Category Archives: physics

Why Physicists Need Their Space

A few weeks ago I attended the Rutgers/Columbia Symposium on the Metaphysics of Quantum Field Theory. This morning in the shower a few things I’ve been thinking about snapped into place relating to that conference and my own hobby-level interest in related questions.

Some background: Ontology, meaning “what stuff is fundamental and what stuff is derived?” is important in the question of the foundations of physics. You can see this going all the way back to Thales (624 – c. 546 BC) who, in the traditional account, is the first “scientist” exactly because he proposed an ontology: water is real, all other phenomena are derived from water. (Note that the idea of supervenience enters into the discussion here: in Thales’ account, for instance, because a rock is fundamentally a sort of water, we can say that the higher level properties of rock supervene upon the fundamental properties of water in some way.) Contrast this with the atomists, who posit that atoms are fundamental objects and other things supervene upon them. Or contrast it with idealists, like Plato, who claim that in some sense forms are ontologically fundamental and that real things supervene upon them.

Now, one of the many ways to see what is hard about QM is that it challenges the ontological status of space itself. This is, in fact, one of the most important ways it’s challenging from a philosophical point of view. That is, for lots of reasons (of which more later), we tend to believe that space is fundamental.

But why do we care so much about space? There are ways of deriving the Schrodinger Equation (which governs the behavior of quantum mechanical systems) from ontologies which don’t include space at all (consequently, space isn’t part of the ontology of these theories at all). See Lee Smolin 2014 – Nonlocal Beables. (NB the vogue is to call observables “beables”). It seems like, if we can find a nice way of getting QM from a more fundamental theory without any of the other weirdnesses (like considering that the wave function is real, for instance) that explains why it seems like wave function collapse constitutes action at a “distance”, then we ought to take it. After all, if we can show that space isn’t ontologically real then we shouldn’t be afraid of some non-spacelike aspects to our theory. Space “emerges” from some low-level dynamics of a non-spatial system. It isn’t fundamentally challenging that some of those dynamics won’t be space like and so we don’t need to grind our teeth and rend our garments about Bell’s Inequality or other Entanglement related phenomena: they are just the fundamentally non-spacey nature of reality peaking around the corners of a low energy/classical limit.

Considering that entanglement presents us with some otherwise very unusual epistemological challenges, this seems to me like a great escape hatch. Or at least it did until I spent some time thinking about how important geometry is to physics.

Believe it or not, action at a distance isn’t a new controversy in physics. It goes back way before entanglement was a twinkle in Schrödinger’s eye. The ancient Greeks were obsessed with it and Descartes and Newton worried a lot about it too. One way of telling the story is to think about planetary motion. The critical insight to planetary motion (this account more or less derives directly from Crowe’s Mechanics from Aristotle to Einstein, 2007) was that objects have momentum (which even Newton conceived of as a kind of force). Without the idea of momentum its hard to imagine what keeps planets in their orbits. The most common explanation at the time of Newton was some sort of substance filling space which had vorticial motion, and thus which carried the planets along in their circular orbits. What was particularly appealing about this to someone like Descartes (for reasons about which I could write a whole other essay) is that it was a theory without action at a distance. The sun might have been the source of a vortex which carried earth around it, but it was the local motion of the fluid which pushed the earth along, and that motion was transmitted from the sun to the location of the earth by local interactions in the fluid itself. That is, there was not some mysterious tendency transmitted over empty space which caused the motion. Everything was local. At the heart of this is both the idea that there is no action at a distance, that inanimate objects don’t move on their own and a deep underlying notion that interactions are always local (which is part and parcel with the sense that space is part of our ontology).

The irony is that Newton, the great hero of the scientific perspective, is the less materialist of the two. In The Principia (1687) he makes such enormous progress by dispensing with the notion that he needs to worry about precisely how the interaction between massive bodies is mediated and instead focuses purely on its mathematical description. In a way, Newton is thus in the “shut up and calculate” camp. Newton doesn’t throw space out of the ontology but he does profoundly weaken its role by at least suggesting that we don’t need to think of every interaction in the universe as mediated in a purely local sense (though he never outright claims gravitation force is nonlocal). If your goal is to calculate the motion of the planets, then this is a great tactic and is, in a way, the essence of good model building: whatever the underlying structure of space-time, its certainly true to a high degree of accuracy that gravity appears to act instantaneously across empty space to produce a force on distant objects. (By the way, Max Jammer’s 1957 Concepts of Force has enlightening things to say on this subject since it helps ground the philosophical notion of force exactly in the physiological experience of pushing or pulling, though we are about to see a compelling reason to believe that the gravitational force is nothing like that at all).

In a way, we can see Newton’s Principia as leapfrogging science’s ability to calculate far ahead of philosophy’s ability to account for what is exactly happening. In that sense, there is an analogy between General Relativity and Newtonian Mechanics and between some heretofore undiscovered ur-theory and Quantum Mechanics: General Relativity provided a kind of philosophical closure between the Cartesian and Newtonian split over the locality of interactions by re-inventing an ontological role for space(time).

General Relativity tells us that no force at all pulls or pushes on the planets. Instead, it says the planets move the way they when the true geometry of space-time is taken into account, they are simply following what locally looks like the plain old Newtonian notion that objects in motion continue to move in a straight line unless acted upon.

Supersymmetry is an attempt to resolve the problems of quantum field theory by imagining that every fermion (boson) in the standard model has a bosonic (fermionic) super-symmetric partner. At this point the theory is out of favor: we’ve never seen these super-symmetric particles in accelerators which means they’d have to be very massive indeed. But one interesting aspect of the theory which was developed in a talk by David Baker at the Rutgers/Columbia Conference is that the addition of such supersymmetric particles introduces aspects of the theory which you could consider elevating to space-time coordinates (however Grassman valued). Why would you want to do that? Well, because its very natural to say that space-time symmetries generate or cause physics. This is the essence of General Relativity and of Yang-Mills style theories, so it underlies both GR and one of the best tools we have to develop useful Quantum Field Theories. Even my passing familiarity with both disciplines is enough to sniff out that these theories are extremely local and geometric. That is practically what differential geometry means.

That is the point of this essay. Modern physics is so used to treating geometry (of spacetime) as ontologically prior that the idea that geometry itself might supervene upon some more fundamental physics is truly challenging. From this point of view, you might prefer to do something like just say the wavefunction is real, even though doing so drastically expands the universe (by introducing a vast number of new observers into it, for instance).

Jovian Prayer

Big slow storms of Jupiter, help sooth us.
Sooth us with your patient weather, ochre,
gamboge, carmine, grey, swirling storms, giant.
And auroras, lightning, huge, cathartic.Screen Shot 2016-07-10 at 10.46.37 AM

Let us be like Galileo’s nameless
daughter, who threw herself into your heart
wrapped in curiosity, down, down, down,
swallowed by knowledge, by your huge brown storms.

Notes on `Quantum Computing Since Democritus, Chapter 1`

For a long time, I’ve been interested in the sorts of questions exemplified by the following example:

Suppose we are Isaac Newton or  Gottfried Leibniz. We have at our disposal two sources of inspiration: data, collected by intrepid philatelists like Tycho Brahe and something like theory, in the form of artifacts like Kepler’s Laws, Galileo’s pre-Newtonian laws of motion (for it was he who first suggested that objects in motion retain that motion unless acted upon), and a smattering of Aristotelian and post-Aristotelian intuitions about motion (for instance, John Philoponus’ notion that, in addition to the rules of motion described by Aristotle, one object could impart on another a transient impetus). You also have tables and towers and balls you can roll on them or drop from them. You can perform your own experiments.

The question, then, is how do you synthesize something like Newton’s Laws. Jokes about Newton’s extra-scientific interests aside, this is alchemy indeed, and an alchemy to which most training physicists receive (or at least I received) does not address itself.

Newton’s Laws are generally dropped on the first year physics student (perhaps after working with statics for awhile) fully formed:

First law: When viewed in an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by an external force.[2][3]
Second law: The vector sum of the external forces F on an object is equal to the mass m of that object multiplied by the acceleration vector aof the object: F = ma.
Third law: When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.

(this formulation borrowed from Wikipedia)

The laws are stated here in terms of a lot of subsidiary ideas: inertial reference frames, forces, mass. Neglecting the reference to mathematical structures (vector sums), this is a lot to digest: and it is hard to imagine Newton just pulling these laws from thin air.  It took the species about 2000 years to figure it out (if you measure from Zeno to Newton, since Newton’s work is in some sense a practical rejoinder to the paradoxes of that pre-Socratic philosopher), so it cannot be, as some of my colleagues have suggested, so easy to figure out.

A doctorate in physics takes (including the typical four year undergraduate degree in math, physics or engineering) about ten years. Most of what is learned in such a program is pragmatic theory: how to take a problem statement or something even more vague, identify the correct theoretical approach from a dictionary of possibilities, and then to “turn the crank.” It is unusual (or it was unusual for me) for a teacher to spend time posing more philosophical questions. Why, for instance, does a specific expression called the “Action,” when minimized over all possible paths of a particle, find a physical path? I’ve had a lot of physicist friends dismiss my curiosity about this subject, but I’m not the only one interested (eg, the introductory chapter of Lanczos’ “The Variation Principles of Mechanics”).

What I am getting to here, believe it or not, is that I think physicists are over-prepared to work problems and under-prepared to do the synthetic work of building new theoretical approaches to existing unsolved problems. I enjoy the freedom of having fallen from the Ivory Tower, and I aim to enjoy that freedom in 2016 by revisiting my education from a perspective which allows me to stop and ask “why” more frequently and with more intensity.

Enter Scott Aaronson’s “Quantum Computing Since Democritus,” a book whose title immediately piqued my interest, combining, as it does, the name of a pre-Socratic philosopher (the questions of which form the basis, in my opinion, for so much modern physics) with the most modern and pragmatic of contemporary subjects in physics. Aaronson’s project seems to accomplish exactly what I want as an armchair physicist: stopping to think about what our theories really mean.

To keep myself honest, I’ll be periodically writing about the chapters of this book – I’m a bit rusty mathematically and so writing about the work will encourage me to get concrete where needed.

Atoms and the Void

Atoms and the Void is a short chapter which basically asks us to think a bit about what quantum mechanics means. Aaronson describes Quantum Mechanics in the following way:

Here’s the thing: for any isolated region of the universe that you want to consider, quantum mechanics describes the evolution in time of the state of that region, which we represent as a linear combination – a superposition – of all the possible configurations of elementary particles in that region. So, this is a bizarre picture of reality, where a given particle is not here, not there, but in a sort of weighted sum over all the places it could be. But it works. As we all know, it does pretty well at describing the “atoms and the void” that Democritus talked about.

The needs of an introductory chapter, I guess, prevent him from describing how peculiar this description is: for one thing, there is never an isolated region of the universe (or at least, not one we are interested in, I hope obviously). But he goes on to meditate on this anyway by asking us to think about how we interpret measurement where quantum mechanics is concerned. He dichotimizes interpretations of quantum mechanics by where they fall on the question of putting oneself in coherent superposition.

Happily, he doesn’t try to claim that any particular set of experiments can definitely disambiguate different interpretations of quantum mechanics. Instead he suggests that by thinking specifically of Quantum Computing, which he implies gets most directly at some of the issues raised by debates over interpretation, we might learn something interesting.

This tantalizes us to move to chapter 2.