Why Quantum Mechanics Is Not So Weird after All

Skeptical Inquirer ^ | July 2006 | Paul Quincey

[snarks_when_bored]

Why Quantum Mechanics Is Not So Weird after All

Richard Feynman's "least-action" approach to quantum physics in effect shows that it is just classical physics constrained by a simple mechanism. When the complicated mathematics is left aside, valuable insights are gained.

PAUL QUINCEY

---

The birth of quantum mechanics can be dated to 1925, when physicists such as Werner Heisenberg and Erwin Schrödinger invented mathematical procedures that accurately replicated many of the observed properties of atoms. The change from earlier types of physics was dramatic, and pre-quantum physics was soon called classical physics in a kind of nostalgia for the days when waves were waves, particles were particles, and everything knew its place in the world.

Since 1925, quantum mechanics has never looked back. It soon became clear that the new methods were not just good at accounting for the properties of atoms, they were absolutely central to explaining why atoms did not collapse, how solids can be rigid, and how different atoms combine together in what we call chemistry and biology. The rules of classical physics, far from being a reliable description of the everyday world that breaks down at the scale of the atom, turned out to be incapable of explaining anything much more complicated than how planets orbit the sun, unless they used either the results of quantum mechanics or a lot of ad hoc assumptions.

But this triumph of quantum mechanics came with an unexpected problem-when you stepped outside of the mathematics and tried to explain what was going on, it didn't seem to make any sense. Elementary particles such as electrons behave like waves, apparently moving like ripples on a pond; they also seem to be instantaneously aware of distant objects and to be in different places at the same time. It seemed that any weird idea could gain respectability by finding similarities with some of the weird features of quantum mechanics. It has become almost obligatory to declare that quantum physics, in contrast to classical physics, cannot be understood, and that we should admire its ability to give the right answers without thinking about it too hard.

And yet, eighty years and unprecedented numbers of physicists later, naked quantum weirdness remains elusive. There are plenty of quantum phenomena, from the magnetism of iron and the superconductivity of lead to lasers and electronics, but none of them really qualifies as truly bizarre in the way we might expect. The greatest mystery of quantum mechanics is how its ideas have remained so weird while it explained more and more about the world around us.

Perhaps it is time to revisit the ideas with the benefit of hindsight, to see if either quantum mechanics is less weird than we usually think it is or the world around us is more so.

Classical Mechanics in Action

When we think of planets orbiting the sun, we usually adopt Newton's view that they are constantly accelerating-in this case changing direction-in response to gravitational forces. From this, we can calculate the motions precisely, and the impressive accuracy of predictions for total solar eclipses shows how well it works.

There is, however, another way of thinking about what is happening that gives exactly the same results. Instead of the Principle of Acceleration by Forces, as we might call it, there is an alternative called the Principle of Least Action, or more correctly, Hamilton's Principle.

It is a principle that was first put forward about fifty years after Newton's, in its earliest form by the Frenchman Pierre Maupertuis, and in its ultimate form by the Irishman William Rowan Hamilton.

The general idea is that when a planet travels through space, or a ball travels through the air, the path that is followed is the one that minimizes something called the action between the start and end points. Action, for our purposes here, is just something that can be measured out for some particular object moving along a particular path. It is exactly defined and is measured in units of energy multiplied by time. The details are not important unless you need to make calculations.

We therefore have two quite different ways of describing situations in classical physics that are equally good in terms of giving the right answer. To give the simplest possible example, we can think of a golf ball travelling across an idealized, frictionless, flat green. In Newton's view (figure 1), the ball moves in a straight line at constant speed, because that is what Newton's Law says it must do. In Maupertuis' view (figure 2), the ball does this because this path is the one that has the least action between the start and end points. This trivial example can be made more interesting by making the green have humps and dips, which are like having forces acting on the ball, but the principles stay the same.

Figure 1. Classical mechanics-Newton's view: the ball moves in a straight line at a constant speed, because that is what things do when there are no forces acting on them.

Figure 2. Classical mechanics-Maupertuis' view: the ball moves in a straight line at a constant speed to any given point on its travels, because that is the path of least action between the start and finish.

Hamilton's Principle is fundamentally equivalent to Newton's Laws, and comes into its own when solving more advanced types of classical problems. But as an explanation, it has a major flaw-it seems to mean that things need to know where they are going before they work out how to get there.

Actually, this is where classical mechanics makes its first big step toward quantum mechanics, if only we look at it another way. The mathematics of Hamilton's Principle can be described in words alternatively like this: given its starting points and motion, an object will end up at locations that are connected to its starting point by a path whose action is a minimum compared to neighboring paths. If locations away from the classical path are considered, no such paths exist-there will always be a path with the least action, but this is not a minimum.

It is an unfamiliar idea, but well worth a little effort to try and digest. One vital change to note is that, while still being classical physics, the emphasis has moved away from knowing the path that is followed to having a test to check whether possible destinations are on the right track. And the crucial factor is being able to compare the actions of different paths.

It leads to a third picture for our moving golf ball, central to the later move to quantum physics, which we can call Feynman's view of classical physics (figure 3).

Figure 3: Classical mechanics-Feynman's view: the ball is found at the black points, which happen to lie on a straight line, and not the white points, because only the black points pass the "action test." This means that there is a path from the start to the black points whose action is a minimum compared to neighboring paths, but there is no such path from the start to the white spots.

If we stay within the world of classical physics, we can choose to ignore this strange new description and stick with the more comfortable idea that things are accelerated along paths by forces, but this would be a personal preference rather than a rational one. The new view prompts the question: "How do things work out whether possible destinations are linked to the start by a path of minimal action?" We should appreciate, however, that the old Newtonian view prompts equally difficult questions like: "How do things respond to forces by accelerating just the required amount, instant by instant?" Moreover, as we will see, the action version is the one that the world around us seems to use.

Roll on, Quantum Mechanics

Suppose we take the action question seriously and give it a rather simple answer: Nature has to check out all possible destinations to see if they are on the right track. It must do this by trying to find out if there is a path of minimal action to each destination. It uses a device that can measure the action along all possible paths to each destination.

The device is a simple surveyor's wheel for measuring action-just a wheel with a mark on the rim (figure 4). There isn't literally a type of wheel that measures action, but we can imagine that there is. The mechanism assigns probabilities to each destination according to whether, with just this simple measuring tool, it can find a path of minimal action.

Figure 4: The single most potent image of quantum mechanics- a surveyor's wheel for measuring action

When the actions it is trying to measure are large compared to the size of the wheel, the system typically works just as classical physics requires. But in some situations the mechanism fails to produce classical mechanics and gives us quantum mechanics instead. We call the circumference of the wheel "Planck's constant," after Max Planck, who discovered its importance by an indirect route in 1900.

You may be wondering how exactly the wheel can tell us what we need to know, but we don't need to go into the details here-those interested should read Richard Feynman's book, QED: The Strange Theory of Light and Matter, or see the summary given in the box on page 43.

Differences from Classical Physics

As we might expect, the introduction of a mechanism for carrying out classical mechanics only makes a difference when the mechanism can't do its job properly. Specifically, if we want to check out destinations that are too close to the start, as gauged by the size of the wheel, the mechanism doesn't work. It cannot say where the object should be going, and there is an intrinsic fuzziness associated with it, with a scale set by the amount of action known as Planck's constant. This is otherwise known as the Uncertainty Principle.

A second feature arises from the simple circular nature of the measuring device. It cannot tell the difference between paths that differ by an amount of action that is an exact whole number of Planck's constants. This can lead to patterns of probabilities that look just like classical waves, because the mathematics of waves is very similar to the mathematics of circular motion.

The most important change comes when we consider objects in very small orbits, like electrons around nuclei. The mechanism gives zero probability unless the orbit (or more correctly the state) has an action that is an exact multiple of Planck's constant. This crude mechanism explains why atoms can only shrink to a certain point, to a state with an action of Planck's constant, where they become stable.

With one extra idea, which we will mention later, the mechanism seems to explain the workings of chemistry, biology, and all the other successes of quantum mechanics, without ever really stopping being classical mechanics.

Three Conceptual Problems with Quantum Mechanics

The way it is normally introduced, quantum mechanics is something quite baffling, and certainly stranger than just classical mechanics with a mechanism. It is worth addressing the three most obvious difficulties directly:

1) Quantum mechanics gives answers that are a set of probabilities all existing at the same time. This is totally unreal. As Schrödinger pointed out, quantum mechanics seems to say that you could create a situation where a cat was both alive and dead at the same time, and we never see this. But this is in fact a very curious piece of ammunition to use against quantum mechanics.

We already have a very good nontechnical word for a mixture of possibilities coexisting at the same time-we call it the future. Unless we believe that all events are predetermined, which would be a very dismal view of the world, this is what the future must be like. Of course, we never experience it until it becomes the present, when only one of the possibilities takes place, but the actual future-as opposed to our prediction of one version of it-must be something much like what quantum mechanics describes. This is a great triumph for quantum mechanics over classical mechanics, which by describing all events as inevitable, effectively deprived us of a future.

Of course, there is now a new big question of how one of the possibilities in the future is selected to form what we see as the present and what becomes the past, but we should not see the lack of a ready answer as a fault of quantum mechanics. This is a question that is large enough, encompassing such ideas as fate and free will, to be set aside for another time. The headline "Physics Cannot Predict the Future in Detail" should be no great embarrassment.

2) Quantum mechanics means that there is a kind of instant awareness between everything. This is quite true, but by introducing quantum mechanics in the way that we have, the "awareness" is of a very limited kind-limited to the awareness gained through the action-measuring mechanism as it checks all possible destinations. It is very hard to see how the only result of this-a probability associated with each destination-could be used to send a signal faster than light or violate any other cherished principle. It is rather revealing that one of the few novel quantum phenomena is a means of cryptography-a way of concealing a signal rather than sending one.

3) Quantum mechanics doesn't allow us to say where everything is, every instant of the time. This is the most interesting "fault" of quantum mechanics, and it can be expressed in many ways: particles need to be in more than one place at a time; their positions are not defined until they are "observed"; they behave like waves. We will summarize this as an inability to say exactly where particles are all the time.

The "classic" illustration of this is the experiment of passing a steady stream of electrons through two slits (figure 5). Instead of the simple shadows we would expect if the particles were just particles, we see an interference pattern, as if the electrons have dematerialized into a wave and passed through both slits at the same time.

Figure 5: A schematic diagram of the two-slits experiment

There are several ways of coming to terms with this. The first thing to note is that the lack of complete information is not really a problem that arose in quantum mechanics-it originates in the third version of classical mechanics. In the Feynman version, the essence of motion is a process of determining if a destination is on or off the right track. Before the move to quantum mechanics, we can do this as often as we like, so that we can fill in the gaps as closely as we like, but the precedent has been set: physics is about testing discrete locations rather than calculating continuous trajectories. If it is inherent in old-fashioned classical physics, not just "weird" quantum physics, perhaps we can relax a little.

The second point is to clarify what the problem is. To take the two-slit example, we never see electrons dematerialize, or rippling through something, we just find it necessary to think that they do to explain the pattern that we see on the screen. If we deliberately try to observe where the electrons go, we see them as particles somewhere else, but the interference pattern disappears. In effect, the problem is that we cannot say what the particles look like only when they cannot be seen.

Now this is an uncomfortable thought, because all our instincts tell us that particles must be somewhere, even when we cannot see them. But if quantum mechanics can accurately describe all the information we can ever obtain about the outside world, perhaps we are simply being greedy to ask for anything more. The headline "Physics Fails to Describe Events That Cannot Be Observed" is, again, rather lacking in impact.

The final point is a little vague but more fundamental. If we accept that the future is not fixed, we expect it to contain surprises. Crudely speaking, this is not very plausible in a world where particles have continuous trajectories and an infinite amount of information is freely available. It is much more plausible in a world that is in some way discontinuous, where the available information is limited. Even though we have set aside the question of how a future full of possibilities turns into an unchanging past, it must involve something that seems pretty weird compared to our normal experience. Perhaps this example of physics not conforming to our expectations is weirdness of the right sort.

The Addition of Spin

It was mentioned earlier that another new idea is needed before the classical physics of electrons and nuclei properly turns into chemistry. That idea is spin, a third property of electrons and nuclei alongside mass and electrical charge. Paul Dirac showed that spin is a natural property of charged particles within quantum mechanics. Wolfgang Pauli showed that the spin of the electron prevents more than one electron occupying the same state at the same time-the Exclusion Principle-a fact responsible for the whole of chemistry. The details are not important here, but quantum mechanics with spin seems to account for pretty much all the world we see around us.

Quantum Mechanics-Bringer of Stability

One of the benefits of viewing the quantum world as not fundamentally different from the classical world is that we can imagine how one changes into the other. With a few simple assumptions, a classical world of point-like electrons and nuclei is blindingly chaotic. Atoms are continually trying to collapse, but are prevented from doing so by the huge amount of electromagnetic radiation that is released in the process. It is not the comfortable place that the word classical implies.

As we imagine moving to the quantum realm by increasing the size of Planck's constant from zero, something remarkable happens. At some point, the blinding light disappears to reveal stable atoms, capable of forming molecules. Far from making everything go weird, quantum mechanics makes it go normal. To be sure, if Planck's constant increases too far, the atoms fall apart and a different form of chaos takes over, but that just makes the story even more interesting.

So it seems that quantum physics is not weird and incomprehensible because it describes something completely different from everyday reality. It is weird and incomprehensible precisely because it describes the world we see around us-past, present, and future.

Reference

Feynman, Richard P. 1985. QED: The Strange Theory of Light and Matter. Princeton, N.J.: Princeton University Press.

About the Author

Paul Quincey is a physicist at the National Physical Laboratory, Hampton Road, Teddington, Middlesex, TW11 0LW, United Kingdom. E-mail: paul.quincey@npl.co.uk.

[PatrickHenry]

By popular demand ...

SciencePing

An elite subset of the Evolution list. See the list's explanation at my freeper homepage. Then FReepmail to be added or dropped.

[Red Badger]

Do quantum mechanics use quantum wrenches?...........

[Quark2005]

A+ post.

Point 2) under "conceptual problems" was especially important, IMO. People who read about quantum entanglement often misconstrue this point (even some otherwise very good physicists I've known).

[MHGinTN]

Interesting post, pipe. May I disagree slightly? Here goes, for what its worth.

There are two dimensions we experience on a comprehensive scale, dimension time and dimension space. We also experience the dimension of life force because we are alive and sensing, and the dimension of spirit because we have a sense of good and evil (well, most people do anyway).

Here's a different way to consider these dimensional aspects. Each dimension has three variable expressions. With dimension space we have linear, planar, and volumetric, with time we have past , present, and future, corresponding roughly in conception to the three variable expressions of dimension space. With dimension life force we have will, emotion, and mind --for want of better terms-- and these also have a similitude to dimensions time and space. I suspect there are three variable expressions to dimension spirit also, but I haven't a clue yet what the variable expressions might be called.

Here's a though regarding the mixing of dimensions time and space. In classical physics there are distances at which the various standard model forces are in effect for the phenomena 'observed'; I would switch this way of describing that, to say that the various forces act in various spatial expressions, as in planar or volumetric, for instance. There may be (and I believe firmly that this is the actual case) 'times' at which the various forces are in effect also, mingled with the various distances (spatial characteristic).

I am working on a paradigm to explain this different perspective using space/time realms or continua as the limits for the various forces. As an example, gravity is a volumetric/past phenomenon, where the temporal aspect is the operant in the force expression, so the entire universe is the realm of gravity action based upon an entanglement of temporal origin related to the start of the disunity to dimension time at the big bang origin of our universe.

Dimensions life force and spirit have been added to the mix of dimensions space and time, broken into constituent expressions, and until some means of mathematically expressing the combinatorial nature of their being mixed into the universe is found, life and spirit will remain metaphysical realms of wonderment, while space and time will continue being explored and codified using a touch of metaphysical perspective, as in quantum field as 'aether' (in a spatio-temporal sense) for standard model force expressions, and entanglement, and action at a distance (each area of exploration being dependent more upon a temporal or spatial expression for fundamental interaction of matter and energy).

Because of this 'different' way of viewing the universe and the standard model for subatomic reality, I have predicted that no graviton particle will be found as mediator of the force of gravity, because gravity is primarily a temporal phenomenon not a spatial phenomenon. Electromagnetic effects are primarily spatial phenomena thus a mediating particle acts as focus of the force exchange because everything in this universe is entangled via temporal containment (everything is existing within a temporal volume in relation to everything else) ... we are in the universe we are in and in which the processes that have resulted in us have occurred, adding dimensional expressions as we have been 'built up' in complexity.

Other 'beings', such as angels, may not have been 'built' in the same fashion from the simplest to the more complex as we have been constructed, for the mind of God can bring things into being by a word, at any complexity level He chooses to assume for them. Parallel universe theory and brane theory and string theory are all hinting at a more inclusive way to define the universe. I think there are recorded examples of events where greater complexity realities have intersected our reality, as in Daniel chptr 5, and the entire of Jesus sojourn on this planet.

Hope this hasn't been too esoteric to have meaning for you.

[BeHoldAPaleHorse]

What we need is a magazine called "Popular Quantum Mechanics."

[Iris7]

Adrian Schwinger (at least as much a big dog physics guy as Feynman was) believed Feynman's view of quantum mechanics to be fundamentally flawed. It has to do with reconciling Maxwell's equations with quantum theory.

If Feynman is correct I read that quantum computation is possible, and, if not, is not.

There is a fairly respectable group of physics people who say that the observed behavior of GPS satellites violates Relativity theory. Therefore relativity theory is wrong. These guys are pretty far up there in the physics world as far as I can tell.

Everybody wants to believe that they know what they are doing. I doubt anyone does.

[<1/1,000,000th%]

The assault on the Copenhagen Interpretation continues.

[Quark2005]

There is a fairly respectable group of physics people who say that the observed behavior of GPS satellites violates Relativity theory.

I don't think that's true. GPS positioning uses a leading order correction based on General Relativity to compensate their positioning. Without it the satellites would lose several meters of accuracy every day.

[Iris7]

I am not in anything like a position to say yea or nay here, for sure.

My impression is that the correction you refer to is empirical in major part and is something of an exercise in curve fitting.

Not claiming special insight here. I just suspect that True Knowledge (term borrowed from Iain Banks, suggests human frailty and the need for enough certainty to have at least some hope for the future, and is a mixture of serious and ironical) is the pot of gold at the end of the rainbow where we endlessly pursue and endlessly do not find. A "chimera", though the analogy is a bit strained.

[linear]

Ping for later

[snarks_when_bored]

Adrian Schwinger (at least as much a big dog physics guy as Feynman was) believed Feynman's view of quantum mechanics to be fundamentally flawed. It has to do with reconciling Maxwell's equations with quantum theory.

If Feynman is correct I read that quantum computation is possible, and, if not, is not.

The Schwinger-Tomonaga operator-theoretic approach to quantum electrodynamics was shown to be equivalent to the Feynman sum-over-histories approach by none other than Freeman Dyson (an act which secured Dyson a permanent faculty appointment at the Institute for Advanced Studies).

[Physicist]

I only skimmed this article, but I didn't like very much what I read. It glosses over some very real philosophical problems associated with QM, and pretends they're not problems.

(N.B.: When I say "problems", I don't mean mathematical inconsistencies in the theory or disagreements between the theory and experimental fact--we know of none--but rather refutations of our naive philosophical expectations.)

For example, with Schrödinger's Cat, he shrugs and says, "QM can't predict the future, no problem". But the problem isn't a question of the future; it's a question of the past.

Suppose the decision whether to release the prussic acid occurs at 4:00, and the chamber is opened at 5:00. The cat is in a superposed dead/alive state at 4:30. It will collapse at 5:00 into one state or the other, sure, but that doesn't mean the cat will live or die at 5:00. The death of the cat, if death is the outcome, will have occurred at 4:00. At 4:30, that event is already in the past. At 5:00, when the mixed state collapses into the death eigenstate, the cat will be an hour dead. It's not the future which is indeterminate, but the past.

Furthermore, the author misleads when he says "we never see this". We may not see it with cats in our sadistic basement experiments, but we see it in the lab, with subatomic particles. Indeed, we exploit it as an experimental tool.

[Aldin]

I thought you might get a kick out of this - I think I'm going to enjoy pondering it quite a bit.

[snarks_when_bored]

It's possible that Quincey might respond by elaborating on these sentences:

But if quantum mechanics can accurately describe all the information we can ever obtain about the outside world, perhaps we are simply being greedy to ask for anything more. The headline "Physics Fails to Describe Events That Cannot Be Observed" is, again, rather lacking in impact.

Puzzles about superposition strike me as being modern instantiations of the problem of the one and the many. If I had more time (and were much, much smarter), I'd say more.

[hosepipe]

[ With dimension space we have linear, planar, and volumetric, with time we have past , present, and future, corresponding roughly in conception to the three variable expressions of dimension space. ]

It does have esoteric and exoteric meaning to me.. Linear, planar and volumn (and time too) might be a 2nd reality.. Probably is.. It could be that "shape" is a 2nd reality.. i.e. all geometry really; including known physics.. Could be that EVERY human is "into" some version of 2nd reality..

Matter/energy (both light and dark energy/matter) could be plasmic in essence.. Like a very good painting/landscape(2 dimensions masking three) can look very real in this paradigm.. Its NOT real(the landscape) but appears to be real.. i.e. a created observation by a human.. This universe could be the same on a spiritual level(God).. except upped a level of reality..

I say that; to posit, that "shape" may be a human observational limitation.. meaning all matter/energy is plasmic.. in essence.. Shape being needed by human eyes and other senses in a limited reality..

This subject is quite deep.. and completely "out of the box"... So I don't discuss this with many.. Everyone I know cannot concieve of a universe without "shape" being integral..

Some people have problems with a tripartite God.. I do not.. It could be God is an amalgam of additional(not mentioned in the bible) Spirits also.. i.e. Father, Son, Holy Spirit plus additional entities not mentioned.. or not.. One way or the other "that" would have no bearing on the bibles message(s) anyway.. Father, Son, Holy Spirit is fine with me..

Some of Stephen Barrs ideas have serious merit...

[kcrackel]

Dean Koontz wrote a good book called "From The Corner Of His Eye" that involved quantum mechanics. Dean gets into some detail about it as he really does his background research when writing books. I would highly recommend this book for entertainment value as well as a for a little quantum mechanics knowledge.

[Doctor Stochastic]

But neither the “world” of relativity nor the quantum world are “visualizable” in the standard sense of that word.

That would depend on how much mathematics is in one's "standard sense."

[Iris7]

I read about that in Dyson's "Disturbing the Universe". The famous trip from the East coast to New Mexico.

My understanding is that Schwinger rejected the Feynman model until the day he died. My hazy recollection is that it had something to do with a "particle's" electrical field. Something about Feynman's analysis seeing a particle as "pointlike". Something about Maxwell's mathematical model.

[dr_lew]

For example, with Schrödinger's Cat, he shrugs and says, "QM can't predict the future, no problem". But the problem isn't a question of the future; it's a question of the past.

In the Copenhagen Interpretation, QM only represents our state of knowledge of a system. With the cat hidden in the box, QM only predicts the probability of what we will find when we open it.

Suppose we put a clock in the box instead of a cat, rigged to stop when the quantum event is detected. When we open the box we will find it running or stopped, and in the latter case we may certainly say that the time it records is the time of the quantum event.

Note that even a dead cat is an evolving system, and we may say by various means such as temperature when it died, even if we weren't watching. The cat is no different than a clock in this way.

This famous paradigm is more a rhetorical exercise than philosophical. The characterizations of "dead" and "alive" as quantum states is entirely unjustified, but the drama of the situation distracts us from noticing.

[<1/1,000,000th%]

With the cat hidden in the box, QM only predicts the probability of what we will find when we open it.

This is certainly a different interpretation than was adopted at Copenhagen. What the Germans said was that the cat is neither alive nor dead until we make an observation of it. Schroedinger's equation allows us to calculate the probability of what we'll find when we make the observation.