## Comments

I could raise some quibbles with the above. For example,

when you mention probability vectors, surely you meant quantum amplitude

vectors. Probability is a real number between zero and one and not a

vector. To be fair, you did say“probability density vector”. then again, you used the word vector 40 times. Maybe you meant to say density matrix. (I see now that others have already posted about this).

I think your point is that quantum mechanics and quantum

field theory have become horribly complicated. A post-doc fellow is going to be

buried in one, two or three corners of theory, while all of the other corners

are bursting out with their own fancy mathematics

There are some overarching principles to help one navigate

the zoo. One application or another of a minimizing principle can always attain

the dynamical equations. What is minimized is the Action and given the symbol S

(not to be confused with the S that is used in other contexts for

entropy). Action has the same units as

Planck’s constant and also the same units a pair of conjugate variables. The

master equation for Action is the following: the variation of S = 0. δS=0.

It is a difficult formula to actually use, yet there it is.

And yes, transient phenomena are not the same as near equilibrium steady-state phenomena

Your essay reminds one of the difficult times in the late

sixties and early seventies when the particle zoo had become a horrible looking

mess. Quarks and a better understanding of gauge theories helped to bring some

unity and order to the zoo.

Although you mention quantum logic quite a few times in your

essay and allude to information theory, your essay gives one no awareness of

the reorganizing and simplification that is going on in work by people like

Erik Verlinde. Our Hammock Physicist here has written a number of posts about

this. I have tried to continue the conversation there at the following link.

http://www.science20.com/hammock_physicist/it_bit_whole_shebang

Some feedback would be appreciated. Will Verlinde’s approach

make it into introductory courses to help make physics more intelligible?

Concerning unitary transformations: they hint at there being a "conservation of information"

principle. I defer to Susskind on that for now. I have not seen the principle clearly stated or widely embraced. The old proverb is that an elephant never forgets.

hoo boy … It did not think that I would read here in Science20.com that “[Dirac] was wrong in two respects” concerning unitary transformations …. and then a quotation that Einstein’s relativity “makes people blind to [its] underlying errors” … not that Helen is subscribing to it … yet gossip repeated becomes fact in some circles.

An excellent primer on Special Relativity is Spacetime Physics by Wheeler
and Taylor.

It was originally a course for freshmen at Princeton.

A classic on Quantum Physics is the same book by Dirac cited by Hans.

For something easier and less confusing perhaps, yet still completely mainstream, you can try the link in my profile.

Seriously Hans, a lot of operators in physics are infinitesimal operators. The transition from infinitesimal movements to macroscopic movements is called integration … on my island. Information is still preserved every step along the way, even if us mortals cannot recover the text of documents burned in a fireplace.

To paraphrase from Wheeler …. a purrfectly classical black hole has no hair. A quantum mechanical black hole, on the other hand, sends out more hair than Tesla with his palms on a mountaintop Van de Graaff machine. In those tuffs of hair, one can in principle, reconstruct exactly how a black hole was formed (though it may take the life of the universe for one to do so). Microphysics is unitary, even at its extremes. It is reversible. At the macroscopic levels, course graining over hidden degrees of freedom causes irreversibility and a flow of time whose “arrow” (not a Hilbert space vector) points in the direction of increases of entropy. It is a more complicated than that perhaps, yet without keystone equations involving temperature, one can scarcely start her up and see if she runs.Hans, you need to get away from this "redefiner" stuff -- you're completely wrong about it. A unitary operator is the most general norm-preserving transformation in Hilbert space. While it does have eigenvectors, that fact does not make it any less general. True its eigenvectors are not "moved", but they are changed (multiplied by the eigenvalue - which is in the unitary case a phase) An analogy is three-dimensional rotations -- any three-dimensional rotation has an axis which is not "moved", but that does not make it less general. It just happens to be a theorem that three-dimensional rotations always have this property. Likewise its a theorem that the most general unitary operator can always be decomposed into actions on one- or two-dimensional eigenspaces. This is not a restriction.

The "trail of infinitesimal unitary transforms" you talk about - a product of unitary transformations is again a unitary transformation. Imagine that! Your redefiner is just another unitary transformation, and yes it will have its own set of eigenvectors and eigenspaces all over again. The redefiner concept is completely redundant.

Only second sentence, already wrong. WF is NOT a PDF. After that, it goes steeply down hill. I applaud your trying to get people interested into QM, but it may be much better if you sleep somewhat more over your stuff before posting it, else it may just do the opposite of clarifying.