String Theory and the Black Hole War

Leonard Susskind gives a two-hour interview.

He is a smart and distinguished physicist, but he has some silly views. He brags about winning the Black Hole War, but he did not. In a recent survey, only 27% agreed with him that information falling into a black hole is preserved in Hawking radiation. Only 11% agreed with many-worlds theory, which he has favored in the past. Not sure if he still does.

The survey had some other curious opinions, such as whether matter falling into a black hole gets crushed into a singularity (29% say yes) and whether the big bang started time with a singularity (only 11% say yes). While you might have heard that the Copenhagen Interpretation is dead, only a minority subscribed to some non-Copenhagen interpretation of quantum mechanics. The survey was given in Copenhagen, so maybe the home team had an advantage.

Information has no physical definition, and has no good reason to be conserved. Susskind would only say that it is conserved because quantum field theory is unitary. That is the same reason he gives for many-worlds. So wouldn't that mean that information could leak into parallel universes, not to be seen again?

He pushes a lot of other wacky ideas, such as anti-desitter space, black hole event horizon firewalls, string theory landscape, entangled wormholes, etc. It is all nonsense. All of it is theoretically dubious, and impossible to observe. Viewers must get a kooky view of Physics when the leading popularizers say such bizarre and unscientific things.

The world is geometrical

In my anti-positivist counterfactual history, here is the first axiom.

Geometry axiom: The world is geometrical.

The most familiar geometry is Euclidean geometry, where the world is R³ and distance squared is given by dx² + dy² + dz². There are other geometries.

Newtonian mechanics is a geometrical theory. Space is represented by R³, with Euclidean metric. That is a geometrical object because of the linear structure and the metric. Lines can be defined as the short distance between points. Plane, circles, triangles, and other geometric objects can be defined.

It is also a geometrical object because there is a large class of transformations that preserve the metric, and hence also the lines and circles determined by the metric. Those transformations are the rotations, reflections, and translations. For example, the transformation (x,y,z) → (x+5,y,z) preserves distances, and takes lines to lines and circles to circles.

Mathematically, a geometry can be defined in terms of some structure like a metric, or the transformations preserving that structure. This view has been known as the Klein Erlangen program since 1872.

The laws of classical equations can be written in geometrical equations like F=ma, where F is the force vector, a is the acceleration vector, and m is the mass. All are functions on Euclidean space. What makes F=ma geometrical is not just that it is defined on a geometrical space, or that vectors are used. The formula is geometrical because all quantities are covariant under the relevant transformations.

Classical mechanics does not specify where you put your coordinate origin (0,0,0), or how the axes are oriented. You can make any choice, and then apply one of the symmetries of Euclidean space. Formulas like F=ma will look the same, and so will physical computations. You can even do a change of coordinates that does not preserve the Euclidean structure, and covariance will automatically dictate the expression of the formula in those new coordinates.

One can think of Euclidean space and F=ma abstractly, where the space has no preferred coordinates, and F=ma is defined on that abstract space. Saying that F=ma is covariant with respect to a change of coordinates is exactly the same as saying F=ma is well-defined on a coordinate-free Euclidean space.

The strongly geometrical character of classical mechanics was confirmed by a theorem of Neother that symmetries are essentially the same as conservation laws. Momentum is conserved because spacetime has a spatial translational symmetry, energy is conserved because of time translation symmetry, and angular momentum is conserved because of rotational symmetry.

Next, we look at geometries that make physical sense.

Experts dispute meaning of Bell's theorem

I mentioned 'tHooft's new paper on superdeterminism, and now Woit links to an email debate between 'tHooft and philosopher of physics Tim Maudlin over it and Bell's Theorem.

The debate is very strange. First of all, these two guys are extremely smart, and are two of the world's experts on quantum mechanics. And yet they disagree so much on the basics, that Maudlin accuses 'tHooft of not understanding Bell's theorem, and 'tHooft accuses Maudlin of sounding like a crackpot.

Bell's theorem is fairly elementary. I don't know how experts can get it wrong.

Maudlin says Bell proved that the quantum world is nonlocal. 'tHooft says that Bell proved that the world is either indeterministic or superdeterministic. They are both wrong.

I agree with Maudlin that believing in superdeterminism is like believing that we live in a simulation. Yes, it is a logical possibility, but it is very hard to take the idea seriously.

First of all, Bell's theorem is only about local hidden variable theories being incompatible with quantum mechanics. It doesn't say anything about the real world, except to reject local hidden variable theories. It is not even particular important or significant, unless you have some sort of belief or fondness for hidden variable theories. If you don't, then Bell's theorem is just an obscure theorem about a class of theories that do not work. If you only care about what does work, then forget Bell.

I explained here that Bell certainly did not prove nonlocality. He only showed that a hidden variable theory would have to be nonlocal.

Sometimes people claim that Bell should have gotten a Nobel prize when experiments confirmed his work. If Bell were right about nonlocality, and if the experiments confirmed nonlocality, then I would agree. But Bell was wrong about nonlocality, and it is highly likely that the Nobel committee recognized that.

At most, Bell proved that if you want to keep locality, then you have to reject counterfactual definiteness. This should be no problem, as mainstream physicists have rejected it since about 1930.

I am baffled as to how these sharp guys could have such fundamental disagreement on such foundational matters. This is textbook knowledge. If we can't get a consensus on this, then how can we get a consensus on global warming or anything else?

Update: Lubos Motl piles on:

Like the millions of his fellow dimwits, Maudlin is obsessed with Bell and his theorem although they have no implications within quantum mechanics. Indeed, Bell's inequality starts by assuming that the laws of physics are classical and local and derives some inequality for a function of some correlations. But our world is not classical, so the conclusion of Bell's proof is inapplicable to our world, and indeed, unsurprisingly, it's invalid in our world. What a big deal. The people who are obsessed with Bell's theorem haven't made the mental transformation past the year 1925 yet. They haven't even begun to think about actual quantum mechanics. They're still in the stage of denial that a new theory is needed at all.

I agree with this. Bell's theorem says nothing about quantum mechanics, except that it helps explain why QM cannot be replaced with a classical theory.

Free will (e.g. free will of a human brain) has a very clear technical, rational meaning: When it exists, it means that the behavior affected by the human brain cannot be determined even with the perfect or maximum knowledge of everything that exists outside this brain. So the human brain does something that isn't dictated by the external data. For an example of this definition, let me say that if a human brain has been brainwashed or equivalently washed by the external environment, its behavior in a given situation may become completely predictable, and that's the point at which the human loses his free will.

With this definition, free will simply exists, at least at a practical level. According to quantum mechanics, it exists even at the fundamental level, in principle, because the brain's decisions are partly constructed by "random numbers" created as the random numbers in outcomes of quantum mechanical measurements.

I agree with this also. No one can have perfect or maximum knowledge, so free will is not really a scientific concept, but it clearly exists on a practical level, except for brainwashed ppl.

But I don't agree with his conclusion:

Maudlin ends up being more intelligent in these exchanges than the Nobel prize winner. But much of their discussion is a lame pissing contest in the kindergarten, anyway. There are no discussions of the actual quantum mechanics with its complex (unreal) numbers used as probability amplitudes etc.

No, 'tHooft's position is philosophically goofy but technically correct. Maudlin accepts fallacious arguments given by Bell, when he says:

Bell was concerned not with determinism but with locality. He knew, having read Bohm, that it was indeed possible to retain determinism and get all the predictions of standard non-Relativistic quantum theory. But Bohm's theory was manifestly non-local, so what he set about to investigate was whether the non-locality of the theory could be somehow avoided. He does not *presume* determinism in his proof, he rather *derives* determinism from locality and the EPR correlations. Indeed, he thinks that this step is so obvious, and so obviously what EPR did, that he hardly comments on it. Unfortunately his conciseness and reliance on the reader's intelligence have had some bad effects.

So having *assumed* locality and *derived* determinism, he then asks whether any local (and hence deterministic) theory can recover not merely the strict EPR correlations but also the additional correlations mentioned in his theorem. And he finds they cannot. So it is not *determinism* that has to be abandoned, but *locality*. And once you give up on locality, it is perfectly possible to have a completely deterministic theory, as Bohm's theory illustrates.

The only logically possible escape from this conclusion, as Bell recognized, is superdeterminism: the claim that the polarizer settings and the original state of the particles when they were created (which may be millions of years ago) are always correlated so the apparatus setting chosen always corresponds—in some completely inexplicable way—to the state the particles happen to have been created in far away and millions of years ago.

No, Bell and Maudlin are just wrong about this. All of that argument also assumes a hidden variable theory, and therefore has no applicability to quantum mechanics, as QM (and all of physics since 1930) is not a hidden variable theory. If Bell and Maudlin were correct about this, then Bell (along with Clauser and Aspect) would have gotten the Nobel prize for proving nonlocality. 'tHooft is correct in accepting locality, and denying that Bell proved nonlocality.

Philosopher did not invent Trump

Filmmaker, and former Princeton philosophy of science grad student, Errol Morris clarifies:

You’re right, I find Kuhn revolting. But I hope I refrained from making a causal connection between The Structure of Scientific Revolutions and the Trump travel ban or Kellyanne Conway’s alternative facts. ...

Was Kuhn merely an expression of a 60s/70s zeitgeist, one among many? Probably. The line that makes me a little queasy is “But I can’t blame Kuhn for Trump, as Morris does.” You suggest this is going too far, and I agree with you. If Kuhn had never lived, in that possible world where Kuhn was never born, there might still be a President Donald Trump. These are counterfactuals I’m not prepared to deal with. On the other hand, do I feel that Kuhn did the world any good by undermining the concept of truth? No, I don't. I’ll leave it to God to decide on the ultimate disposition of his soul. – Errol

Trump believes in "truthful hyperbole". Other politicians have a more lawyerly attitude towards truth.

Thomas Kuhn, aka Professor Paradigm Shift, was in an entirely different category. He denied that science was all about the pursuit of objective truths.

I previously posted:

Errol Morris is a famous filmmaker who is still mad at the late Philosophy professor Thomas Kuhn (aka Professor Paradigm Shift) throwing as ashtray at him and kicking him out of Princeton. ...

Morris thinks that Kuhn ruined the Philosophy of Science in the same way that I think that Einstein ruined Physics.

As with Einstein, the real problem with Kuhn lies in his followers. A whole generation of scholars took his work further, and used it to deny truth as we know it.

Counterfactuals: Quantum Mechanics

Some interpretations of quantum mechanics rely very heavily on a certain style of counterfactual reasoning. Quantum mechanics teaches that an electron has wave and particle properties. It is observed as a point particle, but otherwise it behaves like a wave. The uncertainty principle says that you cannot measure the precise position and momentum at the same time.

J.J. Thomson won the 1906 Nobel Prize for discovering that electrons are particles (his acceptance lecture called them "corpuscles"). His son won the 1937 Nobel Prize for showing that electrons are waves. The subject has confused people ever since.

The interpretations differ in their view of the electron before it is observed. Some say that it is a wave, with no precise location. Others say that it is a particle, but a funny kind of particle that can be many places at once. It thus has multiple histories, unlike anything in our ordinary experience.

The multiple histories get confusing when we consider counterfactuals. Suppose you ask, "where would the electron be if it were in a particular location at a particular time?" This question makes no sense because the electron could not be at a particular location at a particular time because of the uncertainty principle (unless a measurement is disturbing the system). Admitting that the electron could have been in other places as well at the same time only makes the counterfactual meaningless.

To see how this dilemma plays out, consider the Double-slit experiment. An electron beam is fired thru a double-slit, and wave properties cause an interference pattern at the detector. The confusion occurs when you introduce counterfactuals about which slit the electrons pass thru. You can ask "if the electron goes thru the top slit, then where is it detected?" The question has no clear answer. Attempts to answer it involve saying that the electron has some sort of spooky action-at-a-distance effect on electrons going thru the other slit.

The best answer is to refuse to answer the question as a meaningless counterfactual. The question presupposes that the electron is a particle, and it is not a particle. It is a wave that goes thru both slits at once. If you put detectors in the slits then you find the electron in one slit or the other, but without the detector the electron cannot be localized to one slit.

As Asher Peres explained, "unperformed experiments have no results." The electron only looks like a point particle when certain measurement experiments are done. If no such experiment is performed, then there are no point particle consequences.

At this point you are probably wondering why we even talk about the electron as a particle if it is really a wave and if treating it as a particle causes so much trouble. The answer is that treating it as a particle is incredibly useful. Every electron appears identical, with the same mass, charge, spin, and zero radius. We can even see the particle tracks in bubble chamber pictures. R.P. Feynman worked out a diagram calculus for electrons where predictions are based on sums over their many possible histories. Under his interpretation, each diagram is a counterfactual but they all contribute real measurement.

Feynman's quantum mechanics textbook has his version of Peres's slogan:

Another thing that people have emphasized since quantum mechanics was developed is the idea that we should not speak about those things which we cannot measure. (Actually relativity theory also said this.)

The particle interpretation of electrons and photons works quite well as long as you avoid something called counterfactual definiteness. That is, you must not assume that the particles have particular properties that could be obtained by measurement, unless you actually do the measurement.

The 1965 Bell's theorem and subsequent experiments have shown the paradox of quantum mechanics more strikingly than the double-slit. The theorem has been called “the most profound discovery of science.” It is usually explained in terms of correlations between measurements on two equal and opposite electrons.

The correlations are hard to understand, and have two common explanations. Either one measurement has a spooky non-causal effect on the other, or we have to reject counterfactual definiteness.

Many physicists prefer the spooky explanation, and say that this proves that quantum mechanics allows non-locality, meaning one measurement can have an action-at-distance effect on another. As no experiment has ever demonstrated such an effect and we have no mathematical theory for how that would happen, this is indeed a striking conclusion.

The better and more mundane conclusion is that quantum mechanics is not amenable to certain counterfactuals. The disagreement is about whether this conclusion is profound. To some physicists, this proves that scientific realism is impossible. To others, it just shows that some ill-posed questions are unanswerable, just like many philosophical and theological questions, such as "how many angels can dance on the head of a pin?"

There has been no Nobel Prize given for work related to Bell's theorem. While there is talk of such a prize every year, others just shrug it off as just a metaphysical confusion about counterfactuals. All of the Bell test experiments have confirmed the 1930 understanding of quantum mechanics.

Nature is not just the conjunction of quantum particle scenarios. An electron can be measured in a lot of different places, but the electron is not the union of those possibilities because that would not capture its wave properties.

In a mystery novel, Sherlock Holmes might list five possible explanations for a crime, eliminate four, and conclude that the fifth was correct. You cannot do that with quantum particle interpretations because electrons are not really particles.

It does make perfect sense in quantum mechanics to treat electrons and photons as particles with particle histories, as long as you admit that a large number of such histories are possible. The histories are like counterfactuals except that they cannot be said to be definitely true or false. They are just Feynman paths. They allow a particle interpretation of nature and have an extremely powerful predictive theory.

Feynman paths and diagrams are used to explain the simple transmission of light. According to the theory, the simplest interactions involve infinitely many diagrams showing paths and collisions of electrons and photons. The diagrams might involve energy being created or destroyed, particles going backwards in time, and causality violations. Consideration of all of these ridiculous scenarios is essential to calculating an answer that agrees with experiment.

You can choose to believe that all of these scenarios are real if you wish, but it is easier to think of them as counterfactuals. They are wildly implausible assertions that are somehow used to deduce a valid conclusion. You might think that agreement with experiment is strong evidence for the truth of the hypotheses used to make the numerical prediction. But in this case, it is not. The scenarios involve simultaneous precise positions and momenta for photons and electrons. We know that photons and electrons are not really particles, and they do not have specific positions and momenta. We also know that energy is conserved, and that cause precedes effect. We think we know those things, anyway.

Thus it is convenient to think of quantum particles as having multiple counterfactual histories as Feynman paths, and the theory makes predictions as sums over all those paths. One cannot say that some paths are true and some are false, as all must be used to get correct numerical predictions and none can be taken literally. This interpretation is popular but not required, as it is also possible to treat the electrons and photons as fields instead of particles.

For those who argue that time is an illusion, the possibility of multiple histories is very unsettling. They refuse to accept that the past is any different from the future, so they say that the multiple counterfactuals in the past implies that we also have multiple counterfactuals in the future. So they prefer the many-worlds interpretation, where all possible scenarios happen in alternate universes. There can be no physical evidence for alternate universes, but they find it more compatible with their prejudices against time. In my opinion, belief in many-worlds is nothing but a severe confusion about the nature of time and counterfactuals.

The uncertainty principle says that measuring position and then momentum can give a different result from measuring momentum and then position. In quantum jargon, the observable operators do not commute, so the operator order matters. This is hard to understand if you believe in some sort of counterfactual simultaneous observation of position and momentum. But if you follow the Feynman-Peres advice against counterfactual definiteness, then it is plausible that the order of observation can make a difference.

You need to reject counterfactual definiteness in quantum mechanics because the theory predicts observations that disturb the system. A system with an observation is different from one without. You cannot just assume that the system behaves as if everything were observed. If you did, then the electrons and photons would all seem like particles, and you would miss out on the wave properties.

Counterfactuals are understandable by children but troublesome for philosophers. I have posted below about counterfactuals outside the context of quantum mechanics, in order to clarify them without the added quantum confusion.

My conclusion is that the counterfactual is the most confusing thing about quantum mechanics. Understand counterfactuals and you will not be tempted to subscribe to quantum spooky interpretations, to believe in many-worlds, or to deny locality, causality, or realism. All of those mysteries are rooted in misunderstandings about counterfactuals.

Counterfactuals: Reductionism and Objectivity

Reductionism is the idea that the world can be understood as the sum of its parts. Objectivity is the idea that there is an external reality independent of our biases and measurements. Together, these ideas are implicit in much or all of science.

How could these go wrong? Maybe there is some supernatural phenomenon that is not amenable to scientific study. There could be emergent features that do not reduce. There could be objects that behave differently every time you look at them, without any pattern. Maybe you can reduce a system to particles, but find that those particles seem to still have some complexity, but cannot be reduced any further.

Quantum mechanics is a theory that seems to run up against the limits of reductionism and objectivity. Naive reductionism would lead you to reduce an electron to its charge, mass, spin, position, and momentum, but the uncertainty principle prevents it. Attempts at further reduction and realism have nearly always led to some hidden variable theory. However these theories have all failed. We may never reduce electrons to mathematics.

The subject of reductionism and determinism really creeps people out when applied to genomic influence on behavior and IQ. There is overwhelming evidence that many traits are heritable, but we lack a genetic theory to explain it.

To believe in counterfactuals, you have to believe that all possible events can be divided into the real and the fictitious. And that you can analyze them as if they had an objective existence. I have this belief because it seems essential to scientific thinking.

We should not accept a concept 100% just because it is convenient for science. Reductionism is convenient for science, but there may be limits to it. Maybe some counterfactuals do not make any sense. So there may be limits to counterfactual reasoning, but it is hard to imagine science without it.

Counterfactuals: Soft Science

Research papers in the soft sciences usually use a type of counterfactual called a null hypothesis. The object of such a paper is often to disprove a hypothesis by collecting data and applying statistical analysis.

A pharmaceutical company might do a controlled clinical study of a new drug. Half of the test subjects get the new drug, and half get a placebo. The null hypothesis is that the drug and the placebo are equally effective. The company hopes to prove that the null hypothesis is false, and that the drug is better than the placebo. The proof consists of a trial with more subjects doing better with the drug, and a statistical argument that the difference was unlikely to be pure luck.

To see how a statistical disproof of a null hypothesis would work, consider a trial consisting of 100 coin tosses. The null hypothesis is that heads and tails are equally likely. That means that we would get about 50 heads in a trial, on average, with the variation being a number called "sigma". The next step in the analysis is to figure out what sigma is. In this case, for a fair coin, sigma is 5. That means that the number of heads in a typical trial run will differ from 50 by about 5. Two thirds of the trials will be within one sigma, or between 45 and 55. 95% will be within two sigmas, or between 40 and 60. 99% will be within three sigmas, or between 35 and 65.

Thus you can prove that a coin is biased by tossing it 100 times. If you get more than 65 heads, then either you were very unlucky or the chance of heads was more than 50%. A company can show that its drug is effective by giving it to 100 people, and showing that it is better than the placebo 65 times. Then the company can publish a study saying that the probability that the data matches the (counterfactual) null hypothesis is 0.01 or less. That probability is called the p-value. A p-value of 0.01 means that the company can claim that the drug is effective, with 99% confidence.

The p-value is the leading statistic for getting papers published and drugs approved, but it does not really confirm a hypothesis. It just shows an inconsistency between a dataset and a counterfactual hypothesis.

As a practical matter, the p-value is just a statistic that allows journal editors an easier decision on whether to publish a paper. A p-value under 0.05 is considered statistically significant, and not otherwise. It does not mean that the paper's conclusions are probably true.

A Nature mag editor writes:

scientific experiments don't end with a holy grail so much as an estimate of probability. For example, one might be able to accord a value to one's conclusion not of "yes" or "no" but "P<0.05", which means that the result has a less than one in 20 chance of being a fluke. That doesn't mean it's "right".

One thing that never gets emphasised enough in science, or in schools, or anywhere else, is that no matter how fancy-schmancy your statistical technique, the output is always a probability level (a P-value), the "significance" of which is left for you to judge – based on nothing more concrete or substantive than a feeling, based on the imponderables of personal or shared experience. Statistics, and therefore science, can only advise on probability – they cannot determine The Truth. And Truth, with a capital T, is forever just beyond one's grasp.

This explanation is essentially correct, but some scientists who should know better argue that it is wrong and anti-science. A fluke is an accidental (and unlikely) outcome under the (counterfactual) null hypothesis. The scientific paper says that either the experiment was a fluke or the null hypothesis was wrong. The frequentist philosophy that underlies the computation does not allow giving a probability on a hypothesis. So the reader is left to deduce that the null hypothesis was wrong, assuming the experiment was not a fluke.

The core of the confusion is over the counterfactual. Some people would rather ignore the counterfactual, and instead think about a subjective probability for accepting a given hypothesis. Those people are called Bayesian, and they argue that their methods are better because they more completely use the available info. But most science papers use the logic of p-values to reject counterfactuals because assuming the counterfactual requires you to believe that the experiment was a fluke.

Hypotheses are often formulated by combing datasets and looking for correlations. For example, if a medical database shows that some of the same people suffer from obesity and heart disease, one might hypothesize that obesity causes heart disease. Or maybe that heart disease causes obesity. Or that overeating causes both obesity and heart disease, but they otherwise don't have much to do with each other.

The major caution to this approach is that correlation does not imply causation. A correlation can tell you that two measures are related, but the operation is symmetrical and cannot say what causes what. To establish causality requires some counterfactual analysis. The simplest way in a drug study is to randomly gives some patients placebo instead of the drug in question. That way, the intended treatment can be compared to counterfactuals.

A counterfactual theory of causation has been worked out by Judea Pearl and others. His 2000 book begins:

Neither logic, nor any branch of mathematics had developed adequate tools for managing problems, such as the smallpox inoculations, involving cause-effect relationships. Most of my colleagues even considered causal vocabulary to be dangerous, avoidable, ill-defined, and nonscientific. "Causality is endless controversy," one of them warned. The accepted style in scientific papers was to write "A implies B" even if one really meant "A causes B," or to state "A is related to B" if one was thinking "A affects B."

His theory is not particularly complex, and could have been worked out a century earlier. Apparently there was resistance to analyzing counterfactuals. Even the great philosopher Bertrand Russell hated causal analysis.

Many theories seem like plausible explanations for observations, but ultimately fail because they offer no counterfactual analysis. For example, the famous theories of Sigmund Freud tell us how to interpret dreams, but do not tell us how to recognize a false interpretation. A theory is not worth much without counterfactuals.

Counterfactuals: Probability

Once you agree that the past is definite and the future is uncertain, then probability theory is the natural way to discuss the likelihood of alternatives. That is, if you believe in counterfactuals, then different things could happen, and quantifying those leads to probability.

Probability might seem like a simple concept, there there are different probability interpretations. The frequentist school believes that chance is objective, and the Bayesians say that probability is just a measure of someone's subjective belief.

The frequentists say that they are more scientific because they are more objective. The Bayesians say that they are more scientific because they more fully use the available info.

Mathematically, the whole idea of chance is a useful fiction. It is just a way of using formulas for thinking about uncertainty. There is no genuine uncertainty in math. A random variable is just a function on some sample space, and the formulas are equally valid for any interpretation.

Coin tosses are considered random for the purpose of doing controlled experiments. It does not matter to the experiment if some theoretical analysis of Newtonian forces on the coin is able to predict the coin being heads or tails. The causal factors on the coin will be statistically independent of whatever is being done in the experiment. There is no practical difference between the coin being random and being statistically independent from whatever else is being measured.

It is sometimes argued that radioactive decay is truly random, but there is really no physical evidence that it is any more random than coin tosses. We can measure the half-life of potassium, but not predict individual decays. According to our best theories, a potassium-40 nucleus consists of 120 quarks bouncing around a confined region. Maybe if we understood the strong interaction better and had precise data for the wave function, we could predict the decay.

The half-life of potassium-40 is about a billion years, so any precise prediction seems extremely unlikely. But we do not know that it is any different from putting dice in a box and shaking it for a billion years.

All fields of science seek to quantify counterfactuals, and so they use probabilities. They may use frequentist or Bayesian statistics, and may debate which is the better methodology. Only quantum physicists try to raise the issue to one of fundamental reality, and argue whether the probability is psi-ontic or psi-epistemic. The terms come from philosophy, where ontology is about what is real, and epistemology is about knowledge. So the issue is whether the wave function psi is used to calculate probabilities that are real, or that are about our knowledge of the system.

It seems like a stupid philosophical point, but the issue causes endless confusion about Schroedinger's cat and other paradoxes. Physicist N. David Mermin argues that these paradoxes disappear if you take a Bayesian/psi-epistemic view, as was common among the founders of quantum mechanics 80 years ago. He previously argued that quantum probability was objective, like what Karl Popper called "propensity". That is the idea that probability is something physical, but nobody has been able to demonstrate that there is any such thing.

Max Tegmark in the March 12, 2014 episode of Through the Wormhole uses multiple universes to deny randomness:

Luck and randomness aren't real. Some things feel random, but that's just how it subjectively feels whenever you get cloned. And you get cloned all the time. ... There is no luck, just cloning.

There are more and more physicists who say this nonsense, but there is not a shred of evidence that anyone ever gets cloned. There is just a silly metaphysical argument that probabilities do not exist because all possible counterfactuals are real in some other universe. These universes do not interact with each other, so there can be no way to confirm it.

Scott Aaronson argues that the essence of quantum mechanics is that probabilities can be negative. But the probabilities are not really negative. The wave function values can be positive, negative, complex, spinor, or vector, and they can be used to calculate probabilities, but those probabilities are never negative.

There is no experiment to tell us whether the probabilities are real. It is not a scientific question. Even tho the Bayesian view solves a lot of problems, as Mermin says, most physicists today insist that phenomena like radioactive decay and spin quantization prove that the probabilities are real.

Quantum mechanics supposedly makes essential use of probabilities. But that is only Born's interpretation. Probabilities are no more essential to quantum mechanics than to any other branch of science, as I explained here.

Counterfactuals: Causality

The concept of counterfactuals requires not just a reasonable theory of time but also a reasonable theory of causality.

Causality has confounded philosophers for centuries. Leibniz believed in the Principle of Sufficient Reason that everything must have a reason or cause. Bertrand Russell denied the law of causality, and argued that science should not seek causes.

Of course causality is central to science, and to how we personally make sense out of the world.

It is now commonplace for scientists to deny free will, particularly among popular exponents of atheism, evolution, and leftist politics. Philosopher Massimo Pigliucci rebuts Jerry Coyne and others, and John Horgan rebuts Francis Crick.

The leading experiments against free will are those by Benjamin Libet and John-Dylan Haynes. They show that certain brain processes take more time than is consciously realized, but they do not refute free will. See also contrary experiments.

The other main argument against free will is that a scientific worldview requires determinism. Eg, Jerry Coyne argues against contra-causal free will, and for biological determinism of behavior. Einstein hated quantum mechanics because it allowed for the possibility of free will.

A common belief is that the world must be either deterministic or random, but the word "random" is widely misunderstood. Mathematically, a random process is defined by the Kolmogorov axioms, and a random variable is a function on a measure-1 state space. That is, it is just a way of parameterizing outcomes based on some measurable set of samples. Whether or not this matches your intuition about random variables depends on your choice of Probability interpretation.

Wikipedia has difficulty defining what is random:

Randomness means different things in various fields. Commonly, it means lack of pattern or predictability in events.

The Oxford English Dictionary defines "random" as "Having no definite aim or purpose; not sent or guided in a particular direction; made, done, occurring, etc., without method or conscious choice; haphazard." This concept of randomness suggests a non-order or non-coherence in a sequence of symbols or steps, such that there is no intelligible pattern or combination.

In mathematics, the digits of Pi (π) can be said to be random or not random, depending on the context. Likewise scientific observations may or may not be called random, depending on whether there is a good explanation. Leading evolutionists Richard Dawkins and S.J. Gould had big disputes over whether evolution was random.

There is no scientific test for whether the world is deterministic or random or something else. You can drop a ball repeatedly and watch it fall the same way, so that makes the experiment appear deterministic. You will also see small variations that appear random. You can also put a Geiger detector on some uranium, and hear intermittent clicks at seemingly random intervals. But the uranium nucleus may be a deterministic chaotic system of quarks. We can never know, as any attempt to observe those quarks will disturb them.

Likewise there can be no scientific test for free will. You would have to clone a man, replicate his memories and mental state, and see if he makes the same decisions. Such an experiment could never be done, and would not convince anyone even if it could be, as it is not clear how free will would be distinguished from randomness. Free will is a metaphysical issue, not a scientific one.

Even if you believe in determinism, it is still possible to believe in free will.

A debate between determinists Dan Dennett and Sam Harris was over statements like:

If determinism is true, the future is set — and this includes all our future states of mind and our subsequent behavior. And to the extent that the law of cause and effect is subject to indeterminism — quantum or otherwise — we can take no credit for what happens. There is no combination of these truths that seems compatible with the popular notion of free will.

But that is exactly what quantum mechanics is -- a combination of those facts that is compatible with the popular notion of free will.

In biology, this dichotomy between determinism and randomness has been called the Causalist-Statisticalist Debate.

At the core of their confusion is a simple counterfactual:

Consider the case where I miss a very short putt and kick myself because I could have holed it. It is not that I should have holed it if I had tried: I did try, and missed. It is not that I should have holed it if conditions had been different: that might of course be so, but I am talking about conditions as they precisely were, and asserting that I could have holed it. There is the rub. [Austin’s example]

The problem here is that they think that determinism is a philosophical necessity, and so they fail to grasp the meaning of a counterfactual.

In public surveys, people overwhelmingly reject this deterministic view:

Imagine a universe (Universe A) in which everything that happens is completely caused by whatever happened before it. This is true from the very beginning of the universe, so what happened in the beginning of the universe caused what happened next, and so on right up until the present. For example one day John decided to have French Fries at lunch. Like everything else, this decision was completely caused by what happened before it. So, if everything in this universe was exactly the same up until John made his decision, then it had to happen that John would decide to have French Fries.

And so an atheist biologist writes:

To me, the data show that the most important task for scientists and philosophers is to teach people that we live in Universe A.

That is a tough sell, as Universe A is contrary to common sense, experience, and our best scientific theories.

Steven Weinberg has argued that the laws of physics are causally complete, but also that we are blindly searching for the final theory that will solve the mysteries of the universe. A final theory would explain quark masses and cancel gravity infinities.

Einstein had an almost religious belief in causal determinism, and many others seem to believe that a scientific outlook requires such a view. On the other hand, a majority of physicists today assert (incorrectly) that quantum mechanics has somehow proved that nature is intrinsically random.

Quantum mechanics is peculiar in that it leaves the possibility of free will. It is the counterexample to the notion that a scientific theory must be causal and deterministic, or otherwise contrary to free will. If you tried to concoct a fundamental physical theory that could accommodate free will, it is hard to imagine a theory being better suited for free will.

Some interpretations of quantum mechanics are deterministic and some are not, as so, as Scott Aaronson explains, determinism is not a very meaningful concept in the context of quantum mechanics.

If you reject free will and the flow of time, and believe that everything is determined by God or the Big Bang, then counterfactuals make no sense. Most of time travel in fiction makes no sense either. The concept of counterfactuals depends on the possibility of alternate events, and on time moving forward into an uncertain future.

Regardless of brain research and the scientific underpinnings of free will, counterfactuals are essential to how human beings understand the progress of time and the causality of events.

Counterfactuals: Hard Science

Counterfactual reasoning is used all the time in the hard sciences. When you learn the formulas for gravity, the first thing you do is to answer questions like, “If you drop a rock off a 100-foot cliff, how long will it take to hit the ground?”

Dropping a rock from a cliff could also be called hypothetical reasoning, because one can easily imagine conducting the experiment. However physics also has all sorts of thought experiments that have no hope of ever being carried out. For example, explanations of relativity frequently involve spaceships taking people near the speed of light or being swallowed up in a black hole.

Counterfactuals are essential to the scientific method. Science is all about doing experiments that favor some hypothesis over some counterfactual.

The ability to make a precise prediction from a counterfactual is what distinguishes the hard sciences from the soft.

A famous example is Hendrik Lorentz's discovery of space and time transformations (now called Lorentz transformations) to explain the Michelson-Morley experiment. The counterfactual was aether motion, as Lorentz interpreted experiments to show that no such motion was detectable. He then used his formulas to predict relativistic mass, which was then confirmed by experiment. (Einstein later published similar theories, but the consensus of historians is that he paid no attention to the experiments.)

An example that failed to disprove the counterfactual was the 1543 Copernicus heliocentric model of the solar system. The established theory was Ptolemy's, but both theories predicted the sky with about the same accuracy. Experiments and models with much greater accuracy were achieved by Tycho Brahe and Johannes Kepler around 1600. The 20th century theory of relativity taught that motion is relative, and heliocentricity could never be proven.

Kepler's theory was superior not only for its accurate predictions, but for its counterfactual predictions. He had a complete theory of what kinds of orbits were possible in the solar system, so he could have made predictions about any new planet or asteroid that might be discovered. But he did not have a causal mechanism.

Causality is closely connected with counterfactual analysis. If an event A is followed by an event B, we only say that A caused B if counterfactuals for A would have been followed by something other than B. If rain follows my rain dance, I only argue that the dance caused the rain if I have a convincing argument that it would not have rained if I had not danced. A truly causal argument would provide a connected chain of events from the dance to the rain, with every link in the chain causing the next link.

Isaac Newton found a more powerful theory of mechanics by positing a gravitational force between any two massive objects, and saying that the force causes the orbital motion. Laplace argued in 1814 that all of nature is predictable with causal mechanics, given sufficient data.

This Newtonian causality was not true causality, because it required action-at-a-distance. One planet could exert a force on another planet over millions of miles, without any intermediate effects. A truly causal theory required the invention of the concept of field, such as electric or gravitational field, that can propagate thru empty space from one object to another. James Clerk Maxwell worked out such a theory for electric and magnetic fields in 1865, and that was the first relativistic theory.

A field is a physical way of describing certain counterfactuals. Saying that there is an electric field, at a particular point in space and time, is another way of saying what would happen if an electric charge were put at that point. The field is one of the most important concepts in all of physics, because it allows reducing the universe to the mechanics of locally defined objects. Thus physics is rooted in counterfactuals at every level. You could say that reductionism works in physics because of clever schemes for distributing counerfactual info over space and time.

A trendy topic in theoretical astrophysics is the multiverse. This involves a loose collection of unrelated ideas, but they all involve hypothetical universes outside of our observational abilities. It is a giant counterfactual exercise, with no experiment to decide who is right.

A particular fascination is the possibility of intelligent life in other universes. It appears that our universe is finely tuned for life. That is, it is hard to imagine the development of life in most of the counterfactual universes.

The most bizarre approach to counterfactuals is the many-worlds interpretation (MWI) of quantum mechanics. It simply posits that every possible counterfactual has an objective reality in an alternate universe. The extra universes do not really explain anything because they do not communicate with each other. There can be no experimental evidence for the other universes. There is no theoretical reason either, except that some physicists are unhappy with counterfactuals being just countefactuals.

The many-worlds seems like an endorsement of counterfactual thinking, but it corrupts such thinking by declaring the the counterfactuals real. A counterfactualist might argue, "if a new ice age were beginning, then we would probably notice cooler termperatures, but we don't, so we are not in a new ice age." But in many-worlds, all exceptionally improbable events take place in different universes, and we could be in one of them. Thus many-worlds leaves no good rationale for rejecting counterfactuals.

Counterfactuals: Math

Counterfactual reasoning is essential to mathematics. A mathematician might assume some dubious hypothesis, derive an absurd result, and conclude that the hypothesis must be wrong. The method is called reductio ad absurdum. For example, the Greeks proved that there are infinitely many prime numbers as follows. If there were some largest prime N, then all larger numbers could be divisible by primes equal to N or smaller. But you could multiply all those primes together and add one, and get a contradiction. Therefore there must be prime numbers larger than N.

A more trivial example of this reasoning is to prove that there is no largest integer. For any integer N, the integer N+1 is larger. So assuming that there is a largest integer quickly leads to a contradiction. They also used an argument by contradiction to show that the square root of 2 is irrational -- that it cannot be written as a fraction a/b. If it could be, then a² = 2b². But 2 is a factor an even number of times on the left, and an odd number of times on the right, a contradiction. That is why the decimal expansion of the square root of 2 is an endless and non-repeating sequence of digits.

Counterfactual reasoning is also used to create new numbers. Even tho there is no rational square root of 2, we can just hypothesize one anyway. We have to expand our notion of number, and no longer require that a number is a ratio of integers. We still have many other properties, such as every number being less than, equal, or greater than other numbers. We can also lose that property by allowing a counterfactual square root to -1. Other counterfactuals give us infinitesimal numbers and non-Euclidean geometry.

Mathematical logic carefully distinguishes the counterfactual from the false conditional. A statement of the form "if A then B" is always true if A is a false conditional. That is, a false hypothesis allows you to prove anything. For example, if 0 = 1, then I am the Pope. There is no use to a truly false conditional. The value is in a hypothesis that might be true on some alternative universe of mathematical facts.

The statement about the Pope may be proved as follows. If 0 = 1, then add 1 to both sides, getting 1 = 2. The Pope and I are 2 different people. But 2 = 1, so we are 1 person, and I am the Pope. Or you can prove it without this sort of cleverness by just appealing to the meaning of a conditional.

A mathematician might also say, "if pigs have wings, then I am the Pope." That is because pigs do not have wings. If you want to posit some counterfactual world in which pigs have wings, then you need a grammatical modifier or mood to show that.

Sometimes even mathematicians are unhappy with counterfactual reasoning. A century ago L. E. J. Brouwer proved that any continuous function from the disk to itself must have a fixed point, but his proof relied on counterfactual reasoning and gave no way to find such a point. He adopted the view that such a theorem is dubious unless it gives a way to construct the solution.

Mathematician Terry Tao explains his version of counterfactual reasoning in three posts on The “no self-defeating object” argument. As he explains, many elementary theorems are very confusing to students because they are based on constructing some impossible object. There can be no impossible object, so the proof seems like a paradox. The contradiction is avoided by precise mathematical definitions and analysis.

As a simple example, Tao proves that there is no largest integer. The proof is trivial, as any largest integer N would be less than N+1. But the counterfactual subtlety of this argument is sufficient that a child is more likely to learn it from another child on the playground, than from a teacher or textbook.

A very widely promoted AT&T TV commercial focuses on this proof as a way of arguing that bigger is better in phone networks. Sure enough, the kids grasp the concept as the teacher has a difficult time explaining it.

Thus the counterfactual is one of the core concepts in mathematics. You will never learn proofs without it.

Counterfactuals: Time

Time is what distinguishes the past from the future. The chief intuitive difference is that we remember the past, and we cause the future. Time marches forward, and as we cause events, they become the history that we remember.

While this view of time seems obvious to a small child, there is an opposite view that the present flow of time is just an illusion. That view is sometimes called block time, and its roots go call the way back to the ancient Greek philosopher Parmenides. Albert Einstein and other smart people have subscribed to such a view, and even claimed that relativity theory requires it. A 2010 SciAm article says that many physicists argue that there is no such thing as time, and explains:

As you read this sentence, you probably think that this moment — right now — is what is happening. The present moment feels special. It is real. However much you may remember the past or anticipate the future, you live in the present. Of course, the moment during which you read that sentence is no longer happening. This one is. In other words, it feels as though time flows, in the sense that the present is constantly updating itself. We have a deep intuition that the future is open until it becomes present and that the past is fixed. As time flows, this structure of fixed past, immediate present and open future gets carried forward in time. This structure is built into our language, thought and behavior. How we live our lives hangs on it.

Yet as natural as this way of thinking is, you will not find it reflected in science. The equations of physics do not tell us which events are occurring right now — they are like a map without the “you are here” symbol. The present moment does not exist in them, and therefore neither does the flow of time.

That view of time certainly is reflected in science, and in my opinion, adopted by all sensible people. There is not a shred of scientific evidence against it. Most of the fundamental equations of dynamics are expressed directly in terms of the flow of time. I quote the article to point out that more than one view of time is possible.

The scientists who deny the flow of time will typically argue that the fundamental laws of nature are deterministic and reversible, and so the progress of time is an illusion and we have no free will to affect the future. Many argue for retrocausality, as they say the future determines the past as much as the past determines the future. Some people also deny that we can speak definitely about the past, as they say that quantum mechanics allows for multiple histories.

Some argue that relativity is contrary to the flow of time, because time is just another dimension like the three spatial dimensions. That is even the consensus among philosophers. But the flow of time is essential to relativity, as every object travels along its world line into its future light cone. The dynamics of relativity, as well as other physics theories, use the flow of time.

Einstein was unhappy about the flow of time:

Once Einstein said that the problem of the Now worried him seriously. He explained that the experience of the Now means something special for man, something essentially different from the past and the future, but that this important difference does not and cannot occur within physics. That this experience cannot be grasped by science seemed to him a matter of painful but inevitable resignation.

And also:

Three weeks before his death, in 1955, Einstein wrote, “People like us, who believe in physics, know that the distinction between past, present, and future is only a stubbornly persistent illusion.”

Hermann Weyl wrote in 1949:

The objective world simply is, it does not happen. Only to the gaze of my consciousness, crawling upward along the life line of my body, does a section of this world come to life as a fleeting image in space which continuously changes in time.

A recent paper on The flow of time in the theory of relativity demonstrates the confusion over alternate ideas of time:

When we consider any experiment related to the theory of [special] relativity, like the Michelson-Morley experiment (see, e.g., Møller 1955, 26-8), we can always describe it in terms of an intuitive notion of passage or flow of time: light is send through the two arms of the interferometer at a particular moment – the now of the experimenter –, and the process of light propagation takes time to occur, as can be measured by a clock calibrated to the adopted time scale.

However when we consider the theory, in particular focusing on its development in terms of the Minkowski space-time and its application using the Minkowski diagrams, we immediately became puzzled by the implications of the theory regarding our intuitive notion of time, and the passage or flow of time seems difficult or even impossible to ‘find’ in the conceptual-mathematical structure of the theory (see, e.g., Dorato 2010, 1-2).

Of course it is not really difficult to find the flow of time. If you understand how those experiments follow from the theory, then you have the flow of time.

The supposed problem is with "probabilism", which has been defined as the doctrine that "the universe is such that, at any instant, there is only one past but many alternative possible futures". There is also a technical problem that what one person perceives to be the present might differ from what another perceives. But that does not really affect the philosophical issue of time.

Without getting into the subtleties of relativity and quantum mechanics, I am adopting the commonplace view that time flows from the past (that we remember and is certain) to the future (that we cause and is uncertain). In philosophy jargon, I am following the A-theory of time and maybe presentism, instead of the B-theory and eternalism. As the ancient Greek Heraclitus said, it is impossible to step into the same river twice. As the above SciAm article says, how we live our lives hangs on this structure. I want to explain how this view relates to counterfactuals.

Past events are definite, and cannot be changed. Hypothetical events are in the future, and may depend on our free will to choose courses of action. Counterfactual events are in the past, and did not happen. We cannot make them happen. What we can do is to discuss the causal effect of the counterfactual events.

Counterfactual events are always earlier in time than the hypothetical consequences. For example, the counterfactual might be that you jump off a cliff. The consequence is that you fall to your death. Because you understand this causal reasoning, you don't jump off the cliff.

Free will is the idea that you can voluntarily eliminate counterfactuals from your life. At any given time, there could be several counterfactuals in addition to whatever you actually do at that time. If you have the free will to choose what you do, then you are making the decisions that prevent those counterfactuals from happening.

Thus counterfactual thinking is how people imagine alternatives to reality, and make decisions. As such, psychologists and others have attributed poor decision-making to a faulty assessment of counterfactuals. For example, someone might refuse to fly in an airplane because of an exaggerated opinion of the risk of a plane crash.

Again, the Einsteinian physicists and B-theory philosophers reject all of this. Their reasons are more religious than scientific. There are no experiments contrary to the intuitive flow of time, and no generally accepted theory that is inconsistent with it. Their view is deficient, because they cannot grasp counterfactuals.

Update: N. David Mermin recently wrote a paper on trying to escape the B-theory of time:

Rudolf Carnap succinctly stated the problem of the Now in his report of a conversation with Albert Einstein:7 “Einstein said that the problem of the Now worried him seriously. He explained that the experience of the Now means something special for man, something essentially different from the past and the future, but that this important difference does not and cannot occur within physics. That this experience cannot be grasped by science seemed to him a matter of painful but inevitable resignation.”

Mermin says that this is "a longstanding puzzle in classical physics." The problem disappears with a suitable positivistic philosophy, altho Mermin does not exactly express it that way. You just have to rid yourself of warped Einsteinian thinking.

Counterfactuals: Law

Many court actions are contingent on counterfactual reasoning. Tort law is based on the idea that if someone commits a wrong act against you, then you can sue for damages. For example, if someone crashes into the rear end of your car, you can sue for the cost of restoring your car to its condition before the accident.

The court has to somehow figure out what would have happened if the tort had never happened. The counterfactual is the plaintiff's life without the tort. If someone slanders you and you sue for damage to your reputation, then the court has to estimate the dollar value of the difference between your actual reputation and your counterfactual reputation if you had not been slandered.

More common are lawsuits over contract law, and these also depend on counterfactual reasoning. This is one of the most misunderstood points in all of law. If you sign a contract to rent a house from someone for $1000, and you break the contract, then he can sue you for the $1000. But the court will only award the counterfactual damages. If he could have easily found another tenant to pay the $1000, then you may not owe anything. Or you might even owe more than $1000, if he has lost business because of your vacancy.

The debate about Trayvon Martin asked questions like: What if Martin had been white? What if Zimmerman stayed in his car?

At the Zimmerman trial, the prosecutor misunderstood the role of the expert:

Prosecutor Bernie de la Rionda: In order to give an opinion, when someone gives you a hypothetical, it has to based on facts that are accurate and truthful, correct?
Di Maio: A hypothetical doesn't have to be true. A hypothetical is just "suppose this and this happened ...".
Prosecutor Bernie de la Rionda: So we would be speculating, I guess, or potentially speculating?
Di Maio: It is not even speculating. You are giving a presentation and asking what it is.

Di Maio is correct. An excellent expert witness could testify entirely by answering hypothetical questions, and never even look at the facts of the case. For example, a witness might be useful just answering these hypothetical questions: "What does a gunshot would look like if the gun is pressed against the skin? If the gun is 3 inches away? 12 inches? 24 inches? How is that known?" The jury could then apply his knowledge to the facts of the case.

Most witnesses in court are not allowed to speculate, or offer counterfactual reasoning. That is restricted to lawyers making arguments (not under oarh), and expert testimony. A expert must follow the Daubert standard, as codified in US federal court as FRE 702:

A witness who is qualified as an expert by knowledge, skill, experience, training, or education may testify in the form of an opinion or otherwise if:

(a) the expert’s scientific, technical, or other specialized knowledge will help the trier of fact to understand the evidence or to determine a fact in issue;
(b) the testimony is based on sufficient facts or data;
(c) the testimony is the product of reliable principles and methods; and
(d) the expert has reliably applied the principles and methods to the facts of the case.

When the expert describes those reliable principles and methods, he often tells how they apply to hypothetical situations. As the jury (or maybe the judge) determines the facts, testimony about counterfactuals in the most useful. Often there is no need for the expert to offer any opinion about the facts of the case, if the jury is taught how to apply the generally accepted knowledge.

Thus counterfactuals are essential to the law.

Update: A 2010 US Supreme Court decision said that a lawsuit "does not require precise proof of what the Board's policies might have been in that counterfactual world." I mention this because it is understood that lawsuits are all about proving scenarios in counterfactual worlds, even tho that terminology is uncommon.

Counterfactuals: Grammar

Consider the sentence, "if pigs had wings, they could fly." This is a very strange thing to say, as pigs do not have wings. And yet the sentence is readily understandable to children.

The English language has a construction called the "subjunctive conditional" for counterfactuals like this. Statements that describe reality are in the indicative mood, such as "pigs do not have wings" or "pigs do not fly". So are straightforward conditional statements, like "if pigs have food, they eat." If you want to suggest some sort of imaginary world in which pigs fly, you need the verb to be in the subjunctive mood.

Consider this illustration of the English subjunctive:

If he was in class yesterday, he learned it.
If he were in class today, he would be learning it.

The first is a simple statement about a boy learning in class. The second suggests that he was not in class, but it says something about some false scenario anyway.

Here is another example:

If Oswald did not shoot Kennedy, someone else did.
If Oswald hadn’t shot Kennedy, someone else would have.

The first is a true statement because it is indicative conditional with a false antecedent. Oswald did shoot Kennedy. Even if you are not sure that Oswald shot Kennedy but know that Kennedy was shot, then you will still accept the statement as true. It is only an assertion about actual historical events.

The second statement is much more complex. It uses the subjunctive mood to alert you that it is hypothesizing some counterfactual world and trying to reason about that world as if it were real. It is hard to say whether the sentence is true or false because you have to make assumptions about what else might be funny about that unreal world, and speculate how events might play out.

The counterfactual conditional is a false history scenario. In other cases, the counterfactual is a future hypothetical. For example, you could say that "if the Antarctic ice melts, New York would go under water."

The subjunctive is commonly misunderstood. In the famous 1968 zombie movie, Night of the Living Dead, Barbara says, "Johnny asked me if I were afraid." No, Johnny wanted to know whether she was actually afraid. He was not trying to create some counterfactual scenario. The correct grammar is "Johnny asked me if I was afraid."

The subjunctive "were" would be appropriate if Johnny said "I would run if I were you" or "I would be angry if I were you." Obviously Johnny cannot be someone else, and the subjunctive mood alerts the listener that she is getting a superficially nonsensical scenario.

Here is another example:

If he was in line, give him a ticket.
If he were in line, he would be eating by now.

The first is indicative and factual. The second is subjunctive and counterfactual.

The subjunctive is not used often in English, unless there is some counterfactual being expressed. The verb "be" is subjunctive in "I suggest that they be removed." Then sentence does not say that anything has been or will be removed. It creates a hypothetical scenario where something is removed.

The counterfactual concept is essential, and so is the English subjunctive mood for expressing it.

Classics scholar Phuc Tran argues in a TED talk that his Vietnamese relatives are unable to ponder counterfactuals because their language lacks a subjunctive mood.

I am not sure how other languages deal with these concepts. Chinese does not even have past and future tenses, so it has trouble with expressing time as needed for counterfactuals. (I am not sure about all Chinese, as there are at least 300 different varieties of Mandarin that were more or less mutually unintelligible.)

Counterfactuals: Introduction

Counterfactual reasoning is essential to science. It could also be called hypothetical reasoning. It is at the root of many scientific confusions.

Hypothetical reasoning means formulating some hypothesis, and deducing the consequences. For example, a hypothesis might be that CO2 concentrations in the atmosphere might double in the next century. A deduction might be some global warming. The scientific method could be summarized as formulating a hypothesis, deducing consequences, testing those consequences, and ultimately making an inference about the validity of the original hypothesis.

The German philosopher Ludwig Wittgenstein once asked why anyone would think that it logical to assume that the Sun revolves around the Earth. When told that the Sun appears to be revolving, he asked how it would look if the Earth were rotating instead. The point of that anecdote is that science does not just find explanations consistent with observations. It compares the consequences of different hypotheses that may not be true.

Hypothetical reasoning is usually based on the hope that the hypothesis in going to turn out to be true. Counterfactual reasoning is similar, except that the hypotheses are likely to be false. The purpose is not to prove the hypothesis at all, but to elaborate on some artificial scenario.

If you are giving an hypothesis as a scientific explanation for some observed facts, then you are implicitly saying that alternative hypotheses are inconsistent with the facts. Thus even if you want to stick to truth, you must do some counterfactual analysis.

In the 1865 Lewis Carroll book, Alice in Wonderland says, “There is no use trying; one can’t believe impossible things.” The Queen replies, “I daresay you haven't had much practice. When I was your age, I always did it for half an hour a day. Why, sometimes I've believed as many as six impossible things before breakfast.” Carroll was a mathematician, writing for children.

Believing in counterfactuals does take practice, as it is barely distinguishable from believing in nonsense. It is also essential to quantum mechanics.

Aristotle is commonly quoted (incorrectly) as saying, "It is the mark of an educated mind to be able to entertain a thought without accepting it." An educated mind, or the open mind of a child. Or someone who accepts counterfactuals.

A counterfactual argument often starts with a what-if. Someone might ask, “what if the Axis Powers had won World War II?” It is a historical fact that they did not, and any such discussion seems like nonsense. Nevertheless, it is necessary to consider such questions if we are to come to conclusions about whether the war was worth fighting.

Comic books sometimes have counterfactual plots, such as the 1977 comic “What if Spider-Man joined the Fantastic Four?”. These are entirely fictional characters, but the comic was intended for readers who had accepted the story line that Spider-Man was not part of the Fantastic Four, and it was not trying to convince anyone that Spider-Man was joining the Fantastic Four. It was entirely counterfactual, but still made logical sense for its readers. It was like a dream within a dream. Disney recently tweeted that it was banning counterfactual Star Wars stories.

In case you are still wondering what "counterfactual" means, it is an adjective that means contrary to fact. When used as a noun, it is an abbreviation of "counterfactual conditional". But it does not just mean a false conditional, as false conditionals are meaningless. A philosophy site defines it as:

A conditional statement whose antecedent is known (or, at least, believed) to be contrary to fact. Thus, for example, "If George W. Bush had been born in Idaho, then he would never have become President." Unlike material implications, counterfactuals are not made true by the falsity of their antecedents. Although they are not truth-functional statements, counterfactuals may be significant for the analysis of scientific hypotheses.

I have become convinced that children understand counterfactuals better than adults, and that misunderstandings about them pervade many disciplines. I will be posting more on this topic. I will eventually relate this to relativity and quantum mechanics, but first I want to make sure that the concept is crystal clear in other contexts.

Misconceptions about QM and free will

Swedish physicist Sabine Hossenfelder posts 10 Misconceptions about Free Will:

If somebody talks about a “question that science cannot answer” what they really mean is a question they don’t want an answer to. Science can indeed be very disrespectful to people’s beliefs.

No, saying that science cannot answer a question means that there is no experiment or set of observations to resolve the question.

Are sunsets beautiful? Is Obamacare a failure? Is P = NP? These are legitimate questions, but science cannot answer them.

“Do humans have free will?” is a question I care deeply about. It lies at the heart of how we understand ourselves and arrange our living together. It also plays a central role for the foundations of quantum mechanics. In my darker moods I am convinced we’re not making any progress in quantum gravity because physicists aren’t able to abandon their belief in free will. And from the foundations of quantum mechanics the roadblock goes all the way up to neuroscience and politics.

Yes, I just blamed the missing rational discussion about free will for most of mankind’s problems, including quantum gravity.

There you have the folly of modern physics in a nutshell. Yes of course free will lies at the heart of how we understand ourselves. Yes, free will plays a central role for the foundations of quantum mechanics, as QM is unique among modern science theories in that it accommodates free will, as shown by the free will theorem.

But no, an Eisnteinian belief in determinacy will never lead to any progress in quantum gravity.

She lays bare her illogical argument:

So, first the facts.

Fact 1: Everything in the universe, including you and your brain, is composed of elementary particles. What these particles do is described by the fundamental laws of physics. Everything else follows from that, in principle. ...

Fact 2: All known fundamental laws of nature are either deterministic or random. To our best present knowledge, the universe evolves in a mixture of both, but just exactly how that mixture looks like will not be relevant in the following.

Having said that, I need to explain just exactly what I mean by the absence of free will:

a) If your future decisions are determined by the past, you do not have free will.

b) If your future decisions are random, meaning nothing can influence them, you do not have free will.

c) If your decisions are any mixture of a) and b) you do not have free will either.

It would be understandable if she said this in the 19th century. But QM is our leading theory, and it teaches that future decisions are not determined by the past, and that they are only random in the sense of not being predictable by others. In other words, QM is completely compatible with free will.

If you think that QM is somehow incompatible with free will, ask yourself this question: Is it possible for any physical theory to be more compatible with free will than QM? I do not see how. Free will is baked into QM.

If the answer is yes, then ask why no one has ever proposed such a theory. If the answer is no, and you still oppose free will, then your opposition to free will is purely philosophical and independent of any physical principles.

Some ancient philosophers opposed free will, so it is possible to take such a view. Just do not pretend that the view is informed by science, because it is not.

The conflict that doesn't go away is this: There's no sense in which you can change your future. ...

"I could go and jump out of a window. That would change my future dramatically."

No it wouldn't. Your future either does or doesn't contain you jumping out the window. There's nothing you can change about that.

The root of her problem is that she does not believe in counterfactuals. She rejects a concept that is easily understood by little kids. I will post more on that.

She believes in Einsteinian determinism, and even likes superdeterministic hidden variables theories, more commonly known as "conspiracy theories".

Lumo addresses her misconceptions one by one.

Russell denies the law of causality

Explanations of quantum mechanics can get very confusing on the subject of causality. It is odd that people get tripped up on such a simple concept. Apparently there is a long history of smart people saying stupid things about causality.

Bertrand Russell wrote in a 1913 essay on causality:

In the following paper I wish, first, to maintain that the word "cause" is so inextricably bound up with misleading associations as to make its complete extrusion from the philosophical vocabulary desirable; secondly, to inquire what principle, if any, is employed in science in place of the supposed "law of causality" which philosophers imagine to be employed; thirdly, to exhibit certain confusions, especially in regard to teleology and determinism, which appear to me to be connected with erroneous notions as to causality.

All philosophers, of every school, imagine that causation is one of the fundamental axioms or postulates of science, yet, oddly enough, in advanced sciences such as gravitational astronomy, the word "cause" never occurs. Dr. James Ward, in his Naturalism and Agnosticism, makes this a ground of complaint against physics: the business of those who wish to ascertain the ultimate truth about the world, he apparently thinks, should be the discovery of causes, yet physics never even seeks them. To me it seems that philosophy ought not to assume such legislative functions, and that the reason why physics has ceased to look for causes is that, in fact, there are no such things. 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. ...

We may now sum up our discussion of causality. We found first that the law of causality, as usually stated by philosophers, is false, and is not employed in science. We then considered the nature of scientific laws, and found, instead of stating that one event A is always followed by another event B, they stated functional relations between certain events at certain times,

This is all nonsense. Of course gravitational astronomy speaks of causes, as does all other advanced sciences. It is hard to see how something could be scientific without recognizing causes.

I am trying to understand how people could be so confused about time, causality, determinism, and free will.

Russell appears to believe that determinism is some empirical fact, but it cannot be. Charlotte Werndl shows:

The central question of this paper is: are deterministic and indeterministic descriptions observationally equivalent in the sense that they give the same predictions? I tackle this question for measure-theoretic deterministic systems and stochastic processes, both of which are ubiquitous in science. I first show that for many measure-theoretic deterministic systems there is a stochastic process which is observationally equivalent to the deterministic system. Conversely, I show that for all stochastic processes there is a measure-theoretic deterministic system which is observationally equivalent to the stochastic process.

So some formulation of quantum mechanics may be deterministic or not, but that tells us nothing about whether the real world is.

I don't know why Russell was so opposed to causality, except maybe it is related to his atheism. Leftist-atheist-evolutionist Chris Mooney argues that belief in "teleological thinking" or causality is a major deterrent to people accepting evolution over God.