Quantum Mechanics with Dr. Bryan C. Sanctuary

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.

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. 

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 posses 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 posses 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 noting 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 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!”

Empirical or objective?

Lets me summarize here:

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).

If you believe that particles exist and posses values of their attributes whether or not they are known, then you believe in objective reality.

You cannot have it both ways.

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

How Scientist Think

Although the following overview of how scientists think is quite general, in the next few entries to this blog I will be discussing primarily what is involved in acquiring data about the microscopic world and understanding how scientists think about what they measure and what those measurements mean. 

Ontology

This involves trying to understand how information is obtained and how we interpret data leading us to knowledge?  The first thing to confront is the question:

“What is reality?”

This is not a trivial question and one that is at the core of understanding Nature.   In philosophy this is called   Ontology.  Ontology is the philosophy of “being”  and of “reality”. 

The Greeks were the first to develop the ideas:  Parmenides on existence, Plato on separating the mind from the body and Aristotle on metaphysics.

In the macroscopic world we live in  reality is quite intuitive.  We probe our surroundings with our senses and these are automatically interpreted by our minds as perceptions.  We usually believe our perceptions, or maybe misled by them too, but for the most part we are convinced that the objects we see are real.

Normally if you doubt something is real, you simply ask a friend: “Do you see it too?” and seek confirmation.   Yes the moon is really there because when you do not look at it, someone else can, and sees it in a reproducible experiment.

Naive Realism

Our view of the world around us is WYSIWYG .  We do not think much about preparing the object we observe:  we might just pick it up.  Nor do we think about how to measure it: we just look and feel it, maybe shake it, sometimes smell or taste it. We do it without much thought. We perceive and that is our reality.

This is called Naïve Realism

Although this works well in our world, for example animals function very well without any knowledge of physics, Naïve Realism does not work at the microscopic level.

Objective Reality

Objective Reality means that objects around us exist and possess exact values for their properties independently of our intervention.  If, however, an observation is made, then it must be possible for others to confirm it by independent observation.  You see the moon, and others see it too. 

Subjective Reality

Naïve Realism does not extend to the microscopic level, does objective reality?  Some say yes, most say no. Besides objective reality, there is also Subjective reality.

For example, no-one can confirm that God exists because it is a matter of faith.  God is real to all believers and not real to non-believers.  This is not the type of reality of science.  This is called Subjective reality but it plays an important role in the interpretation of objective results

These interpretations must be consistent with the objective results, and be accepted by a large number of other scientists who can agree on some things and disagree on others.

Epistemology

The subjective interpretation of objective reality is knowledge and the branch of philosophy is epistemology—how we know.

In Summary, ontology is the philosophy of the state of being and Epistemology is the philosophy of how we know.

In my next entry I will discuss some common philosophies of science and what they mean.

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What I like about Quantum Mechanics.

My name is Bryan Sanctuary and I would like to tell you what I like about quantum mechanics (QM) in this my first submission to this blog

Purpose of this blog

The purpose of the is blog is to stimulate discussion into the interpretation of qm.  I am sure that you have ideas, questions, comments about qm and reactions to what I say.  I invite you to submit those in my blog and perhaps we can stimulate a lively discussion and even get to some answers as to what qm really means.

Insight into the microscopic world

But what do I like best about qm?  That’s easy.  It is the insight, the deep insight qm give us into the microscopic world.

Now we live in a macroscopic world which is governed by classical or Newtonian mechanics.  If someone tosses you a ball you intuitively put up your hand and catch that ball.  You do not have to understand classical mechanics.  You don’t have to calculate a trajectory.  You don’t need to know anything about forces or gravity.  You simply intuitively put up your hand and catch the ball.

Now in the microscopic world, things are quite different.  The microscopic world is governed by a different mechanics, and that is qm.  And the only way we can get insight into the microscopic world is through the mathematical equations.  I think Heisenberg said it first.  He was one of the founders of qm and said that our ability to visualize in the microscopic world; to gain in intuition; to understand microscopic processes, comes only from understanding the mathematical equations that govern qm.

Now I am not suggesting that you become a mathematician.  Far from it.  There are many people who understand qm.  They work with it daily and they develop an intuition of how the microscopic world works.   So they don’t have to do long complicated calculations.  They know what happens at the microscopic level, so if someone tosses then an electron, they know how to catch it.

The Chemical Bond

The chemical bond can only be described by qm.  It is a100% quantum entity.  Think of all the chemical bonds that are being made and broken everyday, throughout the world, throughout the universe.  They are all governed by the laws of qm.

Spin

Another thing I like about qm is that it can predict properties that do not exist in the macroscopic world, such as spin.  An electron is a particle with a certain mass, a certain charge and a spin of ½ magnitude.  This spin is 100% quantum with no analogue in the macroscopic world.

The hydrogen atom also has spin of ½ which resonates.  This spin is smaller that that of an electron but it is still the same sort of angular momentum.  Other particles have spin.  Carbon-13 has a spin ½ too.  A chlorine atom has a spin of three halves.  Photons have a spin of 1.  Many particles have spin. Today sophisticated instruments have been developed to look at the resonances of many particles and this is called Nuclear Magnetic Resonance (NMR).  These instruments give us spectra and these spectra can all be understood by applying the laws of qm.  That is the position and intensities of all these lines are completely determined by qm. And this is a particularly simple molecule but by understanding such spectra we can obtain important properties of molecules, such as structure, function and reactivity.

Now NMR started way back in the 1940’s when scientist were simply interested to see if they could make the spin of a proton resonate.  This was fundamental research. This was good science, and the two people credited with the discovery of NMR, Felix Bloch and Purcell Pound, had no idea of the tremendous consequences of their experiments.  They did not then know about chemical shifts and that NMR would develop into one of the most useful tools to many areas of scientific research.  And today Magnetic Resonance Imaging (MRI) allows us to non-invasively look inside a body, with great benefit to human-kind and of course medical research too.

The basis of understanding the microscopic world.

QM, therefore, is the basis for our understanding and control of the microscopic world.  Think of microelectronics.  We have microprocessors all around us, based primarily on solid state physics.

New materials.  Just think of new fabrics, new plastics, new polymers all developed in laboratories by scientists doing chemistry or engineering who understand how the quantum world works and are able to create these new materials.

Nanotechnology is a relatively new field of research with tremendous potential.  A nanometer is ten to the minus 9 meters that is 0.000000001 meters.  We know that particles and molecules can self assemble into larger structures.   But scientists can intervene in these processes to assemble the sorts of structures that can do different things.  Here we see a nano tube, but there are many more that can perform different tasks, like nano-size machines.

Today with the use of powerful computers, it is possible to solve the Schrödinger equations to obtain the structures of complicated molecules.  Here we see hemoglobin.  Such structures allow scientists to understand how such complicated molecules function.   There a many beautiful structures of proteins.  In biochemistry and pharmacology for example, scientists can study various biochemical pathways and can intervene in these to control them, and even stop them, when something goes wrong, like cancer.

So quantum mechanics gives us deep and useful insight into how the microscopic world works.  I have talked about chemistry, physics, biochemistry, pharmacology and many other fields of science.  And the ideas that come from this fundamental research, like the example of the resonating hydrogen atom, can be taken over by engineering and companies that do research and development.  These lead to new processes and new products which benefit human kind.

What does qm mean?

But what does quantum mechanics mean?  What is the real meaning of the wave function?  What are the real consequences of quantum mechanics?  How can non-locality happen?  Is Nature really entangled?  Is Nature fundamentally statistical?

These questions have been debated since qm was first formulated in the 1920’s with no real resolution.  Today however many of the gedanken (or thought) experiments of those days can be performed in the laboratory which give us new insight.  However qm is so successful that I believe the vast majority of people don’t care about the real meaning of qm.  It has been debated so long that that they have given up.  It has been debated since the beginning of quantum time with no real clear resolution, so they continue to use qm in their research and are happy to leave it at that.

Richard Feynman

I think the famous Nobel Prize winner Richard Feynman summed it up best.  He obtained his Nobel Prize for formulating qm using what are now called Feynman Path approach.  And about the foundations of qm, Richard Feynman is purported to have said, perhaps with his tongue in his cheek, “Shut up and calculate!”

However I believe, and I am sure that Professor Feynman believed it too, that these questions are fundamental to our understanding of the microscopic world.  We should not give up trying to find the answers.

Coming soon

Well that is all for this first submission.  Next time I want to talk a bit about how scientists approach problems and some of the philosophical consequences of qm.  After that I will tell you what I do not like about qm.

See you then.