When I was a brand new graduate student, I attended one of those “get to know each other” lunches at the beginning of the first semester.  Such events are usually pretty painful.  I hate to perpetuate stereotypes, but physics graduate students (myself included) are by-and-large pretty bad at making pleasantries and light conversation.  Half of us are too loath to engage in it and the other half seem blissfully unaware of their own conversational deficiencies.  Thus discussions among physics students frequently devolve into one or two people monologuing vigorously while the rest look down at their feet and feel awkward.

At this particular event, however, there was one attendee who was well above average at making pleasant conversation, and who therefore found himself at the center of much of our discussion.  He had been teaching physics in high school for the last few years and had decided to return to school to get a graduate degree.  Teaching high school is more “real world” experience than most of us had, so I was enjoying listening to him explain how his classes had been organized and how he had designed various projects to keep the students engaged.

Doing physics?

Until he told one particular story that really bothered me.  One of his projects, he explained, was an assignment to “start a fire using only physics.”

I was mildly horrified.

The intent of the assignment, I suppose, was good — he was trying to get his students to understand how combustion reactions can be started without using ready-made chemical fuel sources.  But by telling his students to “use only physics”, this teacher was spreading the somewhat damaging idea that the world can be compartmentalized into distinct blocks of independent knowledge.  In other words, such an assignment helps solidify the false sense that every phenomenon belongs to some particular class in school: “when a rocket orbits the earth, that’s physics”, or “when you burn gasoline in your engine, that’s chemistry”, or “when cells divide, that’s biology”, or “when a person has brain damage, that’s psychology”, etc.

Nature is Nature, and it doesn’t care what we call ourselves when we describe it.

Richard Feynman said it this way:

…the full appreciation of natural phenomena, as we see them, must go beyond physics in the usual sense.  We make no apologies for making these excursions into other fields, because the separation of fields, as we have emphasized, is merely a human convenience, and an unnatural thing.  Nature is not interested in our separations, and many of the interesting phenomena bridge the gaps between fields.

–The Feynman Lectures on Physics, Vol. I, Ch. 35

It seems to me somewhat of a disservice to teach your students that physics/chemistry/biology etc. is a set of things in the universe rather than a language or a set of tools to describe things in the universe.

$\hspace{10mm}$

$\hspace{10mm}$

It was only much later that I realized that I myself was guilty of employing a similar false dichotomy in my thinking.  What’s more, all the professional scientists around me seemed just as guilty.  For years I had been given assignments by my professors that seemed very much equivalent to “start a fire using only physics”.

Namely, every problem I solve in physics begins by me declaring which of the objects in the problem are classical and which are quantum-mechanical.

Let me elaborate a little bit.  Quantum mechanics (QM), as a theory, is built fundamentally around a sharp distinction between “quantum” objects and “classical” objects.  QM prescribes a particular set of rules for how quantum objects interact with each other — these are the Schrodinger equation, the Dirac equation, the uncertainty principle, etc. — and how quantum objects interact with classical objects — these are called “measurements”.  The set of rules for the two types of interactions (quantum-quantum and quantum-classical) are very different.  I am therefore required to declare at the beginning of the problem which objects are quantum and which objects are classical (i.e. when and where the “measurements” are) so that I know which set of rules to use.

What’s more, QM deliberately refuses to make any predictions about a quantum system that does not interact with a classical object.  QM is a theory whose only goal is to predict the outcome of measurements, and measurements by definition involve changing the state of a classical object.  QM is decidedly agnostic about any situation involving only quantum objects.

Now I don’t mean to make QM sound ugly or arbitrary.  It isn’t (at least not any more than most physical theories).  QM can be quite elegant, and it is completely capable of reproducing classical physics (i.e. the laws of Newton, Hamilton, Lagrange, etc.) in the appropriate limits.  For example, the laws that describe a quantum object of mass m become equivalent to the laws of classical mechanics when m becomes very large.

But that doesn’t mean that QM can stand on its own without relying on classical mechanics.  This is a very unusual situation.  Try contrasting this behavior with, for example, the theory of relativity.  Einstein’s theory of general relativity is an entirely self-sufficient description and is completely independent of the theory it replaced: the laws of Newtonian mechanics and Newtonian gravity.  It is capable of  reproducing Newton’s laws when pushed to the right limit (say, when describing slow-moving bodies), but you are absolutely not required to accept anything Newton ever said in order to use the theory of general relativity.

This seems natural; by comparison, QM is quite strange.

Lev Landau can probably explain this better than I can.  Below is an excerpt from the first few pages of the Landau-Lifshitz Course on Theoretical Physics, Volume 3 (Non-relativistic quantum mechanics).

A more general theory can usually be formulated in a logically complete manner, independently of a less general theory which forms a limiting case of it.  Thus, relativistic mechanics can be constructed on the basis of its own fundamental principles, without any reference to Newtonian mechanics.  It is in principle impossible, however, to formulate the basic concepts of quantum mechanics without using classical mechanics.

… The possibility of a quantitative description of the motion of an electron [for example] requires the presence also of physical objects which obey classical mechanics to a sufficient degree of accuracy.  If an electron interacts with such a “classical object”, the state of the latter is, generally speaking, altered.  The nature and magnitude of this change depend on the state of the electron, and therefore may serve to characterize it quantitatively.

In this connection the “classical object” is usually called “apparatus”, and its interaction with the electron is spoken of as “measurement”.  However, it must be emphasized that we are here not discussing a process of measurement in which the physicist-observer takes part.  By “measurement”, in quantum mechanics, we understand any process of interaction between classical and quantum objects, occurring apart from and independently of any observer.

Thus quantum mechanics occupies a very unusual place among physical theories: it contains classical mechanics as a limiting case, yet at the same time it requires this limiting case for its own formulation.

–Landau & Lifshitz, Course of Theoretical Physics, Vol. 3, Ch. 1

I should make an attempt to show you how ridiculous this sounds.  Imagine that I approached one of my physics professors and asked “Why does it hurt to put my hand on a hot stove?”.

The professor might say something like this:

“Oh, well the stove is hot because the atoms that make up its surface have a high kinetic energy: they are vibrating around very quickly.  When you put your hand on the stove these hot stove atoms begin to collide with the atoms of your hand, thereby transmitting some of that kinetic energy to your hand [of course atoms don’t actually physically touch; they just interact by the electromagnetic force, which transfers momentum from one set of atoms to another].  The atoms on the surface of your hand collide with atoms deeper down in your hand, and so on on, until the heat is transferred a few millimeters past the surface.  Then some nerve fibers in your hand respond to the heat, and the rest is biology.”

You might well object to that phrase “the rest is biology”; it is probably used as a substitute for “I don’t really know what happens next”.  You might want to say: The whole world is made up of atoms, right?  Atoms obey the laws of physics, right?  So surely there must be a “physics” explanation to what’s happening that doesn’t allow the professor to cop out and say “the rest is biology.”

nerve cells: just a bunch of atoms pushing and pulling on each other.

And of course, there is, even though it might be complicated.  If pressed to elaborate, the professor might be able to say something about how the large kinetic energy of individual molecules in my hand causes cell walls to break apart (these walls were previously held together by strong electrostatic bonds, but the bonds are now weaker than their constituent molecules’ kinetic energy).  When the cell walls break, chemicals inside the now-broken cells can diffuse around.  When the right chemical diffuses into the right nerve cell, it triggers a channel in the nerve cell to open and let in sodium ions from the surrounding salt water.  This in turn triggers nearby channels to open, and there is a wave of nerve channel openings that travels up a long nerve fiber into my brain.  [Biologists out there: I apologize if I got some of the details wrong here.  Please correct me.]

My point is this: in principle, my question can be completely answered by describing the motion of individual atoms (or, if you prefer, electrons and quarks) as they push and pull on each other by fundamental forces.  Even the expletive-laden thoughts that cross my mind as I pull my hand off the stove can be described as a process of many atoms being pushed one way or another in my brain.

There is absolutely nothing real about the distinction between “physics” and “biology” in this explanation.  There is only one reality; you can call yourself what you want as you describe it.

$\hspace{10mm}$

Now imagine that I asked the professor a different, more quantum question.  For example, “What happens when I fire a single photon at a thin slab of metal?”

The professor might say something like this:

“Well, with a particular probability $P_R$ the photon is reflected, with some other probability $P_T$ the photon is transmitted through the slab, and with a third probability $P_A = 1 - P_R - P_T$ the photon is absorbed by the slab.  [The professor can then calculate all these probabilities if I ask him to.]  If the photon is absorbed, then the slab moves forward with the momentum it gained from the photon, as dictated by the laws of classical mechanics.”

Here I might object to the professor’s phrase “as dictated by the laws of classical mechanics” in the same way I objected above to the phrase “the rest is biology”.  The slab might be big, but it is still made of electrons and protons and neutrons: each of these are quantum objects.  So doesn’t the photon (a quantum object) just alter the quantum states of all the constituent particles in the slab?

The atoms in my brain are quantum objects.

For that matter, I myself am made of electrons and protons and neutrons.  When I interact with the metal slab (perhaps just by watching its motion) doesn’t this change the quantum states of all my little constituent particles?  Can’t you tell me what is happening in a consistent way where everything that we know to be a quantum object behaves like a quantum object?

The answer is no.  The professor can only tell me what will happen when I let quantum objects interact with classical ones.  If I refuse to let him tell me that the metal slab (or myself) is a “classical object” and I insist that everything is ultimately made of tiny particles that must respect QM, then the professor has nothing to tell me.  QM refuses to make any statements about a “reality” independent of classical objects.

In short, QM cannot describe a universe made only of quantum objects, even though that is apparently the case in reality.

What a strange and impertinent way to be treated by history’s most successful scientific theory.

$\hspace{10mm}$

$\hspace{10mm}$

Personally, I find it very disconcerting that such a strong dichotomy — quantum versus classical — should be so central to our thinking as physicists.  We even have an obvious identifier to tell the two types of objects apart: quantum objects always have Planck’s constant $\hbar$ somewhere in their description and classical objects never do.

Somehow this doesn’t fit with my sense of aesthetics, which says that there can be only one universe that doesn’t care what we call classical and what we call quantum.  I am left to speculate, or perhaps just to hope, that ultimately QM will be replaced by some theory that can stand on its own and make independent claims about reality.  Because a theory that “contains classical mechanics as a limiting case, yet at the same time requires this limiting case for its own formulation” is a hard pill to swallow.

$\hspace{10mm}$

Perhaps this should teach me to be a little more kind to science teachers.

9 Comments leave one →
February 2, 2011 8:28 am

Is there a difference between the objects of a theory and the theory itself? Or, are they inseparable?

February 2, 2011 8:52 pm

Fuzzy-Observable is the buzzword.

3. February 4, 2011 5:35 am

I read in a book by Robert Laughlin that the idea that the classical world is a limiting case of the quantum world is an assertion that has never been shown rigorously. Do you have a citation to support the idea that QM is”completely capable of reproducing classical physics (i.e. the laws of Newton, Hamilton, Lagrange, etc.) in the appropriate limits”?

Has the limiting case been explored mathematically?

May 28, 2012 12:21 pm

Isn’t this essentially the Correspondence Principle?

4. Raphael R permalink
February 8, 2011 3:10 am

Landau & Lifshitz is certainly a superb book, but things have changed quite a lot in quantum mechanics with respect to the understanding of the process of measurement since its publication. The controversy given on your text only appears if you follow the Copenhagen Interpretation. By employing the density operator formalism, decoherence and modeling the apparatus as a quantum object it is possible to explain a lot related to the measurement process in quantum mechanics.

[video src="http://media.physics.harvard.edu/video/index.php?id=SidneyColeman_QMIYF.flv" /]

This excellent Sidney Coleman lecture from the 80’s (or 90’s) already explained most of the things that seem confusing to you.

However, it is really rare for a QM course today to discuss density operator formalism, measurements and everything else in a deep way, since that’s an actual topic of research. Hence, they prefer to explain things in the way you just described, which is really traditional and based on Copenhagen’s interpretation, which is outdated, just like some of the ideas being propagated here.

5. April 1, 2011 5:10 pm

Correct. The usual explanations of QM are logically deficient (as Einstein realized). See http://www.math.rutgers.edu/~oldstein/ and http://www.mathematik.uni-muenchen.de/~bohmmech/BohmHome/bmstartE.htm .