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Stan Shunpike

23:04

@ACuriousMind does every eigenstate have an observable operator for which it is the eigenvector?

ACuriousMind

@StanShunpike What's your definition of eigenstate?

Stan Shunpike

@ACuriousMind A state vector that is an eigenvector for an operator. Is that a valid definition?

NeuroFuzzy

@StanShunpike even better than that, I can give you an observable which has every state as its eigenstate, with eigenvalue one!

Stan Shunpike

@NeuroFuzzy do tell lol

NeuroFuzzy

@StanShunpike you're not going to like it.

ACuriousMind

23:13

@StanShunpike Ah! I though were asking about a tautology

NeuroFuzzy

It's the identity.

ACuriousMind

But you put observable in there

Stan Shunpike

Who me?

ACuriousMind

@StanShunpike Yeah, you

0celo7

I must be high. My estimate for the velocity of the ISS is off by like a factor of 30. Is $$v=\sqrt{\frac{GM}{r}}$$ not the formula?

Stan Shunpike

23:14

Are there operators besides observables that have eigenstates?

@ACuriousMind ^

0celo7

@StanShunpike Anything that's not hermitian is an operator but not an observable.

ACuriousMind

@NeuroFuzzy The identity is self-adjoint, but it not clear it is an observable. $C^*$-algebra folks probably wouldn't call the identity an observable

@StanShunpike As you say, an eigenstate is an eigenvector of an operator. Nothing in that definition says self-adjoint or observable

It's just linear algebra

Every matrix can have eigenvectors, they just don't necessarily span the whole space

Stan Shunpike

@ACuriousMind it's funky linear algebra lol

Sofia

@ACuriousMind pleeeease! Don't encourage closing this question. I see there things that have to be elucidated: quantum communication without the help of classical qubits. It's essentially faster-than-light. So, let's make light what's going (I believe that smth. is wrong). The user indeed searched material, made effort.

ACuriousMind

@StanShunpike Well, the details of the spectral theorem and such are. The concept of an eigenstate isn't

0celo7

23:19

@ACuriousMind What the hell am I doing wrong?! I swear to god $\sqrt{GM/r}$ is orbital velocity.

I get 242 km/s, it should be like 7.

ACuriousMind

Not all at once! :D

NeuroFuzzy

@ACuriousMind Hm. Interesting.

@0celo7 details plz!

0celo7

@NeuroFuzzy I need to calculate the velocity of the ISS for something.

$r$ should be like 6800km.

NeuroFuzzy

@0celo7 wolframalpha.com/input/…

-shrug-

0celo7

@NeuroFuzzy ::eye twitches::

km.

NeuroFuzzy

23:23

hehe

ACuriousMind

@Sofia I have not voted to close that question because, much to my personal dismay, quantum interpretation questions are not off-topic. I may comment however I like, though.

0celo7

Seems I thought the Earth radius was 6km.

@NeuroFuzzy wolframalpha.com/input/…

ACuriousMind

@NeuroFuzzy Yeah. In the $C^*$-approach, you explicitly specify the algebra of observables, which may well only be a subset of the whole algebra of self-adjoint operators when realized on a Hilbert space.

0celo7

@ACuriousMind ""Could QM be describing a non physical reality of information"...I have no idea what that means. " Translation: is QM the matrix?

Stan Shunpike

That's philosophy not physics

Sofia

23:25

@DavidZ I saw a question with all sort of voting for close. The user indicates articles in the scientific literature that seem to support faster-than-light communication. I see many VTCs. Please, I would like to see what's going and I need time. Debugging an article needs time. I'd say that our site is supposed to clarify such things.

ACuriousMind

@0celo7 No, that's not what I think it is meant to mean, but it is about as much physics, in my opinion.

0celo7

@NeuroFuzzy So I was calculating the time dilation of the ISS and I got an orbital frequency of 30rad/s during the process.

Freaking units.

Sofia

@ACuriousMind very well that you didn't VTC. I would like to get into at least one of those articles seriously and see what exactly goes there.

NeuroFuzzy

@Sofia So, I'm just at the level of introductory physics so forgive me, I think it's like this: arguments EITHER tell you that quantum mechanics necessitates faster than light "communication" (pilot wave theory?) OR that quantum effects are real and fully describe everything.

And that this exact thing was discussed in a lecture which my QM professor made us watch, thiss thing ("this implies FTL effects") has it backwards.

@Sofia this is the lecture I'm referring to and I apologize because it's an hour long and the video player is horrible. media.physics.harvard.edu/video/?id=SidneyColeman_QMIYF

@Sofia I'll try to find the exact moment where he states that so that you don't have to watch the whole thing.

0celo7

@ACuriousMind 'Twas a joke.

ACuriousMind

23:33

@0celo7 Oh. Sorry. In these matters, I'm having trouble getting jokes because even most serious contributions seem laughably absurd or confused to me :P

NeuroFuzzy

@ACuriousMind is a $C^*$ approach something like a different flavor formulation of QM?

Stan Shunpike

Are there analytical solutions to a particle under the force of a coulomb potential? I'm not really sure what I mean by analytical solution, but all the related models I was looking at were called that on Wikipedia.

@ACuriousMind "What kind of question is that?" Lol

0celo7

@ACuriousMind Do you think I read that question and seriously thought "oh he's talking about the matrix"? :/

ACuriousMind

@0celo7 Honestly, no idea. I simply don't get these people, perhaos they are talking about the matrix and you understand them and I don't? :D

@NeuroFuzzy What I call $C^*$-algebra approach is a way of approaching QM rigorously by first specifying the algebra of observables and then constructing the space of states by the GNS construction. It's basically the "Hilbert space approach" turned up to eleven ;)

NeuroFuzzy

@Sofia around 18:00 . at 19:50: "As John Bell pointed out, there is no way of refuting this position [of QM implying FTL], and he gave a specific example of a classical theory that on this level reproduces quantum mechanics, the de Broglie Bohm pilot wave theory."

user54412

23:38

@StanShunpike Um... like conic sections?

user54412

(attractive EM being the same as gravity)

ACuriousMind

@StanShunpike Are you talking abut the hydrogen atom?

Sofia

@ACuriousMind did you change your mind about this post? Where from did you take "Words like "fundamental", "real", "ontic" and "epistemic" are philosophers' tools."? But, bottom line, words are your problem? It's Faster-than-light there. Let's make light! I take it.

Stan Shunpike

Basically, but I was wondering if that applied to just any charged particle pairs as opposed to having to consider the hydrogen atom. Like what about two electrons?

ACuriousMind

@Sofia "Fundamental" and "real" are used in the post itself. "ontic" and "epistemic" occur on the first page of the linked arXiv paper.

Stan Shunpike

23:40

@ChrisWhite here's where I found the phrase analytical en.m.wikipedia.org/wiki/…

I don't really know what that means

user54412

Really important fact: "closed-form" and "analytic" as used colloquially are basically meaningless. What you mean is "subjectively simple expression in terms of functions that I like." Is the sine function closed-form? It is if you say it is, it isn't if you say it isn't. After all, sine is only computable in the limit of infinitely many arithmetic operations, but we gave it a special name. So perfectly well-defined solutions to well-posed differential equations can be non-"analytic" to some simply because no one bothered to give those solutions a special name. — Chris White Jul 4 '14 at 23:08

Stan Shunpike

Well said

ACuriousMind

@Sofia The question is not about FTL, but about the idea that exchange of information without exchange of matter, as it happens in quantum teleportation, implies something about the ontology we should imbue our theory with.

Stan Shunpike

I'll add that to my book of quotes lol

Sofia

@NeuroFuzzy I would be very glad to have the reference where John Bell said it. I knew that he said, but I don't have the reference, and someone downvoted me because that. If you can give me the reference, I'd be very glad. Now, another thing, John Bell said that smth. goes FTL, but we can't lay our hand on that, and do FTL communication.

alarge

23:43

@KyleKanos For some reason I thought you already had the interview. Just out of curiosity, what are you expecting them to ask?

NeuroFuzzy

@ACuriousMind oh neat! That actually sounds interesting and is the first actual definition I've heard of a C^* algebra

ACuriousMind

My problem is not the words, but the word games that are played with this. None of this debate has any empricially testable impact, as I've repeatedly said. The difference between a theory that is "real" and one that is "real but not physical" and one that is "unreal, but about information" can only lie in a difference in the predictions. If the predictions are the same, then all we're are doing is playing word games, and not physics.

Tangential remark: I predict now that that comment thread is either going to get a gold mine for hilarious quotes or ugly real fast. Possibly both. (I won't say more there, however)

NeuroFuzzy

@Sofia Well I'm paraphrasing my link too much. You can quote Sidney Coleman from that lecture. He's saying that it's either nonlocal hidden variables or totally local quantum mechanics. But that if you want to look at things as nonlocal hidden variables then there's nothing stopping you. Again, I'm not that good at this so I don't have all the details.

ACuriousMind

@NeuroFuzzy When I first heard of them, I had one of these "Why did no one mention these before?" moments ;)

Sofia

@ACuriousMind, look at this : existing quantum-information transfer schemes require a physical medium, and it was unclear if quantum information can be transferred without transmitting any physical particles – but this paper suggests that it can. As to wording, "Fundamental", "real", "ontic" and "epistemic", since when I care of words? What, shouldn't we (I) clarify what's going because there is phraseology there?

0celo7

23:50

@ChrisWhite I would tell past Chris White that an analytic solution is one that does not require perturbation theory.

I feel like that might be wrong.

ACuriousMind

@Sofia Yeah, quantum teleportation is possible. That's not the question. The question is "Could this point to matter being like playdough or pixels on the screen and there's a fundamental reality of information that informs matter as to what states it can be in?" and "Could Quantum Mechanics and General Relativity be describing 2 different things?"

Which is completely non-sensical in any rigorous way to me.

Except for the fact that QM describes the small/three of the four forces and GR describes the big/the other force, so, yeah, they describe two different things, duh.

Sofia

@ACuriousMind please see this : Zhang continues: the minimum information unit is quantum state-encoded qubit. However, to date, schemes for the transfer of an unknown quantum state required physical particles to travel – for example, quantum teleportation needs prior entanglement sharing and classical comm., and both entang. sharing and classical comm. cannot be done without transmitting physical particles. In our scheme, entang. sharing and classical comm. are not needed.

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