Tag 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.

In defense of “The Thin Line Aesthetic”

I was lucky to be one of the guest artists at the Code+Art Student Visualization contest at NCSU library recently, where parts of my generative art work Clocks were displayed. In preparation for the show, I wrote specific pieces for the space, which uses a large screen made out of Christie Micro-tiles. These are modular screens which can be used to construct large and even irregular displays. While the Micro-tiles gave me the largest amount of screen real-estate I’d ever worked with, they posed their own challenges. In particular, the luminance tends to vary between tiles in such a way that art works with predominantly white backgrounds can be distracting, since each tile making up the whole screen will appear at a different brightness. The effect is less noticeable when darker colors are supplied.

Thin Lines!

Thin Lines!

During these discussions, it was suggested that using dark backgrounds might help get us away from “the thin line aesthetic” so predominant in generative art. I agree, thin lines, typically dark on white, are extremely common in generative artworks. But here I will say a few words in their defense.

Clock 10 is a thin-line clock. I’ve had occasion to think very carefully about why this clock works as a generative art piece, and it is typically the clock I talk about when talking about the project as a whole because it has a relatively simple, but non-trivial, account. Briefly, Clock 10’s charged particles want to distribute themselves evenly over the face of the clock (since they are all positively charged, and hence repel one another). The clock hands persistently frustrate this tendency by moving particles from the second hand to the hour or minute hand. As such, the particles are constantly seeking, but never attaining, their low energy equilibrium state. Critically, there is not just one such equilibrium state: there exists a family of states related by symmetry transforms (continuous and discrete rotations).

What this boils down to is that Clock 10 traces out the symmetries of the ground states. This is why, if you let the clock run for a half hour, you see concentric rings appear: these rings are the places that particles would like to be modulo rotations, were they allowed to find those states without interference.

cant-number-3

A few aesthetic choices support the relationship of Clock 10 to this interpretation. The color of the trace left by each particle is adjusted in such a way that it only darkens as the particle settles down, so that paths near equilibrium are dark while those far from it are white. And, of course, we use thin lines, which allow lots of information about those trajectories to appear on the face of the clock.

I am a barbarian, so far as artistic pedigree is concerned, but if Clock 10 lives anywhere in the landscape of the practice of generative art, it is in the school of Complexism. Complexism suggests one role of generative art is to explore complex systems. In the sense the Clock 10 is an aesthetically pleasing visualization of the ground states of a certain physical system, it meets this criterion. And thin lines help it operate in this way because they allow us to see a lot of different trajectories in a small amount of space. They give the clock non-trivial texture: tendencies of the motion can be apprehended at a large scale while details of the motion are still discernable.

I tried a variety of other ways of visualizing the trajectories, but none were particularly satisfying because they obscured the fine-scale variations in a way which significantly reduced the information content of the visualization. Part of the impact of generative art is that it imitates nature, to an extent, in that it can compound over and over again many fine motions. The accumulation of so many effects is part of the immediate perception of a work, and undermining it undermines one of the fundamental advantages of using computers, systems capable simultaneously of great precision and great, repetitive patience.

So use thin lines! Or, if you are seeking alternative aesthetic choices, try to find ones which capture the same benefits, packing lots of precise detail into the image in such a way that larger trends are also made visible.

cant-number-1.5