mitchellmckain » May 23rd, 2018, 10:12 am wrote:I think I understand what you mean, but the first and last sentences need work in order to be stated correctly. Scientists consider a superposition to be a particular objective state. Say rather that QM tells us that the universe does not consist of point particles with particular positions and velocities. So the billiard ball conception of the universe is certainly unworkable.
Furthermore you can grant that the universe is rather machinelike on a large scale, but yes QT does indeed throw a wrench into works of the this conception if you try to take it too far. In particular the rug has been pulled out from beneath Laplace's demon
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ar old conceptualization of "material"? It seems to me, our conception of "material" is something that has be constantly changing and with greater rapidity as we approach the present.
hyksos » May 23rd, 2018, 6:51 pm wrote:mitchellmckain » May 23rd, 2018, 10:12 am wrote:I think I understand what you mean, but the first and last sentences need work in order to be stated correctly. Scientists consider a superposition to be a particular objective state. Say rather that QM tells us that the universe does not consist of point particles with particular positions and velocities. So the billiard ball conception of the universe is certainly unworkable.
It is true that scientists consider a superposition to be a particular objective state. I can agree with a full heart. However, the further problem is that we puny humans have no access to that. Whenever we measure a system, it only presents one of the eigenstates of that superposition to us.
There is the issue of the "eigenstate selection"/"measurement problem"/"wave function collapse" thing. I dunno, for brevity call it ESMPWFC or maybe WFC.
Yourself, or others, could begin to linguistically associate the Universal Wave Function (which contains all the superpositions nicely) as The One Objective Reality. Nothing in physics forbids this reshuffling of terms. In that instance the act of measurement/WFC would be considered a transient phenomenon, a derivative of what is "actually real". Sort of like dipping a drinking straw into an ocean.
While this might seem all very coherent and tidy at first glance, the implications of doing this are certainly not. The room you are in contains transparent glass and objects with certain stable colors. The above framework would be like denying that color exists.
hyksos » May 23rd, 2018, 6:51 pm wrote: To back up a little bit on that briefly  the reason that anything in the room has color is because electrons can only emit a particular wavelength of light, and the reason is exactly because we only see electrons in the eigenstates of their wave function. This would be like denying that any surface emits color as an objective fact. Whether you like this or not, it is rather forcibly attached to this methodology. It is a corner one paints one's self into, if you have committed to the One Objective Reality is the Universal Wave Function itself.
hyksos » May 23rd, 2018, 6:51 pm wrote:So in any case  I hear and understand "Scientists consider a superposition to be an objective state" but they do so in a narrow academic context that is quite divorced from our experience of the universe.
hyksos » May 23rd, 2018, 6:51 pm wrote:They might have "mathematical reasons" inside the discipline for stating this in narrow academic contexts.
hyksos » May 23rd, 2018, 6:51 pm wrote:I am not disagreeing with the statement on factual grounds. However, I ask you to consider the narrow context and narrow setting in which that position is adopted.
hyksos » May 23rd, 2018, 6:51 pm wrote:Furthermore you can grant that the universe is rather machinelike on a large scale, but yes QT does indeed throw a wrench into works of the this conception if you try to take it too far. In particular the rug has been pulled out from beneath Laplace's demon
...
ar old conceptualization of "material"? It seems to me, our conception of "material" is something that has be constantly changing and with greater rapidity as we approach the present.
I don't know what to make of this bizarre situation that we find ourselves in. On one hand , we begin to try to reach absolute monism in our metaphysics, we are forced, in some way to a singular Universal Wave Function.
hyksos » May 23rd, 2018, 6:51 pm wrote:But that UWF has pieces we cannot measure. Are they real? David Deutsch says if we "take it literally" then they must be as real as we are. We are forced into the corner with Everettian Many Worlds. Two photons going through two slits in two realities is okay. We can sleep on that.
hyksos » May 23rd, 2018, 6:51 pm wrote:In that corner there are copies of you in other universes. But wait  that's a plurality! In our desperate attempt to obtain perfect monism, we encounter a kind of extreme plurality. The most extreme : the Many Worlds Interpretation. This situation is like a genie that fulfills wishes, but only at a price. The bigger the wish, the steeper the price. "Genie of the lamp, grant me perfect monism." "It is done." "Wait  now there are a trillion copies of me in trillion other realities! That's not what I asked for!"
So your claim that we only see eigenstates is wrong because the eigenstates themselves are superpositions of other eigenstates.
Because these "other worlds" are not measurable, then this is not a matter of objective scientific results but of subjective interpretation. Another interpretation, as I have explained in the other thread, is that these are nothing but real possibilities which did not actually happen.
perhaps what you means to say is that these superpositions in science suggest to you a philosophical view of reality as lacking in particular objective states. That is not a philosophical viewpoint which I am going to be at all hostile to.
Remember, it is my frequent argument that we have no objective evidence that reality is exclusively objective and good pragmatic reasons for believing there is an irreducibly subjective aspect to reality as well. Isn't this is practically saying the same thing in different words?
I have no reason to back down from nor amend this paragraph. This debate is very real. Even if not a single poster on this forum is engaging it, it still exists, and research scientists are still throwing big money at it.hyksos » May 22nd, 2018, 12:10 pm wrote:The metaphysical grist of Quantum Theory does not pivot on a inescapable plurality. Rather the metaphysical pivot point in QM is that it suggests that the universe is not in a particular objective state at time t. The universe is not a grand machine made of "gears" whose orientations are objectively determined at any given instant. Even if the universe were "one singular substance" (lets say) that substance would not be in a particular configuration/state at time t.
hyksos » May 23rd, 2018, 9:50 pm wrote:So your claim that we only see eigenstates is wrong because the eigenstates themselves are superpositions of other eigenstates.
Our communication has severely broken down. An eigenstate is most assuredly not a superposition, at all. It is practically speaking the opposite of one. Perhaps we are reading different textbooks here. Would you prefer that I ditch "eigenstate" and instead use the phrase "stationary state"?
7. The uncertainty principle. Now you can see (qualitatively) how the
uncertainty principle arises. The eigenstates of one operator are not in
general the same as the eigenstates of a different operator. So when you
make a state with a definite value of one observable, it will in general not
have a definite value of the other observables. For example, a plane wave,
which is an eigenstate of the momentum operator, has a definite value of
the momentum. But plane waves are completely spread out in space, so the
plane wave contains all eigenstates of the position operator, so the position
is then completely uncertain
To suggest that some are real and others are not is kind of like saying that only certain times on the clock are real and that when the time reads between them then these are not objective states of time. That would seem rather silly to most people, wouldn't it? But we see the exact same sort of circular continuity in what we call orthogonal measurements. So the problem is a little bit more fundamental than perception by scientists, because this is not a subjective thing at all. If these superpositions are not particular objective states then there would be no particular objective states at all  and the evidence does not support that either.

The eigenstates are relative to the measurement operator. Pick a different measurement operator and the eigenstates are different even in the same measurement space. Thus the eigenstates of one operators will be combinations (superpositions) of the eignstates of the incompatible (noncommuting) operator.
"Thus the eigenstates of one operators will be combinations (superpositions) of the eignstates of the incompatible (noncommuting) operator."
A
has "collapsed" to an eigenket by an operator Y
, A
will appear concomitantly in physical reality, along with a superposition of the observable B
which is noncommuting with A
.combinations (superpositions) of the eignstates
Because the eigenstates of one operator is a linear combinations of the eigenstates of the other operator you cannot measure both at the same time and we call them noncommuting because you get different result depending on which you measure first.
Bottom line: An (single) eigenstate is not a (single) superposition.
the eigenstates of the momentum operator are a linear combination of all the eigenstates of the position operator, and visa versa.
mitchellmckain » May 27th, 2018, 9:17 am wrote:The only thing I have to say about hidden variable theories, is that they have been experimentally proven wrong.
Perhaps my philosophical offerings are equally diverse and too much for the sensitive digestion of those more accustomed to simple fare.
hyksos » May 27th, 2018, 4:36 am wrote:The differentiation between eigenstate and superposition is quite rigid, and it has to do with matrices. There is actually something in a matrix called an eigenvalue. They represent the Schroedinger wave as a "state" in a Hilbert Space and give a matrix for that state, wherein each entry in the matrix is a complex number.
For a given matrix, there will be an eigenvector, and that eigenvector is called an "eigenket" in quantum mechanics textbooks.
hyksos » May 27th, 2018, 4:36 am wrote:But it it is far far too specific to glean a DEFINITION of "eigentstate". The word eigenstate in is a very broad term in quantum mechanics, and while momentum is certainly an example of a particular eigenstate observable, it is a by no means the only example. There is also an eigenstate for angular momentum, which if observable, will correspond to what is regularly called a "spin state". There are eigenvalues of a wave matrix that are not even observable at all.
I cannot emphasize enough how broad "eigenstate" is. It is broadest way possible to refer to an aspect of Matrix Mechanics that comes up in this universe. If I wanted to avoid the word, and risk "Talking down" to an audience, I would say something else like "standing wave". While "standing wave" would make a lay audience nod in understanding, a physics geek in the room would be cringing because the word choice does not adequately capture the nuances of QM.
hyksos » May 27th, 2018, 4:36 am wrote:Nevertheless, a standing wave is the simplest, clearest pedagogical example of an "eigenstate" money can buy. When you enhance and upgrade your education to textbooks, these simple examples must be dispensed with and replaced by more allencompassing mathematical procedures. You upgrade from 2D waves to vectors in infinite dimension Hilbert Spaces. You must then depart from simple PBS Nova TV explanations and start dealing with things like eigenvalues of a matrix. These more abstract , more foundational tools will capture a much broader range of physical phenomena.
During unitary wave evolution (when the system is not observed, measured, or probed) that the vector in the Hilbert space representing the Schroedinger wave is definitely NOT an eigenvector. Consequently you could never claim that the state the wave is in at that time is an eigenstate. It is vehemently not an eigenstate, and furthermore, it could not be a "linear combination" of them either.
mitchellmckain » May 27th, 2018, 11:53 pm wrote:Yes the operators can be matrices which operate on a space of vectors. The eigenvectors are those in this space which give a particular eigenvalue in the eigenvalue equation. But the point here that you keep glossing over is that the all of this is completely relative to which matrix you have in your eigenvalue equation. With a different matrix (a different measurement operator in QM) you get a different set of eigenvectors and different eignvalues to go with them
And while the eigenvectors of the one matrix are independent (not a linear combination of the other vectors), they are a linear combination of the eigenvectors of the OTHER matrix.
so matrix A
2 1 0
1 2 1
0 1 2
gives eigenvalues with eigenvectors:
2 with a1 = (1 0 1),
2+sqrt(2) with a2 = (1 sqrt(2) 1)
2sqrt(2) with a3 = (1 sqrt(2) 1)
BUT a different matrix B
1 2 0
3 2 3
1 0 1
gives you these eigenvalues with eigenvectors:
1 with b1 = (0 0 1)
1 with b2 = (1 1 1/2)
4 with b3 = (2 3 2/3)
You can normalize these eigenvectors if you want but it is not required for this demonstration.
So for example we can see that b1 = .25 a2 + .25 a3  .5 a1
Thus we see that the eignevectors of one matrix operator is a linear combination of the eigenvectors of a different matrix operator.
NO! The terms in science and mathematics are VERY specific  there is nothing "broad" about them. Ok, sure. You appropriate the terminology of science for a pseudoscientific gobbledeegook for a lot of subjective philosophy in such things as motivational speaking or selling products in some pyramid scheme. But I hope you don't seriously expect everyone to buy into such nonsense!
Switching to a different set of scientific and mathematical term which you want to appropriate for your rhetoric is only going to get this reply: "fool me once shame on you, fool me twice shame on me." I am hardly going to waste the time digging into another set of math and science terms see if there is any substance there, when the first such effort led nowhere.
hyksos » May 27th, 2018, 11:44 pm wrote:You want page numbers?
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