Parallel Universes

[Finster]

Re: Parallel Universes

... Because these Bell's theorem experiments prove that the bizarre non-local affects predicted by Quantum Mechanics really do exist, they therefore show that no "common sense" (local affects only) theory (such as TEW) can possibly be correct.

However a new result Disproofs of Bell, GHZ, and Hardy Type Theorems and the Illusion of Entanglement (April 2009, Oxford University, Joy Christian) purports to demonstrate that Bell's theorem is fundamentally flawed, and that the experiments demonstrating Bell's theorem do not demonstrate quantum mechanical non-locality.

This is good news for Little's TEW. It's main stumbling block, Bell's theorem, may have just been shot down..

John Bell, ironically, was himself a sympathizer of Einstein and others on interpretations of QM. Not long before his death, he stated in a published article that "... however legitimate and necessary in application, [the following words] have no place in a formulation with any pretension to physical precision: system, apparatus, environment, microscopic, macroscopic, reversible, irreversible, observable, inflationary, measurement ... on this list of bad words, the worst of all is "measurement" ... It would seem that the theory is exclusively concerned with the "results of measurement" and has nothing to say about anything else. What exactly qualifies some physical system to play the role of measurer? Was the wave function of the world waiting to jump for billions of years until a single-celled living creature appeared? Or did it have to wait a little longer, for some better qualified system ... with a Ph.D.?..."

[Finster]

Re: Parallel Universes

The establishment picture is not of a wave or particle traveling together, but rather an exercise in linear algebra: particles and waves are viewed as alternative basis sets in which a given state can be represented, and notionally, you could imagine a system being in an eigenstate of one of these representations (i.e. a "pure" particle or wave) -- but the mathematical relationship between the representations is such that states which are simultaneously eigenstates of both representations don't exist....

I think it's more than that, Ash. The two-slit experiment and the photoelectric effect, as examples, require the physicist to consider both particle and wave models, well before you get into the mathematics. In fact the debate about the nature of light being particle or wave was in full thrust even back in the days of Newton. Then of course De Broglie proposed the reverse: that matter - even stuff previously thought to clearly be particulate, like the electron - might itself disply wave characteristics. All quite independent of abstract algebra.

My QM text, Eugen Merzbacher's Quantum Mechanics, which does go through the linear algebra, goes so far as to state matter-of-factly that [the amplitude of the wave function squared] "is proportional to the probability of finding the particle at position x".

[vinoveri]

Re: Parallel Universes

guys, if you're willing to subscribe to a theory postulating parallel universes (untestable as far as I can tell, and the real world consequences of such a state still escape me), then I suppose man-made global warming doesn't seem out of the question .

QM works, and I've met many who are proficient mechanics using the theory, but few (if any) who really understand "what it means". Even Richard Feynman admitted it to be "strange".

[ASH]

Re: Parallel Universes

I think it's more than that, Ash. The two-slit experiment and the photoelectric effect, as examples, require the physicist to consider both particle and wave models, well before you get into the mathematics. In fact the debate about the nature of light being particle or wave was in full thrust even back in the days of Newton. Then of course De Broglie proposed the reverse: that matter - even stuff previously thought to clearly be particulate, like the electron - might itself disply wave characteristics. All quite independent of abstract algebra.

My QM text, Eugen Merzbacker's Quantum Mechanics, which does go through the linear algebra, goes so far as to state matter-of-factly that [the amplitude of the wave function squared] "is proportional to the probability of finding the particle at position x".

I agree about the historical antecedants of the modern formulation -- the "corpuscular" theory of light, and so forth, down through Einstein with the photoelectric effect and de Broglie. It's definitely true that the respective particle and wave models have played an important historic role. What I'm stating is that the unifying picture that eventually emerged from all this is rooted in linear algebra.

It is common to teach quantum mechanics starting with Schroedinger's equation and wave functions. I think that is probably because it used to be that students of physics would have encountered the classical Hamiltonian already in their study of mechanics, and because most students would have some familiarity with differential equations, so Schroedinger's treatment is the most familiar. I'm not familiar with Merzbacker (except that it is one of the standard texts), but it sounds like he follows this normal development. Generally, after covering basic computation in the position representation, such texts will introduce the transformation into the momentum representation and show how Schroedinger's equation can be re-written using momentum as coordinates instead of position, with solutions for which the amplitude of the wave function squared is "proportional to the probability of finding the wave with momentum p." Along the way, the superposition principle will have been introduced, and hopefully orthogonality and operator algebra (stuff like commutators and ladder operators). At this point, things will start sounding an awful lot like linear algebra, and eventually it will be revealed that the position or momentum wave functions are projections of a general state vector onto the basis vectors corresponding to classical "particle" or "wave" states. The object described by this state isn't a particle or wave itself in the classical sense of these terms, but idiomatically, most physicists still use the word "particle" because it is convenient. At that point in the course material, explicit wave funtions for specific representations aren't used very much, and the notation switches to Dirac's bra-ket notation in order to talk about the state vectors in a more general way. (And after that, those bastards mix in special relativity, my head explodes because I don't have a deep enough "stack" for all the indices, and I go my separate way to do semiconductor device physics, leaving smarter folks to continue the slog.)

Anyway, my feeling is that although QM is often taught starting with the Schroedinger equation, that treatment is probably the least useful in terms of teaching the important concepts. The Sakurai book I mentioned above is great, because it skips the historic development and gets immediately to "the good stuff".

[Finster]

Re: Parallel Universes

Yes, the Merzbacher text is probably pretty standard mainstream. He remarks in the preface to the third edition (my copy) to the effect that (unlike in earlier editions) he now presumes the student to have already been exposed to quantum mechanics, even saying that "the bra-ket notation is already familiar to all students". The Schröedinger equation is introduced alongside operator algrebra.

One of the things that intrigues me is how it happens that a tool originally developed to deal with systems of linear equations turns out to be so useful in modeling the behavior of elementary physical entities.

[ASH]

Re: Parallel Universes

One of the things that intrigues me is how it happens that a tool originally developed to deal with systems of linear equations turns out to be so useful in modeling the behavior of elementary physical entities.

Yes. This is where I get all wild-eyed and start semi-mystical metaphysical mumbling about how math is Truth, and the universe is just a very complicated mathematical expression that sums to zero. But yeah -- I'm kind of preoccupied with the observation that the behavior of physical entities matches the properties of abstract mathematical objects so well... and that in many cases, the math was developed for largely abstract purposes far in advance of the discovery of physical systems with the same properties. I'm about the least spiritual guy I know, but as much as anything, this connection between "pure" math and the tangible world is my 'religion'. At some level, I guess I do believe that it must all be math. Since I was in high school, and first exposed to popularized accounts of various cosmological theories, I have thought that mathematical self-consistency and "summing to zero" might be sufficient criteria for the universe to exist. At the time, I think I was taken by speculation about how the universe might have been born as a vacuum fluctuation, and that the negative potential energy of bound states in the universe might balance the positive energy associated with the matter and energy in the universe, thereby "summing to zero". Sadly, my intellect proved inadequate to pursue this sort of thing professionally, so my day-to-day concerns are far more prosaic... such as how to reduce the dark current in my photodiodes and make a buck or two by solving the decoy problem (for MDA).

Cheers,
Andrew

[cobben]

Re: Parallel Universes

"There has been a lot of writing that seems to sensationalize the "weird" aspects of QM, even suggesting that it implies some kind of moral relativism. "

Up a level of complexity or a few, it's been some years since I studied just complexity theory, revisited Keirsey's site

Relational Science: Towards the Technology of Comparative Complexity
http://edgeoforder.org/ccomp.html

Mathematics Itself: On the Nature, Origin, and Fabrication of Structure and Function in Logic and Mathematics

http://edgeoforder.org/mathitself.html

" . . .
2.1 Science, Math, and Modeling

2.1.1 An Initial Look at Some History of Science

Again to give an indication of a problem, let us look at the new developing fields of string theory and loop quantum gravity from on high, before we plunge into the depths. That high perch partly being a function of time.
In relatively recent ancient times, the Greek astronomer Ptolemy devised a method to model the heavens -- those pinpoints of light in the night sky. The problem came in that there were “wandering stars” and these things, called planets, seemed pretty predictable, but not completely. In fact, Ptolemy had to devise a pretty complicated model using his “perfect” and "simple" circles by including the notion of epicycles. Through sheer doggedness, he “fit” these paths of the planets and provided mariners and clerics, useful tables that were “good enough for government work” that held sway for about 1300 years.
Of course, along came Copernicus, who suggested a better model, which was instantiated, modified, and refined into mathematical form by Kepler, and then converted and generalized into a simple differential equation by Newton. Newton, in creating and applying calculus, started the trend in using simple to sophisticated differential equations to model the world. Bernoulli, Lagrange, and others continued the process in the development of a kind of implicit recursive function theory in modeling physical processes.
More recently, in the 1800's physicists have used mathematical methods, namely the Fourier transforms and the Taylor series as general “fitting” strategies. It is well known that one can approximate any single line curve using either a Fourier or a Taylor series, given enough terms (with real coefficients). This strategy, the strategy of building up a model by cobbling together a set of mathematical pieces -- is similar to Ptolemy's strategy. It should be pointed out that Newton's laws of motion are essentially a two-term cutoff of a Taylor's series expansion of 1/(x-1)[Chapter 4, Life Itself]. Slightly more complicated version of Newton's laws, Lagrangian and Hamiltonian differential equations have been the mainstay of much of physics. Renormalization groups, a range-limited form of differential equations (there is a scale cutoff) is yet another form of these kinds of recursive functions even more sophisticated. Of course, there was a crisis in physics that started to brew with Max Planck's discovery of quanta in the domain of the very small and Einstein's discovery of relativity in the domain of the very large.
There is a problem here, of course, what does one mean by "large" and "small" and what is the relationship between those concepts and "in" and "out".
Tensors, the next step in mathematics proper, is the next generalization of differential equations using recursive function theory in multiple dimensions. Werner Heisenberg's quantum mechanics in the form of non-communitive matrix algebra was shown to be "mathematically equivalent" by Erwin Schrödinger wave mechanics, a recursive function formulation. Both men were hoping this method of modeling would have the Church/Turing thesis to be true. Unfortunately, Church's thesis is not true [Rosen 91].
In some sense, similar to Riemann's dreams, tensors are a general way of adding dimensions to the modeling problem whether the dimensions be large in the case of Einstein's relativity or small in the case of Planck's quanta. In the final analysis, similar to Ptolemy, it is now hoped by modern string theorists that cobbling together enough “dimensions” and in the right way (26 or less – 11 seems particularly attractive at this point) they can model the universe: large or small. The technical term for this wish is called M-theory.
. . ."

[Finster]

Re: Parallel Universes

... Tensors, the next step in mathematics proper, is the next generalization of differential equations using recursive function theory in multiple dimensions... In some sense, similar to Riemann's dreams, tensors are a general way of adding dimensions to the modeling problem...

Oh great ... and we were just stretching to get our arms around the abstract algebra ... ;)

[Finster]

Re: Parallel Universes

Yes. This is where I get all wild-eyed and start semi-mystical metaphysical mumbling about how math is Truth, and the universe is just a very complicated mathematical expression that sums to zero. But yeah -- I'm kind of preoccupied with the observation that the behavior of physical entities matches the properties of abstract mathematical objects so well... and that in many cases, the math was developed for largely abstract purposes far in advance of the discovery of physical systems with the same properties. I'm about the least spiritual guy I know, but as much as anything, this connection between "pure" math and the tangible world is my 'religion'. At some level, I guess I do believe that it must all be math. Since I was in high school, and first exposed to popularized accounts of various cosmological theories, I have thought that mathematical self-consistency and "summing to zero" might be sufficient criteria for the universe to exist. At the time, I think I was taken by speculation about how the universe might have been born as a vacuum fluctuation, and that the negative potential energy of bound states in the universe might balance the positive energy associated with the matter and energy in the universe, thereby "summing to zero". Sadly, my intellect proved inadequate to pursue this sort of thing professionally, so my day-to-day concerns are far more prosaic... such as how to reduce the dark current in my photodiodes and make a buck or two by solving the decoy problem (for MDA).

Cheers,
Andrew

As you're probably aware, to Einstein's objection that "God does not play dice.", Bohr (perhaps apocryphally) retorted "Stop telling God what to do!" I have the feeling many of these scientific pioneers did feel they were somehow looking for, if not God himself, then his handiwork, the set of rules by which everything would work. It's hard to study fundamental physics, for me anyway, without coming away awestruck, as if having glanced the dust of creative Genius.

Alas, I can make no claim of genuine expertise in the field either. Not only is the math demanding intellectually, but of time, too. Fortunately you can fashion a sort of middle ground between the science-for-non-scientists and the science-for-those-who-are-into-symbolic-abstraction by drawing from both kinds of sources. The attraction of the summing-to-zero point of view is easy to sympathize with; especially when you look at the various symmetries such as particle-antiparticle ... electron-positron annhilation, for example, always fascinated me. Far as the nominal subject of this thread goes, however, I could never see much sense in the many-universes theory. One seems quite enough to handle...

I do get the impression, though, that somewhere physics has wandered off course. There are just too many particles. Especially these virtual particles that are said to mediate forces between real particles ... it just smacks of artificiality. Can a design so complex and flaky actually have been robust enough to build a whole universe on? And then there's this great search for the Grand Unified Theory Of Everything, that supposedly will complete physics by unifying gravity with the other three "fundamental forces". I suppose we will need a particle for that, too. But wouldn't that be repudiating Einstein's General Theory Of Relativity? The whole point was that gravity is not a "force"; it's a warping of the structure of space-time itself. If General Relativity is correct, and unification is correct, then wouldn't the sensible strategy be to show how all forces are somehow curvatures in dimensions of space-time?

[cobben]

Re: Parallel Universes

Has the can of worms been opened, or has the worm turned?

QM!?

Why not Quantum Biochemistry and Quantum Genetics?!

Robert Rosen:

http://en.wikipedia.org/wiki/Robert_Rosen

http://www.rosen-enterprises.com/Rob...bert_main.html

" . . .
Rosen's research was concerned with the most fundamental aspects of biology, specifically the question "What is life?" or "Why are living organisms alive?". Major themes in the work of Robert Rosen were:

• developing a specific definition of complexity that is based on relations and, by extension, principles of organization
• developing a rigorous theoretical foundation for living organisms as "anticipatory systems"

Rosen came to realize that the contemporary model of physics - which is still based on the Cartesian/Newtonian world of mechanisms - was inadequate to explain or describe the behavior of biological systems; that is, one could not properly answer the question "what is life?" from within a scientific foundation that is entirely reductionistic. Approaching organisms with reductionistic scientific methods and practices always sacrifices the whole in order to study the parts, but what Rosen discovered was that the whole could not be recaptured once the organization had been destroyed. His conclusion was that the very thing about living organisms biologists should be studying, the organization, was the first aspect of all biological systems to be thrown away in scientific analysis. This is regarded as a limitation of the part of contemporary science which regards the machine or automaton as a model for all systems in the universe. Rosen came to regard the machine metaphor as the single biggest impediment to scientific exploration of questions in biology and concluded that the paradigm needs to be expanded beyond purely reductionist capabilities. In order to do this properly, he said there must be a sound theoretical foundation underlying the expansion and that relational complexity provided such a foundation. So it was that, rather than biology being a mere subset of already-known physics, it turned out that biology had profound lessons for physics, and science in general.^[3]

. . ."

[ASH]

Re: Parallel Universes

There are just too many particles. Especially these virtual particles that are said to mediate forces between real particles ... it just smacks of artificiality.

I think the whole virtual particle thing is on pretty solid experimental ground. A lot of the examples I've heard of concern virtual bosons, but I think the influence of virtual fermions can also be measured. "Spontaneous" emission of light by an excited state is actually stimulated by virtual photons; one can measure the Casimir force due to a mismatch between the number of virtual photon modes outside an optical cavity versus inside, where the boundary conditions of the cavity eliminate some of the possible modes; the zero-point motion of the ground vibrational state of a chemical bond can affect the rate of some chemical reactions, and the ground state vibrational excitation is a virtual phonon. I think charge-screening effects and "vacuum polarization" due to virtual fermions can also be measured experimentally.

I do get the impression, though, that somewhere physics has wandered off course.

...

And then there's this great search for the Grand Unified Theory Of Everything, that supposedly will complete physics by unifying gravity with the other three "fundamental forces". I suppose we will need a particle for that, too. But wouldn't that be repudiating Einstein's General Theory Of Relativity? The whole point was that gravity is not a "force"; it's a warping of the structure of space-time itself. If General Relativity is correct, and unification is correct, then wouldn't the sensible strategy be to show how all forces are somehow curvatures in dimensions of space-time?

I'm personally hoping that these points will become clearer during my lifetime. QM and GR are right around 100 years old... give the physicists another couple of decades, and I think the state of theory may be more satisfactory.

[Finster]

Re: Parallel Universes

Has the can of worms been opened, or has the worm turned?

QM!?

Why not Quantum Biochemistry and Quantum Genetics?! ...

I'll take Darwinian Physics for $500, Alex...

[Finster]

Re: Parallel Universes

I think the whole virtual particle thing is on pretty solid experimental ground. A lot of the examples I've heard of concern virtual bosons, but I think the influence of virtual fermions can also be measured. "Spontaneous" emission of light by an excited state is actually stimulated by virtual photons; one can measure the Casimir force due to a mismatch between the number of virtual photon modes outside an optical cavity versus inside, where the boundary conditions of the cavity eliminate some of the possible modes; the zero-point motion of the ground vibrational state of a chemical bond can affect the rate of some chemical reactions, and the ground state vibrational excitation is a virtual phonon. I think charge-screening effects and "vacuum polarization" due to virtual fermions can also be measured experimentally.

Since I don't have a better theory (yet...;)) guess I'm not standing on solid enough ground to complain. (Personally, I don't believe there is any such thing as point particles in the first place, it's all fields). But will point out that the evidence is - as it must be for anything on that scale - decidedly indirect and circumstantial. But more to the point, it is not at all unknown for multiple theories to be in perfect accord with the experimental evidence, and the choice boils down to esthetics. Or more specifically, simplicity and elegance. For example, alternatives to special relativity have been proposed that are built on a purely Newtonian foundation in the sense that they assume time and space to be invariant. But they require some mathematical convolutions to get there that relativity doesn't. The situation is reminiscent of the Ptolemaic model of the solar system. Yes, you can accurately predict planetary orbits, but the Copernican model does the same with simplicity and elegance.

I'm personally hoping that these points will become clearer during my lifetime. QM and GR are right around 100 years old... give the physicists another couple of decades, and I think the state of theory may be more satisfactory.

Maybe physics is at a juncture not unlike it was around the time of the Michelson-Morley experiments. And that messy zoo of virtual particles will go the way of the æther...

[ThePythonicCow]

Re: Parallel Universes

Unfortunately, Church's thesis is not true [Rosen 91].

Thank-you, cobben. You saved the day (or at least a snippet of my pride.)

Having re-ignited this thread (elsewhere, before the good Finster brought it back here) I was now feeling inadequate to keep up with the discussion between Finster and ASH. Even before I could form a reaction to one detail, Finster and ASH would have woven a rich tapestry with that and far more.

But I chased the [Rosen 91] link you provided and was delighted (even before noticing you had expanded on it in a subsequent post.) The last I had known of this inquiry was the work of Church and Alonzo long ago. Good progress has been made since then.

So I shall order Rosen's book from Amazon and once again happily leave quantum mechanics to those with more adept minds.

Life is good.

[cobben]

Re: Parallel Universes

"Thank-you, cobben. You saved the day "

Well, at least you caught the brass ring - Finster doesn't seem to want to play outside the medieval ring wall . . . .

I have not spent nearly as much time & energy on these ideas as I should have when I first ran across them, got sidetracked I suppose, this thread jogged my memory.