Quantum Interpretations: Exploring the Validity of Non-Local and Local Models

[WaveJumper]

WaveJumper, please read the articel again.
"If the electrons of the H atom have decohered 4.5 billion years ago into single electrons" - electrons never decohere until you entangle electorns with a thermodinamically irreversible system with a huge number of states.

So? What are you saying? That electrons in the atoms of water have not decohered?? Then may i ask how do you see water? Do you think you see wavefunctions?

 

[Dmitry67]

2 colorSpace

Decoherence shows how a macroscopic system interacting with a lot of microscopic systems (e.g. collisions with air molecules or photons) moves from being in a pure quantum state—which in general will be a coherent superposition (see Schrödinger's cat)—to being in an incoherent mixture of these states. The weighting of each outcome in the mixture in case of measurement is exactly that which gives the probabilities of the different results of such a measurement.

So after you detect a photon in a matrix of your camera, the interference is lost and you get for 1 megapixel matrix something like :

1/1000000 * (photon detected by pixel at (0,0)) + ...

 

[Dmitry67]

So? What are you saying? That electrons in the atoms of water have not decohered?? Then may i ask how do you see water? Do you think you see wavefunctions?

In order to decohere some electrons it is not enough to 'look' at water, you need to measure *individual* propeties of some electrons.

Until then they are not decohered.

As an example, you can make lens of water and perform all sorts of interference experiments using such lens and reflection from the surface of water. Interference is not lost in all these cases.

 

[WaveJumper]

In order to decohere some electrons it is not enough to 'look' at water, you need to measure *individual* propeties of some electrons.

Until then they are not decohered.

As an example, you can make lens of water and perform all sorts of interference experiments using such lens and reflection from the surface of water. Interference is not lost in all these cases.

And very definitely i see liquid water because all the particles have already decohered. Otherwise, very definitely, i wouldn't be able to see water. No one has ever seen a wavefunction. You see physical objects because their wavefunctions have "collapsed" to a single state.

The case with water is special, because H has only 1 electron, which means that if it's decohered, water molecules would fall apart, which is very definitely not the case.

 

[colorSpace]

2 colorSpace

So after you detect a photon in a matrixof your camera, the interferenc eis lost and you get for 1 megapixel matrix something like :

1/1000000 * (photon detected by pixel at (0,0)) + ...

Right. Once the wavefunction is decoherent, the probabilities can't cancel each other out (interact) anymore, as they do in an interference pattern.

Let me approach it from a slightly different side:

In CI, the selection of a possible result has no mechanics which explains why that result happens, and not one of the other possible ones. The missing mechanics are called "randomness".

Now, MWI assumes that all possibilities remain real (unless they cancel each other out, which is a very strange thing), and so removes the name "randomness". But the mechanics of why things happen this way in one world, and that way in another, are still missing. How is it possible that a photon which could have been seen by one observer (if there had been one) and a photon which could have seen by an alternate observer, cancel each other out, and are not seen by anyone? In MWI, that's just two complex numbers adding up to zero, but how can two photons disappear by nothing else than mathematical addition? The mechanics for that are still missing, they just don't have the name "randomness" anymore.

Now an MWi proponent could say: that's simply what the wavefunction says will happen. However, the same thing could be said by the CI proponent: it's simply random according to the wavefunction. That's not a scientific difference or even Occam's razor, it just seems a personal preference: Would you rather believe in randomness, or in trillions alternate versions of yourself and everyone else coexisting in trillions of alternate universes.

 

[Dmitry67]

1
We start with what you call "back-references" but it is going back to the true fundamentals of science...the experiment. Get too far from this and you begin arguing about things no-one can observe and that is a theological debate, not science.

2
No of course not. At some point the mathematical terms must be related to the physical...that by the way is the true interpretation of the theory. How a ket or Hermitian operator relates to an actual experimental device.

3
How can we define anything without "we"? Science is what scientists do.

I think I found why our views are so different.

3
Take the Classical mechanics. let's take F=ma. Do you see any 'we', 'our knowledge about'? For that reason Hilbert wanted to find the axiomatisation of physics.

1
No, the fundamental of science is a THEORY. An experiment is just a tool to prove or disapprove it. Without theories, the science would be just a heap of recepies... like alchemistry... This is what science about: the underlying formulas!

Let me ask some questions again

What do you think about the max Tegmark program 'physics from scratch'
We define TOE is a pure mathematical form, TOE(f)=0. So there are only equations, no words. Then we derive everything from there. We ask 'what a complicated system would percieve?" building frog's view from the equations?

Or do you believe that there are some 'physical' axioms which can not be expressed in forms of equations?

Do you agree that MWI is the best to be expressed in the TOE(f)=0 form?

Do you agree that MWI (when we pay a contre-intuitive price of accepting parralel realities) saves not only determinism, but also realism?

 

[Dmitry67]

1
Now, MWI assumes that all possibilities remain real (unless they cancel each other out, which is a very strange thing), and so removes the name "randomness". But the mechanics of why things happen this way in one world, and that way in another, are still missing.

2
it just seems a personal preference: Would you rather believe in randomness, or in trillions alternate versions of yourself and everyone else coexisting in trillions of alternate universes.

1
This is a very good question, I remember I was thinking about it when I learned the MWI...
I would say this is "no-issue": let's take dead/alive cat.
So what MWI predicts is that BOTH observers would say "I understand that there are alternative branches of reality where cat is alive/dead, but why *I* get this result, not another one? Why *my* consiousness is in THAT branch of reality?"
This is exactly what happens!
So MWI predicts BOTH (any) observer to be surprised and believe in randomness!

2
True
But again, waht is wrong with trillions alternative universes when our universe is INFINITE (in space at least)? If you multiply infinity by billion, the result is not bigger.

 

[Dmitry67]

And very definitely i see liquid water because all the particles have already decohered. Otherwise, very definitely, i wouldn't be able to see water. No one has ever seen a wavefunction. You see physical objects because their wavefunctions have "collapsed" to a single state.

The case with water is special, because H has only 1 electron, which means that if it's decohered, water molecules would fall apart, which is very definitely not the case.

Sorry, this is a nonsense
Please check how QED explains why light moves slower then C from water.

Hint: photons are slowed down because they are absorbed/reemitted by atoms, putting these atoms for a very short peiod of time into an excited state. That causes a delay. However, the process is absolutely reversible, so after photon had passed thru the water, there is no way to tell which atom had actually slowed the light down.

 

[colorSpace]

1
This is a very good question, I remember I was thinking about it when I learned the MWI...
I would say this is "no-issue": let's take dead/alive cat.
So what MWI predicts is that BOTH observers would say "I understand that there are alternative branches of reality where cat is alive/dead, but why *I* get this result, not another one? Why *my* consiousness is in THAT branch of reality?"
This is exactly what happens!
So MWI predicts BOTH (any) observer to be surprised and believe in randomness!

2
True
But again, waht is wrong with trillions alternative universes when our universe is INFINITE (in space at least)? If you multiply infinity by billion, the result is not bigger.

To 1) No problem with the surprise factor, the appearance of randomness is a given.
However unless there is decoherence (which is the trivial case in both MWI and CI), MWI says the probabilities interact simply by mathematical operation, the physical process, the mechanics are still missing.

To 2) The problem is not the largeness of the number, but the belief that there would be (many) multiple alternate versions of each living being and non-living thing coexisting at the same time. Why would they not collide? Just because they are different terms in a wave function which can't be added mathematically? Doesn't that require a "how", a physical explanation?

 

[WaveJumper]

Sorry, this is a nonsense
Please check how QED explains why light moves slower then C from water.

Why should I? What the heck does this have to do with anything that i was talking about?

Hint: photons are slowed down because they are absorbed/reemitted by atoms, putting these atoms for a very short peiod of time into an excited state. That causes a delay. However, the process is absolutely reversible, so after photon had passed thru the water, there is no way to tell which atom had actually slowed the light down.

No, what you say is completely not what i was talking about. I never spoke of light or c. You are talking about a subject of your choice, that i had no intention of discussing. Hint: Decoherence does not happen only when waves of matter hit photon waves.

 

[Dmitry67]

1. Mechanics is described in the Wiki article. It actually begins from the chapter "Mechanisms" :) There are all formulas you might need.

2. Why would they not collide? - because of the loss of coherence. Non-diagonal elements of the density matrix vanish, and branches lose the ability to influence each other. Check the "Density matrix" chapter.

 

[Dmitry67]

Why should I? What the heck does this have to do with anything that i was talking about?

Because it is directly related to the subject we discuss:
OPTICAL effects (refraction, reflection, etc) are reversible and collapse-free. Put an aquarium behind 2 slits and still you will be able to see an interference pattern. This is an absolute proof that when photons pass thru water, they do not leave and 'which-path' traces, so there is no 'collapse' at all. So you can not say that 'photon had been slowed down by this and this hydrogen atom'. If you can say it then you know thepath and there would be no interference.

 

[Hurkyl]

Just because they are different terms in a wave function which can't be added mathematically? Doesn't that require a "how", a physical explanation?

If the wave function represents the physical state, then that is a physical explanation.

Why would they not collide?

MWI worlds are not Sci-Fi parallel universes; they do not consist of distinct collections of matter living in parallel dimensions. Worlds are just another wave phenomenon, a product of evolution according to the Schrödinger equation. In principle, they could interfere, but that's incredibly unlikely for large systems, and essentially impossible for nonisolated systems.

 

[The Dagda]

That's just explaining-away the randomness. To me the real paradox of quantum physics is that the probabilities of flying through either slit will interact with each other, but in the end the photon will appear only in one place, not smeared out like butter. And trying to measure the path will strangely make the interference go away. MWI doesn't seem to change that.

Yeah people seem to get all goose pimply when we say it's absolutely random, not chaotic but there is no way to know what state photons are in without a measure. MWI is I suppose just a semantic/philosophical issue, it makes no difference to scientists experiments or what actually is, except they have the notion that the wavefunction an abstract mathematical object is actually representing the pictorially and really the nature and image of photons, which of course we can't know. Strange times.

 

[vanesch]

Yes but this is the same as CI for all practical purposes, if so what's the point of it? I mean I can dream up anything to make QM deterministic does that mean my dreams exist?

First of all, the fundamental difficulty with QM in the CI is not its random character, but rather two other things:
1) the distinction in physical description of what is "observation" and what is "physical process". In other words, there are magical things out there which are called observers, and whenever they enter the picture, the way to solve the problem is different and mathematically incompatible with whatever are the rules when we consider physical processes. In other words, the way quantum theory is usually done (as in CI), it is impossible to analyze, from within the theory, what is the physical process of observation.
You cannot analyze detectors quantum-mechanically, in principle. You cannot write the Schroedinger equation of a detector. Of course, you can, but then your detector is no detector anymore.

2) The problem with Bell, if we insist on locality.

If in experiment QM is random, and in MWI which in experiment appears random where's the difference and isn't that just semantics?

Again, the problem is not the randomness per se. It is the fact that in CI, it is in principle impossible to describe the detection process. This is the problem that MWI tries to solve, and you get as two bonuses, that Bell isn't a problem anymore, and that on top of that, the objective reality (contrary to the subjectively perceived reality) became deterministic.

In how much this is actually *true* is a totally different (and in my opinion even irrelevant) matter. What you do get from it is a much clearer picture of how things are behaving *according to quantum theory*, because there's a whole lot of fuzzy handwaving contradiction that is gone now. It's why I like it.

Yes, I'm god, but don't tell anyone, I'm incognito

 

[vanesch]

To 2) The problem is not the largeness of the number, but the belief that there would be (many) multiple alternate versions of each living being and non-living thing coexisting at the same time. Why would they not collide? Just because they are different terms in a wave function which can't be added mathematically? Doesn't that require a "how", a physical explanation?

The answer to that is simply the fact that the time evolution operator is a linear operator. You cannot influence the result of a linear operator acting on something, by adding something to the argument.

U (a + b) = U(a) + U(b).

U(a) is independent of whether there was a b or not.

Now, there is a "non-linear" part somewhere, which is the amplitude-> probability change. Indeed, if U(a) and U(b) have a common component, then the amplitude -> probability change will be influenced by the presence or not of b and hence U(b).

However, if a is a vector in many many dimensions and so is b, and they are essentially orthogonal, then (because U is not only linear, but also unitary), U(a) will also be orthogonal to U(b). As such, in the amplitude -> probability transition, you will not have any effect of the presence or not of b (and U(b) ).

That's what decoherence essentially tells you. Whenever you get hopelessly entangled, every "world" is essentially orthogonal to any other, and this will remain so. So the presence of another world or not will not influence whatever happens to one.

As long as a and b are not hopelessly orthogonal, you do have effects in the amplitude -> probability transition of the presence or not of b, and that is exactly what we call quantum interference.

 

[The Dagda]

First of all, the fundamental difficulty with QM in the CI is not its random character, but rather two other things:
1) the distinction in physical description of what is "observation" and what is "physical process". In other words, there are magical things out there which are called observers, and whenever they enter the picture, the way to solve the problem is different and mathematically incompatible with whatever are the rules when we consider physical processes. In other words, the way quantum theory is usually done (as in CI), it is impossible to analyze, from within the theory, what is the physical process of observation.
You cannot analyze detectors quantum-mechanically, in principle. You cannot write the Schroedinger equation of a detector. Of course, you can, but then your detector is no detector anymore.

2) The problem with Bell, if we insist on locality.
Again, the problem is not the randomness per se. It is the fact that in CI, it is in principle impossible to describe the detection process. This is the problem that MWI tries to solve, and you get as two bonuses, that Bell isn't a problem anymore, and that on top of that, the objective reality (contrary to the subjectively perceived reality) became deterministic.

In how much this is actually *true* is a totally different (and in my opinion even irrelevant) matter. What you do get from it is a much clearer picture of how things are behaving *according to quantum theory*, because there's a whole lot of fuzzy handwaving contradiction that is gone now. It's why I like it.

Yes, I'm god, but don't tell anyone, I'm incognito

See that's why I don't like it, it's too convenient. It's like string theory: what physics would be like if God was a mathematician. But I suppose it's all hand waving at the end of the day to try and solve handwaving issues.

As physicists say the universe has no regard for what you expect to be true only what is.

 

[vanesch]

See that's why I don't like it, it's too convenient. It's like string theory: what physics would be like if God was a mathematician.

I'm not a mathematician (but I play one on TV...)

The way I view MWI is not as some "ultimate truth", but rather as the bare bones logical consequence of the theory of quantum mechanics if you want to keep to the math and the logic all the way down. The price to pay is that it doesn't fit at all with any preconceived ideas of what could be reality, but what you win from it is a crystal-clear view on the wheels and gears of the quantum-mechanical formalism, and that all so-called paradoxes disappear in a puff of logic. There are no difficulties anymore in viewing any EPR experiment, or any quantum eraser experiment or anything. It all comes out very clear.

(ok, what becomes incomprehensible in this view is general relativity of course...)

In other words, to me, MWI is the picture I try to keep in my mind when doing quantum mechanics, in order to "understand" and "get a feeling" for how the theory behaves. You can't do that if you are having a machinery which produces you apparently paradoxical situations, and so the fact of removing those, and even removing all the ambiguity of "do I measure this here now or not ? " or "is the information still available or not ? " or "did this polarizer actually measure the polarisation or not" and all the handwaving that comes with CI-style views on some more subtle experiments disappears completely from an MWI viewpoint.

Questions raised by CI, such as: if the detector clicks, but I don't look, is there a measurement or not ? And if I destroy the record ? And if I throw it in a black hole ? and over which one can have heated philosophical debates become a trivial issue from the MWI viewpoint.

 

[The Dagda]

I'm not a mathematician (but I play one on TV...)

God is on TV playing a mathematician! :D I must notify The Vatican?!??

 

[Dmitry67]

but what you win from it is a crystal-clear view on the wheels and gears of the quantum-mechanical formalism, and that all so-called paradoxes disappear in a puff of logic. There are no difficulties anymore in viewing any EPR experiment, or any quantum eraser experiment or anything. It all comes out very clear.

Very good description of the 'enlightment' I felt whan I realized the beauty of MWI!

The second enlightment I experienced when I read the Max Tegmark article about the Mathematical Universe... what do you think about it?

 

[vanesch]

God is on TV playing a mathematician! :D I must notify The Vatican?!??

Not in every universe, of course, but in some, He (I) is (am)

 

[vanesch]

The second enlightment I experienced when I read the Max Tegmark article about the Mathematical Universe... what do you think about it?

Don't know what it is. Are you talking about his classifications of infinity in different universes ?

 

[WaveJumper]

Because it is directly related to the subject we discuss:
OPTICAL effects (refraction, reflection, etc) are reversible and collapse-free. Put an aquarium behind 2 slits and still you will be able to see an interference pattern. This is an absolute proof that when photons pass thru water, they do not leave and 'which-path' traces, so there is no 'collapse' at all. So you can not say that 'photon had been slowed down by this and this hydrogen atom'. If you can say it then you know thepath and there would be no interference.

I never ever said anything about light. I don't agree that only light can "collapse" the wavefunction of H. I don't agree with Decoherence because we can only observe particles, not waves. Do you understand? When you are looking at a glass of water, its atomic particles have collapsed, if they weren't you wouldn't see water. Any system that is isolated from interactions with the environment, according to Decoherence, is invisible. The fact that a cup of water is visible, means that ALL(each and every damn particle) has already collapsed?

And Decoherence is strictly an irreversible process, once decohered particles are particles, not waves.

And what happens to the 1 electron H atoms in the H2O molecule? It breaks apart, because the electron has collapsed to a single state and can no longer be at multiple places all at once and keep the covalent bonds between atoms in the molecule.

If you haven't grasped what I am saying, i will no longer reply to your posts.(and notice I am not talking about any light whatsoever).

 

[Dmitry67]

I'm not a mathematician (but I play one on TV...)

Offtopic: Dont know what is the show, but just curious, did you change the scripts? Did you ever tell them "I will not repeat this because it does not make any sense?"

You know, things like "Switch on the wormhole drive! Oh, no, the graviton emitter does not function! Somebody has to go there and repair a Higgs particle reflector plate manually!" :)

 

[Dmitry67]

Don't know what it is. Are you talking about his classifications of infinity in different universes ?

http://arxiv.org/abs/0704.0646v2
It had really opened my eyes!
He touches slightly MWI, but it is not the point.
THe main point is that PHYSICS = MATHEMATICS

 

[Dmitry67]

And Decoherence is strictly an irreversible process, once decohered particles are particles, not waves.

That is why I provided you a proof that when light interacts with water, there is no decoherence/collapse.

Just peform the 2 slit experiment in water. Result will be the same.

You are wrong saying that 'we can observe only particles, not waves'. When you observe water with gamma rays, their wavelength is short enough so they hit an electron in H, measuring its position, so it irreversibly flies away leaving a detectable track.

Visible light has a wavelength much longer then an atom, so it does not reveal any 'particle' nature of electron in atom. This process is resersible, it does not leave any detectable tracks in water. There is no collapse/decoherence

 

[Hurkyl]

I don't agree with Decoherence because we can only observe particles, not waves.

What do you mean? Decoherence is a reality, both theoretical and experimental.

And Decoherence is strictly an irreversible process, once decohered particles are particles, not waves.

No it's not. The simplest model for decoherence is given by unitary evolution -- a process that is by definition reversible.


The way you talk about "particles" and "waves" makes it sound like you're thinking of their meaning in classical mechanics, which is definitely incorrect...

 

[colorSpace]

1. Mechanics is described in the Wiki article. It actually begins from the chapter "Mechanisms" :) There are all formulas you might need.

2. Why would they not collide? - because of the loss of coherence. Non-diagonal elements of the density matrix vanish, and branches lose the ability to influence each other. Check the "Density matrix" chapter.

To 1) I'm not talking about decoherence from a mathematical point of view, all the formulas may be there... but they appear as a high-level formula with a missing low-level explanation, which is a problem of the wavefunction in general. A sum of probabilities with a complex amplitude that can interact with each other, or not. In my view that is not a physical explanation. The "wavefunction" isn't similar to the description of a classical wave. In a classical wave, there is a physical explanation of why it behaves that way. In quantum physics, MWI postulates that the wave function should be taken for granted, even as a physical reality. That would be some odd reality to take for granted.

To 2) That's a purely high-level mathematical statement. It doesn't say how it can be possible that two photons cancel each other out. Just because the formula says so?

MWI doesn't solve the mystery of the probability-nature of quantum physics, just a tiny fraction of it, if at all, at the expense of asking us to believe that there are trillions of worlds with trillions of alternate versions of each human being.

 

[colorSpace]

If the wave function represents the physical state, then that is a physical explanation.

If it is, then it is. If not, then not. For me that would be like believing that floating point numbers have a physical existence.

MWI worlds are not Sci-Fi parallel universes; they do not consist of distinct collections of matter living in parallel dimensions. Worlds are just another wave phenomenon, a product of evolution according to the Schrödinger equation. In principle, they could interfere, but that's incredibly unlikely for large systems, and essentially impossible for nonisolated systems.

But each world would have conscious human beings, you would be conscious in each of many worlds which result from you observing a quantum phenomenon, since there is no explanation why most of those would be only mathematical constructs and only one of them with real conscious human beings. So how is this not "parallel universes", as a result for us human beings?

 

[Dmitry67]

ColorSpace, regarding the physical explanations

There are some constants (like water density at 0C) which can be derived from c,h,and other parameters of the Standard Model.
However, the fundamental constants like G, h,c can not be calculated this way

The same for the laws. Some things, like viscosity, have someunderlying mechanisms, so you can give a physical explanation of a phenomena. However, fundamental physical laws do not have any futrher explanations and do not have any sub-components... just formulas

 

[Dmitry67]

since there is no explanation why most of those would be only mathematical constructs and only one of them with real conscious human beings.

No, no!
ALL these branches DO contain conscious human beings!
You should not ask 'why I am in that particular branch' or 'why may can is dead, not alive'
You exists in multiple copies in all branches, you do not randomly 'fall' into one branch!

 

[jambaugh]

I think I found why our views are so different.

3
Take the Classical mechanics. let's take F=ma. Do you see any 'we', 'our knowledge about'? For that reason Hilbert wanted to find the axiomatisation of physics.

No! Hilbert's program was to axiomatize all of mathematics with proven mutually consistent sets of axioms. But Godel blew that out of the water with his incompleteness proof.

But take F=ma. What is an acceleration? Define (interpret) it for me. Tell me how to measure the acceleration of an object without using observers with clocks and measuring rods. This isn't a trivial question considering Einstein's equivalence principle. There's all kinds of "we" implicit in the semantics of F=ma. What's more you can define force via F=ma in terms of the acceleration of a test particle. It isn't any longer an axiom, it is a definition. More generally you define F=dP/dt and the F=ma is simply the P=mV definition.

1
No, the fundamental of science is a THEORY. An experiment is just a tool to prove or disapprove it. Without theories, the science would be just a heap of recepies... like alchemistry... This is what science about: the underlying formulas!

No the fundamental root of science is the way we decide if your theory is better than my theory. It is the epistemology! Without experiments science would be just a heap of theologies. You invoke alchemy but you fail to note that it was not the empiricism in alchemy it was the underlying "theory" based on a mystic world view which kept it from being a science. When one sticks to the epistemological root then the theories branching from it are well grounded and not subject to floating off into la la land.

Let me ask some questions again

What do you think about the max Tegmark program 'physics from scratch'
We define TOE is a pure mathematical form, TOE(f)=0. So there are only equations, no words. Then we derive everything from there. We ask 'what a complicated system would percieve?" building frog's view from the equations?

You keep invoking Termark but a quick glance at his website shows me he acknowledges:"...

Termark: "Every time I've written ten mainstream papers, I allow myself to indulge in writing one wacky one, like my Scientific American article about parallel universes."

I don't think Mr. Termark takes this as seriously as you do.

I'll have to study his "mathematical universe" stuff in some detail to answer your question but I'll make two comments "off the cuff"...

Firstly he starts with the question of which mathematical model is isomorphic to "the universe" and so his axiom is that the universe is equivalent to some mathematical model. It isn't a conclusion it is an assumption. As to the validity of that assumption, his ERH...

It is exactly the problem of holding onto an absolute objective reality while accepting QM which, to avoid the fact that these two are incompatible in their essence, one must re-interpret QM. It is again exactly analogous to holding onto absolute simultaneity while accepting the predictions of SR which requires one to invoke a preferred frame along with the unobservable aether which defines it.

I think he'd be well facilitated by updating his ERH to an EAH (External Actuality Hypothesis).

Or do you believe that there are some 'physical' axioms which can not be expressed in forms of equations?

Any statement S can be reformulated in equation form... I don't get your point here. But I think the phrase "physical axioms" is an oxymoron. There are physical interpretations of mathematical constructs. Then axioms about these constructs will map to physical assumptions. But the form of the axiom is dependent on our choice of interpretation. I think you're seeing this in this discussion.

Note that mathematics is an inherently "we" based system. Mathematics says nothing until "we" choose a particular set of axioms, choose a particular set of "interesting" definitions, and then apply deductive logic. Consider how Godel mapped axiomatic systems to numbers...Here is the list of all axiomatic systems: 1,2,3,... Which is the one for the universe?

The richness of the mathematics is not in the axioms. It is in the definitions and how they relate to what we do with the math...what we do with the math!

Push any subject far enough and you will find a mirror.

The role of mathematics in physics it to assure that our logic is consistent and to see where assertions have operational meaning. When two axiomatic systems when interpreted in terms of physical models yield identical empirical predictions we then recognize that the difference in the axioms is not a difference in the physics but rather a choice of viewpoint, a choice of convention (like c = exactly 299,792,458 m/s).

We could btw formulate GR as a theory of variable speed of light with the metric interpreted as the covariant permittivity tensor. We would then have a "fixed geometry" and variable vacuum dynamics. The equivalence principle is an equivalence (two way mapping) not a one way street. I cringe when people say "gravity is just geometry"... it isn't any more than "geometry is just gravity".

Do you agree that MWI is the best to be expressed in the TOE(f)=0 form?

No. I can't as I don't know what you mean by TOE(f)=0. You'll have to parse it down to the operational meaning of what observable predictions it makes and procedures it describes and I suspect you'll find that when this is done the predictions will be independent of any assumptions about other worlds.

Do you agree that MWI (when we pay a contre-intuitive price of accepting parralel realities) saves not only determinism, but also realism?

Whether or not "parallel realities" is intuitive or counter-intuitive is immaterial. Intuition is just our hidden assumptions and integrated knowledge bubbling up from our subconscious. What concerns me is what "parallel realities" means physically. Can you smell them? Can you traverse them? Can you in other words falsify your assumption of them?
(Again refer to our earlier discussion in the other thread.)

As far as saving determinism, QM dynamics is deterministic (In CI as in any other interpretation)
in that any observation may be assured (in principle) by prior preparation of the system an arbitrary period of time earlier.

The fact that the wave-functions in-deterministically collapse is only your problem when you confuse them with the physical system. Again you are objecting to CI by assuming a non-CI interpretation of the wave-functions.

As for reality ("what is") I don't think it needs saving, rather I think it needs updating to actuality (what happens).

 

[jambaugh]

A note to other posters/readers. I know I get long winded so let me know if you are weary of my sermons. I'll move this one into a private message domain.

 

[Dmitry67]

jambaugh,
regarding Hilbert you mix 2 things:
Hilbert's program http://en.wikipedia.org/wiki/Hilbert's_program
and Hilbert's problems http://en.wikipedia.org/wiki/Hilbert's_problems
Check 6th problem pls.

Regarding other questions, do you plan to read Max Tegmark's article?
If so I would rather wait until we are on the same page...

 

[Hurkyl]

No! Hilbert's program was to axiomatize all of mathematics with proven mutually consistent sets of axioms. But Godel blew that out of the water with his incompleteness proof.

To axiomatize physics was the 6th out of Hilbert's famous list of 23 problems. And the intent, I assume, was merely to put the mathematical aspects of physics on a rigorous footing -- e.g. to have a fully rigorous formal theory of 'particles', 'forces', and whatnot, so that the physical content of classical mechanics is nothing more than making the assertion "reality is a model of this formal theory".

As far as saving determinism, QM dynamics is deterministic (In CI as in any other interpretation)
in that any observation may be assured (in principle) by prior preparation of the system an arbitrary period of time earlier.

Now come on; that statement is blatantly false! "Identical preparation yields identical results" is simply not true in the basic formulation of QM; to get that, you either have to add hidden variables (e.g. Bohm) or drop the assumption of definiteness (e.g. MWI).