Pages Menu
TwitterRssFacebook
Categories Menu

Posted by on Mar 15, 2010 in Quantum Mechanics Research | 2 comments

005 Micro and macroscopic reality 1

Microscopic and Macroscopic reality is different

In this entry I will discuss the difference between reality at the microscopic and macroscopic levels.

Last time I talked about where quantum mechanics fits and called the domain that lies beyond measure the quantum.  Let us suppose that the statistical nature of quantum mechanics can somehow be bridged, so that quantum noise can be resolved into structure by a deeper sub quantum theory.

An Objective Realist would expect a complete microscopic theory to have pure dispersion-free properties in the limit of one particle.  Also causality should be restored, so we can predict the states of particles from initial conditions and the known forces.

Empiricists would worry about how to measure such a particle, but need not because, as I said, a sub-quantum theory is beyond measure.  Quantum mechanics, in contrast, is a theory all about measurement.

Differences between the microscopic and macroscopic

I think we all have a really good idea of the reality around us.  We know fact from fiction, and even though we might be fooled, we can usually work it out.  But here is a question that is worth considering:

Is reality at the one particle level the same as in our macroscopic surroundings?

Many who believe that quantum mechanics is the most fundamental theory criticize microscopic objective reality and label such sub-quantum theories as “Classical” .

But it is well known that correlation exists between microscopic particles that cannot be explained by any classical theory.  In quantum mechanics the property that describes these quantum correlations is called entanglement, about which I will come back to later. But are those critics right?  Are local realistic sub-quantum theories classical?

No! Absolutely not. So be ready to consider that reality is different between the micro and macroscopic.

Quantum and Classical Mechanics differ

First off the mechanics of any sub-quantum theory will be completely different from Classical Mechanics.  Here we see Professor Lewin put his life on the line by demonstrating his faith in the Conservation of Mechanical Energy.  But he knew that he was safe because he knows that the pendulum cannot exceed its amplitude.

However if that were a quantum pendulum, the ball could extend beyond the classical range and hit him.  This is quantum tunneling:

Consider a quantum pendulum

There is the classical turning point right at Professor Lewin’s chin which in this case is a physical barrier, like a wall.  A quantum pendulum can tunnel right through his chin.

In other words, classical and quantum mechanics are quite different in many ways.  It is more likely that a sub-quantum theory be closer to quantum mechanics than to classical mechanic, so there will not be too much that can be called “classical” in a sub-quantum theory.

Those who call a sub-quantum theory “classical” are incorrectly applying notions from our macroscopic surroundings to the microscopic.

Moreover reality is different between the micro and macroscopic even though both are objectively real; both are local, complete and deterministic.

Indistinguishability

Reality is different between the microscopic and macroscopic levels because of  Indistinguishability and Resonance.  These properties do not exist classically.

You can always find differences between any two macroscopic objects but you cannot tell one Hydrogen atom from another, or one electron from another.  They are indistinguishable.

That is, indistinguishablity is a property that cannot be found in our macroscopic world.

Resonance is another property unique to the microscopic. There are forms and structures that flip between one and the other without any obstacles.

However if you want to apply a mathematical description, say by writing down the Hamiltonian in quantum mechanics to understand the hydrogen bond, we label them so we can keep track of them.

But labeling the two H atoms makes them distinguishable and if we keep the labels, we will get the wrong answer.

A hydrogen molecule bond is one of the simplest.  Recall that the protons, A and B are positively charged and the electrons are negative.  Since like repels like and unlikes attract, we have two repulsions (between the two protons and two electrons; and four attractions between electrons and protons. )  It is impossible for us to apply quantum mechanics to any problem without labeling the parts to distinguish them so we can apply the mathematical equations.

But labeling the two H atoms and two electrons makes them distinguishable and if we keep the labels, we will get the wrong answer.

In order to correct this, we have to make the two atoms indistinguishable in our calculation by symmetrizing the two forms.  This is done frequently in quantum theory.  In this case, shown schematically here, the symmetrized sum is called the exchange term in quantum chemistry.

Remarkably if we do not do symmetrize then the calculation misses 90% of the bond strength!!  That is, this purely microscopic property of indistinguishable particles cannot be ignored.

This is a major difference between the macro and microscopic worlds.

In other words, indistinguishability predicts new phenomena that cannot exist macroscopically.

(this is continues in entry 005b)

2 Comments

  1. I like this series about quantum, classical, micro and macro reality. Thanks for sharing.

    You write that indistinguishability cannot exist in macroscopic reality. It seems to me that it can be simulated in macro reality, provided you define proper procedures for measuring the state of the system. For example, in a black box with ordinary particles, the state can be held indefinite by not looking at it with your eyes, but just recording ineraction events. It is then impossible to characterize the exact state of the system.

  2. In principle you could build up two macroscopic structures so they are identical in every way, put in practice there will always be some slight differences, defects etc. But even supposing that you had two identical macroscopic objects, they would not be able to display the resonance or exhange contribution to, say, the hydrogen molecule bond (the example I used). Microscopic indistinguishably leads to properties that do not exist macroscopically. It is a difference between classical and quantum mechanics.

Post a Reply

Your email address will not be published. Required fields are marked *

*

You may use these HTML tags and attributes: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <strike> <strong>