David

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David

Apr 8, 2018 07:02

@JohnRennie Perhaps what I can say is that the Riemann integral, along an interval of the x axis, is not a generalization of a discrete sum, consisting of a finite number of terms, into "continuum sum”, that is a sum containing a non-countable number of terms. It is, rather, a generalization of a discrete sum, containing a finite number of terms into a sum containing a countably infinite number of terms.

David

Apr 8, 2018 06:52

but the function is never evaluated at the irrationals in calculating the areas.

David

Apr 8, 2018 06:51

@JohnRennie Could you please tell me where my reasoning went wrong, above?

David

Apr 8, 2018 06:50

@JohnRennie But do you agree that it seems that Riemann integrals seems to skip over the irrational values of the variable of integration? I never learned that and think it is interesting and probably telling of something...

David

Apr 8, 2018 06:44

@JohnRennie Thank you for your response. But there seems to be a contradiction by assuming that a variable takes on a continuum of values, but integration over that variable skipping the irrational ones. The link you provided assumes that position can have irrational values, so I think it is different than where I am coming from.

David

Apr 8, 2018 06:39

Oh, you are talking to Mr. Meurer

David

Apr 8, 2018 06:38

no, no interview. Do I sound cranky?

David

Apr 8, 2018 06:38

Hi, well, even that they cannot be irrational is kind of a big thing and means that there are no physical variables that are truly a continua.

David

Apr 8, 2018 06:24

Possible Insight, Based on Set Theory, On Quantization of Position: The set of all integers is a countable infinity. The rational numbers are also a countable infinity but the irrational numbers are a non-countable infinity. You can make a one to one mapping of the infinity of all integers to the infinity of all rationals, and vice versa. You can even map the infinity of all integers to the infinity of all rationals that are between 0 and 1. The real numbers are the combination of the rationals and the irrationals and are represented by the real number line, such as the continuum of point…

Discussion between ACuriousMind and D…

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David

Feb 15, 2016 01:41

You mentioned evolving and that is via the hamiltonian in schroedinger's eq.

David

Feb 15, 2016 01:33

Did you downvote me twice?

David

Feb 15, 2016 01:20

I don't think tbis question fits yiur downvote criteria. I did research tgis and put effort into it. Anyway, as I said, I think the composite WF will evolve correctly wothout the wjrstion I Ask if I inckude the self-hamiltonians.

David

Feb 15, 2016 01:09

I think the answer is to also include the self hamiltinian of system a, not just the interaction hamiltonian that entangles systems a and b. Theae (-) votes for questions that are not obviously rediculous are what drives people from this site.

David

Feb 15, 2016 01:07

@ acuriousmind I asked the question because I was confused about something and that confusion may show in the wording. Howver, I don't think the question, once it is clear enough, is bad and does not deserve a (-) vote, in my view.

David

Feb 15, 2016 01:01

Is there a chat room to go to?

David

Feb 15, 2016 01:01

Or better yet, just refrain from commenting on this question.

David

Feb 15, 2016 01:01

@ ACuriousMind Instead of finding every possible flaw, and dinging from your position of superiority, could you please try to understand and constructively comment on the spirit of the question?

David

Feb 15, 2016 01:01

The Gaussian distribution is part the specifics of the problem I am trying to solve. Maybe it is not critical to state. It is explaining how the expectation value is changing over time. In any case, if it is not important, then please ignore it.

David

Feb 15, 2016 01:01

Maybe $O_A$ can be the charge of a two parallel plate capacitor (in an LC circuit) that has no side walls and the probe is an electron that passes between those plates. The states of the charge are just the possible charge values (1 coulomb, 2 coulomb, etc.) . By $O_A$ I was not referring to an operator. Also, I meant measuring the momentum of the probe, whose possible momentum values (states) are entangled with the charge states.

Discussion between David and CuriousOne

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David

Dec 24, 2015 08:48

Good night (or morning or afternoon, depending on your location).

David

Dec 24, 2015 08:47

Yes, the weak measurement is not related, but very interesting in its own right.

David

Dec 24, 2015 08:46

Agreed. Anyway, it is 3:45 AM where I am. Have to go, now. Thank you for your interest and your insights! I welcome any further thoughts that you have.

David

Dec 24, 2015 08:45

I know I have a valid point here, somewhere...

David

Dec 24, 2015 08:44

I see. Again, beyond me at the moment. I do find weak measurements interesting though. It seems like a bit of an attempt to introduce a kind of determinism.

David

Dec 24, 2015 08:42

Anyway, if the wave function of X consists of W1 and W2 waves, superimposed, and W1 can interacts with system A while W2 does not, but instead interacts with system B, and then there is a measurement of X, wiping out W2, what happens to how B evolved since interaction with W2?

David

Dec 24, 2015 08:40

Aharonov is Mr. Weak Measurement, isn't he? I am only familiar with ordinary QM, not QFT or QED. Just a B.S. in physics and an enduring interest in the nature of wave functions. SQUIDs are beyond what I know. weak measurement with SG I have read about.

David

Dec 24, 2015 08:38

Well, my attempt to create that experiment clearly was not clean enough...

David

Dec 24, 2015 08:36

right. there would be a lot of overlap in those Gaussians.

David

Dec 24, 2015 08:35

Whatever we call it, the two superimposed parts of the same wave function each become linked to a different part of the environment. I find that interesting and am trying to follow that idea through.

David

Dec 24, 2015 08:34

Yes,, let's forget Stern Gerlach. It was perhaps a clumsy visualization tool

David

Dec 24, 2015 08:33

does dotted line mean you left the chat?

David

Dec 24, 2015 08:30

Well, in the double slit experiment, if you put a parallel polarizing filter over one slit and a perpendicularly polarizing filter over the other slit, the two emerging waves (which are part of the same wave function; superimposed) each entangle with a different polarization eigenstate. The result is they no longer interfere. So, different superimposed parts of the same wave functions can interact differently with their environment.

David

Dec 24, 2015 08:27

Then, somehow, a measurement selects Gaussian 1. Does the effect that Gaussian 2 had on the "something else" get nullified at that time?

David

Dec 24, 2015 08:25

In any case, I am wondering if a wave function can be created such that it has two non-zero Gaussians, separated in space, and Gaussian 1 can entangle with one thing and Gaussian 2 can entangle with something else.

David

Dec 24, 2015 08:23

Oh, you mean photons produced by the apparatus interacting with the particle? Is it a changing magnetic field?

David

Dec 24, 2015 08:23

@CuriousOne You mean photons from the environment? Let's keep it simple and say there are none. The Stern Gerlach part was just to set up the questions, so they can be visualized. Stern Gerlach is not essential to the questions.

David

Dec 24, 2015 08:23

@CuriousOne, the wave function's disjoint (but superposed) packets have a trajectory, but the position of the particle is still uncertain and governed by quantum probabilities.