So rmax, do you know how a gyroscope works? A little interaction of gravity (mathematicians would call that 'torsion') makes things a bit more interesting, doesn't it?N

QuoteOriginally posted by: Nrmax,HUP looks great if you do your work in 1 or 2 dimensions, but from simple classical mechanics, you know that angular momentum in 3 dimensions is not in Hilbert space (Riemann manifold).Thought about this when I went to get my lunch... At the risk of admitting how stupid I am: I don't understand. Any pointers for the intellectually challenged?

QuoteOriginally posted by: rmaxQuoteOriginally posted by: Nrmax,HUP looks great if you do your work in 1 or 2 dimensions, but from simple classical mechanics, you know that angular momentum in 3 dimensions is not in Hilbert space (Riemann manifold).Thought about this when I went to get my lunch... At the risk of admitting how stupid I am: I don't understand. Any pointers for the intellectually challenged?Sure...The Hamiltonian is defined on a symplectic manifold and not on a Riemann manifold. This is well known, but those QM dudes (like Feynman) insisted on ignoring math and classical physics.

- Cuchulainn
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Quoteignoring math and classical physics.Do this at your peril. As far as Hilbert spaces are concerned, they are useful but only to a certain extent. For classical PDE they need to be extended.

Last edited by Cuchulainn on March 22nd, 2006, 11:00 pm, edited 1 time in total.

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Quote Hamiltonian is defined on a symplectic manifold and not on a Riemann manifoldOK -at the risk of getting myself into some serious discussion hot water I am not going to understand!1/ When I did Physics N years ago we didn't approach QM in this way - why is QM on the symplectic manifold and not on a Riemann manifold?2/ Why does this make a difference as far as UP is concerned? The simplest formulation is just the wave used to probe the position or momentum of the wave particle. Edit: Corrected quote tags

Last edited by rmax on March 22nd, 2006, 11:00 pm, edited 1 time in total.

N,sometimes even SU(2) is sufficient in NMR, depends what you do. As cuch has implied we don't have the luxery of saying 'here's an idea, universe conform to it' and you have to remember that math is tool for us and nothing more. I think theoreticians shouldget in the lab occasionally and try some experiments and vice versa and the hard sciences would be a much more productive industry. If our work and conjectures don't benefit mankind in some way then what's the point? Long story short, how does your conjecture benefit (say) my NMR-QC project?

QuoteOriginally posted by: rmaxQuote Hamiltonian is defined on a symplectic manifold and not on a Riemann manifoldOK -at the risk of getting myself into some serious discussion hot water I am not going to understand!1/ When I did Physics N years ago we didn't approach QM in this way - why is QM on the symplectic manifold and not on a Riemann manifold?2/ Why does this make a difference as far as UP is concerned? The simplest formulation is just the wave used to probe the position or momentum of the wave particle. Edit: Corrected quote tagsrmax,As long as you don't use the Hamiltonian, you're cool. Obviously the sum of the torsions (and forces of course) must be zero, therefore the 3-dim Jacobian must exactly zero. Riemann manifolds do not have zero torsion.The simplest correct QM formulation is the 'nonlinear Schroedinger's wave equation'. Angular momentum in 3-dim is not trivial as you suggest.N

QuoteOriginally posted by: zetaN,sometimes even SU(2) is sufficient in NMR, depends what you do. As cuch has implied we don't have the luxery of saying 'here's an idea, universe conform to it' and you have to remember that math is tool for us and nothing more. I think theoreticians shouldget in the lab occasionally and try some experiments and vice versa and the hard sciences would be a much more productive industry. If our work and conjectures don't benefit mankind in some way then what's the point? Long story short, how does your conjecture benefit (say) my NMR-QC project?z,This is not a conjecture but simply well understood classical mechanics. How does your NMR-QC project benefit from good math? You'd use the correct transform/geometry rather than guessing that a Hadamard transform does something good for you (it might if you were working with quarterions). There would be *no* noise in your result -- How's that?n,BTW, what's a lab?Edit: In case you're interested, the signal you're seeing is called an L-function in math.

Last edited by N on March 22nd, 2006, 11:00 pm, edited 1 time in total.

>> I'm losing faith in physicistsI'm shocked.

>> I'm losing faith in physicistspauper,I guess your prayer session for me last week didn't help. Edit: I pray for more math types on Wilmott. It'd be fun to discuss somthing like 'vertex algebras'.

Last edited by N on March 22nd, 2006, 11:00 pm, edited 1 time in total.

I don't know about l functions for signals N; signals have pretty easy eigenvalues not requiring any sexy number theory.Orientational dependence from tensor interactions (eg., quadrupoles) introduce spectral broadening but even then they oftenmay be simulated numerically using an average hamiltonian.noise is interesting, but I'm not sure what sort you mean. mechanical noise is taken care of via signal averaging. QM noise or decoherence is v interesting and requires novel pulse sequences and phase cycling to eliminate artifacts. you probably know of an early innovation called the spin echo which helps overcome spin-spin decoherence (eg., the dipole coupling) by (in the simplest case) refocussing/rotating magnetization. phase cycling is important paerticularly for quadrupole spins I>1/2 where multiple quantum transitions take place. NMR pulses have specific attributes which manipulate the spins, but the phase allows one to (over the course of many scans) ED: select particular MQ transitions which over the course of time (much like phasors in EE) cancel or coadd. multiple pulses and transitions give rise to large numbers of pathways; one of my papers is on using Galois fields and zech log permutations to reduce phase tables which in the case of NMR-QC will hopefully mean faster clocks and more qubitsthis is an example of theory and experiment nicely meshing N; why not set up a real experiment or even a gedunken to test your ideas?

Last edited by zeta on March 22nd, 2006, 11:00 pm, edited 1 time in total.

- phenomenologist
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Physics is to Math what Sex is to Masturbation --Richard Feynman

- phenomenologist
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Another one:One day in class, Richard Feynman was talking about angular momentum. Hedescribed rotation matrices and mentioned that they did not commute. Hesaid that Sir William Hamilton discovered noncommutivity one night when hewas taking a walk in his garden with Lady Hamilton. As they sat down on abench, there was a moment of passion. It was then that he discovered thatAB did not equal BA.

QuoteOriginally posted by: NI'm losing faith in physicistsIs this thread about physics, or is it about you, N? What, did you pick up that "I'm losing faith in" line from your wife? Nobody gives a fuck if he has your faith.

QuoteOriginally posted by: farmerQuoteOriginally posted by: NI'm losing faith in physicistsIs this thread about physics, or is it about you, N? What, did you pick up that "I'm losing faith in" line from your wife? Nobody gives a fuck if he has your faith.Do you say your prayers with that potty mouth

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