A Central Point in ‘Physics & Philosophy’

On Thursday, a friend and I watched the first half of Copenhagen, a film adaptation of Michael Frayn’s play of the same name about the mysterious meeting between Werner Heisenberg and Neils Bohr in 1941 in Copenhagen. It may have been the fact that he was played by Daniel Craig, or that every time I try to focus on the mind-body problem¹ I invariably wind up slamming right into quantum mechanics, but the first thing I did yesterday was rush to the library to get Heisenberg’s Physics & Philosophy. I finished it last night. I don’t agree with all of it—and certainly don’t understand even more of it—but I was blown away by the clarity of thought. Ultimately on Heisenberg’s interpretation, physics is neither epistemologically nor ontologically neutral, and that is something worth unpacking.

But before we get to that, it’s important to emphasize that this is a discussion of Heisenberg’s book, his contributions to quantum mechanics, and his interpretation. Not Bohr’s, or Bohm’s, or Schrödinger’s, or anyone else’s explicitly. I also couldn’t possibly address every point in the book without rewriting it. (Hence: A Central point in Physics & Philosophy. This review will look at the tension between determinism and indeterminism specifically.)

Contemporary physics demands that we revise our conception of the universe and our relation to it. At the heart of this revised view is Heisenberg’s uncertainty principle, and nowhere in physics are the implications for our conceptions of determinism and free will more severely challenged than in this principle. In this revised view, we are forced to ask “what do experimentally verified theories of contemporary physics affirm?” And, more importantly, how are we to think about ourselves in relation to the universe in light of what they affirm?

Heisenberg draws an implicit distinction between several different meanings of the terms causality and determinism. By the former we generally mean the relation between different states of the same object (or the same system of objects) at different times t₁ and t₂. Importantly, the following must be kept in mind:

1. The description of the state of any physical system at any specific time t
2. Some time equation—namely, Schrödinger’s equation—that relates the state of the physical system at time t₁ to its different state at any other time t₂

In other words, a description of the state of a physical system plus an equation that describes how that system will evolve gives us the causal relation between different states of that physical system at different times. But what is the nature of this relation? There are three possibilities.

The first, which is the weakest possible relation, is that the state of the physical system at t₂ is related to the state of the physical system at t₁ only by temporal succession—in other words, the only relation they have is that one comes after the other in time. There is no probability—not even a minuscule probability—that t₂ will follow outside of the temporal order. The relation isn’t necessary.

The second and third possibilities are necessary relations. We come to know what the necessary relation is only by knowing the future state (ie. time t₂). How do we come to know the future state? We can either wait around for it to arrive, or we can deduce the future state from what we have seen of final states of similar systems before.

When this is the case, the causal relation between the states of a physical system at t₁ and t₂ is teleological, meaning that changes in the system with time are determined by the final state. Teleological causation is intuitively “backwards causation” in that future states (ie. the state of the physical system at time t₂) explain the present state (ie. the state of the physical system at time t₁). This is the second possibility, and is the view affirmed by Aristotelian physics.

The third possibility is that the causal relation between the states of a physical system at t₁ and t₂ is given by the initial state at t₁. On this view, given knowledge of the initial state of the system, assuming isolation, any and all future states can be deduced. The “knowledge of the initial state” includes the two things we’re keeping in mind:

1. The description of the state of the physical system
2. A time equation that relates the state of the physical system at time t₁ to its different state at any other time t₂

Given the state at t₁, all one has to do to get the future state at anytime  t₂ is solve the equation. This relation exemplifies mechanical causation; the evolution of the state of a physical system with time is deterministic.

Now we’re faced with the question of what factors or variables we need to define the state of the physical system, and what features these variables might have. There are two possibilities here:

1. Probability is a variable used to define the state of the system
2. Probability is not a variable used to define the state of the system

Heisenberg calls the former of these two weak mechanical causation and the latter strong mechanical causation. By the latter we get a causal relation that is both mechanical and deterministic, while by the former we get a causal relation that is mechanical but not deterministic. At this point the question is whether or not probability is a relevant factor in defining the state of a physical system.

Classical physics wants to say that probability is not a relevant factor in defining the state of a physical system, thus committing to mechanical and deterministic causality. To put it hard and fast, determinism is identical with strong mechanical causation. Causality in classical physics is also identical with strong mechanical causation, and thus causality and determinism are one and the same thing in classical physics—mechanical and deterministic.

Contemporary physics, on the other hand, wants to say that probability is a relevant factor in defining the state of a physical system. In other words, causality in contemporary physics is identical with weak mechanical causation, committing contemporary physics to mechanical but not deterministic causality.

So which one is it? To resolve the issue, the question we must ask is this: are the deductive experimental consequences of each theory confirmed by experiment or not? This is the question repeated over and over again in science, and a true theory is any theory that, when it’s spelled out, leads you to answer “yes” to this question.

At first blush, this doesn’t clash with anything in classical physics; there, too, theories must be confirmed by experiment. However, in contemporary physics, no theory is just a description of experimental facts or something deducible from such a description as is the case in classical physics. In breaking with Newtonian physics, we realized that no object of scientific knowledge can be known directly by observation. Thus, objects of scientific knowledge can only ever be known by speculative means, by deducing the conclusions of various theories about the objects from their axioms and postulates. The theoretic assumptions will correspond to experimental consequences, and once they have been deduced speculatively, we can see if they match up with experiment, thereby affirming or denying the theory.

Heisenberg argues along these lines to show that probability is a relevant factor in defining the state of a physical system, that the state of a physical is system is ultimately not well-defined. While the state of a physical system evolves deterministically with time when it’s not being measured, as soon as it is measured probability becomes a relevant factor. One striking aspect of the difference between classical and contemporary physics is that whereas classical mechanics presupposes that exact simultaneous values can be assigned to all physical quantities, quantum mechanics denies this possibility, the prime example being the position and momentum of a particle. According to Heisenberg’s uncertainty principle, the more precisely the position (momentum) of a particle is given, the less precisely can one say what its momentum (position) is.

1. We cannot know the object of scientific knowledge by direct observation, but only by speculative means of axiomatic theoretic construction/postulation.
   • There is no a priori or empirical motivation to define an object of scientific knowledge in any particular way. The only criterion is: which set of theoretic assumptions, when pursued to their deduced experimental consequences, is confirmed by experiment?
2. The deduced experimental consequences of the well-defined theoretic conception of classical mechanics, in which the definition of the state of a physical system is given only in terms of well-defined position and momentum, are not confirmed by experiment.
   • The well-defined theoretic conception of classical mechanics is false.
3. The deduced experimental consequences of the probabilistic theoretic conception of quantum mechanics, in which the definition of the state of a physical system is given in terms of probabilistic position and momentum, is confirmed by experiment.
   • The probabilistic theoretic conception of quantum mechanics is true.

Probability, in other words, is a relevant factor in defining the state of a physical system. Causality is mechanical but not deterministic. “The courage which it took to make this step away from the unqualified determinism of classical modern physics may be appreciated if one recalls that even such a daring, creative spirit as Einstein balked.”²

There is so much more to be said on the wealth of insight in Physics & Philosophy, on a range of topics that extends beyond the topic of (in)determinism. But even on this single topic there is a great deal more to be said.

Thank you Ben for showing me Copenhagen, and for your comments. As ever, you’re a spectacular sounding board. Looking forward to finishing the movie, and hashing out relativity!