Foundations of Quantum Mechanics and Physical Chemistry

httpvh://www.youtube.com/watch?v=6wQyMxYuR_s

Positivism, empiricism and objective reality

In my last entry I talked a bit about reality and introduced the ideas of Ontology (the philosophy of being) and Epistemology (the philosophy of knowledge).  In this entry we move down to the microscopic level where things are quite different.  Our intuition in the macroscopic Naïve Reality in which we live changes dramatically.

Positivism

In fact the last holdout who denied the existence of microscopic particles was perhaps the famous and influential 19th century physicist and philosopher, Ernst Mach (you have heard of Mach force and Mach number).  He was a Positivist who believed that what we can know is restricted to our sensory perception alone.   Therefore he did not believe in the existence of atoms and molecules.

Ernst Mach

So Mach would only accept what he can see macroscopically.  This is different from Naïve Realists because Positivists do not ever think about what lies deeper.

Positivists maintain this stance because they only need a way to calculate the observed objective data without trying to understand it.

This is because Positivists abhor the metaphysical: questions that do not have a measureable answer.  If they interpret, then paradoxes and difficulties can arise and a Positivist does not want to get into that game.

Ontology

Is the Microscopic world real?  Are microscopic particles real?

It is difficult to find scientists today who do not believe particles are real objects.  Microscopic particles do exist.  Here you see iron on copper as viewed by using a scanning tunneling microscope. This technique does not see particles the same way light or electron microscopes do by use of diffraction.  Rather the scanning microscope detects the electrons in atoms and molecules and makes use of the quantum phenomenon of tunneling.  The changes in electric field as the probe passes over a surface are changed into images.

Scanning Tunnel Microscope of Iron and Copper

The resolution is about 0.1 nano meters (1 nanometer is 10 to the minus 9 meters), this is down to the dimensions of single particles.

All matter is composed of smaller particles.  Quantum mechanics cannot directly describe one particle.  Rather only the collective effects of many particles prepared in a similar way fall under the purview of quantum mechanics.

Since we use instruments to probe the microscopic, we cannot use our normal naïve perceptions to interpret what we observe.

We also need a different mechanics.

What is microscopic reality?

However there is disagreement as to how we obtain microscopic properties and describe them.  Basically the question is:

• Do we observe the microscopic properties of individual particles,

or

• Do we measure the microscopic interaction between many particles and a measuring instrument?

The former view is that of an Objective Realist: objects possess real attributes that naturally exist even if they are too small or too fragile to observe.

The latter is that of an Empiricist:

Discussions of the interpretation of quantum mechanics cannot ignore the famous and important Einstein-Bohr debates.  At this stage I wish to discuss the ideas that are most prevalent today rather than the rich and exciting history of quantum mechanics.   I will come back to the early debates later.  At this stage, let us generally consider that Einstein was a realist and Bohr was an empiricist.

Empiricism

So what do Empiricists believe?  They recognize that microscopic interactions are manifested macroscopically.

These readings constitute the objective reality of measurement.

They are macroscopic real numbers, not the properties of individual particles, because they are obtained by the amplification of individual interactions of many particles within a measuring instrument.

In contrast to Positivists, Empiricists gain knowledge by experimentally testing the assumptions and hypotheses of our logical description of Nature.  They want to interpret the experimental data within quantum mechanics.

Empiricists are therefore concerned about what we measure  and not primarily about whether microscopic objects possess real values or not.

However empiricists accept that quantum mechanics might not be a complete description of Nature but work within its framework to resolve difficulties.

Objective Realism

Let’s leave empiricism for a while and discuss how an objective realist views Nature.

In object reality, all attributes of a system are real and dispersion free whether we measure them or not.

In our classical surroundings, this is not a problem.  We figure we can measure as accurately as our instruments allow and our challenge is to build instruments to measure the exact values of the properties of a system with as little error as possible.

When we know all these attributes, the only error is in the final digits of our instrument accuracy, and this is called dispersion. We believe this can reduce by improving the instrument.

An accurately known quantity has small dispersion (or error).

In a nutshell, an Objective Realist believes that microscopic objects possess values which have no dispersion.  All attributes have exact values that exist simultaneously.

This is not true of Quantum mechanics and it is impossible to describe all attributes without fundamental error arising that we cannot surmount by improving equipment.  But look at this image from IBM—it is a bit fuzzy, but that is instrumental error.  A single molecule can be seen and it looks real.

Heisenberg Uncertainty Principle

Of course the fundamental error in quantum theory is succinctly expressed by the Heisenberg Uncertainty Principle which puts a limit on quantum theory.  I will talk more about this later but it is important to note that there is nothing in the derivation of HUR that has anything to do with measurement

All you need is two non-commuting Hermitian operators and a bit of math.

If you believe fundamentally that objects are real, then you cannot accept quantum mechanics as a complete description of nature because some attributed disrupt each other.

What to believe?

If you believe Quantum mechanics is the most fundamental theory of Nature then you have to accept that reality changes depending on how it is observed.

That is the reality we associate with the result from one measurement, say position of a particle, is different from the reality we associate with another measurement, say of the momentum of a particle.

If you believe this then you are in good company even if the company is not very large. Einstein could not accept that quantum mechanics was complete, and he sought a sub-quantum theory to understand the statistical nature of quantum mechanics—and we all know his famous quote:

“God does not play dice.”

Although many would like to believe that quantum mechanics is incomplete, after trying unsuccessfully since the late 1920’s to complete it, you can understand why Richard Feynman might have said:

“Shut up and calculate!”

Summary

Lets me summarize here:

1. You believe that quantum mechanics is complete, then you must accept that Nature is statistical and that reality changes depending upon how you look at it (that is performing different experiments).
2. If you believe that particles exist and posses values of their attributes whether or not they are known (that is you are an objective realist), then you must accept that quantum mechanics is incomplete.

You cannot have it both ways.

Next time I want to explain where quantum mechanics fits into our description of Nature.