## 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.

real physical states carom off the planes and subspaces through which they

would be confined by unitary transformations? What would be the experimental

evidence for this? Chemical reactions?

When you have a system tooling along in its subspaces … and then introduce

an entirely new element into the system from outside, then yes, you have to

redefine where you now are, because physics cannot predict when the long arm of

a scientist or gremlin is going to drop something new (eye-of-newt) into a

beaker.

As Bohr indicated, when you change the experimental

conditions -- the boundaries and/or framework -- you need to include these

changes in your description. The redefinition of the apparatus works its way all

the way down to the eigenstates. For Bohr, this was simply an extension of

Einstein’s lesson concerning the dependence of variables on one’s frame of

reference.

Your approach is not yet comprehensible to me. I’ll ask again, what is its stance on conservation of information?

The gee-whiz -- isn’t this remarkable -- method of introducing people to quantum

physics can be counterproductive. A different civilization may feel that it is

classical physics that is counter-intuitive.

The Bell inequalities are proven using classical logic. One can tediously

illustrate and prove them using Venn Diagrams. It’s all about Boolean logic and

the classical assumption that things are either with you or not with you. The

Biblical predecessor is that things are either with you or against you. The

quantum-logical tolerance and acceptance of off-diagonal cross product terms is

unthinkable.

The difficulties and limitations of classical logic for many particle

systems were sensed by the pioneers of quantum physics, including Einstein,

long before Dirac and von Neumann. It was evident in the way one had to use the

cross-product (tensor product) of state spaces H1 x H2 x H3 …. for many body

systems and not a classical sum H1+H2+H3 …. The cross-products give one a

higher dimensional arena and sophisticated ways for objects to be entangled

that classical logic completely misses.

A mnemonic for these cross-products is a Totem Pole or for that matter, any

mythological beast that is an incongruous juxtaposition of seemingly

irreconcilable objects. Such objects are rather common in non-western art and

logic. The classical alternative is more like a painting of the Great Judgment;

objects are sorted into separate sets and hierarchies; off-diagonal terms are

not even considered.

I realize that this may all sound far fetched. Nobody writes about quantum

logic in this way. Or do they? When Bohr pleaded passionately about an “open

world” tolerance and acceptance, was he not applying the quantum logic that had

become natural to him?

A more familiar issue is in the way Quantum Operators do not commute. Here

too one can ask what is so sensational about that? One can even consider

operators that fail the associative law. They exist algebraically in a higher

dimensional analog of Hans’ waltzing quaternions. This was pointed out to Sir

William Rowan Hamilton by a colleague long ago, and yet Hamilton kept toiling

with his beloved quaternioins.

procedures being non-commutative. Suppose we start with a freshman student for

which I’ll give the state vector |Fresh>.

Let B stand for Bathing, U stand for the operation of putting on one’s

Underwear and let P stand for putting on one’s Pants. The sequence of operations

PUB acting on |Fresh> will put the our freshman in a prepared state PUB|Fresh>

for performing a wide range of tasks, whereas a change in the order of PUB to

BUP, for example, is going to be … disastrous.

That’s a tough fish of bones to swallow, even for a cat

Why would quantum electrodynamics have dynamics in its name

if it did not include dynamics?

Newtonian mechanics includes Newtonian dynamics using

classical logic.

Quantum mechanics includes Newtonian mechanics. It covers it

completely and extends it using traditional quantum logic. It has all of

Newton’s dynamics in it and more. So how can you say that is not a logic that

includes dynamics?

Can someone else help me here?

((I only have a couple of days left here before I head north to remote areas of British Columbia. I presume the Hammock Physicist is already on a sabbatical of sorts.))“Is it your conviction Hans that even when recording devices are not present, real physical states carom off the planes and subspaces through which theywould be confined by unitary transformations?”

To which he replied:

“Instruments are not required. This is about mathematics ..."

In my inquiry, I was checking to see if Hans' “dynamics” has anything to do with the so-called measurement problem. He signals that it does not.

To understand you Hans, I have to start from something familiar. Since I originally specialized in General Relativity and the singularity theorems of Penrose and Hawking, I have long been familiar with Penrose.

Readers here may be aware that Penrose puts all of the operators of dynamical quantum physics into two distinct classes. One of them he calls U for unitary. The other class he calls R for reduction. This latter class has to do with the measurement problem and the projection of states into subspaces. Both classes have dynamics; maybe not dynamics as you imagine dynamics to be, Hans. You seem to be on a solitary trip.The whole notion of “dynamics” can be a chimera. If you flow along with the particles … if your coordinate system itself is tied to the particles themselves …. as one would do with 19^{th} century Lagrangian coordinates …. then what changes may be an average distance from one molecule (or galaxy) to another. However, in the overall scheme of things, the total energy, momentum, angular momentum, charge, and more exotic flavors never change. Not even the information. I don't believe in evolution. Everything is as sophisticated as it has ever been.

It is a matter of taste and efficiency as to whether one considers "dynamics" to be an active rotation (for example) or a passive one. When it comes to down to what is measurable, it makes no difference if you want view things from on or off the merry-go-round. There is a coordinate

transformation from one frame of reference to another. This is why “dynamics” is a bugaboo. Einstein's equivalence principle taught us that before anyone here was born.

Neither stance is more fundamental. It is one of those duality thingies. Ladies' choice.

I don’t know if anyone is reading this blog or can follow it. I still have the feeling that you are making up theory where none needs to be made.

I mentioned the annihilation and creation operators because these basic raising and lowering operators include the smallest changes that the quantum of action will allow.

You wrote that you are interested “when two very small quantum physical items influence each other … The small quantum physical items hardly influence each other’s state. Still there is some influence … it is sensible to also investigate what moves the tiny objects. ... this is NOT described by plain unitary transforms. The situation is much more complicated.”

**What would Feynman say to that?**

Methinks you have chosen a pretty lonely path for yourself.

A funny thing happened on the way to the forum.

You have not given us Hans, a real physical situation in which your more complicated theory can calculate something at a higher degree of precision than can quantum mechanics. You have not even shown that you can do calculations with your theory.

If your theory is better at describing an array of microphenomena, then it should be able to account for something that standard quantum mechanics misses. Good luck with that.

In my posts I have indicated that quantum mechanics is sufficient and complete enough. No additional layers of complexity are needed, no additional hidden variables and no transformations unforeseen by Dirac and his students Penrose and Feynman. If it ain’t broke, why fix it.

An excellent thin book on the merits and meaning of Dirac’s bra kets is Primer of Quantum Physics by Marvin Chester; he had Feynman as a teacher. It needs to be supplemented with a standard presentation of experiments.Currently, I am reviewing statistical physics because Erik Verlinde’s approach offers a simplification of what we already know. Occam’s razor still rules in the sciences. Theology is different.

I’ll leave with a word from Feynman in his Lectures, Volume I

**“ … although most problems are more difficult in quantum mechanics than classical mechanics, problems in statistical mechanics are much easier in quantum theory.”**

We accepted the complications of General Relativity because it allowed us to calculate at a higher degree of precision. Much later (long after Tesla), we learned how to make the theory simple and natural in our understanding of it. It took gifted teachers like John Wheeler to do so; he practically created a new generation of physicists conversant in Einstein's lessons.

In the same vein Hans, you need to simplify and show where you can do more accurate calculations than can current theory.

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.