004 Where quantum mechanics fits.

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Where quantum mechanics fits.

Last time I discussed a bit about how scientists view Nature at molecular dimensions. One of the reasons scientists think that quantum mechanics is a complete theory of the microscopic is because it is capable of explaining all objective data.  Well as we will see, not quite all.  There is one experiment that causes trouble but otherwise with no evidence of anything deeper.  How can we know if a sub-quantum domain actually exists?

Requirements of a physical theory

The least we should expect from a physical theory is that it is consistent with reality; completely explains all phenomena; and deterministically allows for events to be predicted from some initial cause.  We also should expect interactions to be local.

Quantum mechanics fails in all these.

Particles are real and we have many ways of determining and confirming the structure and function of molecules—that is chemistry.

Interactions fall off with some inverse power law—so interactions are local.  Near a source the intensity drops off the further you are, like the light from a distant star.  This is an example of an inverse power law and all forces (well there are only four) become weaker with separation until they are negligible and can be ignored.

Evolution is deterministic.   Here is an example of cause and effect.  In our world where classical mechanics is applicable all processes are deterministic, but not in quantum mechanics.

We’d also expect a physical theory to describe all properties of a system accurately.  Quantum fails there too.

Maybe these are not failures of quantum mechanics, maybe quantum mechanics is complete and accurately reflects the way Nature is.

So maybe reality does change and we can let philosophers argue the ontological difficulties.  Maybe Nature is not deterministic, and only gives probabilities and God really does roll dice.

But that is not very satisfying as attested to by the large number of attempts to understand and interpret quantum mechanics.

Troubling issues with quantum mechanics

Right from the beginning, scientists have been troubled by these issues yet wowed by its success.

It started about the time of this famous photograph showing the participants of the 1927 Solvay conference in Brussels which was chaired by the well known grandfather of physics Hendrick Lorentz.  The focus of the conference was the interpretation of the wave function and most were on the side of Niels Bohr who believed quantum mechanics a complete theory, but with Louis de Broglie and Einstein as notable exceptions.  In his summary at the end of the conference, Lorentz expressed what has been echoed many times since: dissatisfaction with the rejection of determinism in quantum mechanics.  Let us look at a chronological list of some of the many attempts to interpret quantum mechanics since that time

Many interpretations

Consider all these approaches.

1. Ensemble interpretation—Born 1926
2. Copenhagen—Bohr and Heisenberg 1927
3. Hydrodynamic—Madelung 1927
4. Projective measure—von Neumann 1932
5. Quantum Logic—Birkhoff  1936
6. Bohmian mechanics—Bohm 1954
7. Many-worlds—Everett  1957
8. Stochastic mechanics—Nelson 1966
9. Many minds—Zeh  1970
10. Statistical-ensemble—Ballentine 1974
11. Consistent histories—Griffiths 1984
12. Objective collapse theories—GRW 1989
13. Transactional—Cramer  1986
14. Rational—Rovelli  1994
15. Incomplete measurement  de Dinechin  2006

All accept quantum mechanics to be a complete description of Nature except the ensemble approaches (1 and 10) and David Bohm’s Bohmian sub-quantum mechanics, 6.

Notably is the Copenhagen interpretation which today is still perhaps one of the most accepted, and first articulated by Bohr at the 1926 Como conference in Italy.  It too assumes the completeness of quantum mechanics.

Quite a few interpretations require the wave function collapse upon measurement.  This is also called “reduction of the wave function”.  I remember when I was taking a course in quantum physics as a grad student at UBC.  I was not really paying attention when suddenly I heard the professor say, “..and the wave function collapses…”  He suddenly had my attention and I had a strange image of quantum mechanics falling apart.  But the more I looked at it, the less sense it make.  I had no answers of course, but it needled me from then on.

The Statistical-Ensemble Interpretation

There is a notable paper by Leslie Ballentine where he explains the statistical interpretation of quantum mechanics and compares it to other approaches.  In that paper regarding the enormous number of papers on the theory of quantum measurement,  Ballentine states,

“The reader can shorten his task greatly by ignoring all papers which try, without modifying quantum theory, to accommodate the reduction of the state vector and which also assume the state vector to describe an individual system.”

Cross out 4, 12 to 15  because  they all require  wave function collapse.  Of the remaining interpretations of quantum mechanics, only the Statistical-Ensemble approach leaves open the door for sub-quantum theories.  All the others maintain that quantum mechanics is a complete theory of the microscopic.  So since we are discussing the possibilities of sub-quantum theories, let us cross them out too.

Only the statistical-ensemble interpretations, as discussed in that paper by Ballentine, allows for a sub-quantum theory to complete quantum mechanics with properties that satisfy local realism, causality and determinism.  That a suitable sub-quantum theory has not been found is a human failing and nothing more.

I am not including number 6, Bohmian mechanics, because it is a sub-quantum theory rather than an interpretation of quantum mechanics. Also I am not rejecting the other interpretations just noting that they all consider quantum mechanics is complete.

Where does quantum mechanics fit?

So to what systems is quantum mechanics applied?  Since we can recover classical mechanics from quantum mechanics, we could move into the cosmos, but let’s not go too far.  Let us not consider the cosmos and questions of quantum gravity, black holes and dark matter etc.  The cosmos is big. Cosmologists estimate the number of starts in units of sextillion.

How about our macroscopic surroundings:  we know that quantum effects are manifested in many ways, but they are indirect.  They are there but you can safely ignore them without hindering your ability to function normally.  In fact from an empiricists point of view, we can only see microscopic effects indirectly as numbers on meters and deflections of needles.

Quantum mechanics becomes relevant when Planck’s constant becomes important.  Planck’s constant is a very small number.  He first discovered his constant while studying blackbody radiation in 1898.  As you heat a black body, say by turning on your stove, it starts to glow and give out radiation.  The intensity and colour depend upon the temperature of the body.

One of his critics, James Jeans, who tried unsuccessfully to use classical mechanics to describe BlackBody radiation and which led to the ultraviolet catastrophe, said “The real value of Planck’s constant is zero.”  In classical mechanics he is right, but quantum mechanics describes phenomena where its value is non-negligible.

This is where quantum starts to be relevant.

Many people incorrectly think that Planck’s constant the smallest quantum of energy, but that is not correct.  It has the units of Joule seconds which is angular momentum.

Likely the value of Planck’s constant was fixed at the time of the Big Bang and after that, along with other fundamental constants, …, our periodic table was set.

The limit of quantum mechanics

But back to the fit of quantum mechanics in Nature.  Earlier I mentioned that the Heisenberg Uncertainty Relations  have nothing to do with measurement, but they do put a limit on how we prepare a system for a measurement.  That preparation fails unless it satisfies the Heisenberg Uncertainty Relations .  If preparation is impossible, then measurement is impossible.  Quantum mechanics is a theory about measurement of the microscopic and the Heisenberg Uncertainty Relations  give the limit of its applicability.

Quantum Noise

Let us call the microscopic domain that lies below the Heisenberg Uncertainty Relations  the quantum noise.  Is it only noise : that is uncertainty, dispersion and random events?  This is the sub-quantum domain.

Here I do not mean quantum noise in any experimental sense, like shot noise. Quantum noise is defined here by the statistical nature of quantum mechanics as determined by the Heisenberg Uncertainty Relations.

Sub-quantum theories are beyond measure.

This gives us a big hint.  If Quantum mechanics is a theory of measurement which is limited by the Heisenberg Uncertainty Relations, then we can surmise that one of the properties of a sub-quantum theory is that is cannot be directly measured.  We can ignore the measurement problem in developing a sub-quantum theory.  Quantum mechanics does the job very well and even sets limits of applicability.

So what good is sub-quantum theory if it cannot be measured?

Well just as quantum effects indirectly affect our macroscopic surroundings, so a sub-quantum theory can lead to measureable effects indirectly on quantum mechanics.  In other words, unless something new emerges from a sub-quantum theory, then we might as well forget it.  New predictions and results are needed and these must be consistent with quantum mechanics.  This is one of the difficulties with Bohmian mechanics—an intriguing sub-quantum theory, but nothing new is predicted, so it cannot be confirmed.

Summary

Here is a summary: Cosmology down to our Classical Earth, and then into the quantum world where Planck’s constant rules and finally perhaps to the elusive hidden variable sub-quantum mechanics that restores Objective Reality to Nature and restores ontological sense to science.

Of course a complete unified theory is still a holy grail of physics.  Perhaps some clues lie in trying to understand if something lies below Quantum Mechanics, and if so what?

The truth about reality would be nice.  So in my next entry I want to talk a bit about how objective reality at microscopic dimensions differs from that of our macroscopic surroundings.