we cannot imagine how this happens. We just postulate this. And interaction confinement postulate, formed on results of an experiment, does the job.
Author Mikalai Birukou replied on May. 1, 2013 @ 14:46 GMT
Reflecting back on all of this, we have a bit more formal approach to postulates 3 and 4 in essay, and we may use experiment with qubits to form postulate 4. I specifically chose double-slits for this essay, to highlight for more general audience that bizarre slits are related to EPR, i.e. it is the same fundamental aspect of nature. But rigorous formulation, with observation of no-show of +-/-+ results, is much simpler.
So, would you like to co-author a paper? :) Your pressure was instrumental in fleshing these details out.
Jochen Szangolies replied on May. 1, 2013 @ 15:20 GMT
OK, so from your posts, it seems like you have reached some sort of conclusion on the issue, which sadly for me is still lacking... What I think you're saying now is that for some reason I can't take the perspective of the qubits when talking about the measurement in the +/- basis, since this disagrees with what we observe. At least that's what I take from you saying:
"Let's say that logical insistence that Q(0/1) perspectives must also correspond to L perspective, the way original Q perspective did, is ruled out by experiment. It is a mathematical reasoning branch, which is physically not applicable."
Is that correct?
If that's the case, then first of all, that's something simply not present in your original formulation; but furthermore, it makes the formulation arbitrary: you can derive consequences from it that disagree with experiment, and to remedy this, you suggest throwing these consequences away. But then it's kinda hard to accept this as a viable theory at all...
Besides, I don't think the Q perspective ever corresponded to the L perspective in the case of measurement in a different basis. And the problem is not a 'relative' one: going from one starting point (say, the perspective of L) simply gives a different result, for L, than going from another (say, the Q-perspective). But since both should be equally valid, the theory simply makes inconsistent predictions.
Or maybe there's a language problem? Can you write down, perhaps, what happens from the qubits' perspective upon measurement in the +/- basis?
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Author Mikalai Birukou replied on May. 1, 2013 @ 19:35 GMT
On "don't think the Q perspective ever corresponded to the L perspective". I am talking about the very-very first setting before any interactions took place. It was just
[equation]
just three system, all in pure states. At this moment Q's and L perspectives have just this. 0 denotes one state, + denotes another, but these are just pure states.
On "If that's the case, then...
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On "don't think the Q perspective ever corresponded to the L perspective". I am talking about the very-very first setting before any interactions took place. It was just
just three system, all in pure states. At this moment Q's and L perspectives have just this. 0 denotes one state, + denotes another, but these are just pure states.
On "If that's the case, then first of all, that's something simply not present in your original formulation". Nope. The postulate 4 is there. We just have a different articulation of it, using perspectives for writing formulas. Think about how qubits experiment tells us (there are no -+/+-'s) not to use classical like succession of perspectives Q->Q(0/1), like we would in classical case. This is the same as double-slits use. Double slits are more dramatic (for essay), but qubits give clean systematic way to tell folk at ICQ which of their experimental statistics is a key for quantum phenomena.
On "Can you write down, perhaps, what happens from the qubits' perspective upon measurement in the +/- basis?". So, looking at 2nd interaction (L's measurement in +/-), should be done from not one qubits' point of view, but from two, Q0 and Q1, simultaneously. There is no way to human-logically join the two, but statistics (absence of -+/+-) says that only L's perspective produces correct result. And L perspective can be connected by us only to Q, but not to Q(0/1). Therefore, may be nature tells that the question is ill-posed. It is a usual-logic branch that leads away from experiment. (Math is not the king, experiment is.)
On "it makes the formulation arbitrary: you can derive consequences from it that disagree with experiment, and to remedy this, you suggest throwing these consequences away". So, we have this tried-and-true in our classical world logic. Using what we have, we assemble a formulation for a phenomenon, which might be different from our usual classical world. Formulation runs into a crossroad. You settle it by looking at experiment. Experiment gives you new mathematical rule, or postulate, which allows us to have a descriptive formalism that works. I see no problem here. Also, let's not forget that entire mathematical apparatus is based on some axioms/postulates anyway, math did not fall from the sky, and there is Godel around this corner ;) .
This, forming math rules to fit experiment, has a taste of how Einstein did SR, by introducing strange rule with light speed constancy, and GR, by introducing equivalence principle, which asked for newer curvilinear manifolds math. Notice also that we do not argue to make new rules for every new experiment. No, we make formulation for one, but key experiment, and rules we get are applicable to all other instances.
I can derive "thermodynamics of blackholes" basing myself on concepts of usual thermodynamics and GR description of spacetime. No need to introduce anything new. A smooth derivation of QM out of classical information concepts, has been shown to be impossible by Bell's theorem (and interaction confinement shows it as well). So, in talking about quantum phenomenon, we do not have a luxury of smooth derivation through endless equality signs. There is abruptness, and it should not be arbitrary, but should be dictated by nature. Yet, we do have a luxury of having a historical meta-insight on how good theories were formed under similar constraints.
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Jochen Szangolies replied on May. 1, 2013 @ 21:11 GMT
The postulate 4 may be there, but it doesn't tell me that I can't describe certain interactions from a certain perspective that should be a perfectly valid one in the theory. I mean, think about the absurdity this entails: you venture to solve the measurement problem by introducing a definite state for interacting systems; but then, you posit that you can't describe any further interaction using this state. Or say you replace one of the qubits with a conscious observer performing measurements: as soon as somebody else were to measure him, his perspective ceases to become valid. That's worse than the original measurement problem ever was: there, one just has an ambiguity in the description; but in your formulation, a certain description is actually false.
And I'm sorry, but simply stipulating that 'everyday logic fails' is a lazy way to solve this issue. With such a sentence, I can make every observation vacuously consistent with every theory; if there is no way to decide from the fundamental principles themselves what the theory actually predicts, it's simply empirically inadequate. Usually, when a theory entails a conclusion that does not agree with experiment, one doesn't question logic, but considers the theory to be falsified.
Besides, if you stipulate that the qubit perspective isn't valid for the description of the measurement, why should I accept that it's valid at all? It does not determine any further interaction, so it has no observable consequences. In particular, simultaneously claiming that the measurement problem is solved through the existence of this perspective, of the definite state the qubits see, and then claiming that this perspective is actually wrong for describing the further dynamics, seems simply inconsistent to me.
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Author Mikalai Birukou replied on May. 1, 2013 @ 23:08 GMT
On "simply stipulating that 'everyday logic fails' is a lazy way". Consider refactoring into prime numbers. In classical logic you need certain number of steps to find prime devisers. Deutsch algorithm makes it in less number of steps. So, when IBM refactored 15 into 3 and 5 in less steps than it is possible in classical logic, nature showed clearly that our everyday logic is not the last word in...
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On "simply stipulating that 'everyday logic fails' is a lazy way". Consider refactoring into prime numbers. In classical logic you need certain number of steps to find prime devisers. Deutsch algorithm makes it in less number of steps. So, when IBM refactored 15 into 3 and 5 in less steps than it is possible in classical logic, nature showed clearly that our everyday logic is not the last word in math. And to fit it to quantum world, some rules are to be added/adjusted. When you insist that classical logic should unconditionally apply to quantum information flows, you should at least provide such classical logic algorithm, for classical computer, which would be no slower than Deutsch's on a quantum computer. Short of that, people should be allowed to doubt supremacy of classical information flows (logic) in quantum domain.
On "why should I accept that it's valid at all? It does not determine any further interaction, so it has no observable consequences". Actually, we have specific observable consequences in each perspective. And, it seems to me, that by having "observable consequences" you mean having a description in one globally applicable description/perspective. Too bad, that nature does not make one global informational perspective. And, by the way, nature also has a speed limit on things. Strange, but true.
On "you venture to solve the measurement problem". Nope. We venture to formulate QM in simpler terms, where all interactions are fundamentally same, i.e. there are no two types of interactions. And postulate 4 tells you the difference between measurement and non-measurement, and since measurement is getting information, it is a postulate about natural quantum information.
On "simultaneously claiming that the measurement problem is solved through the existence of this perspective, of the definite state the qubits see, and then claiming that this perspective is actually wrong for describing the further dynamics, seems simply inconsistent to me". How about that high-school problem about objects in a field of gravity, where you throw away one negative solution. Does it make use of quadratic equation inconsistent?
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Paul Reed replied on May. 2, 2013 @ 04:48 GMT
Guys
I think you both need to ask yourselves what is the measurement problem, bearing in mind:
-What happened has happened, the act of measuring just invokes a time/spatial definition on that, ie what amongst all the events you are trying to discern
-The subsequent processing of physical input received has no effect on the physical circumstance
-What is received, in the case of sight, is a physically existent photon based representation of what happened, not what happened
In simple language, is the problem innate to physical existence, and if so what is it, or is it a function of our inability to differentiate a discrete physically existent state?
Paul
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Jochen Szangolies replied on May. 2, 2013 @ 05:56 GMT
First of all, Grover's prime-factoring algorithm was of course arrived at through classical logical reasoning: he wrote symbols down on a page, and derived consequences from them. The same procedure in your case fails: the symbols don't produce what experiment needs them to produce. Second, of course I can simulate any quantum effect on a classical computer---in general, this will incur an exponential slowdown, but this says that classical logic isn't wrong, it's just not as fast.
About the observable consequences: well, one consequence would have been that from the qubit perspective, there is no entanglement. But you throw out this consequence, so what's left?
Anyway, I'm happy that you've finally come around to recognizing that your approach makes no headway on the measurement problem; if you recall, that was my question to you which sparked this discussion, in response to which you claimed that postulate 3 applies to all interactions, thus eliminating the measurement problem. Since you seem to no longer be claiming this, I think the discussion has served its purpose. But then you should perhaps revise the part in your essay where you claim that your formulation produces QM without the usual interpretational problem.
The problem, by the way, is wholly disanalogous to discarding unphysical solutions: such solutions refer to mathematical possibilities, which are simply precluded by the physics (negative distances, imaginary masses, retrocausality etc.). The solution obtained in your formulation is perfectly sensible physically: it merely amounts to a difference in statistics from what is actually observed. So your theory predicts (at least) two incompatible, but physically perfectly sensible, observations, making it inconsistent.
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Jochen Szangolies replied on May. 2, 2013 @ 11:50 GMT
Above, I meant Shor's prime-factoring algorithm... Grover's is quantum search. I should just not write anything when my brain hasn't reached its proper caffeination level...
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Author Mikalai Birukou replied on May. 2, 2013 @ 16:03 GMT
On "prime-factoring algorithm was of course arrived at through classical logical reasoning". The question is how it works in the lab. Algorithm exploits informational flow that is not present in classical logic. So, again nature has informational flows that differ from those we are accustomed in everyday life, the classical logic. Highlight again, nature has, without any regard to what you and me...
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On "prime-factoring algorithm was of course arrived at through classical logical reasoning". The question is how it works in the lab. Algorithm exploits informational flow that is not present in classical logic. So, again nature has informational flows that differ from those we are accustomed in everyday life, the classical logic. Highlight again, nature has, without any regard to what you and me may think about it.
On "from the qubit perspective, there is no entanglement. But you throw out this consequence, so what's left?". Entanglement is left in lab's perspective, which we experience, where we have wonderful and useful quantum computers. Now, recall, that 70 posts ago, I told you that this is relative state thingy. Just like Everett's one, but, thanks to your pressure, I put this relative states concept into formal form. But it is still that same relative states arrangement. And do not mix it with multi-worlds, which use relative states, but also draw this picture of parallel existence, which, as we have already noticed, may be self-contradictory (splitting goes as in classical case of essay equation 5, giving to human reader a sense of satisfaction, by fitting it to how everyday logic flows, while eq5 is opposite to eq6, which leads to unitarity, which is simply postulated in many-worlds).
On "you've finally come around to recognizing that your approach makes no headway on the measurement problem". I told you, some 70 posts ago, that we do not have such problem, exactly like Everett's relative states concept does not. It does not arise cause you do not have to square two types of interaction with a democratic view of physical systems (i.e. none is special).
On "The problem, by the way, is wholly disanalogous to discarding unphysical solutions". We are in the same boat as in early 1900's. Galileo's concepts of adding velocities were producing mathematical results that did not fit results of Michelson-Morley experiment (our analog of eq5). Some stayed the course of sticking with existing mathematical concepts. Constructed aether also defied properties of all known matter, but existing math concept was saved. The other guy, noticing aether's ridiculousness, suggested fitting mathematical concepts to nature's shape (choice of eq6, and related rules about perspectives, which we fleshed out). And a big amount of electricity, which your computer uses this very moment, is now produced thanks to fitting math to experiment (or physical reality, if you wish). How one wise man said, choose you road carefully.
On "So your theory predicts (at least) two incompatible, but physically perfectly sensible, observations". In different perspectives! In common life, and logic we use every day, there is no analogue of different perspectives. It is, again, relative states idea, started by Everett. And sticking to necessity of having one, true for all perspective does "mak(es theory) inconsistent". But it is you who is trying to sneak in a bit of this old-fashion one-perspective-for-all. And I've been telling you not to do so from the very beginning. And I even wrote a little formalism to drive you an idea, that it is relative states we have here, and that one perspective, true for all, so psychologically pleasing to us, humans, is NOT what NATURE has.
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Jochen Szangolies replied on May. 2, 2013 @ 17:25 GMT
"Now, recall, that 70 posts ago, I told you that this is relative state thingy. Just like Everett's one, but, thanks to your pressure, I put this relative states concept into formal form."
Which produces, unfortunately, wrong predictions. On Everett's relative state notion, it doesn't matter what perspective you choose, you get a consistent theory out of it---that's its strength. On your view, one perspective gives false predictions.
"It does not arise cause you do not have to square two types of interaction with a democratic view of physical systems (i.e. none is special)."
But you have to square two different perspectives, one of which yields the wrong predictions.
"Galileo's concepts of adding velocities were producing mathematical results that did not fit results of Michelson-Morley experiment (our analog of eq5). Some stayed the course of sticking with existing mathematical concepts."
Which is what you're doing: your math produces the wrong result, but you decide to come up with an arbitrary rule to forbid that result. But of course, then as now, the correct response was to change the theory that gives the wrong prediction.
"one perspective, true for all, so psychologically pleasing to us, humans, is NOT what NATURE has."
This is an idea that I could get behind; unfortunately, in your formulation, it's not present: there's one correct perspective (the lab perspective), and a wrong one.
In any case, this isn't going to get us anywhere, is it? I was hoping that eventually we could go on to discussing the other problems of your formalism, but I think now that's not gonna happen. So all that's left I guess is for me to wish you good luck in the contest, and to hope that maybe, you'll at some point revisit your ideas with a critical eye and try and refurbish them in a way that stands up to scrutiny. So, good luck!
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Author Mikalai Birukou replied on May. 3, 2013 @ 15:55 GMT
The question we forgot to ask is, whether upon second measurement, in a peculiar different basis, perspectives Q(0/1) seize to exist. Each physical interaction is reshuffling of particle events, making it an active change of what systems, therefore, information is at the moment.
Now, on a heat note, I am challenging you to put Everett's concepts into formal language, like I did. Then you will notice this strange thing, that upon doing interactions in different basis, you invariable have perspectives like Q(0/1) with states +-/-+, which have to somehow merge/cancel out to provide proper lab's experience. You will also find exactly this thing, the need to merge already split many-worlds, which we talked about. You will also see that insisting that Everett's thing is correct and mine isn't, is like saying that verses in a book become incorrect by virtue of translation into a different language (except that here languages won't be too different).
Author Mikalai Birukou replied on May. 3, 2013 @ 16:17 GMT
Yes, this idea of perspectives being actively destroyed, due to specific setup of fundamental events (+/- basis vs 0/1), relies on first two postulates and removes the problem, just like non-preferred basis never show up, as they need an active reshuffle of events.
Let's not forget that nature of these particle events is that of QFTs. In particular, when you receive an electron at detector (where it annihilates) you cannot tell 100% sure how many there were self energy loops, involving virtual particles. By the way, word "virtual" comes from exactly this fact that we cannot tell how many loops there were.
I think, we have our final answer.
Jochen Szangolies replied on May. 6, 2013 @ 17:55 GMT
I think this would be a nightmare scenario, both from a personal viewpoint, and as far as the ability to do science is concerned: if I interact with a system, then I have the perspective of someone 'in' the system; but if something then interacts with the system I am part of from outside, then this perspective is destroyed. But this in particular implies that there are no measurement records, since those only exist 'in' the system. So not only is your personal experience at this very moment liable to be destroyed in the next, there is also no way to globally account for stable measurement records, which are a prerequisite for theory building. So if one were to believe your theory, one would have to conclude that there is no actual physical evidence for doing so!
As for formalizing Everett, well, that's just the ordinary Hilbert space quantum mechanics; and yes, branches can be merged, but this doesn't imply the destruction of some perspective (at least not if you don't want to impose the strictest many-worlds reading, but this I believe contains other problems anyway).
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Author Mikalai Birukou replied on May. 6, 2013 @ 19:38 GMT
The facts are things from the past, to which everyone may agree. Perspective is gone in a sense that any statement about the future from it will not work.
On "to globally account for stable measurement records, which are a prerequisite for theory building". When you have such "ledger" how would you know that it is truly global? It has to be consistent with that of systems, with whom you have informational (interactional) contact, but you cannot possibly compare it to systems that are not (or not yet) in interaction with you.
If we do not push interpretations, like Everett's, for stricter reading, we may loose a hope on making them falsifiable, or experimentally distinguishable and provable, which ever way you like it. If it is not falsifiable, it is just many-worlds. There were people, trying to see how branch splitting/merging can be connected to spacetime (recall Equivalence principle, gravity is just rippling of spacetime). The local/global reading is paramount there, as GR is a local theory.
Author Mikalai Birukou replied on May. 6, 2013 @ 22:30 GMT
It will be useful to identify in more details, using fundamental particle events, why perspective is destroyed, and to make sure that the fact of such destruction is universally agreed upon.
A stricter definition of system and chains of events, which can be called "my past", are needed here. This will provide ground for an observed funny behaviour of systems, which are all effective, let's not forget. Such definition should be done in line with use of events in QFT, so that (a) it is not out-of-the-blue, and (b) it is consistent with actual practice at lowest level.
Paul Reed replied on May. 7, 2013 @ 03:50 GMT
Guys
Your basic problems are:
-in order to have any form of sense you are working with ‘definitive one at a time physically existent state in sequence’, otherwise it would be physical anarchy. But the theory you are considering embodies a contrary assertion about how physical existence occurs
-one of the mechanisms for rationalising this inherent contradiction is the role of measurement/observer. This cannot have a role, as it cannot affect the physical circumstance, because that occurred before the measurement/observervation.
Paul
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