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Axioms of choice

Could it be that the general interpretative framework of the standard model of quantum physics is not falsifiable as per Popper?

Christos Tombras
21 July 2020
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The headlines did not conceal the excitement of the journalists. There were 53 excess events observed in the XENON1T Dark Matter Experiment. They were unexplained and additional to the 232 anticipated by the theory. They could prove the existence of axions, hypothetical solar particles resembling photons, and also provide evidence for the existence of the elusive dark matter. They could indicate that there is a whole world, above and beyond the one described by the so-called standard model of particle physics – hence the excitement.

Axions were first hypothesised in the 70s, in an attempt to clear up some problems involving axial quantum symmetry anomalies. Their name evokes axioms – fundamental statements, or propositions, in mathematics and logic – but in reality they were named after Axion, a then famous brand of laundry detergent.

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For some philosophers of science, falsifiability is the fundamental feature of any scientific endeavour. Karl Popper considered this to be the criterion that would demarcate science from pseudo-science. His critique of psychoanalysis (and Marxism) was famous in this respect. The claims of psychoanalytic theory, he argued, cannot be properly tested because the theory is equipped with all necessary conceptual tools to turn everything to its opposite – if needed. Psychoanalysis is a belief system, he concluded, that is, non-scientific.

Addressing such criticisms, Freud countered that psychoanalytic hypotheses are tested all the time in the clinic, by competent practitioners. Still, Popper was not convinced. Clinical observations are not concrete facts, he said, they are “interpretations in the light of theories […] and for this reason they are apt to support those theories in the light of which they were interpreted.”

That is, this is all circular.

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Scientists hope now to be able to comb through the mass of collected data and weed out possible sources of error. There are three possible explanations of the unexpected 53 detections at XENON1T. It might have been a case of contamination of the experimental setting; of some yet unaccounted feature of current theories; or indeed of an indication that axions do exist. There are now three possible ways forward: to ignore the data and start anew; to adjust current theories; or to bring in a general overhaul of the standard model of particle physics. The debate has just begun.

In contrast to axions, which are hypothetical and have yet to be proven, axioms do not need a proof at all. They are true by definition. Or, better, you assert they are true. And that’s it. But axioms are not cast in stone. You can pick and choose. As soon as you have finalised your choice, this has consequences, results. Different axioms lead to different results. It’s the results that indicate whether your choice has been a successful one or not.

Axioms form the bedrock on which conceptual and theoretical structures of mathematics and logic are built. As such they are not falsifiable. They are prior to any methodology of falsifiability.

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What do data show? Do they represent facts? Do we ever have access to facts? Is it ever possible to see things as they really are? The answer might seem obvious. We only need to keep our eyes open and our minds free from biases.

But is that indeed so? What are facts if we consider them outside some framework of understanding? Take the 53 excess events. Are they facts? In what sense? Or perhaps the raw data collected by the detector. Do they represent facts? Can they say anything to anyone who does not have a competent working knowledge of the experimental design and its underlying theoretic assumptions?

Assuming Popper was correct in his response to Freud, i.e. that clinical observations cannot constitute evidence because they are interpretations in light of theories, then what can we say in the case of the experimental design that allowed the detection of 53 excess events? Are they not interpretations in light of theories? Are they not, as such, apt to support the theories in light of which they were interpreted?

It would appear that the general interpretative framework of the standard model of quantum physics is not falsifiable as per Popper. Or, perhaps, it is the case that Popper’s criterion of falsifiability needs to be a little refined.

Who knows?

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“I was reading your piece regarding conspiracy theorists”, my friend GG said the other day, “and I have a problem.”

“Yes?”

“You claim that what motivates conspiracy theorists is a ‘need to keep a check on fear and despair’. That’s fine with me. But then you add, ‘Perhaps not only them’. Not only them? Then you can only mean ‘us’. Is this not opening the doors to alternative facts and a dangerous relativism? I am not happy with that.”

Admittedly I am not happy with that either. It feels wrong and counterintuitive. But a response is not so easy. Indeed it is impossible unless we decide to look a bit more closely at the one thing that is missing from the discussion. It’s missing because it is taken as self-evident.

I am referring to truth.

We need to look at truth a bit more closely.

This piece was first published in the July Splinters column.

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