Is Hilbert space an isomorphism with the field of n-dimensional complex numbers?

[SimonA]

I recently made a post here asking questions that where clearly rediculous. I guess I need to be more obtuse. The reason I asked it here is that I'm looking for any possible way in which the 'tornado-like' rotation of galaxies could be explained by any kind of possible atomic structure in 3D space. Baryonic matter is a no-go. I suggested H+ ions as a kind of last chance saloon - but it seems no one found that convincing. And hot dark matter is a silly idea if you want to reproduce the dynamics that we are trying to explain.
That leaves cold dark matter - WIMPS, crumbly matter etc. So what I'm curious about is the possibility of any possible atomic construction of such particles that doesn't involve extra dimensions.
As always, any suggestions will be appreciated greatly. I realize I'm not au fait with the mathematics of QM. Thats the reason I'm troubling the people here who are. Einsteins broad horizon is disapearing as he predicted.
My challenge to you is to construct a 3D particle, from first principles, that has mass enough to hold galaxies together - but will not tend to concentrate in the centre of galaxies.
As I'm being verbose and hoping for criticism I'll lay my cards on the table. My suspicion is that QM deals with a multi dimensional universe in ways that relativity doesn't. Thats not surprising - Einstein made his great advances mainly by considering a 4D universe. In Einsteins world the vacuum energy is negligable (hence the mistake that was not a mistake but in the end is an inaccurate assumption). Feynman has the correct value, kind of, for the vacuum energy. He just was unable to grasp the multi-dimensional nature of the universe hinted at (rather than described implicitly) by QM.
Discuss. Please.
Simon

 

[SpaceTiger]

I think you'll find this paper interesting:

http://lanl.arxiv.org/abs/astro-ph/9909386"

Also, it seems that the cuspy halo problem is becoming less of one as the simulations get better. See, for example:

http://lanl.arxiv.org/abs/astro-ph/0310576"

 

[ComputerGeek]

it was just shown that Dark matter is not needed if you use the equations correctly, as was shown in the papers above.

 

[SimonA]

I think you'll find this paper interesting:
http://lanl.arxiv.org/abs/astro-ph/9909386"

Unfortunately not at all. Speculation based on speculation based on lack of common sense.

Also, it seems that the cuspy halo problem is becoming less of one as the simulations get better. See, for example:
http://lanl.arxiv.org/abs/astro-ph/0310576"

So put your money where your mouth is. I'm not rich, but I'll go against the odds and offer a wager of £1000 that neither of those papers will be accepted as likely explanations for galaxy rotation dynamics by the three most cited theoretical physicists between 2014 and 2015.

Interested ?

 

[ZapperZ]

Excuse me, but YOU asked for feedback and discussion, which is one reason I'm letting this go on rather than deleting it. If you're going to get SNAPPY when someone presented a contradictory paper, which by the way something you have NOT done at all to support anything you have to say, then you should say good night quickly because this thing will end.

And don't be too quick to dismiss something simply because you think it's speculation. Go read your original post and tell me if you remember writing "...My suspicion is that QM deals with a multi dimensional universe in ways that relativity doesn't..." Suspicion? And this is better than putting a quantitative model out in the open for the experts in the field to test?

Zz.

 

[SpaceTiger]

it was just shown that Dark matter is not needed if you use the equations correctly, as was shown in the papers above.

No, it wasn't.

https://www.physicsforums.com/showthread.php?t=92716"

 

[SpaceTiger]

So put your money where your mouth is. I'm not rich, but I'll go against the odds and offer a wager of £1000 that neither of those papers will be accepted as likely explanations for galaxy rotation dynamics by the three most cited theoretical physicists between 2014 and 2015. Interested?

Uh, no, because the cusp problem isn't about rotation dynamics. You should probably read the papers. Also, theoretical physicists tend not to know a whole lot about astronomical observations, so I wouldn't take their opinions as anywhere near the most important ones for this problem.

 

[SimonA]

ZapperZ - Fair point. I didn't mean to be "snappy" - obviously my naturally sunny disposition doesn't shine through :)


SpaceTiger -

Uh, no, because the cusp problem isn't about rotation dynamics.

Of course it is. Because the rotational dynamics require extra mass according to Newton an theoretical non baryonic substance is proposed that according to models should have a high cuspy density at galactic cores - which is not see in indirect observations.

However I was tired last night and have to admit I missed the point I now think you where reffering to in that first paper. Self interacting dark matter, that interacts weakly with normal matter. If you're thinking what I'm thinking then I like the way you're thinking

Simon

 

[SpaceTiger]

SpaceTiger - Of course it is. Because the rotational dynamics require extra mass according to Newton an theoretical non baryonic substance is proposed that according to models should have a high cuspy density at galactic cores - .

These are two separate problems. The rotational dynamics of galaxies is one -- dark matter is one possible solution to that. However, once you introduce dark matter, you run into another problem when you include it in cosmological simulations -- that they predict cores that are too cuspy. This is also commonly called the "small-scale structure problem". The papers I cited are looking for a solution to that. The solution to the rotation dynamics problem is pretty much universally accepted already -- dark matter.

 

[Jonny_trigonometry]

this gets me thinkin'. Being that I don't know what spin is, I might as well relate it to anything, including dark matter (which I have no clue what that is, besides matter we can't see) so here goes. I know I'm wrong with this, and I think it's rediculous, but I got to ask, is spin up=matter, and spin down=antimatter or dark matter, or vice-versa?
In an atom, the culoumb force dominates, so gravity means nothing, so matter and antimatter behave basically the same (they don't repel each other sufficiently enough to cause any noticable effect). I know, this is unreasonable because they would annhialate each other, but due to the exclusion principle, they never come in contact with each other in an atom. All this fails when two atoms collide though, unless the matter-antimatter interactions all spontaneously recreate electrons with correlated momenta rather than EM waves and a loss of matter. This Is where I realize that this idea is a bunch of hooey.
What is spin? I know people have explained that it has something to do with the failure of two operators to commute or something... isn't that the uncertainty principle? maybe I'm getting things mixed up here, but what is spin? don't tell me about the stern Gerlauch (or however you spell it) experiment, I just don't get it. Why is it called spin when it has nothing to do with spin in the classical sense? I can understand the angular momentum quantum number, and the magnetic quantum number (because the electron is moving through space, and has a mag field around it since it has a charge), but I don't understand spin. If the electron has a dipole mag field cause by it's spin, wouldn't it be oriented in any direction, rather than just two? Suppose it just has a mag field but as a monopole, (huh?) then it would'ne be directional, but it could have two different values, inward flux or outward flux, but a dipole has both inward and outward flux just oriented on opposite sides. Does spin mean that universally, all electrons are oriented in only two ways? is there a universal north and south, as if all electrons are tiny compasses that align themselves automatically. what is spin? arghhh!

 

[vanesch]

this gets me thinkin'. Being that I don't know what spin is, I might as well relate it to anything, including dark matter (which I have no clue what that is, besides matter we can't see) so here goes. I know I'm wrong with this, and I think it's rediculous, but I got to ask, is spin up=matter, and spin down=antimatter or dark matter, or vice-versa?

No, spin doesn't determine whether something is matter or antimatter.

 

[Norman]

Jonny Trig,
Please read these:

https://www.physicsforums.com/showthread.php?t=75234&highlight=spin

https://www.physicsforums.com/showthread.php?t=88970&highlight=spin

https://www.physicsforums.com/showthread.php?t=83078&highlight=spin

that should help

 

[Jonny_trigonometry]

"Now, what does this mean ? Well, let's look at QM and how the J-operator is connected to rotations. A QM-system is invariant under rotations if

1) the normalization of the wavefunction is preserved
2) the expectation value of any observable is preserved
3) if the Hamiltonian does NOT change under rotations."

So, would a conformal mapping be an invariant transformation?

 

[Jonny_trigonometry]

The QM prof. was indroducing Dirac's change into matrix notation today, and I was wondering if all the restrictions and operations of bound states and the hilbert space that they dwell in combined, form a field, and that field is an isomorphism with the field of n-dimentional complex numbers and operations. Is that why things can be switched over into matrix form?

 

[Jonny_trigonometry]

Ok, I get the point about how spin arises from the way we model physics, but what does it mean, physically? How can I think of spin as an attribute of a particle? You might say, it's an intrinsic constant angular momentum of the particle which can only have two orientations... but what does that mean? how can there only be two orientations when a point isn't oriented in any particular direction?

Does the Stern Gerlach experiment use a velocity selector before it sends them through the nonhomogeneous mag field?

 

[selfAdjoint]

The QM prof. was indroducing Dirac's change into matrix notation today, and I was wondering if all the restrictions and operations of bound states and the hilbert space that they dwell in combined, form a field, and that field is an isomorphism with the field of n-dimentional complex numbers and operations. Is that why things can be switched over into matrix form?

Yes the Hilbert space is n-fold complex (in the limit, infinite dimensional). It is acted on by an algebra of linear operators. In the finite dimensional case, and in some suitable basis, the algebra consists of a set of nXn complex matrices {A} closed under the inner product <A,B> = A^*B, where * indicates the adjoint, in this case just the conjugate-transpose. The complex numbers by themselves form a field, which supplies the constants to the algebra. (An algebra, in case you didn't know, is just a vector space closed under a linear inner product, or if you prefer a ring which is also a vector space).