- “I'm not aware of too many things
I know what I know, if you know what I mean”
~ Edie Brickell
Mermin comments on the “bad habit of physicists to take their most successful abstractions to be real properties of our world.” He starts with commenting on the reality of the quantum state:
[T]he recognition that quantum states are calculational devices and not real properties of a system forces one to formulate the sources of that discomfort in more nuanced, less sensational terms. Taking that view of quantum states can diminish the motivation for theoretical or experimental searches for a “mechanism” underlying “spooky actions at a distance” or the “collapse of the wavefunction”—searches that make life harder than it needs to be.He then goes on to distinguish between the real and the abstract on the example of quantum field theory
I hope you will agree that you are not a continuous field of operators on an infinite-dimensional Hilbert space. Nor, for that matter, is the page you are reading or the chair you are sitting in. Quantum fields are useful mathematical tools. They enable us to calculate things.and the spacetime continuum
[S]pacetime is an abstract four-dimensional mathematical continuum of points that approximately represent phenomena whose spatial and temporal extension we find it useful or necessary to ignore. The device of spacetime has been so powerful that we often reify that abstract bookkeeping structure, saying that we inhabit a world that is such a four- (or, for some of us, ten-) dimensional continuum.He warns of the consequences of mistaking abstractions for reality
So when I hear that spacetime becomes a foam at the Planck scale, I don’t reach for my gun. (I haven’t any.) But I do wonder what that foam has to do with the macroscopic events that spacetime was constructed to represent and the macroscopic means we use to locate events.(Referring to Stephen Hawking's remark “When I hear of Schrödinger's cat I reach for my gun.”) Mermin concludes with
Quantum mechanics has brought home to us the necessity of separating that irreducibly real experience from the remarkable, beautiful, and highly abstract superstructure we have found to tie it all together.I completely agree with Mermin. One shouldn't mistake mathematical tools for reality, and mixing up both leads to confusions. Our task as physicists is to explain observations and make predictions for experiments, not to unravel the fundamental nature of reality (wink, wink). However, one should not throw out the baby with the bath water. We have a clear goal, but no map telling us how to get there. And while some might find the philosophy of science a waste of time, and others might say taking abstractions too seriously only creates artificial problems, these considerations could contain the clue, or the inspiration, necessary for progress.
Thus, while I personally am not too enchanted by taking maths to be reality, I think one should not simply dismiss these studies on the basis of gut-feeling. I was therefore put off, not by the actual opinion Mermin expressed, but by it being uninsightful, and - in its polemic way - potentially counterproductive by encouraging shallow argumentations.
So I wrote the following letter:
“I hope you will agree,” David Mermin writes, “that you are not a continuous field of operators on an infinite-dimensional Hilbert space. Nor, for that matter, is the page you are reading or the chair you are sitting in.” His comment is a nice example of the logical fallacy known as “appeal to belief”: Most people believe X is true, so X is true. That many people believe they are not operators in Hilbert spaces, believe they do have free will, or do or don’t believe in global warming makes no difference as to whether a statement is true or false. I have no basis on which to decide what I “really” am. And though I personally think any such argument is a waste of time because it can never be decided anyway, and though I am sympathetic to the opinion Mermin expresses, his article dismisses the relevance of both quantum foundations and the philosophy of science out of hand in a rather polemic and not very insightful way.Sabine Hossenfelder
Waterloo, Ontario, Canada
To which Mermin replies
Sabine Hossenfelder takes my rhetorical flourish as an attempt to argue, fallaciously, for the truth of that proposition. That was not my intent any more than I intended, by calling attention to the agreement among most of us that the ether is not real, to establish thereby its unreality. Although Hossenfelder takes my column as a shallow, polemical dismissal of both philosophy of science and quantum foundations, I had viewed it as an amateurish attempt to contribute to both disciplines.It leaves me to wonder though why Physics Today prints such amateurish attempts. It's like opening a journal on medicine and reading a column proclaiming talking is a bad habit since, I hope you will agree, the human body is not made of words. And then find it explained as being an amateurish contribution to psychology.
In any case, I will now go act on some wave-functions.
“Philosophy is the talk on a cereal box
Religion is the smile on a dog
I'm not aware of too many things
I know what I know, if you know what I mean
Choke me in the shallow waters
Before I get too deep
What I am is what I am
Are you what you are or what?
~Edie Brickel, What I am