Carlo Rovelli is a big fan of loop quantum gravity, and of physics in general, and this book recaps the whole history of modern physics, at least partly in order to show how elegantly loop quantum gravity fits into place as a reasonable extrapolation. It’s an interesting and believable history, and the case for the plausibility of loop quantum gravity looks convincing to me. But then, I think I was an easy mark — since I already agreed with a series of strange (from the layperson’s point of view, at least) assertions Rovelli makes about known physics.
Rovelli inserts helpful diagrams every so often to summarize the history (and sometimes potential future) of “what there is” in the physical world according to physics. I can’t quite do justice to them so I use a table (please read it as one table).
Covariant quantum fields
In the transition from special relativity (1905) to general (1915), fields and spacetime are absorbed into “covariant fields”. This is because spacetime, Rovelli asserts (and I instinctively agree), is the gravitational field. So other fields like the electromagnetic field are covariant fields – fields that relate to each other in circumscribed ways. The curvature of spacetime depends on the energy (e.g. electromagnetic) present, and the behavior of electromagnetic fields depends on that curvature.
Rovelli likes to sum up some key features of each theory, and these summaries are very helpful. For QM, Rovelli lists three key principles:
Information is finite;
There is an elementary indeterminacy to the quantum state;
Reality is relational (QM describes interactions).
As a fan of Everettian QM, I don’t think we really need the indeterminacy principle. But it’s still true that we face an inevitable uncertainty every time we do a quantum experiment (it’s just that this is a kind of self-locating uncertainty).
Loop quantum gravity refines the “information is finite” principle to include spacetime as well. Not only are energy levels discrete; spacetime is also discrete. There is a smallest length and time scale. Rovelli identifies this as the Planck length (and time).
Rovelli explains loop quantum gravity as the quantization of gravity, deriving from the Wheeler-DeWitt equation. This equation can only be satisfied on closed lines aka loops. Where loops intersect, the points are called nodes, and the lines between nodes are called links. The entire network is called a graph, and also a “spin network” because the links are characterized by math familiar from the QM treatment of spin. Loop quantum gravity identifies the nodes with discrete indivisible volumes, and each link with the area of the surface dividing the two linked volumes.
Rovelli is at pains to point out that the theory really says what it’s saying. For example: “photons exist in space, whereas the quanta of gravity constitute space itself. … Quanta of space have no place to be in, because they are themselves that place.” This warning might seem too obvious to be necessary, but that’s because I didn’t reproduce the graphs of spin networks in Rovelli’s book. (I lack the artistic talent and/or internet skillz.) You know, graphs that sit there in space for you to look at.
OK, that’s space, but what about time (and aren’t these still a spacetime)? This deserves a longish excerpt:
Space as an amorphous container of things disappears from physics with quantum gravity. Things (the quanta) do not inhabit space; they dwell one over the other, and space is the fabric of their neighboring relations. As we abandon the idea of space as an inert container, similarly we must abandon the idea of time as an inert flow, along which reality unfurls.
[…] As evidenced with the Wheeler-DeWitt equation, the fundamental equations no longer contain the time variable. Time emerges, like space, from the gravitational field.
Rovelli, chapter 7
Rovelli says loop quantum gravity hews closely to QM and relativity, so I assume we get a four-dimensional spacetime which obeys the laws of general relativity at macroscopic scales.
In a section of Chapter 11 called Thermal Time, Rovelli uses thermodynamics and information theory to explain why time seems to have a preferred direction, just as “down” seems to be a preferred direction in space near a massive body. When heat flows from a hot zone into the environment, entropy increases. Since entropy reductions of any significant size are absurdly improbable, these heat flows are irreversible processes. And since basically everything in the macroscopic world (and even cellular biology) involves irreversible processes, time “flows” for us. Nevertheless, at the elementary quantum level, where entropy is undefined (or trivially defined as zero – whichever way you want to play it) time has no preferred direction. All of this will be familiar to readers of my blog who slogged through my series on free will. This is the key reason scientific determinism isn’t the scary option-stealing beast that people intuitively think it is.
There was one small section in Chap. 10 on black holes that seemed to fail as an explanation. Or maybe I’m just dense. Since spacetime is granular and there is a minimal possible size, loop quantum gravity predicts that matter inside the event horizon of a black hole must bounce. The time dilation compared to the outside universe is very long, so an observer would see no effect for a very long time, but then the black hole would “explode”. But surely “explode” is not the right word? Intuitively it would seem that any bouncing energy should emerge at a comparable rate to that at which it entered, at least for matter entering during a period of relatively stable Schwarzschild radius. Maybe by “explode” Rovelli just means the black hole would “give off substantially more energy than the usual Hawking radiation”?
In a recent interview with Nigel Warburton, neuroscientist Anil Seth mentions (around 3 minutes + 30 sec) John Locke’s distinction between primary and secondary qualities. For primary qualities, the way in which it appears in our experience is pretty directly related to how things are in the world, such as solidity and movement. But there are things like colors which are secondary qualities, where the relationship between what we experience and what’s out there is more indirect and requires the participation of the observer to generate that quality.
But then, at around 6:30 in the video, Anil Seth tells us that all perception works mainly in the top-down, or inside-out direction – from high-level descriptive guesses about the world “down” to details that then fit in to or revise that picture, and from the central nervous system “out” to the periphery. From what little I know of neurology, this inside-out direction of influence is indeed quite important. But that observation threatens, or perhaps we should say trivializes, the primary/secondary distinction. (Seth may well understand this; I’m not sure. The mention of primary/secondary may only be made in order to move beyond it.)
If our perceptions of solidity and of motion are indeed primarily driven from the inside of the brain outward to the periphery, what sense can we make of the idea that our “experience is pretty directly related to how things are in the world”? Our experience is driven from guesses in the central cortical region outward, in both color and solidity experiences. It would seem that all qualities are secondary qualities.
But then, all qualities are also primary qualities, if all it takes to be a primary quality is that it can be specified without reference to an observer. For example, we can define three zones of spectral radiance, one centered at 420 nm, one at 530 nm, and one at 560 nm, each giving less weight to other wavelengths as one gets further from that peak. We can then define “red” things as those whose radiance in that highest-wavelength band bears sufficiently high ratios to the radiance in the other two bands. Of course, I had to lean on human experience of colors to get those wavelength numbers. Yet, I have to lean on human experience of solidity before I could attempt to define that, as well. The alleged primary/secondary distinction is not to be found here.
Seth points out that the solidity of a bus can impact you even when you’re not observing it. OK, but a bacterium which photosynthesizes using only rhodopsin will flourish in green light more easily than in red light of the same total intensity – regardless of whether anyone is looking. Again, no difference here.
Did you hear the latest news from the courts? They’re overhauling the rules for legal arguments in front of a jury. The rules for lawyers will be much looser. Want to ask a witness an irrelevant question? One that lacks foundation? One that the witness has already answered, but you didn’t like the answer? Want to skip the questions and just testify to the courtroom on behalf of your side? Go right ahead!
The other side can object, of course, and the objections will be noted for the record. But then the questioning, or testifying, can go on as if nothing happened.
Badgering the witness? Go for it! Hearsay? No problem! Lay witness testifying about a subject he has no expertise in? Let the jury beware!
Expert witnesses also need no particular qualifications any more. If the witnesses are good enough for one side, they’re good enough for the court. It’s strictly He said, She said, from here on out. The court will not attempt to instruct the jurors regarding which witnesses are credible or have genuine expertise. Jurors will be on their own regarding whom to believe.
OK, relax. I’m just kidding. This isn’t going to happen. But if it did, it would be a disaster. Lawyers would race to the bottom to use underhanded tricks to con jurors onto their side. Truth and evidence would largely go out the window. It’s widely known that the legal rules of evidence and argument are there to prevent just such a disaster, and there is no massive wrecking ball on the horizon headed toward destroying these rules.
OK, don’t relax. Indeed, low-grade panic would be appropriate. This isn’t going to happen to the courts, but it has already happened to the press. The mainstream US print, radio, and TV media, with the exception of a few open partisans, treat “objectivity” as if it demanded a courtroom without any rules. More precisely, with only one rule: that “both sides” will get a chance to speak. And never mind how the number of sides gets magically reduced to two. Journalists have become stenographers or videographers. Fact checking is relegated to a special segment, if it exists at all. And news outlets are embarrassed if some important figures are found to be stating falsehoods on a regular basis, especially if that looks “unbalanced”.
In recent years there has been a lot of well justified hand-wringing about our post-truth society. “How did we get here?” authors ask. To me the mystery is rather: why did it take so long?
The BBC recently came out with a three-part series on free will. Part 2 is about physics. If you’re going to infer lessons from physics, it helps to get the physics right. They don’t. Part 2 of the BBC series can be found here: https://www.bbc.com/reel/playlist/free-will?vpid=p086tg3m
The picture above analogizes a series of physical events to a chain of dominoes, in order to talk about cause and effect. But there’s something odd about this metaphor, if the dominoes are supposed to represent the physical universe: look at that first domino, in black. What makes it tip over? Something from outside the universe, a “god” so to speak, intervenes to set the whole thing in motion. We seem to have jumped from physics to theology.
This would just be a nit-pick, if the negligent treatment of the “start” in the model did not affect the conclusions drawn. But it does, as we will see.
But first let’s look at some additional physics mistakes in the video. Jim Al-Khalili says “When we think we’re making free choices, it’s just the laws of physics playing themselves out.” Well no, the laws of physics alone don’t cause anything. The laws of physics are rather abstract. If you want to understand how a concrete action came about, you need not just laws of physics but also what physicists call “boundary conditions”, AKA concrete reality. Especially bits of concrete reality that heavily interact with the action in question. For example, you. Of course, perhaps Al-Khalili didn’t mean “just the laws of physics” quite so literally. But it matters how you phrase things, especially when you accuse people of only thinking they’re making free choices. Your grounds for calling them mistaken had better not be based on distorted depictions of the physics.
From the “libertarian” side of the philosophical debate, Peter Tse makes a different mistake – or maybe just poorly worded statement: “Patterns of energy don’t obey the traditional laws of physics.” Unless he means “classical physics” (in which case: say “classical”), that’s not true. The Wikipedia article on Lagrangian mechanics is a good resource for seeing just how deeply physics treats patterns of energy. “The kinetic and potential energies still change as the system evolves, but the motion of the system will be such that their sum, the total energy, is constant.”
Since Einstein, physicists have known that space and time are not independent, but aspects of a single four-dimensional manifold, spacetime. For observers in different inertial reference frames, which direction counts as “time” will differ. A metaphor called the “block universe” is sometimes used to describe this, where we only depict two spatial dimensions and then repurpose the third to represent time. Jim Al-Khalili uses a loaf of bread, with different times being different slices.
The block universe is like a loaf. OK, let’s go with this metaphor: one end of the loaf is very hot (we call it the Big Bang) and the other is cold. There are certain patterns that stretch from one end of the loaf to the other. If we know the pattern (laws of physics) and we know the boundary conditions (full state of any slice) we can derive the state of any other slice. Why say that the hot end caused the cold end to be the way it is? Why not say that the cold end caused the state of the hot end? After all, the mathematical derivation works equally well in that direction. Better yet, why not admit that “causality” is a useless concept at the level of a complete description of the universe, and just look at the bidirectional laws of nature instead? Why not start your analysis in the middle (but nearer to the hot side), and work your way toward both ends? The last option is a lot more practical, since that middling point is where you are.
The idea that the Big Bang is the Big Boss and we are just its slaves has no basis in science. Remember that “god” that tipped over the first domino? He’s creeping back in through the back door of Al-Khalili’s thinking. He thinks the Block Universe is dominated by its early times. You can only get such domination by swapping out a scientific view of time and causality, and sneaking in an intuitive picture of time and causality in its place.
Al-Khalili does that when he says “The past hasn’t gone … the future isn’t yet to be decided.” The narrator does that when she says “every single frame of that animation already exists and will exist forever.” Argh, no! Time is within the loaf! If you’re going to use a metaphor, stick with the structure you used to create it – don’t sneak your intuitive conception of time into the background while leaving scientific time in the foreground, now portrayed spatially.
Al-Khalili says “the future … is fixed, even though we don’t know it yet.” This conclusion would repeal the very laws of physics Al-Khalili was claiming to honor. The future is dependent on us because, to repeat myself, laws of physics must be applied to boundary conditions to derive a prediction about the future, and those boundary conditions include us.
Modern physics does destroy the traditional “solution” to the “problem of free will”. What these commentators don’t seem to notice is that it also destroys the traditional “problem” of free will. When you notice that your intuitive ideas of time and causality conflict with science, you need to figure out the full consequences of the science, not take one point from science and then re-apply your intuitive ideas. The future isn’t set in stone. It’s set in spacetime. And spacetime is lighter than air.
(B) Unidirectional, making for controllers and the controlled
But not more than two of (A)-(C). Causality is unidirectional and scientific, but not universal. Laws of nature are universal and scientific, but not unidirectional. Determinism as imagined in the Consequence Argument is universal and unidirectional, but not scientific. That’s why the Consequence Argument fails.
We think of the past as fixed and the future as open. Some people think science has shown that the fixed past is real and the open future is an illusion, but the truth is almost diametrically opposite. The idea that the whole past is fixed is an overgeneralization. It is a natural, and even rational, inference from our experiences as macroscopic beings, but still a mistake.
Even though (the evidence indicates) the past only depends microscopically on the present, what is advocated here is not a version of Lucretius and the “swerve”. It’s not that we get our freedom from microscopic past phenomena (such as quantum phenomena) in particular. The idea that freedom has to be handed down from past to present is wrongheaded to begin with. If in some particular case, a macroscopic past state did perfectly correlate with our macroscopic present action, that would still not be a problem: that macroscopic past state would then be up for grabs. (Aside for the really nerdy: This is why I am not a big fan of Christian List’s reply to the Consequence Argument, even though it may have a solid point. It concedes too much.)
An additional group of anti-free will arguments, vaguely similar to the Consequence Argument but different, are called sourcehood arguments. Let me just quote the first premise from the Stanford Encyclopedia of Philosophy article:
1. We act freely … only if we are the ultimate sources (originators, first causes) of at least some of our choices.
This one wears its allegiance to a certain picture of time and causality on its sleeve. Why ultimate source? Why not just source? Because the proponent of the argument mistakenly thinks that physical events are in the general habit of bossing each other around, so that the only way we can avoid being controlled is to conjure something ex nihilo. Hopefully, we’ve covered this ground enough that the reader can see what’s wrong with that premise.
People often do bad things when they could have done better things. Does that mean Retributivism is justified? (Hint: No.) Retributivism, on one definition, is the view that it’s intrinsically morally better that a wrongdoer suffer than that they do not, provided that they could have done otherwise.
Retributivism is not a metaphysical mistake. But in my view, it’s a moral mistake. Instead, punishment is justified when justifiable rules call for it, and discovering those rules depends on free and open moral dialogue among people who will be affected by the rule; people who are intent on reasoning together about how to get along. Others may not care to get along. We need a backstop to enforce livable social rules on those who would otherwise harm anyone who got in their way, and those who are a little more pro-social yet still go off the rails sometimes. But not everyone needs suffering to keep them in line, and those who do should not receive more than the minimum required.
There’s a more humane approach to justice that is common in many indigenous societies, and is making something of a comeback in ours. Here’s part of a transcript of an interview about restorative justice. Michel Martin is a show host, and Sujatha Baliga is a recent MacArthur Fellowship winner who works on restorative justice.
MARTIN: I’m glad you raised that as a crime of violence because I think many people may be familiar with a concept of restorative justice in connection with, you know, teenaged mischief, for example. Let’s say you deface somebody else’s football field before the big game, and they find out that you did it. And the consequence is you have to clean it up. In matters like this, in matters of serious crime and serious harm, where someone’s life is taken, where someone is seriously harmed, what, in your view, is the societal benefit of taking this approach?
BALIGA: Actually, restorative justice works best with more serious harms because we’re talking about people who are actually impacted. In that face-to-face dialogue, you can imagine it not having any heat or any value, really, in terms of the wake-up or the aha moments when we’re talking about graffiti versus when someone has actually entered someone’s home and taken their things, right? That’s a situation that calls for accountability, calls for a direct dialogue where someone takes responsibility for what they’ve done. So, to my mind, restorative justice – and it’s not just to my mind. There’s international data that shows that restorative justice is actually more effective with the more serious harms that people do to one another.
Emphasis added. A humane approach to justice doesn’t depend on the denial of free will or moral responsibility. Quite the opposite, in this case.
Intuitively, we think of the future as open and the past as fixed. Meaning that the future is up to us; dependent on our actions. And the past is not; it’s independent of our actions. This way of thinking is very natural and goes deep. We think that being in the past makes those events fixed. But that’s wrong: it’s an oversimplification. It’s the fact that those events (that we are thinking of) represent a lower entropy state that makes them fixed. And an occurrence of a lower entropy state requires a large number of microscopic states which all count as the same state at some coarse-grained level, such as “the pressure of the air in this tire.”
Let us count the Ways
If all you know about “entropy” is that it’s related to “disorder” (true in a limited range of cases), the fact that entropy is only defined statistically will come as a surprise. But the classic definition for entropy given by Ludwig Boltzmann is S = k ln W. S is entropy, k is the Boltzmann constant, and W is the probability, given by the count of the ways that the macroscopic state can be realized by various microscopic arrangements. Because the numbers of microscopic states in question are enormous (18 grams of water contains 6 x 10^23 molecules for example), the probabilities quickly become overwhelming for macroscopic systems. Ultimately, the increase of entropy is “merely” probabilistic. But those probabilities can come damn close to certainty.
Why are so many processes irreversible? By reversing a process, we mean: removing a present condition, to give the future a condition like the one had in the past. For example, suppose I dropped an egg on the kitchen floor, making a mess. Why can’t I undo that? The molecules of egg shell and yolk are still there on the floor (and a few in the air), and they traced in-principle reversible paths (just looking at the micro-physics of molecular motion) to get there. So why can’t I make an intact egg from this?
The answer is entropy, and therefore the count of the Ways. There are many ways to get from a broken egg to a more-broken egg. There are many orders of magnitude fewer ways to get from a broken egg to a whole egg. One would have much better odds guessing the winning lottery number, rather than trying to find a manipulation that makes the egg whole. There is some extremely narrow range of velocities of yolk and shell-bits such that if one launched the bits with just those velocities, molecules would in the immediate future bond to form whole egg-shell, with yolk inside – but finding those conditions, even aside from implementing them, is impossible in practice. Because the more-broken egg states so vastly outnumber the whole-egg states, our attempts to reverse the mess have vanishing probability of success.
On a local level, some macroscopic processes are reversible. I accidentally knock a book off a table; I pick it up and put it back. The room is unchanged, on a suitably coarse-grained analysis — but I have changed. I used up some glucose to do that mechanical work. I could eat some more food to get it back, but the growth of the relevant plants ultimately depends on thermodynamically irreversible processes in the sun. On a global analysis, even the restoration of the book to its place is an irreversible process.
The familiar part of the past is fixed …
Entropy thus explains why we can’t arrange the future to look just like the past. The different problem of trying to affect the past faces similar obstacles. The “immutability of the past” arises because the events we humans care about are human-sized, naturally enough, i.e. macroscopic. Macroscopic changes in practice always involve entropy increases, and always leave myriad microphysical traces such as emitted sounds and reflected and radiated light and heat. These go on to interact with large systems of particles, typically causing macroscopic consequences. While phonons (quanta of sound) and photons follow CPT-reversible paths, that does not mean we can collect those microscopic energies and their macroscopic consequences in all the right places and arrange to have the past events that we want. As in the broken egg case, even if we had the engineering skills to direct the energies, we face insurmountable information deficits. We know neither where to put the bits, nor with what energy to launch them.
In addition to the time-asymmetry of control over macroscopic events, we have time-asymmetric knowledge, for closely related reasons. Stephen Hawking connected the “psychological arrow of time”, based on memory, to the “entropic arrow of time”, which orients such that lower-entropy times count as past, and higher as future. Mlodinow and Brun argue that if a memory system is capable of remembering more than one thing, and exists in an environment where entropy increases in one time-direction, then the recording of a memory happens at a lower-entropy time than its recall. Our knowledge of the past is better than our knowledge of the future because we have memories of the past, which are records, and the creation of records requires increasing entropy.
Consider an example adapted from David Albert. Suppose we now, at t1, observe the aftermath of an avalanche and want to know the position of a particular rock (call it r) an hour ago, at t0, the start of the avalanche. We can attempt to retrodict it, using the present positions and shapes of r and all other nearby rocks, the shape of the remnant of the slope they fell down, the force of gravity, our best estimates of recent wind speeds, etc. In this practically impossible endeavor, we would be trying to reconstruct the complete history of r between t0 and t1. Or we might be lucky enough to have a photograph of r from t0, which has been kept safe and separate from the avalanche. In that case our knowledge about r at t0 is independent of what happened to r after t0, although it does depend on some knowledge of the fate of the photograph. As Albert writes [p. 57], “the fact that our experience of the world offers us such vivid and plentiful examples of this epistemic independence [of earlier events from later ones] very naturally brings with it the feeling of a causal and counterfactual independence as well.”
Contrast our knowledge of the future
position of r an hour from now. Here
there are no records to consult, and prediction is our only option. Almost any feature of r’s environment could
be relevant to its future position, from further avalanches to freak weather
events to meddling human beings. The
plenitude of causal handles on future events is what makes them so manipulable.
Note that it is not that our knowledge of the macroscopic past puts it beyond our control: we cannot keep past eggs from breaking even if we did not know about them. Nor is it our ignorance of the future that gives us control over future macroscopic states (nor the illusion of control). Rather, it is the increase of entropy over time, and the related fact that macroscopic changes typically leave macroscopic records at entropically-future times but not past times, that explains both the time-asymmetry of control and of memory. A memory is a record of the past. And a future macroscopic event (for example, a footprint) that we influence by a present act (walking in the mud) is a record of that act. If we could refer to a set of microphysical past events that did not pose insurmountable information deficits preventing us from seeing their relation to present events, might they become up to us?
…But not the whole of the past is fixed
Yes, some microphysical arrangements, under a peculiar description, are up to us. We’ve been here before, in Betting on The Past, in the previous post in this series. There, you could guarantee that the past state of the world was such as to correspond, according to laws of nature, to your action to take Bet 2. You could do so just by taking Bet 2. Or you could guarantee that the microphysical states in question were those corresponding to your later action to take Bet 1. When you’re drawing a self-referential pie chart, you can fill it in however you like. Dealing with events specified in terms of their relation to you now is dealing in self-reference, regardless of whether those events are past, present, or future. Of course, you have no idea which microscopic events, described in microscopic terms, will have been different depending on your choice. But who cares? You have no need to know that in order to get what you want.
We’re used to the idea of asymmetric dependence relations between events, such as one causing another. And we’re used to the idea of independent events that have no link whatsoever. We’re not used to the idea of events and processes that are bidirectionally linked, with neither being master and neither being slave. But these bidirectional links are ubiquitous at the microscopic level. It is only by using our macroscopic concepts, and lumping together event-classes of various probabilities (various counts of microscopic ways to constitute the macroscopic properties), that we can find a unidirectional order in history.
There’s nothing wrong with attributing asymmetric causality to macroscopic processes – entropy and causality are reasonably well-defined there. But if we overgeneralize and attribute the asymmetry to all processes extending through time, we make a mistake. Indeed, following Hawking and Carroll  and others, we can define “the arrow of time” as the direction in which entropy increases.
This gets really interesting when we consider cosmological theories which allow for times further from our time than the Big Bang, but at which entropy is higher than at the Big Bang. Don Page has a model like this for our universe. Sean Carroll and Jennifer Chen  have a multiverse model with a similar feature, pictured below:
The figure shows a parent universe spawning various baby universes. One of the ((great-(etc))grand)babies is ours. The parent universe has a timeline infinite in both directions, with a lowest (but not necessarily low!) entropy state in the middle. Observers in baby universes at the top of the diagram will think of the bottom of the diagram, including any baby universes and their occupants, as being in their past. And any observers in the babies at the bottom will return the favor. Each set of observers is equally entitled to their view. At the central time-slice, where entropy is approximately steady, there is no arrow of time. As one traverses the diagram from top to bottom, the arrow of time falters, then flips. Where the arrow of time points depends on where you sit. The direction of time and the flow of cause and effect are very different in modern physics than they are in our intuitions.
Another route to the same conclusion
So far we’ve effectively equated causation to entropy-increasing processes, where the cause is the lower-entropy state and the effect is the corresponding higher-entropy state. But there’s another way to approach causality, one which finds its roots in the way science and engineering investigations actually proceed. On Judea Pearl’s approach in his book Causality, an investigation starts with the delineation of system being investigated. Then we construct directed acyclic graphs to try to model the system. For example, a slippery sidewalk may be thought to be the result of the weather and/or people watering their grass, as shown in the tentative causal model below, side (a):
Certain events and properties are considered endogenous, i.e. parts of the system (season, rain…), and other variables are considered exogenous (civil engineers investigating pedestrian safety …). To test the model, and determine causal relations within the system, we Do(X=x) where X is some system variable and x one of its particular states. This Do(X=x), called an “intervention”, need not involve human action, despite the name. But it does need to involve an exogenous variable setting the value of X in a way that breaks any tendencies of other endogenous variables to raise or lower the probabilities of values of X. In side (b) of the diagram this shows as the disappearance of the arrow from X1, season, to X3, sprinkler use. The usual affect of season causing dry (wet) lawns and thus inspiring sprinkler use (disuse) has been preempted by the engineer turning on a sprinkler to investigate pedestrian safety.
As Pearl writes,
If you wish to include the entire universe in the model, causality disappears because interventions disappear—the manipulator and the manipulated [lose] their distinction. … The scientist carves a piece from the universe and proclaims that piece in – namely, the focus of the investigation. The rest of the universe is then considered out. …This choice of ins and outs creates asymmetry in the way we look at things and it is this asymmetry that permits us to talk about ‘outside intervention’ and hence about causality and cause-effect directionality.
Judea Pearl, Causality (2nd ed.): 419-420
It’s only by turning variables on and off from outside the system that we can put arrow-heads on the lines connecting one variable to another. In the universe as a whole, there is no “outside the system”, and we are left with undirected links.
In Judea Pearl’s exposition of the scientific investigation of causality, causality disappears at the whole-universe level. In the entropy-based definition of causality, causality doesn’t apply between fully (microscopically) specified descriptions of different times because irreversibility only applies where the number of ways of making up the “effect” state is far greater than the number of ways of making up the “cause” state – but the number of ways to make a fully-specified state is 1.
The bottom line
Laws of nature / Causality / Determinism can be:
(A) Universal, applying to everything
(B) Unidirectional, making for controllers and the controlled
Choose not more than two.
Albert, David Z. After Physics. Cambridge: Harvard College, 2015.
Carroll, Sean M. From Eternity to Here: the Quest for the Ultimate Theory of Time. New York: Penguin, 2010.
The law of causality, I believe, like much that passes muster among philosophers, is a relic of a bygone age, surviving, like the monarchy, only because it is erroneously supposed to do no harm.
Bertrand Russell, Selected Papers
Scientific determinism isn’t sufficient for causality, as we pointed out last time. That’s because the laws of nature we actually have allow us to derive the past states from a complete description of the present, every bit as much as they allow us to derive the future from the present. Consider some very simple possible universes called checkerboard worlds (modeled after Carroll [2010: 127]), shown in the following figures. They have one dimension of time, which will be displayed along the vertical, and one of space, along the horizontal. To establish conventions, say that time t increases from t=1 at the bottom to t=10 at the top row, and position increases from x=1 at left to x=10 at right. Discrete spacetime regions can have either of two states, portrayed as white or gray. Our job as scientists is to come up with a most elegant statement of the rules, or patterns, embodied in the universe. We can further imagine that after hazarding a hypothesis, more of the universe (more time and/or space) will be revealed to test it. Our first checkerboard universe is C, below.
The law of nature of C is simple, and shown in the caption. Note that it can be stated as a rule for deriving later-time descriptions from earlier ones, or as a rule for deriving earlier descriptions from later ones. Let’s call that kind of law of nature bidirectional in time. That doesn’t mean that the direction of time make no difference. If we flip universe C in time, around the middle of the diagram, we get C-prime:
Note that the law is different, in that the state at position x matches the previous state at position x+1 in C’, not the position at x-1. In three spatial dimensions, if we flip all spatial directions at once, physicists call that parity reversal. Universe C has Parity-and-Time (PT) reversible laws. The best accounts of the laws of physics of our actual universe, general relativity and the Schrödinger equation of quantum mechanics, are Charge-Parity-and-Time (CPT)-reversible.
It’s worth staring at picture C’ and asking: does row 8 make row 9 have gray cells at positions 4 and 8? Or does row 9 make row 8 have gray cells at 5 and 9? Or does the whole metaphor of physical states bossing each other around lose its grip here?
Let’s look at a checkerboard universe that doesn’t have bidirectional laws. This one has four possible states for any spacetime location, which will be represented as white, light gray, dark gray, or black.
A black pattern moves to the left (lower x) with time, but ends if it collides with a dark gray column. Similarly, a light gray pattern ends if it collides with a dark gray column. And a dark gray square can appear “out of nowhere” (that is, when no other dark gray square is within +/- 1 spatial location) – at least when the local neighborhood contains only white squares. It looks like universe M might contain at least one probabilistic law: something like “if x-1 through x+1 are white squares at t-1, then the probability of dark gray at t,x is 0.01”. If not for this last feature, universe M would have been unidirectionally deterministic. Information about the past would be lost, but the future could still be derived from the present. But with the addition of the probabilistic law, universe M loses information in both temporal directions.
M is for macroscopic. The world we can observe with our unaided senses, and which we are accustomed to acting on and caring about, is like M. In the human-scaled world the same effect can come about from multiple causes, and different results can issue from the same situation. On the latter point, to vary our earlier example, a cup of cool water could be caused by leaving a cup of cool water in place, and no heat exchange taking place. Or it could be caused by leaving a cup of hot water with some ice in it for a long time, instead. So, tracing from the same state (same in macroscopic terms) and going backward in time, different possibilities appear, which all converge on the same present state. And likewise forward in time: the weather, and human decisions, are notoriously unpredictable. We can offer Alice the choice of lunch destinations, and sometimes she picks Mexican and other times Korean, without any observable difference (such as how long it’s been since her last visit to these places) to explain it. Her futures diverge from the same macroscopic present state.
It’s the convergence of macroscopic causality – the fact that the cause (ice water left in the room) guarantees the effect (cool water) but not vice versa – that leads to the idea that the cause is master, and the effect its slave. From our everyday experience, we infer that there is a power differential which is explained precisely by time-order: the past has power over the present, which has power over the future, in a one-way chain of relationships. And that’s a reasonable inference to a simple and elegant theory which neatly fits the macroscopic data – but it’s wrong, as our best theories of microphysical processes reveal. It’s lower entropy, not being in the past as such, which explains why different past states converge on the same macroscopic present state. (More on that next time.)
When someone tells us that the divergence from the present state into multiple future states is an illusion, but neglects to tell us (or notice) that the convergence from past to present states is also an illusion, they’re telling half truths. Half truths can be misleading. This one is.
The Future-Rewound Argument
“I can prove you don’t have free will,” says your strangest friend. “If you had free will, that would mean you’d be able to do something different, even keeping all facts about the future beyond that act fixed. So for example, you think it was up to you where you took your last winter vacation. But if we hold fixed the fact that you were in New York on December 31, and rewind the movie of the universe from there, we find that necessarily, you arranged to travel to New York earlier. So in fact, you had to arrange to travel to New York.”
That’s a crazy argument, which no one would make. The crazy is easy to spot, it’s the idea of keeping all facts about the future beyond that act fixed. You shouldn’t keep those facts fixed, because they are not independent of your decision. But in a universe of bidirectional-in-time fundamental laws, the complete (microscopically detailed) past state of the universe is also not independent of your decision.
But many future facts, like being in New York, are not only not independent of your decision, they are caused by your decision. Causation involves an additional condition: a one-way relationship from cause to effect. Maybe it’s only this one-way causation from your decision to the future that frees you from the need to “keep fixed” those future facts? No: a symmetric relationship will suffice. We can see this in the next two thought experiments.
Self-Referential Pie Chart
The pie chart makes two statements, both of which are true, and it has two pie slices of different size. The size of the reddish slice doesn’t cause the corresponding statement to be true in an asymmetric way: the reddish slice being the size it is, is identical with the truth of the corresponding statement. Once we have a convention that the color of a slice stands for the portion of the chart which is that color, we don’t even have to leave room for a statement written in the same color-range.
Readers are invited to make their own self-referential charts. Be careful in sizing portions and choosing colors: you wouldn’t want to get it wrong! (In the original XKCD comic, Randall Munroe makes his pie chart only partially and indirectly self-referential. So he actually did need to be careful. I call self-nerdsniping.)
The same logic of self-reference that frees us, in this chart-making, from the need to match an independent reality, also applies to our relation to the past under time-symmetric determinism.
Betting on the Past
In my pocket (says Bob) I have a slip of paper on which is written a proposition P. You must choose between two bets. Bet 1 is a bet on P at 10:1 for a stake of one dollar. Bet 2 is a bet on P at 1:10 for a stake of ten dollars. […] Before you choose whether to take Bet 1 or Bet 2 I should tell you what P is. It is the proposition that the past state of the world was such as [to correspond, according to laws of nature, to your action to] take Bet 2.
Ahmed 2014, p. 120
If we take Bet 2, we pocket a dollar. Our usual ignorance about which present states relate to microscopic past details has been removed, thanks to the logic of self-reference. Instead of trying to control a specific macroscopic past event – which is how we usually think about “affecting the past” – here we refer to a present macroscopic event, our taking Bet 2, and work backwards to refer to a widely scattered set of past events, down to the microscopic details.
It’s vital that proposition P is about you. If Bob’s proposition is about what Alice will take when offered this bet, it no longer makes sense to take Bet 2 unless you are Alice. What is up to you depends on who/what you are, including where you stand in the universe. This shouldn’t be surprising.
You might wonder how Bob is supposed to know that the past state of the world was such as to lawfully correspond to your taking Bet 2. But that is easy, if we suppose that Bob is a scientific determinist. He will take our choice as sufficient evidence. Does this mean that we only care about the future, i.e. Bob’s reaction? No: we are honest bettors, who want to take Bob’s money, but only by genuinely satisfying the winning conditions of the bet.
Let’s go back to those counterfactuals. What would happen if we had taken Bet 1? We would have lost a dollar, that’s what. The experiment can be repeated as many times as you like: it would support the hypotheses that “if you had taken Bet 1, you’d lose money” and “if you had taken Bet 2, you’d win money”. Normally, experiments don’t have logically foreseeable results like this; we normally need to know what the specific laws of nature are, not just that they are deterministic. But apart from that, these experiments support “would” statements just as other experiments support more ordinary statements such as “if I dropped this cup, it would fall.” (Remember, even well grounded scientific laws and meta-statements (like determinism) about laws can be supported or undermined by experiments.)
If we can show in more detail that there’s no need to posit an objective Power Hierarchy of Time in which earlier times rule over later ones, then counterfactuals can reach into the past just as easily as into the future. This doesn’t mean that we can change the past, as if some particular past time could be one way – Kennedy was assassinated on Nov 22, 1963 – and then be another way – Kennedy retired after two full terms. Nor does it mean that we can affect the past, if “affect” is a causal verb. It just means that if we had taken Bet 1, we would have lost a dollar. The fact that the consequent follows from the antecedent plus the natural laws, seems like a sufficient reason to accept that counterfactual.
It’s worth noting that even under time-symmetric determinism, the proponent of the Consequence Argument has one last-ditch option to preserve premise
(2) The distant past state of the universe is such that, for every action A you could take, if you did A, that past state would still obtain.
They can assert as an additional premise that there is only one action you could take: the one you did take. So in other words, they simply assume you have no options – they don’t need no stinking reason! This eliminates the Consequence Argument in favor of a Consequence Assertion. There is nothing to recommend such an assertion.
Next up: we show in more detail that there’s no need to posit an objective Power Hierarchy of Time in which earlier times rule over later ones. Hint: entropy explains the irreversible behavior of macroscopic processes. Second hint: the scientific and engineering approach to understanding systems explains how we understand causality.
As we said last time “alpha is unavoidable for you” means “For every action A you could take, if you did A, alpha would (still) happen / be true”. A key concept here is a would statement, which logicians call a “counterfactual conditional”. For example, if I had written that logicians call a would statement “the cat’s meow”, you would think I was joking. The term “counterfactual” is a bit misleading because there can be would-counterfactuals with factual antecedents. For example if I had written that the Consequence Argument was formulated by Peter van Inwagen, you would have read the name Peter van Inwagen. And I did; and you did. What the would statement adds, beyond the simple statement that I did so write and you did so read, is the idea that there’s a robust connection between those things. A counterfactual is a bigger claim than the “if” from propositional logic (which logicians often symbolize with “⊃” — so A ⊃ B simply means that it’s not the case both that A is true and B is false.) Note that counterfactual antecedents and consequents (the “if…” and “would…” parts, respectively) range over processes, events (including boring events like a particular state obtaining at a particular time), and actions.
The premises of the Consequence Argument that we’ll question are (and here let’s spell out the counterfactuals contained in the shorter versions):
(2) The distant past state of the universe is such that, for every action A you could take, if you did A, that past state would still obtain.
(3) The laws of nature are such that, for every action A you could take, if you did A, those laws would still obtain.
And we won’t question premise (1) from the last post, nor the formulation of scientific determinism from which it follows, but we will take a good hard look at that formulation. It turns out not to say some of the things that we might on first glance think it says.
The Best Systems Analysis has a model in Algorithmic Information Theory, for which a very crude model is a .zip file, such as you might create from a .txt document on a computer. The .zip file contains compression rules plus compressed data (and the program that reads and writes zip files, say 7zip, contains additional compression rules). The compression rules (including those in the zip-making program) are like the laws of nature, such as the mass and charge of an electron; the remaining data is like the remaining facts, such as the locations of electrons at particular times. Different programs, say 7zip vs the Windows file compressor, might make somewhat different decisions about how to divide up the totality of information in a text file into “compression rules” vs “raw data”. And of course, if you put a different text file into the zip program, you typically get output containing both different “rules” and different “raw data”. For example, if I have a text file where most lines consist of a lot of spaces, the compressor program might make a rule where one special character represents 9 consecutive spaces and another represents 3 consecutive spaces. Then a line consisting of 13 spaces can be abbreviated with 3 characters. But if the text file instead contains a lot of consecutive z’s and no consecutive spaces, the rules part of the compressed file will contain rules representing z’s instead.
It’s this last point that casts doubt on the immunity of laws of nature to human action. If human actions were distributed differently, the totality of physical facts of the universe would be different, so different “compression rules” might most-efficiently summarize the total physical information. If all that laws of nature are, are just efficient summary rules for physical information, then they depend on all that information: the human related bits included every bit as much as the rest. The individual ground-level facts, including what people are doing, are fundamental, on the Best Systems Analysis. The laws are consequences of those facts, not governors of them.
Now, it would be nice if I could say whether the Best Systems Analysis is correct. But all I can do is register my hazy suspicion that it’s not. (My thoughts on that aren’t even worth setting down.) So it seems we are stuck on this part. But wait! What’s that smell? Yes, it’s the sweet smell of unnecessary work! (Hat tip: Dilbert comic.) There’s a chance we don’t have to decide about Premise 3 of the Consequence Argument, and thus we don’t have to decide about the Best Systems Analysis of laws. We don’t need to evaluate Premise 3 if we can undermine Premise 2 of the Consequence Argument. And we can.
Let’s look again at Premise 1 of the Consequence Argument, or better yet, at our definition of scientific determinism (abbreviated SD), from which Premise 1 followed:
(SD) Determinism requires a world that (a) has a well-defined state or description, at any given time, and (b) laws of nature that are true at all places and times. If we have all these, then if (a) and (b) together logically entail the state of the world at all other times (or, at least, all times later than that given in (a)), the world is deterministic.
Stanford Encyclopedia of Philosophy entry on “causal determinism”
SD says that the laws plus a complete description can logically entail the state of the world, either symmetrically both into the past and future, or asymmetrically just into the future. But the actual laws of physics that science has given us to this point are time-symmetric in exactly this sense, at least when they are deterministic. Conservation of information in quantum mechanics is a case in point. (There are deterministic interpretations of quantum mechanics, such as the Everett Interpretation, which interpret quantum probabilities as statements of rational expectation in the face of partial ignorance.) Because of conservation of information, the final state of a quantum system plus the environment, after an interaction, must contain the information that the system had beforehand. In other words, from the later state plus the laws of quantum mechanics, the earlier state is logically implied. Scientific determinism is a two-way street.
But now notice: “causality” is supposed to be a one-way street. A cause is not supposed to be itself caused by the very thing it supposedly caused. Let’s make this part of the definition of “cause”: causation is asymmetric, so that “A causes B” and “B causes A” are contraries. It immediately follows that
(Determinism ≠ Causality) The existence of laws of nature that logically entail state B at one time given state A at another, does not suffice to show that A causes B.
Causation is not interdependence, but one-way dependence. For example, a room-temperature cup of water could be caused by leaving a cup of steaming hot water in the room until the temperature equilibrated with the room. Or it could be caused by leaving a cup of ice water in the room for a long time, instead. The effect is guaranteed by the cause, but no particular cause is guaranteed by the later state. Without this kind of asymmetry in the relationship, causality is lacking, as physicist Sean Carroll explains in this 3-minute video. “There’s just a pattern that particles follow,” he says. “Kind of like how the integer after 42 is 43, and the integer before it is 41, but 42 doesn’t cause 41 or 43, there’s just a pattern traced out by those numbers.”
So where does causality come from? I’ll give two answers reflecting different interpretations of “causality” – both of them useful in different ways. On one reasonable interpretation (used by Sean Carroll), causality comes from entropy. On another reasonable interpretation, given by Judea Pearl in his book Causality, causality comes from our division of the world into a system of interest vs exogenous variables.
Now let’s look again at the Consequence Argument’s premise
(2) The distant past state of the universe is such that, for every action A you could take, if you did A, that past state would still obtain.
Is it true? If the “distant past state” is given macroscopically, describing such things as glasses of water and their temperature, then (2) is true, but not adequate for the argument, because (as we’ll see later) the present state of the universe doesn’t follow from the past macroscopic state. But if the “distant past state” is given in microscopic detail, then it is not independent of the present state including what we are doing now.
There is no reason to believe (2), where the states in question are described in microscopic detail. Or rather, there is a reason, but it evaporates once you realize that there’s another explanation for why we never observe the past depending on the present or future. We don’t need to posit a magical “flow of time”, or a universal master/slave relationship between past and future. The idea that the past has power over the future but not vice versa is an overgeneralization from our experience of the macroscopic world: our experience of states and processes large and complex enough for entropy to be well-defined and increasing in only one temporal direction.
All this has gone by way too fast, and there are many points that need further justification and explanation. Along the way, we’ll use modern science to deeply challenge our intuitive conceptions of time and causality, then show how those wrong intuitions about how our universe works have affected our views of the free will “problem”. Scientific determinism isn’t the problem – our misconceptions of it are. The traditional free will problem doesn’t hinge on the definition of “free will”, but of “determinism” and “causality”.
Let’s start with some popular versions of what I call “the main type of argument” against free will. Here’s Jerry Coyne, from the conference called Moving Naturalism Forward:
(stolen from Anthony Cashmore) Free will is defined as the belief that there is a component to biological behavior that is something more than the unavoidable consequences of the genetic and environmental history of the individual and the possible stochastic laws of nature.
Jerry Coyne, Free Will and Incompatibilism: Jerry Coyne et al – YouTube, at 2:00
There are two words there that are doing a lot of work: “unavoidable” and “consequences”. The “unavoidable” becomes both more and less clear, in different ways, when Jerry comments on the “stochastic laws of nature” part of the definition.
My definition used to be: If you put yourself in the same situation in the same universe with every molecule in the same place, free will would mean that if you come to a decision point you could make more than one decision. But then I realized that quantum indeterminacy if it acts on the neuronal level could make you make a [conscious and] different decision.
ibid., at 2:22
What gets less clear after this explanation is why the word “unavoidable” is appropriate. when it is hypothesized that human behavior might be different even putting yourself in these highly restricted conditions. And worse, the “same universe with every molecule in place” includes all of you. If something flows from you, that seems an especially poor reason to call it unavoidable. But what gets more clear, I think, is why a non-stochastic (deterministic) view is thought to make behavior “unavoidable”. Genetic and environmental history, after all, can be traced back before you were born. And the universe before your birth doesn’t include you. So let’s forget about stochastic laws of nature at least temporarily, and just get clear on the basic argument, assuming that the laws of nature are deterministic. We will use the scientific meaning (not, say, a theological meaning) of determinism:
Determinism requires a world that (a) has a well-defined state or description, at any given time, and (b) laws of nature that are true at all places and times. If we have all these, then if (a) and (b) together logically entail the state of the world at all other times (or, at least, all times later than that given in (a)), the world is deterministic.
So we’ll assume now that our universe is deterministic in this sense, and formalize the argument against free will. If we need to see if it generalizes to the case of stochastic laws (teaser: we won’t need to), we can check that later. We can interpret the phrase “consequence of genetic and environmental history” (from Cashmore and Coyne) as the logical entailment mentioned in the definition of determinism. And we can add two plausible premises: the state of the past before your birth is for you unavoidable, and the laws of nature are unavoidable. (To save words later, “the past before your birth” is abbreviated “the distant past”.)
Here’s how we’ll understand “unavoidable”: “Alpha is unavoidable for you” means “For every action A you could take, if you did A, alpha would (still) be true”.
The argument we get is the Consequence Argument, a famous (infamous?) argument in modern philosophy. The original formulation was by Peter van Inwagen, but that relied on an inference rule which was invalid. A better version was later constructed by van Inwagen, David Widerker and Alexander Pruss. It goes like this:
(1) The distant past state of the universe, together with the laws of nature, together logically entail your action now.
(2) The distant past state of the universe is unavoidable (for you).
(3) The laws of nature are unavoidable.
(4) If a proposition X expresses a fact unavoidable for you, and X logically entails Y, then Y is also unavoidable for you.
(5) Therefore, your action now is unavoidable for you.
The argument so formulated actually makes premise (4) a tautology, and I want to continue assuming for the sake of argument that (1) is true. But premise (3) is controversial and (2) even more so. We’ll take them up in the next part.
Pruss, Alexander 2013. Incompatibilism Proved, Canadian Journal of Philosophy, 43/4: 430–437
Van Inwagen, Peter 1983. An Essay on Free Will. Oxford: Clarendon Press.
Widerker, David 1987. On an Argument for Incompatibilism. Analysis, 47/1: 37–41.