## Monday, October 02, 2006 ... //

### Falsifiability in physics

In humanities, one can create a lot of sentences that satisfy the rules of grammar but that don't admit any kind of experimental test that would decide about their validity. Some examples are:

• The sunshine is female.
• The supernovae are evil.
• Green ideas are sleeping furiously.
If I want to be more accurate, the last sentence used to be meaningless 40 years ago but it recently became a meaningful description of the intellectual quality of the environmental movement.

Physics works differently. When it's done properly, physics talks about objects that can be observed and quantified i.e. described by numbers: this is why we call them observables or quantities. Classical physics talks about distances that can be measured by sticks and time intervals that can be measured by clocks. It also talks about voltages that can be measured with voltmeters and dozens of other quantities. The laws of classical physics dictate the relationships between these quantities and their evolution with time in various situations. The most fundamental laws of classical physics are usually expressed as differential equations.

Quantum physics can often talk about the same observables but they become operators and their measured values may fail to be continuous: the physicists say that the spectrum of some observables may become discrete. Moreover, quantum physics no longer claims that the measured values follow from the initial conditions deterministically: quantum mechanics only predicts the probabilities of different outcomes - different values of various observables. The probabilities are often interpreted as decay rates, cross sections, and other quantities of statistical character. Quantum mechanics can predict their values and they can be measured using detectors (almost) exactly by repeating the same experiment many times.

Can these predictions be falsified?

Start with classical physics and try to describe the motion of Mercury orbiting the Sun. Write down any differential equation for the position. Can your equation be falsified? You bet. Unless you write the exact right equation as Newton did plus minus small corrections that can't obscure that what you have written down are still essentially Newton's equations with small additions, your theory will be instantly falsified. The physicists from the early 18th century will need a couple of minutes to see that your theory is incompatible with observations.

Write down some dynamical laws for the electromagnetic field. Again, unless you write something that is essentially equivalent to Maxwell's equations, the physicists at the end of the 19th century or later will be able to disprove your theory within minutes. In 1800, it would be much harder for the physicists to make the right verdict but 100 years later, it was already trivial.

Go back to the early 20th century and suggest any theory that is meant to be a replacement for special relativity: write down your new rules for the relativistic momentum or energy that doesn't have the right features such as the Lorentz invariance. The physicists in 1910 will also need just a few minutes to rule your theory out.

In 1927, you may write down a new equation meant to replace Schrödinger's equation to capture physics of the Hydrogen atom. Again, they will need a few minutes to prove you wrong unless you write something that was designed to reduce to Schrödinger's equation in the right limit.

As physics advances, we are interested in ever more abstract and complicated classes of processes but we are learning about an ever increasing set of natural phenomena and we are learning what their outcomes are more and more precisely. Because more experiments have been made before 2006 than those that had been completed before 1906, the possible natural laws are constrained more than they were ever constrained in the past.

If you randomly propose a new law of physics, be sure that it is much more likely that it is going to be demonstrably wrong than if you wrote the same candidate law centuries ago. Also, the physicists know more than they knew and they got better in various calculations and in various kinds of reasoning, so they will need a shorter time to disprove your theory than they needed centuries ago. On the other hand, the students must attend more classes these days before they get to the cutting edge.

In physics - I mean real physics - we always talk about meaningful and measurable quantities. Any prediction about such quantities is either correct or wrong. Predictions can also be "slightly wrong" but there is usually a way to refine them so that the issue can be settled.

Needless to say, particle physics is no different. In high-energy physics, the theories predict the spectrum of particle masses and cross sections - the probabilities of different processes such as production of new particles or elastic scattering into given angles. You can always decide whether a prediction is correct or wrong just like you can decide whether you see 5 cows or 7 cows (unless you observe new kinds of double-cows whose existence, again, either agrees or disagrees with your theory).

String theory is no different. In all of its known formalisms, it has fixed Lagrangians and quantitatively accurate and rigorous formulae just like renormalizable quantum field theories. Again, it predicts various masses and cross sections. Moreover, it has no continuous non-dynamical adjustable parameters. On the other hand, it has a large discrete set of classical solutions - possible universes. The number of them that have a chance to be compatible with the basic features of reality is probably finite. Each of them accurately predicts the values of the usual quantities used in quantum field theory - masses and couplings.

In many cases, especially those with unrealistically high supersymmetry, these quantities can be calculated analytically. In less supersymmetric cases, we can still compute some quantities but it is hard to compute others. In the vacua without spacetime supersymmetry, we're not sure that we fully understand the quantitative rules to calculate all quantities we need with an arbitrary accuracy at generic (or stabilized) values of the coupling constant. But given the obvious progress and unique results with the supersymmetric vacua, we are confident that an answer to these questions exists in the non-supersymmetric case and it will be unique just like it was in the supersymmetric cases.

Surely, it is completely clear that the question whether one of the vacua of string theory agrees with reality is an extremely sharply defined question and the answer is either Yes or No. Every high-energy theoretical physicist who was not completely decoupled from the community knows that. Everyone knows that only nutcases are ready to suggest, with a serious face, that string theory could be unfalsifiable. Surely it is falsifiable.

I predict that the word "nutcase" is the only word that the nutcases will be able to comprehend and learn from this article: they will ignore the rest, thinking that they don't need it to be upgraded from nutcases to something else.

As Barton Zwiebach wrote, the prescription to decide about the validity of string theory is straightforward: simply list all possible vacua of string theory, calculate their properties with a sufficient precision, and compare them with reality. Either one of them will match the reality or not.

The answer just can't be ambiguous just like the answer whether "232,582,657-1" is a prime integer cannot be ambiguous. And you bet it is a prime. The greatest known prime as of today. A naive critic of mathematics could say that the question whether the number is prime is not even wrong because one would have to test the potential divisors up to the square root of the number i.e. up to "216,000,000" or so. One would need "216,000,000" units of time. It is even more than the number of the flux vacua and it's not possible to check it. That's why, the critic would argue, it's not science, it's not even wrong, there are troubles with mathematics, blah blah blah. The reality is that one computer in GIMPS needed one month or so to verify that the number is indeed prime (and a faster computer rechecked it in a few days). There exist more sophisticated and faster methods to decide about the validity of a statement than the primitive critic of mathematics could imagine. The case of physics is analogous.

If it turns out that the properties of the non-supersymmetric vacua in string theory can't be consistently well-defined, string theory is wrong, too. At any rate, an answer exists. So far the theory is still alive.

This is a proof in principle. But a proof can still be difficult in practice. Indeed, if we talk about theories in which the characteristic phenomena occur at the Planck scale, it is rather difficult to test them in the most straightforward way.

If we could measure the spectrum of masses of all objects that are comparable to the Planck scale plus minus a few orders of magnitude, we could surely say a lot about the vacuum - presumably string theory vacuum - in which we live. Unfortunately, there objectively exist technical limitations that prevent us from making the tests in the most straightforward manner. But this just means that all theorists and especially experimenters are objectively facing difficult problems: it has nothing to do with the falsifiability of a theory. Moreover, as the prime integer example above suggests, there are usually much more effective ways to decide about the validity of an assertion than the most straightforward test you could invent.

In reality, it will probably be impossible to falsify string theory because string theory is probably correct and you can't ever falsify correct theories. ;-) But if string theory were wrong, there would be thousands of ways to falsify it, even in the very near future. Although string theory predicts many new phenomena whose details are not uniquely known, it also implies that many old principles are exactly valid. If string theory is correct, the superposition principle of quantum mechanics, Lorentz invariance, unitarity, crossing symmetry, equivalence principle etc. are valid to much higher accuracy than the accuracy with which they have been tested as of 2006.

If you believe that string theory is wrong, just prove any of the theories predicting all the bizarre phenomena like Lorentz symmetry breaking, breaking of unitarity, locality, rotational invariance, and so on. I think that all these things are badly motivated - but it's mostly because I know that it seems that they can't be embedded in string theory. If you don't believe string theory, you should believe that anything can occur and every new test of Lorentz invariance has a potential to falsify special relativity. Every new test has a potential to falsify the equivalence principle. And there are dozens of such examples. Without string theory, all these laws are approximate accidental laws and symmetries. I assure you that string theory will pass every new test of this type and its foes will always lose. String theory allows us to redefine what proposals about new physics are reasonable and what proposals are not, even without the exact knowledge of the vacuum.

String theory also gives us new tools (AdS/CFT correspondence) to calculate previously uncalculable properties of the quark gluon plasma at RHIC and other experiments: the experimenters are in love with holography, Joshua F. told us again. But I don't want to talk about these things because in this setup, only a portion of string theory toolkit is used. In this situation, string theory is not used as a unified theory of all interactions including four-dimensional gravity.

Instead, let me say that there are many predictions of string theory that are independent of the detailed choice of the vacuum. Some of them directly follow from the validity of the principles such as unitarity, Lorentz symmetry, and crossing symmetry at all energy scales: this validity seems to be a simple consequence of string theory.
have derived various inequalities satisfied by the electroweak interactions at the TeV scale. What is needed for you to falsify string theory is to observe that these inequalities are violated and various light states don't exist. Then all of the string theory vacua, whether or not the number 10^{500} seems large to you or not, will be falsified.

If Jacques' and his friends' paper is not one of the most thrilling things for most of their colleagues, it is because they know that such inequalities obviously can be derived and some of them are similar to those advocated by Nima Arkani-Hamed and various groups including your humble correspondent; Jacques' rules look more old-fashioned, in fact. There is certainly no reasonable particle physicist who would have doubts that general predictions like that can be derived. Once again, only nutcases can have such doubts.

One such a nutcase has been writing this kind of garbage and nothing else for more than two years, if not twenty years, hoping that a lie repeated 1000 times becomes the truth. But what happened instead is that he became much greater a nutcase than he was at the beginning. String theory is undoubtedly falsifiable and those who don't understand why are just too severely limited to join any meaningful discussion about the subject.

In Jacques' paper, a sentence "string theory would be falsified" was changed to "generic models of string theory would be falsified" when they upgraded from v3 to v4, and they generalized the title because the violation of the inequalities would falsify not only string theory but many other models sharing certain principles with string theory.

The nutcase who obviously can't understand a single formula from Jacques' paper noticed this difference using the methods of comparative literature and wrote a blog article about this sentence because he thought that such a treatment of one sentence and the title could hurt string theory. He's just such a pathetic and obnoxious mug of vitriol. The v4 formulation of the sentence is an example of a standard careful scholarly jargon but the meaning is effectively the same: if you observe a violation of inequalities that follow from the old-fashioned assumptions implied by string theory, string theorists will be shocked if not screwed. ;-)

In fact, the "alternative physicists" who have recently advocated the same kind of silliness about "unfalsifiability", attracting a huge attention of dozens of stupid journalists, must also completely misunderstand the very spirit of the elementary facts written in this article. They must misunderstand that it has become very easy to falsify a generic new theory talking about some well-established observables unless the author of the theory has been thinking very hard.

Invent some crazy theory - for example that our universe is a f*cking universe that produces mutated children inside the black holes that evolve into new universes and follow Darwin's rules of natural selection, which is why our universe must be optimized for black hole production.

If you think that this theory is far too crazy, believe me that it has been seriously proposed by a physicist. In fact, this physicist, a darling of the media, still proposes this nonsense even though at least a dozen of people have explained him why his theory is easily falsified.

Just like in the examples at the beginning, you need a few seconds or minutes to falsify such a theory. It is trivial to adjust the parameters of the Standard Model so that the black hole production will be strengthened. Virtually every parameter of the Standard Model, if changed in the right direction (one of the two directions), will calculably increase the black hole production.

Moreover, there are many other profoundly bad features of the "theory" that make it not only wrong but also ill-defined: it is hard to define what a black hole means because according to everything we know, there is no qualitative difference between black holes and heavy elementary particles. It is also unclear how to count the "children" if two black holes merge. Finally, the evolution of the children into new universes seems to lead to a loss of the information - something that we have extremely good reasons to consider to be impossible.

But even if you start with a relatively vague theory like cosmological natural selection, it is not hard to falsify it.

Today, it is, on the contrary, extremely easy to falsify random theories as long as they are just a little bit quantitative. In serious physics, it has become harder, not easier, for theories to survive. String theory remains the simplest known theory that is more complete than the conventional Quantum Field Theory and GR and that has not yet been falsified. When I was defining the crackpots, the third feature I included was their inability to falsify a conjecture by a comparison with the most elementary data or facts about the Nature. We see that many people fit this description. This is why they propose us to spend decades with theories that can be falsified within minutes. And because they are also unable to realize their own limitations, they think that if they can't falsify a theory, no one else can do it either. But they are completely wrong. Other physicists are simply much smarter than they are.

We have acquired so many accurate measurements, general rules, insights, principles, theorems, and methods in physics that we can instantly rule out whole classes of theories even if these classes look "large" to some people. It doesn't matter that they look large. The available tools are strong enough so that they can kill these classes instantly; it is enough that these classes share certain properties that imply, via one of the numerous arguments we have learned, some predictions that can be falsified or - more usually - have already been falsified. If the Lorentz symmetry or equivalence principle etc. are violated in an experiment, it will likely falsify all 10^{500} of vacua of string theory that are often included as members of the "F-theory landscape". The number 10^{500} doesn't mean that the laws of mathematics or rational reasoning break down, even though some people apparently think otherwise.

On the other hand, using purely theoretical arguments and experimental data already available to Archimedes (if not Adam and Eve), we can rule out all the discrete models of quantum gravity. The observation of the violation of Bell's inequalities has instantly falsified all local theories of hidden variables even though many people thought that this was the future of physics.

Those who still work on the hidden variable theories or discrete quantum gravity theories differ by the shape of the wooden earphones and they think that the shape is the most interesting question in physics that everyone should work on for decades or centuries. But there are smarter physicists who can simply show that this whole discrete quantum gravity industry is just wrong, narrow-minded, misled, and incompatible with the observations. And they only need a few minutes to do so. These physicists prefer to work on theories that are still alive and that lead to new fascinating discoveries that expand our knowledge as well as imagination.

Summary

Because we know more than we knew in the past, it has become much easier to falsify randomly proposed theories. Those who think that it has become harder to falsify theories only say so because they don't know what they should know if their job is physics.

And that's the memo.