Can Quantum Mechanics and System Approaches Coexist Without Conflict?

[SW VandeCarr]

I've argued in other threads in this and other forums against strict determinism (non probabilistic) on philosophical grounds. The probabilistic formulation of quantum mechanics is still the standard view, but it seems to irritate some who post in PF. They would seek a fully deterministic theory of nature that would satisfy those who take Einstein's view that "God does not play dice". The linked article proposes a view that there are no causal laws but that the probabilities of physical processes are invariant under a group of symmetries.

http://arxiv.org/PS_cache/physics/pdf/0112/0112020v6.pdf

 

[Muppetmaster]

I've argued in other threads in this and other forums against strict determinism on philosophical grounds. The probabilistic formulation of quantum mechanics is still the standard view, but it seems to irritate some who post in PF. They would seek a fully deterministic theory of nature that would satisfy those who take Einstein's view that "God does not play dice". The linked article proposes a view that there are no causal laws but that the probabilities of physical processes are invariant under a group of symmetries.

http://arxiv.org/PS_cache/physics/pdf/0112/0112020v6.pdf

That's because some people are deterministic in their approach to life. Everything in its place and a place for everything.

They literally are that anal thus MWI for example speaks to them of their dream to have everything neatly in a box and not to have to think about things.

To think the fundamental laws of nature are probabilistic is to admit there is something they have no control over, thus idiotically they are doomed to be determined despite being free.

 

[SW VandeCarr]

To think the fundamental laws of nature are probabilistic is to admit there is something they have no control over, thus idiotically they are doomed to be determined despite being free.

I wouldn't be that harsh. Science has always been about cause and effect. Given that mind-set, it's difficult to accept that causal laws may be artifacts of our limited powers of observation. The idea of a strictly relational reality governed by probabilistic laws seems to set limits on science that some simply cannot accept. Einstein was one such person, yet he still made great contributions to science and to fundamental ways of thinking about nature. However, I would agree that some posters in this and the classical physics forum (re chaos theory) just don't get it. Chaos theory, IMHO, is a deterministic approximation to nature, but not the reality of nature itself.

 

[Muppetmaster]

I wouldn't be that harsh. Science has always been about cause and effect. Given that mind-set, it's difficult to accept that causal laws may be artifacts of our limited powers of observation. The idea of a strictly relational reality governed by probabilistic laws seems to set limits on science that some simply cannot accept. Einstein was one such person, yet he still made great contributions to science and to fundamental ways of thinking about nature. However, I would agree that some posters in this and the classical physics forum (re chaos theory) just don't get it. Chaos theory, IMHO, is a deterministic approximation to nature, but not the reality of nature itself.

If a tree falls in the forest and no ones around to see it what colour is it?
If a tree falls in the forest and no ones around to hear it does it make a sound?

 

[SW VandeCarr]

If a tree falls in the forest and no ones around to see it what colour is it?
If a tree falls in the forest and no ones around to hear it does it make a sound?

What do you mean, there's no one around to hear it? In a forest, there's a myriad of 'critters' who will "hear" the "noise". If you read the paper, you'll find that the relational view of reality requires an interaction. In this case, a disturbance in the air results in changes in the nervous systems of forest animals creating a record. The disturbances in the atmosphere itself can also be considered an interaction between the falling tree and the atmosphere which in principle is observable (as with a recording device). If a rock on the moon is dislodged from a formation by a moonquake, it's still a potentially observable event that creates a record which could be discovered by an astronaut.

Philosophical issues regarding solipsism (your or my first person reality) are off topic. This thread is about whether causal laws should be part of a fundamental scientific theory.

 

[Chronos]

Without causality you have chaos. Is chaos theory a better candidate to explain the universe in which we reside? I think not. It comes into play at the beginning of the universe and degenerates into causality.

 

[SW VandeCarr]

Without causality you have chaos. Is chaos theory a better candidate to explain the universe in which we reside? I think not. It comes into play at the beginning of the universe and degenerates into causality.

We have chaos theory because we (still) have chaotic systems we want to understand. It's a deterministic theory which I accept as an approximation to the behavior of chaotic systems. However, the proximity of initial conditions need not have a lower limit. That is, differences in initial conditions could be at quantum (probabilistic) scales.

The author of the linked paper in post 1 (which you might want to read) takes a different approach. He/she calls "metaphysical" causality as the causality of Newton (the clockwork universe) and "Einstein" causality as a causality consistent with the Lorentz Group of symmetries. All physical theories today have CPT (charge, parity and time) symmetry according to author. Causal laws are asymmetric with respect to time. Therefore, according to the author, causal laws are not consistent with CPT symmetry and should be discarded for quantum mechanics. That is (my interpretation), probabilities are fundamental and looking for a deterministic substratum to QM is not warranted. The author goes into much greater depth defending this thesis, getting into some technical areas that most non physicists (including myself) might not follow completely. However, most of the paper can be read by those possessing a fair knowledge of the issues involved.

 

[apeiron]

We have chaos theory because we (still)have chaotic systems we want to understand. It's a deterministic theory which I accept as an approximation to the behavior of chaotic systems. However, the proximity of initial conditions need not have a lower limit. That is, differences in initial conditions could be at quantum (probabilistic) scales.

Hi VandeCarr - I'm in general agreement with your points and also Anandan's Polyverse paper. But I'll pose a few questions.

Chaos theory is interesting because it is "determined" in the sense that it is about free dynamical systems reaching their steady equilbrium - the point where all further micro-state change ceases to produce a macro-state change.

This is why we can talk about things like Universality constants.
http://en.wikipedia.org/wiki/Feigenbaum_constants

So the equilibrium story is an important characteristic of dynamic systems that the (yes, deterministic) maths of chaos theory captures with great precision. And it is a truth that is independent of the nature of the systems - whether classical or quantum.

The message of chaos theory, I believe, is that random processes (local degrees of freedom) can have determined outcomes (globally coherent relations). And the randomness can be either classical or quantum in principle, so it does not require that we invoke quantum indeterminancy as the reason for real-world chaotic systems. Classical level randomness is enough.

I realize many want to argue differently of course.

All physical theories today have CPT (charge, parity and time) symmetry according to author. Causal laws are asymmetric with respect to time. Therefore, according to the author, causal laws are not consistent with CPT symmetry and should be discarded for quantum mechanics.

I did not take that part seriously. The relational view and the polyverse story is the right kind of thinking. But the second law of thermodynamics is an asymmetric causal law - one that is necessary to correct for the way that causal direction is erased in classical and relativistic modelling.

And this is the way to improve QM also - update the existing formalisms via some kind of thermodynamic principles, such as decoherence.

 

[SW VandeCarr]

Hi VandeCarr - I'm in general agreement with your points and also Anandan's Polyverse paper. But I'll pose a few questions.

Chaos theory is interesting because it is "determined" in the sense that it is about free dynamical systems reaching their steady equilbrium - the point where all further micro-state change ceases to produce a macro-state change.

First, thanks for your thoughtful response apeiron. It's clear you understand the argument.
My understanding is that, according to chaos theory, chaotic systems tend to diverge despite very small differences in initial conditions and this behavior is completely determined by each system's precise initial conditions. As with the first example of chaos with the rounding of decimal fractions, there is no random element. So the theory goes. I'm thinking that in nature, can we put a lower limit on the magnitude of difference in initial conditions? If we get down to quantum scales, it seems random elements could enter in. Feigenbaum's constants seem to come out of computer generated simulations. Can this be applied to nature, particularly QM "randomness"?

So the equilibrium story is an important characteristic of dynamic systems that the (yes, deterministic) maths of chaos theory captures with great precision. And it is a truth that is independent of the nature of the systems - whether classical or quantum.

Well, as I said, chaos theory doesn't factor in randomness at all. In the case of the original example of decimal expansions, the two calculations continue to diverge in a deterministic way, while quantum outcomes are probabilistic. So it would seem the nature of the system
is important.

I did not take that part seriously.

Why not ( re CPT symmetry)? It seems to be a straightforward argument. If CPT symmetry is true, can asymmetric causal laws exist at the quantum level?

But the second law of thermodynamics is an asymmetric causal law - one that is necessary to correct for the way that causal direction is erased in classical and relativistic modelling.

Lord Kelvin said something to the effect that you can challenge any theory except the second law of thermodynamics. But that was before QT and QM. Anandan is only addressing QM as a fundamental theory. Asymmetries arise in larger scale phenomenon, but I don't think anyone really understands exactly why.

And this is the way to improve QM also - update the existing formalisms via some kind of thermodynamic principles, such as decoherence.

Well, that's above my pay grade, but please keep me informed. Thanks

 

[apeiron]

My understanding is that, according to chaos theory, chaotic systems tend to diverge despite very small differences in initial conditions and this behavior is completely determined by each system's precise initial conditions.

More the other way round. If we are talking about dissipative structures (which is what "chaos" theory was really about).

Released from almost any initial conditions, a system will find its way to an attractor - another word for its dynamic equilibrium.

Initial conditions are a calculational issue because rounding-errors multiply exponentially rather than linearly. They are not well-behaved and become intractable. And so a butterfly wing's flap can trigger a typhoon. But that just means many other flaps did not lead to anything much. And all that really happened is that the Earth's weather patterns exhibits turbulence over powerlaw scale. Looking for local causes is actually futile because of the measurement and calculation issues. But you can know exactly the equilibrium result that must emerge regardless of the local mechanics.

I tend to forget how much chaos theory was mis-sold. It is really a theory about natural order as far as I'm concerned.

Traditionally we think of order as being a very static and linear thing. But natural order is dynamic and non-linear as a rule. The order of attractors and equilibriums and dissipation.

Well, as I said, chaos theory doesn't factor in randomness at all.

Well, taking the example of fractals, you can generate a fern frond or menger sponge either by iteration of an equation starting from some fixed input, a set of numbers, or by a stochastic process. You can build up exactly the same thing from probabilities.

see wiki for example...
http://en.wikipedia.org/wiki/Fractal_landscapes

Iterated function systems – These have a fixed geometric replacement rule. Cantor set, Sierpinski carpet, Sierpinski gasket, Peano curve, Koch snowflake, Harter-Highway dragon curve, T-Square, Menger sponge, are some examples of such fractals.

Random fractals – Generated by stochastic rather than deterministic processes, for example, trajectories of the Brownian motion, Lévy flight, fractal landscapes and the Brownian tree. The latter yields so-called mass- or dendritic fractals, for example, diffusion-limited aggregation or reaction-limited aggregation clusters.

while quantum outcomes are probabilistic.

But not ordinary probabilities. Entangled probabilities, which is fundamentally different. Weird even.

Why not ( re CPT symmetry)? It seems to be a straightforward argument. If CPT symmetry is true, can asymmetric causal laws exist at the quantum level?

Well we know that CPT does not in fact apply to our universe. The symmetry is actually broken - and the reason we can exist. So CPT is an idea, not a reality. Gauge symmetry is the current best explanation for why this asymmetry is intrinsic to reality. Which sort of gets you down to the quantum level explanation I guess.

Lord Kelvin said something to the effect that you can challenge any theory except the second law of thermodynamics. But that was before QT and QM. Anandan is only addressing QM as a fundamental theory. Asymmetries arise in larger scale phenomenon, but I don't think anyone really understands exactly why.

I would question your notion of fundamental. QM may be about the fundamentally small and localised, but from a systems point of view, it has to be matched by a theory of the fundamentally whole and global.

Personally, I would rename the second law the first law. I believe that the open and developing view comes before the closed and stabilising one.

But even if you don't want to go that far, the second law is still a truth of reality that would have to be incorporated into any ToE.

It could be just an emergent feature of things (that would be the more common approach). But the incompleteness of QM and GR (and the first law of thermodynamics too) would say that the second law has to be part of the final mix.

 

[SW VandeCarr]

Well we know that CPT does not in fact apply to our universe. The symmetry is actually broken - and the reason we can exist. So CPT is an idea, not a reality. Gauge symmetry is the current best explanation for why this asymmetry is intrinsic to reality. Which sort of gets you down to the quantum level explanation I guess.

From this recently dated source, CPT symmetry might be broken, but it hasn't been observed yet.

http://media4.physics.indiana.edu/~kostelec/faq.html

I need to leave now. I'll try to respond to your other points later. Anyone else, feel free to jump in.

 

[apeiron]

From this recently dated source, CPT symmetry might be broken, but it hasn't been observed yet.

Sorry, you're quite right about that. I was thinking of CP rather than CPT.

 

[SW VandeCarr]

Released from almost any initial conditions, a system will find its way to an attractor - another word for its dynamic equilibrium.

Chaos theory is defined in terms of initial conditions. I'm thinking about the original example of chaos theory again, the rounding initial conditions of a decimal fraction. What is the attractor here? The two representations of the fraction are of finite length and the difference is multiplied in the calculating process so that the results of the calculations drift further and further apart.
http://home.earthlink.net/~srrobin/chaos.html

I would question your notion of fundamental. QM may be about the fundamentally small and localised, but from a systems point of view, it has to be matched by a theory of the fundamentally whole and global.

I think everyone would agree that QM is incomplete but QFT is a relativistic formulation. What's missing from QM is the fourth interaction, gravity. The still undiscovered particle is the graviton. However, all efforts I know of toward unification are from the particle side: the Extended Standard Model, Supersymmetry (sparticles), string theories, Loop Quantum Gravity and others. I know of no proposed or developing theory where the fundamental objects and relations are large scale phenomenon. Of course, that doesn't mean much because I'm not a physicist, but I think I would have heard about such a proposal just from following the "Beyond the Standard Model" discussions in PF if not in my general reading on the subject..

It could be just an emergent feature of things (that would be the more common approach). But the incompleteness of QM and GR (and the first law of thermodynamics too) would say that the second law has to be part of the final mix.

Can you give me a reference where the second law is discussed as part of a proposed or developing fundamental theory?

 

[apeiron]

Chaos theory is defined in terms of initial conditions. I'm thinking about the original example of chaos theory again, the rounding initial conditions of a decimal fraction. What is the attractor here? The two representations of the fraction are of finite length and the difference is iterated in the calculating process so that the results of the calculations drift further and further apart.
http://home.earthlink.net/~srrobin/chaos.html

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

I think everyone would agree that QM is incomplete but QFT is a relativistic formulation. What's missing from QM is the fourth interaction, gravity. The still undiscovered particle is the graviton. However, all efforts I know of toward unification are from the particle side: the Extended Standard Model, Supersymmetry (sparticles), string theories, Loop Quantum Gravity and others. I know of no proposed or developing theory where the fundamental objects and relations are large scale phenomenon. Of course, that doesn't mean much because I'm not a physicist, but I think I would have heard about such a proposal just from following the "Beyond the Standard Model" discussions in PF if not in my general reading on the subject..

Relativity is a global theory.

Can you give me a reference where the second law is discussed as part of a proposed or developing fundamental theory?

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

 

[SW VandeCarr]

Relativity is a global theory.

General Relativity (GR) is a successful theory of gravity. However, it doesn't explain the three other (currently thought to be) fundamental interactions. Afaik, no reputable "top down" proposal that explains how to go from GR to a unified theory has ever been advanced. (Einstein's late-in-life attempts notwithstanding). The closest I know of are the large set of possible string theories such the 10+1 dimensional theory with its four extended spatial dimensions. But the motivation for the whole string theory movement was its early success in linking gravity with QM at the microdimensional level. The problem with string theories is that there seems to be a string theory for perhaps 10^500 possible worlds and none of them seem to be testable at available energies.

As far as including some explanation for the second law in a fundamental theory, I would agree that this would be desirable. Anandan mentions it only indirectly with a reference to decoherence. I think the author would explain such asymmetries in terms of a relational reality where two non-entangled entities must interact under an action-reaction principle to create a reality. Without interactions, there is no reality, only probabilities.

While it is true the second law of thermodynamics is asymmetric with respect to time, it is only valid in a closed system. Eventually equilibrium is reached and symmetry is restored if there is no further disturbance of the system.

EDIT: Note all the current proposals for a possible TOE are referred as theories (or hypotheses) of quantum gravity.

 

[apeiron]

Afaik, no reputable "top down" proposal that explains how to go from GR to a unified theory has ever been advanced.

And I would argue it is in fact not possible to reduce the global scale causality to the local scale causality in the way you are thinking. This is exactly why current approaches are a washout (and I just spent a few days hearing about latest ideas at a GR conference).

So GR is a global level description. It is not a pure theory of global scale downward constraint though. It is just a suitable extension of mechanics that does the job.

The way to get to a unified theory, IMHO, would be to form a dichotomy and thus a hierarchy out of the available formalisms.

So your starting points for the dichotomy would be QM and GR as the local bottom-up and global top-down sources of action. QM produces the creative grain of events, GR embodies the prevailing system of constraints. Standard systems theory. Then the interaction of the local and the global, the QM and the GR, gives you flat classical Newtonian spacetime. This is their "average" or equilibrium outcome, when QM and GR are mixed (renormalised) over all spatiotemporal scales.

Note of course we are talking about dynamic equilibriums (and dynamic versions of the second law) not the kind of closed, static, gaussian, ideal gas, models you will be thinking about. Rather the kind of open, phase transition, Prigogine, Tsallis, Renyi, critical, powerlaw, dissipative equilibriums of a systems approach to modelling thermodynamic reality.

So, hey, the universe turns out to be a dissipative structure that cools by expanding. Not some static deal. And open systems equilibriums can be either a story of a static system pushing entropy through it (perhaps the idea you are familiar with from dissipative structure theory) or it can be like the universe - a system in effect becoming its own expanding heat sink.

Of course the second law would have to be rewritten to account for what is actually going on here.

The conventional framing is now in crisp microstate counting. So the only gradient recognised is from order to disorder - min-entropy => max-entropy.

But I support the addition of another more basic dimension to the modelling of reality (a fifth dimension I guess, though actually it could be a better description of time, the fourth dimension). Anyway, this is the dimension, the development gradient, from the vague to the crisp.

So step back, reframe the second law, and we start talking instead of a natural developmental gradient, an arrow of "time", that is max vagueness => max crispness.

Now apply that re-termed second law to the big bang~heat death story of our universe. We would treat its (quantum scale) origins as a maximally vague state. Neither the container nor its contents really exist as yet, neither the spacetime context nor the local particle-like events.

However as the universe expands and cools, both these things can come into crisper existence. The second law is being fulfilled. We can say it is itself emerging crisply into view as a global law.

Then roll forward to the end of time. The universe is as large and cold as it can be. It is maximally crisp in these two dichotomistic aspects encoded in the Planckscale, in quantum measurement. Location is as generalised as possible. And so is momentum. The second law also now exists in its strongest possible fashion. Where in our current era, the second law is still swimming its way towards existence out of vagueness, at the head death, it is as definite truth as it can be.

Adopt the lenses of the systems perspective and you will see a different world. Your choice.

I study both reductionist and systems approaches. I can see the value of both. And I can also see which is the more fundamental. Stick with reductionism and you will forever be tieing yourself in knots and actually misapplying this otherwise useful intellectual tool.

 

[apeiron]

Are reductionist and system approaches mutually exclusive?

Yes. Done right, they ought to be. Being mutually exclusive would make them dichotomistic. You would be coming at reality from the two limiting extremes of points of view that would be possible. Yin and Yang.

QM, as a probabilistic formulation, is not really reductionist since it's not strictly deterministic.

It is certainly an attempt to be as deterministic as possible about the smallest scale. The fact that you actually encounter vagueness at the limit simply supports my position.

The systems approach is an internalist perspective. And QM is framed in an externalist, reductionist fashion. Which is what creates a lot of confusion over observers, and measurement, and non-locality (or globality).

So for example, I would see the wavefunction as the global constraints that a system - the universe - puts around a locale, some event space. Then within that event space is a vagueness (entangled probabilties rather than ordinary classical crisp variety). The making crisp of that event space, a phase transition from vague possibility to crisp actuality, is decoherence.

Except again, this is reductionist talk. I would prefer to call it "making coherent" as I would say the quantum state is vague rather than coherent. And after decoherence, that event space of possibility has in fact become a crisp mark, a crisp state of information, now woven into the developing classical history of the universe. Once something has crisply happened, it can't unhappen.

The formalism of QM works great. But the "how" of how it works would have two views, one from inside the system, one from the outside - or rather, if you are a reductionist, from the below the fundamental smallness of the system. You are down there wondering where the crisp hidden variables or crisp multiple worlds are which make what you are seeing possible.