Evidence and Theory in Physics. Tim Maudlin, NYU Evidence in the Natural Sciences, May 30, 2014

Transcription

1 Evidence and Theory in Physics Tim Maudlin, NYU Evidence in the Natural Sciences, May 30, 2014

2 Two Features of Physics Physics displays two interesting features: 1) Programmatically, it aspires to be completely universal. 2) Predictively, it has produced the most accurate and highly tested predictions in human history. It also applies the most stringent standards for the statistical significance of evidence.

3 Predictive Power The best current theoretical calculation of the anomalous magnetic moment of the electron is (± 86). The best current theoretical value of the anomalous magnetic moment of the electron is (± 28).

4 Standard of Evidence In order for the evidence of the Higgs boson to count as strong enough to be considered a discovery, it had to be statistically significant at the 5σ level. Roughly, that means that the probability of getting the result just by chance is one out of 3.5 million.

5 What Does This Mean? Clearly, this means that physics is getting something right. But what, exactly? At the simplest level, it means that at least certain parts of physics are, in fact, highly predictively accurate and we can expect the predictions to continue to be highly reliable. In the case of the Higgs, we can confidently expect that in future experiments, effects of the particle will continue to appear.

6 More Ambitiously It would be nice to be able to say something stronger that this. In particular, it would be nice to be able to say that this predictive accuracy and high level of evidential standard means that the basic picture of the world given to us by contemporary physics is true or approximately true or at least on the right track.

7 But. Richard Feynman once wrote: [W]e always have had (secret,secret, close the doors!) we always have had a great deal of difficulty in understanding the world view that quantum mechanics represents. At least I do, because I m an old enough man that I haven t got to the point that this stuff is obvious to me. Okay, I still get nervous with it I cannot define the real problem, therefore I suspect there s no real problem, but I m not sure there s no real problem. (Simulating Physics with Computers,1982)

8 What is the World View of Quantum Mechanics? Before we can even ask whether the predictive success of quantum theory is good grounds to think it is (approximately) true, we need to have some account of what quantum theory claims about the physical world. At present, there is no agreement at all about this. Further, there are still fundamental problems understanding how the theory can make any predictions at all (in a principled way).

9 The Scope of Physics Physics was once characterized as the theory of matter in motion. As such, everything that can be correctly described as matter in motion in principle should be subject to physical analysis. This includes all of the systems studied by biology, chemistry, psychology, economics, meteorology, astrophysics, cosmology, geology, etc.

10 The Measurement Problem Since all experiments involve matter in motion, in order for physics to be internally coherent it must not only produce predictions for how experiments will come out but also be capable of modeling the experiments themselves as physical processes. One way of trying to do this leads to the Schrödinger cat problem: if there is no collapse of the wavefunction and the wavefunction is a complete physical description of a system, then the cat does not end up either alive or dead.

11 A Deeper Problem If we are to describe a physical situation as matter in motion, then the physics must specify where there is matter. In quantum theory, though, there is no agreed account of exactly what sort of matter there is, according to the theory, located in space and time.

12 For Example Here are some pictures of electron orbitals :

13 Possibilities The electron is, at all times, smeared out in this shape. The electron is orbiting the nucleus. This is like a time-lapse photograph. The electron pops in and out of existence. This is like a timelapse photograph. The electron is nowhere at all until a position measurement is made. This shows where it might show up. Each electron is at rest. This shows the positions of many, many electrons, superimposed.

14 Possibility 4 is Incoherent If electrons aren t anywhere until measured, then the electrons in the measuring apparatus aren t anywhere until measured by something else. This will not end well.

15 The Measurement Problem Quantum theory provides extremely accurate techniques for predicting the outcomes of measurements of observable quantities. These techniques require characterizing an experiment as a measurement of the observable. But the programmatic universality of physics requires that one should also be able to simply treat the experiment as a physical interaction, without needing to characterize it as a measurement of anything.

16 Ontology and Beables The notion of an observable is tied to the notion of a measurement. But in order to have measurements, there must be something that is just there, independently of its being measured. In philosophical terminology, the things that are postulated to exist according to a theory constitute the ontology of the theory. John Bell, in discussing this problem, invented a new term for this: the beables of a theory.

17 Bell on Beables In particular we will exclude the notion of observable in favor of that of beable. The beables of the theory are those elements which might correspond to elements of reality, to things which exist. Their existence does not depend on observation. Indeed observation and observers must be made out of beables. (Beables for Quantum Field Theory)

18 More Bell on Beables The concept of observable lends itself to very precise mathematics when identified with selfadjoint operator. But physically, it is a rather wooly concept. It is not easy to identify precisely which physical processes are to be given the status observations and which are to be relegated to the limbo between one observation and another.

19 Bell con t. So it could be hoped that some increase in precision might be possible by concentration on the beables, which can be described in classical terms, because they are there. The beables must include the setting of switches and knobs on experimental equipment, the currents in coils, and the readings of instruments. Observables must be made, somehow, out of beables. The theory of local beables should contain, and give precise physical meaning to, the algebra of local observables. (The Theory of Local Beables)

20 Local Beables Among the beables of a theory, Bell particularly emphasized the local beables, that is, local in space and time. It is only local beables that can be attributed motions through space-time by the theory. A theory with no local beables cannot be a theory of matter in motion, and hence not physics as we understand it. But there is no accepted account of what the local beables in quantum theory are! That is why the world view the quantum mechanics represents is so obscure.

21 Local Beables and the Measurement Problem Suppose a physical theory postulates 1) That there are some local beables. 2) That everyday matter (protons, neutrons and electrons) are composed of these beables. 3) A dynamics (deterministic or stochastic) for the these beables. 4) Whatever else is needed to complete the dynamics (which may include non-local beables).

22 Results Such a theory, in principle, should make predictions (deterministic or probabilistic) about how everyday matter will behave given a complete physical specification of a situation. Therefore, such a theory will make predictions about what the empirical data produced by an experiment will be, if the experiment is described in sufficient physical detail. It is irrelevant whether the experiment is described as the measurement of any observable.

23 Bell again Not all observables can be given beable status, for they do not all have simultaneous eigenvalues, i.e. do not all commute. It is important to realize therefore that most of these observables are entirely redundant. What is essential is to be able to define the positions of things, including the positions of pointers or (the modern equivalent) of ink on computer output. (Beables for Quantum Field Theory)

24 How has Physics Managed Without Local Beables? The original approach to understanding quantum theory was pioneered by Bohr, in the so-called Copenhagen interpretation. Bohr described his approach this way in 1949:

25 Bohr on Evidence For this purpose, it is decisive to recognize that, however far the phenomena transcend the scope of classical physical explanation, the account of all evidence must be expressed in classical terms. The argument is simply that by the word experiment we refer to a situation where we can tell others what we have done and what we have learned, and that, therefore, the account of the experimental arrangement and of the results of the observations must be expressed in unambiguous language with suitable application of the terminology of classical physics.

26 Copenhagen Bohr tried to insist on two points: 1) The evidence for a theory must be expressed in classical terms, by which he just means in terms of the positions and motions of macroscopic objects in space and time. 2) Quantum systems cannot be described in classical terms: electrons and protons and neutrons do not have any location or follow any definite trajectory through space-time.

27 Ergo If one tries to hold both of Bohr s principles at the same time, the only conclusion is that macroscopic objects cannot be described by quantum theory, or even that macroscopic objects cannot be composed of quantum objects, and hence macroscopic objects are not just collections of electrons, protons and neutrons. Bell called this Bohr s dual kinematics.

28 Bell on Copenhagen The kinematics of the world, in this orthodox picture, is given by a wavefunction (maybe more than one?) for the quantum part, and classical variables variables which have values for the classical part: (Ψ(t,q ),X(t) ). The Xs are somehow macroscopic. This is not spelled out very explicitly. The dynamics is not very precisely formulated either. It includes a Schrödinger equation for the quantum part, and some sort of classical dynamics for the classical part, and collapse recipes for their interaction. (Against Measurement )

29 Note The evidence for the theory is determined entirely by the behavior of the classical part: it is only through this that we have any reason to accept the quantum theory. But on Bohr s picture, the classical part is not given by a quantum-mechanical description at all. The observable motion of matter is not derived from the quantum state.

30 Bell s Solution It seems to me that the only hope of precision with the dual (Ψ,x) kinematics is to omit completely the shifty split [between classical and quantum], and let both Ψ and x refer to the world as a whole. Then the xs must not be confined to some vague macroscopic scale, but must extend to all scales. In the picture of de Broglie and Bohm, every particle is attributed a position x(t). Then instrument pointers assemblies of particles have positions, and experiments have results.

31 Bell con t. The dynamics is given by the world Schrödinger equation plus precise guiding equations prescribing how the x(t)s move under the influence of Ψ. Particles are not attributed angular momenta, energies, etc., but only positions as functions of time. Peculiar measurement results for angular momenta, energies, and so on, emerge as pointer positions in appropriate experimental setups.

32 Recapitulation Ultimately, the evidence for a physical theory is the motion the location and shape through time of macroscopic objects. Due to the programmatic universality of physics, predictions for those motions should be derivable from the physical description of an experiment. In its present state, this cannot be done in quantum theory.

33 Solution Bell s solution is to postulate the existence of some local beables at microscopic scale, beables that are just there independently of being observed or measured. The locations and motions of macroscopic objects is then determined by the locations and motions of their microscopic parts.

34 Possible Local Beables 1) Particles (that always have definition locations) 2) Matter density (that has a definite value at each space-time point) 3) Strings (with definite trajectories) 4) Flashes (point events)

35 Reprise Here are some pictures of electron orbitals :