Varieties of Time Travel

My kids have been reading lots of books over the break, including an adventure series that involves time travel. Knowing vaguely that dad is a theoretical physicist, they asked me how time travel works.

1. Can one change history by influencing past events?      

OR

2. Is there only one timeline that cannot be altered, even by time travel?

I told them that no one really knows the answer, or the true nature of time.

I gave them an example of 1 and of 2 from classic science fiction :-)

1. Ray Bradbury's short story A Sound of Thunder:

... Looking at the mud on his boots, Eckels finds a crushed butterfly, whose death has apparently set in motion a series of subtle changes that have affected the nature of the alternative present to which the safari has returned. ...

(Note this version implies the existence of alternative or parallel universes.)

2. Ted Chiang's one pager What's expected of us, which also notices that a single time line seems deterministic, and threatens Free Will. (More ;-)

... it's a small device, like a remote for opening your car door. Its only features are a button and a big green LED. The light flashes if you press the button. Specifically, the light flashes one second before you press the button.

Most people say that when they first try it, it feels like they're playing a strange game, one where the goal is to press the button after seeing the flash, and it's easy to play. But when you try to break the rules, you find that you can't. If you try to press the button without having seen a flash, the flash immediately appears, and no matter how fast you move, you never push the button until a second has elapsed. If you wait for the flash, intending to keep from pressing the button afterwards, the flash never appears. No matter what you do, the light always precedes the button press. There's no way to fool a Predictor.

The heart of each Predictor is a circuit with a negative time delay — it sends a signal back in time. The full implications of the technology will become apparent later, when negative delays of greater than a second are achieved, but that's not what this warning is about. The immediate problem is that Predictors demonstrate that there's no such thing as free will.

There have always been arguments showing that free will is an illusion, some based on hard physics, others based on pure logic. Most people agree these arguments are irrefutable, but no one ever really accepts the conclusion. The experience of having free will is too powerful for an argument to overrule. What it takes is a demonstration, and that's what a Predictor provides. ...

I attended a Methodist Sunday school as a kid. I asked my teacher: If God knows everything, does he know the outcomes of all the decisions I will ever make? Then will I ever make a free choice?

I also asked whether there are Neanderthals in heaven, but that's another story...

EPR and Bell for pedestrians

My old friend Mark Alford (WUSTL) was on campus last week for the inaugural meeting of the FRIB-TA (Facility for Rare Ion Beams Theory Alliance). Over beers he told me he had come up with a pedagogical way to explain Bell's inequality in a single picture. Here it is.

Ghostly action at a distance: a non-technical explanation of the Bell inequality

Mark G. Alford

We give a simple non-mathematical explanation of Bell's inequality. Using the inequality, we show how the results of Einstein-Podolsky-Rosen (EPR) experiments violate the principle of strong locality, also known as local causality. This indicates, given some reasonable-sounding assumptions, that some sort of faster-than-light influence is present in nature. We discuss the implications, emphasizing the relationship between EPR and the Principle of Relativity, the distinction between causal influences and signals, and the tension between EPR and determinism.

FIG. 4: One trial in the EPRB measurement of polarization for two photons. The final result in this trial is that photon 1 encountered a filter of type B and reflected off it, while photon 2 encountered a filter of type C and passed through it. According to the Bell inequality (Eq. (3)) this sort of result, where the two photons do different things when encountering different filters, should happen no more than 2/3 of the time.

... When polarizations of pairs of spin-singlet photons are measured in real-world experiments, it is found that they do show agreement in same-axis measurements, but when we perform different-axis measurements the two photons only show the same behavior 1/4 of the time; 3/4 of the time they show different behavior: one bounces off its filter and the other passes through. This violates the Bell inequality. Such violation has now been seen in many experiments ...

Strategic War (with cards)

War is a simple card game played by children. The most common version does not require decisions, so it's totally deterministic (outcome is determined) once the card order in each deck is fixed. Nevertheless it can be entertaining to watch/play: there are enough fluctuations to engage observers, mainly due to the treatment of ties. The question of how to determine the winner from the two deck orderings (without actually playing the entire game, which can take a long time) was one of the first aspects of computability / predictive modeling / chaotic behavior I thought about as a kid. This direction leads to things like classification of cellular automata and the halting problem.

My children came home with a version designed to teach multiplication -- each "hand" is two cards, rather than the usual single card, and the winner of the "battle" is the one with the higher product value of the two cards (face cards are removed). I thought this was still too boring: no strategy (my kids understood this right away, along with the meaning of deterministic; this puts them ahead of some philosophers), so I came up with a variant that has been quite fun to play.

Split the deck into red and black halves, removing face cards. Each hand (battle) is played with two cards, but they are chosen by each player. One card is placed face down simultaneously by each player, and the second cards played are chosen after the first cards have been revealed (flipped over). Winner of most hands is the victor.

This game ("strategic war") is simple to learn, but complex enough that it involves bluffing, calculation, and card counting (keeping track of which cards have been played). A speed version, with, say, 10 seconds allowed per card choice, goes very fast.

Has anyone seen heard of this game before? It's a bit like repeated two card poker (heads up), drawing from a fixed deck. Note the overall strength of hands for each player (combined multiplicative value of all cards) is fixed and equal. Playing strong hands early means weaker hands later in the game. The goal is to win each hand by as small a margin as possible.

Are there strategies which dominate random play (= select first card at random, second card from range not exceeding highest card required to guarantee a win)?


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Dennett and Intuition Pumps

At the bookstore today I spent some time looking at Intuition Pumps And Other Tools for Thinking, Daniel Dennett's new book. I highly recommend his Darwin's Dangerous Idea, discussed earlier here. I'm not a big fan of Dennett's work on free will and determinism (for my views, see this old post and also here), but we seem to share the same opinion of John Searle's Chinese Room.

For more Dennett, see this Stanford Humanities Center lecture (iTunes video).

NYTimes: ... The new book, largely adapted from previous writings, is also a lively primer on the radical answers Mr. Dennett has elaborated to the big questions in his nearly five decades in philosophy, delivered to a popular audience in books like “Consciousness Explained” (1991), “Darwin’s Dangerous Idea” (1995) and “Freedom Evolves.”

The mind? A collection of computerlike information processes, which happen to take place in carbon-based rather than silicon-based hardware.

The self? Simply a “center of narrative gravity,” a convenient fiction that allows us to integrate various neuronal data streams.

The elusive subjective conscious experience — the redness of red, the painfulness of pain — that philosophers call qualia? Sheer illusion.

Human beings, Mr. Dennett said, quoting a favorite pop philosopher, Dilbert, are “moist robots.”

“I’m a robot, and you’re a robot, but that doesn’t make us any less dignified or wonderful or lovable or responsible for our actions,” he said. “Why does our dignity depend on our being scientifically inexplicable?”

If he hadn’t grown up in an academic family, Mr. Dennett likes to say, he probably would’ve been an engineer. From his beginnings in the philosophical hothouses of early 1960s Harvard and Oxford, he had a feeling of being out of step joined by a precocious self-confidence.

As an undergraduate, he transferred from Wesleyan University to Harvard so he could study with the great logician W. V. O. Quine and explain to him why he was wrong. “Sheer sophomoric overconfidence,” Mr. Dennett recalled.

As a doctoral student at Oxford, then the center of the philosophical universe, he studied with the eminent natural-language philosopher Gilbert Ryle but increasingly found himself drawn to a more scientific view of the mind.

“I vividly recall sitting with my landlord’s son, a medical student, and asking him, ‘What is the brain made of?’ ” Mr. Dennett said. “He drew me a simple picture of a neuron, and pretty soon I was off to the races.”

In 1969, Mr. Dennett began keeping his “Philosophical Lexicon,” a dictionary of cheeky pseudo-terms playing on the names of mostly 20th-century philosophers, including himself. (“dennett: an artificial enzyme used to curdle the milk of human intentionality.”) Today, his impatience with the imaginary games philosophers play — “chmess” instead of chess, he calls it — and his preference for the company of scientists lead some to question if he’s still a philosopher at all.

“I’m still proud to call myself a philosopher, but I’m not their kind of philosopher, that’s for sure,” he said. The new book reflects Mr. Dennett’s unflagging love of the fight, including some harsh whacks at longtime nemeses like the paleontologist Stephen Jay Gould — accused of practicing a genus of dirty intellectual tricks Mr. Dennett calls “goulding” — that some early reviewers have already called out as unsporting. (Mr. Gould died in 2002.)

Mr. Dennett also devotes a long section to a rebuttal of the famous Chinese Room thought experiment, developed by 30 years ago by the philosopher John Searle, another old antagonist, as a riposte to Mr. Dennett’s claim that computers could fully mimic consciousness.

Clinging to the idea that the mind is more than just the brain, Mr. Dennett said, is “profoundly naïve and anti-scientific.”

Free Will in Waking Life

I discovered this video while looking for some course material on determinism and free will. I haven't seen Waking Life, but it looks interesting.

Economics, ant farmers and free will theorems

Wow, it's been almost a week since my last post. I was pretty busy at the Perimeter Institute -- my brain is occupied trying to digest all the new things I've learned :-)

The conference had its origins in an essay Can science help solve the economic crisis? written by several of the organizers. The essay received responses from several prominent thinkers, and led to an exchange between Stanford economist Paul Romer and mathematician turned quant Eric Weinstein (see further down the page at the link above). Romer agreed to debate Weinstein, but then failed to show up! [Note added: in a private communication to me, Paul Romer writes that there was a misunderstanding and he never agreed to participate in a debate.]

The meeting went full speed from 9 AM until late at night for four days. The attendees were a mix of theoretical physicists (with particle physics and complexity theory, especially the Santa Fe Institute, well represented), practitioners from Wall St. (often from a math or physics background), academic economists (Barkley Rosser, Richard Freeman, etc.) and evolutionary biologists. See here for video recordings of talks. There were many good talks but I especially recommend Doyne Farmer's for the physicist's complex systems view of economics.

Too much ground was covered for a short summary, but one area of interest for almost all attendees was the possibility of going beyond the neoclassical paradigm via simulations of interacting agents. Examples of such simulations were discussed in several of the talks, including by Santa Fe "ant farmers" Bruce Sawhill and Jim Herriot, who used agents to model air traffic for the ambitious DayJet startup (see here and here).

The technology is certainly there to do some massive, quasi-realistic simulations of an actual economy (as opposed to an isolated financial market or sub-economy). The main problem, which wasn't given as much attention as I might have liked, is that the results are limited by the quality of the individual agents, who must have at least rudimentary learning capabilities to be realistic. Hence one is led full circle back to problems related to AI, machine learning and even psychology or cognitive science.


When I wasn't at the conference I managed to have several interesting physics discussions. Below are links to some recent work by John Conway and Simon Kochen that came up in two separate conversations I had at Perimeter -- one with Rob Spekkens (he and I were discussing related issues, although he didn't mention these papers specifically) and with Nima Arkani-Hamed, who was visiting from IAS.

The Free Will Theorem

http://arxiv.org/abs/quant-ph/060407

On the basis of three physical axioms, we prove that if the choice of a particular type of spin 1 experiment is not a function of the information accessible to the experimenters, then its outcome is equally not a function of the information accessible to the particles. We show that this result is robust, and deduce that neither hidden variable theories nor mechanisms of the GRW type for wave function collapse can be made relativistic. We also establish the consistency of our axioms and discuss the philosophical implications.

See also the Strong Free Will theorem.

I feel the name of the theorem is a bit misleading, but inevitably so as it is quite difficult to define free will. The main feature of the papers is the great clarity of thought and presentation. In content, they are not so different from the older GHZ result which was formulated in terms of what the authors called local realism. To be honest I don't quite agree with Conway and Kochen's interpretation of their own results -- it's obvious that the results are easily consistent with many worlds quantum mechanics, which does not (at least from my spacetime perspective) allow for free will.

Here are 6 lectures on the theorem and related topics, given by Conway recently at Princeton. See also 'tHooft's response to their result.

More than this

I discovered today that one of my colleagues also loves this song. Bryan Ferry of Roxy Music had real artistic insight into chance and determinism. I like the 10,000 Maniacs version better, which is in the lower screen.

More Than This

I could feel at the time
There was no way of knowing
Fallen leaves in the night
Who can say where they're blowing

As free as the wind
And hopefully learning
Why the sea on the tide
Has no way of turning

More than this - there is nothing
More than this - tell me one thing
More than this - there is nothing

It was fun for a while
There was no way of knowing
Like dream in the night
Who can say where we're going

No care in the world
Maybe I'm learning
Why the sea on the tide
Has no way of turning

More than this - there is nothing
More than this - tell me one thing
More than this - there is nothing

Free will and determinism: a physicist's perspective

This is an amusing topic I've discussed with many people over the years. My opinion: if our current understanding of physical laws is correct, humans have only the illusion of free will.

What do I mean by free will? Well, that is hard to define. But the absence of free will or deterministic behavior is not hard to define. In classical physics the future evolution of a system is completely determined by the state of the system (including time derivatives) at any instant. For example, suppose that at some instant t I know all of the positions and momenta of every molecule or atom in the universe. Then, in a classical universe, I could in principle predict with certainty its future evolution. Another universe prepared in the identical state would evolve identically. So, in a classical universe everything that has happened since the big bang could (again, in principle) have been predicted at that moment. Such a universe is deterministic, and no subcomponent of that universe (i.e., a dog, a human, a robot, or a martian) can have free will.

Note that chaos does not help. Suppose the classical evolution is nonlinear, and exhibits chaos. Then initial states which are very similar may, after only a short time, have evolved into radically different configurations. This makes the job of predicting the future behavior of some initial data very hard, but nevertheless possible in principle.

Does quantum mechanics help? Well, a quantum universe is not deterministic. (In the many-worlds description, the evolution of the wavefunction describing all possible universes is deterministic, but only a single branch of the wavefunction is perceived by any macroscopic observer, and the path followed by a particular observer at each branching is not predictable.) However, it seems that the functioning of our brains is almost entirely classical. The number of atoms involved in the firing of a synapse, or other chemical reactions in brain functioning, is quite large, and there is little quantum coherence. As far as we know, our brains are readily simulated by purely classical processes.

Still, the inputs received by our brains may be non-deterministic in a quantum world. For example, the clicks of a geiger counter (which detects the photons from individual radioactive decays) are intrinsically random according to quantum theory. But, it is hard to see how introducing occasional random inputs amounts to granting free will to an otherwise deterministic machine. A classical robot which is fed occasionally random data does not seem to me to have free will. If prepared in an identical state and fed the same inputs, it would behave the same way every time.

If the previous discussion is correct, all we really have left is the illusion of free will. It seems like I chose what to have for lunch today. The conscious part of my brain didn't know what the answer was until going through what seemed to be a decision process. But, given that there are lots of lower-level brain processes that my consciousness has only a vague awareness of, it seems quite plausible to me that the "decision" was made in a deterministic way without my knowledge.