The Foundations of Spacetime Physics:
Philosophical Perspectives

by Antonio Vassallo, ed.
Routledge, 2013, 289 pages
reviewed by T. Nelson

The physicist Steven Weinberg in his essay “Against Philosophy” from Dreams of a Final Theory wrote

[U]ntil the introduction of the post office, the chief service of nation-states was to protect their peoples from other nation-states. The insights of philosophers have occasionally benefited physicists, but generally in a negative fashion—by protecting them from the preconceptions of other philosophers.

Weinberg said that after Einstein, physics gave up on the mechanistic worldview. By this he meant the clockwork mechanism of Newton. But despite its mathematical elegance, fundamental physics has always been descriptive, not mechanistic. How, for example, does an excited atom decide to reduce its energy state by emitting a photon? Physics does not answer this question; it only tells us that it does. A mechanism would have to invoke a lower level process, and here we're stuck in the muck of quantum indeterminacy.

Now, just when the last piece of metaphysical rubbish has been cleared away, physics is grappling with questions like whether space is real and how to make the jump from mathematics to an emergent spacetime in the absence of any instrumentation remotely able to do measurements at small enough scale. With so little to go on, physical theories must take leaps of faith and even, perhaps, scrape up a few broken shards of metaphysics.

This collection of ten essays starts out with a discussion of the hole argument, which is a problem that Einstein struggled with and solved in his famous paper on general relativity. The authors describe it this way:

[B]y the hole argument we understand the philosophical argument that derives the negation of determinism from the existence of hole diffeomorphisms. The mathematical fact that such a diffeomorphism exists is not affected by any metaphysical considerations regarding essential properties.

A diffeomorphism is essentially a bijection, which is to say a map of one manifold onto another. Einstein's dynamical equation G_ab = 8πT_ab, which says that the Einstein tensor G_ab is proportional to the stress-energy tensor T_ab, is famously diffeomorphism-invariant, whereas Newton's formula is not. A ‘hole’ happens when a warp in spacetime occurs, supposedly leaving you at the same coordinates but in a different place. The argument seems weird today, as relativity is now second nature to every sci-fi fan, but it is evidently a big topic in philosophy.

The debate was kicked off by philosopher Tim Maudlin, who is noted for his views that time and space are real and fixed. Maudlin claimed that the hole argument makes general relativity indeterm­inis­tic. In other words, he believes in what is called metric essentialism, which is the idea that the geometrical structure of spacetime is fixed.

This debate, which the authors describe in Chapter 1 in the most confusing way imaginable, introduces the debate about substan­tival­ism vs relation­alism in the first half of the book. Substan­tival­ism says that space and time are ontologically self-sufficient and not dependent on the existence of matter. Relation­alism says they're not.

Since nobody has the faintest clue what space and time may or may not be, the arguments aren't scientific but depend on fine points of logic. By Chapter 4 by Vassallo et al., we finally get a classic sociology-style philosophical debate on the topic.

Part of the problem is that philosophers can't be authoritative on how physics should be interpreted, so it's hard to tell whether their ideas are based on physical insight or just intuition.

Then in Chapter 5, “Rotating Black Holes As Time Machines,” Juliusz Doboszewski goes way out on a limb by saying maybe Kerr black holes are time machines and maybe they aren't. Of course he knows they're not, but we start getting into what real physicists think about Cauchy horizons and the Cosmic Censorship Hypothesis.

In Chapter 7, Vera Matarese presents Weyl's argument that quantum spacetime can't consist of repeated units or ‘tiles’ because this would violate the Pythagorean theorem. That is to say, if space consisted of tiny cubes, the distance going, say, right by 5 units would be different than the distance going at a 45° angle by 5 units. (This is false, by the way: it's easy to envision a scheme in quantum gravity in which it's tiled yet also isotropic.)

In Chapter 8, Vincent Lam et al. throw out a lot of interesting ideas: does quantum indeterm­inacy mean ontological inde­term­inacy? Could spacetime be in a quantum super­pos­ition? Is there always a link between eigen­states and eigen­values? Philosophers, they say, are skeptical of meta­phys­ical indeterm­inacy.

Chapter 9 talks about different types of singularities and how to get rid of them in our formulas, and in Chapter 10 Daniele Oriti discusses his spinfoam model for quantum gravity he calls tensorial group field theory, or TGFT. Asking Oriti to describe spinfoams would get you a whole book, so Oriti skips the math and just focuses on the philosophical issues about spacetime emergence:

In the end, assigning ontological status to the new non-spatiotemporal entities suggested by quantum gravity approaches calls for the development of an ontology that is not spacetime-based, which is a philosophical work yet to be tackled, and of the utmost importance. . . . These are still far from a theory of continuum fields and spacetime and in fact generic discrete configurations appearing in the perturbative expansion would not even correspond to well-behaved simplicial geometries.

In layman's terms this means that the fundamental problem is that spacetime needs to be defined in terms of something that is neither 'spacey-wacey' nor 'timey-wimey.' For this, we will need to think “outside the usual effective field theory mindset.” Oriti is struggling to do that, and he's enthusiastic about his theory, but what physicists need are some experimental clues on which to base a theory. Otherwise they could end up with schemes that reproduce the phenomena but are funda­ment­ally wrong, as the Earth-centered Ptolemaic model was.

Oriti says we need a new ontology that is not grounded on space and time notions. I couldn't agree more. Where did we put those philosophers? Maybe we shouldn't have burned all of them at the stake. Oh well, too late now.

jun 29, 2024

Causal Reasoning in Physics

by Mathias Frisch
Cambridge, 2014, 256 pages
reviewed by T. Nelson

You might think from the title that you'll learn about new insights about causality. Or maybe about how physicists have started using clever new forms of causal reasoning to understand the mysteries of the universe.

Fat chance. It turns out there are people who think physics doesn't use causal reasoning at all.

The claim that physicists don't use causal reasoning conflicts with almost every textbook. Here is physicist Lee Smolin criticizing the causal set theory model of space for being not causal enough:

Nowhere in physics do we have a theory that explains why individual events occur. . . . There are, to my knowledge, no deterministic causal set models; instead those causal set models that have been studied take a stochastic or quantum approach to dynamics. They therefore do not attempt to answer the question of why particular causal sets may occur. (The Singular Universe and the Reality Of Time, p.384)

The standard twelve-pounder on relativity, Gravitation by Misner, Thorne, and Wheeler, has an entire section on causal relations that begins with explicit definitions of causality:

P ≺ Q or Q ≻ P (“the event P causally precedes the event Q; the event Q causally precedes the event P”) means there is at least one future-directed causal curve that extends from P to Q. (Gravitation, p. 922)

(Side note: Amazon says this 1300-page book is for readers “age 1 and up” but I think they will need to study partial differential equations first.)

The point is that establishing causality is what science is all about. It is the explicit reason for a control in an experiment. In fact, any words like ‘thus’, ‘therefore’, ‘what happens’ and ‘why’ are abundant in all branches of science, including physics. Even in particle physics, the overwhelming emphasis is on ‘interactions’. These are all direct appeals to cause and effect, as philosopher Nancy Cartwright correctly pointed out.

You could even argue that physicists shouldn't talk about causality because when you define something you're not supposed to use a word in its own definition. Another reason may be that the term ‘causation’ sounds too metaphysical.

Why, then, do some philosophers say it doesn't exist? Frisch describes the idea of Woodward and Field, as expressed in The Oxford Handbook of Metaphysics, this way:

Physical theories provide us with complete models of the phenomena in their domain, constructed from the data on complete lightcone cross sections as input, which do not permit a distinction between causes and background conditions. Therefore, there is no place for causal notions in physical theories. [p.59]

This is false, Frisch argues, because we'd have to know the state of every particle within the past light cone of an event to attribute cause and effect, which is impossible.

I don't have my copy of that handbook handy, but it seems to me that there's a much simpler counter-argument. Frisch gives an example of what caused him to hear Beethoven's Tempest Sonata on the radio. Was it, he says, the background conditions where the initial electromagnetic field was zero at some point? According to W&F, it would have to be. He writes as if it's a big mystery how people figure things like this out, but in fact a vast background of scientific knowledge goes into our everyday reasoning. We know already what physical processes are important and which we can ignore. When studying protons, for instance, we can ignore the phase of the Moon and the fact that Ben Affleck and JLo are divorced because countless other experiments have shown that these events have no effect on our protons.

Bertrand Russell said functional dependencies have replaced causes in theories. And what does a ‘functional dependency’ mean? A cause!

But all this was just a red herring before Frisch gets around to the main argument, which starts on page 124, where Frisch finally states the problem that philosophers have with causality. If the laws are time-symmetric, they say, there is no way to distinguish one temporal direction from the other. A classic example is an astronomer viewing a star through a telescope. If physical laws are time-agnostic, how do we know the light went from the star to the telescope and not the other way around?

Maybe we can blame on the science popularizers, who told us that QM has proved that the laws of nature are non-deterministic, that there was no time before the Big Bang, and that because time is not explicitly coded in the equations everything could just as easily run back­wards if it wanted to. But even Einstein struggled with it, as the chapter on the Einstein-Ritz debate shows.

But the answer is very simple. Equations are simplifications and can have solutions that aren't physically realizable. Their job is to make the principle understood, so they might omit time because the physicist knows, or at least hopes, the reader is in possession of a certain common sense knowledge. Photons travel from a star to the observer and not the other direction because the reverse direction violates entropy and probability and many other physical laws. This is, of course, obvious and it is why no one bothers to include time explicitly in any optics equation.

As Quine put it, a theory doesn't exist in isolation but as part of a vast bundle of previously demonstrated knowledge. We call this “common sense,” which is a shorthand for saying “every stupid fact about nature that has been discovered over the past 1000 years need not be restated every single time.”

Frisch says much the same thing in greater detail. The reason, he says, is that inferences in physics are “severely underdetermined” and that observational data don't always determine the causality, so causal assumptions play an important inferential role.

To back this up he cites Green's theorem, where we constrain the boundary value such that it depends only on variables in its past. He uses the Markov condition implied by the principle of common cause (PCC) to get the correct solution. And he quotes John Earman, who said the reverse would be a “near miracle.” Then he devotes a chapter to linear response theory, which is explicitly time-dependent, adds some math to justify his boundary conditions on the Green's formula, and another chapter on radiation asymmetry and entropy.

So there you have it. By gum, that dead horse is going to stay dead.

If this were fiction, it would be a story where they argue a bit over some triviality, nobody really disagrees with each other, and you know from the start it will have a happy ending. And maybe I just spoiled the ending.

jul 11 2024