*Volume 4, Issue 1, pages 142-146*

Louis Marchildon [Show Biography]

Louis Marchildon is Professor of Physics (Emeritus) at Université du Québec à Trois-Rivières (UQTR). He obtained his B.Sc. and M.Sc. from UQTR, and his Ph.D. from Yale University in 1978. After postdoctoral work at Institut des hautes études scientifiques (France), he returned to UQTR where, in addition to research in relativity, he collaborated with a group investigating dielectric properties of materials. His book Quantum Mechanics: From Basic Principles to Numerical Methods and Applications was published by Springer in 2002. He served as President of the Canadian Association of Physicists in 2007-2008. He has now been working on quantum foundations for more than 15 years, and is also interested in science popularization.

Kastner (this issue) and Kastner and Cramer (arXiv:1711.04501) argue that the Relativistic Transactional Interpretation (RTI) of quantum mechanics provides a clear definition of absorbers and a solution to the measurement problem. I briefly examine how RTI stands with respect to unitarity in quantum mechanics. I then argue that a specific proposal to locate the origin of nonunitarity is flawed, at least in its present form.

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Prof. Marchildon's objections are based on numerous misunderstandings, which I've tried to correct in emails (apparently unsuccessfully). I will try again here.

First, he is still looking for empirical predictions from RTI that differ from standard quantum theory. But as I've repeatedly noted in an email exchange with him, RTI is empirically equivalent to standard QED (up to the non-unitary transition); **this is a theorem**, as noted in Kastner/Cramer 2017 (https://arxiv.org/abs/1711.04501).

The only sense in which RTI differs from standard QM/QED is in predicting collapse (i.e. predicting that we will get definite outcomes, which we DO in fact get). In contrast, the unitary-only theory fails to predict what we see; i.e., definite outcomes. Thus, to the extent that it differs from standard QM/QED (i,e only in predicting the measurement transition), RTI is empirically corroborated; while the unitary-only theory is not.

Now for the next problem: Prof. Marchildon states that "he charge is not associated with the amplitude of a physical process". But this assertion is exactly contradicted by Feynman, the founder of QED, who correctly noted that the charge is the amplitude for an electron (or positron) to emit a real photon. The fact that each Feynman diagram represents a term in a sum in no way refutes this interpretation of the coupling amplitude. Such sums express situations in which no real photon was in fact emitted (usually because the photons are off-shell and/or their emission would violate the conservation laws). But the amplitude still functions as Feynman stated.

Prof. Marchildon's remaining objections are also off-target. Getting specific behavior for the mesoscopic realm (including Buckeyballs) obviously requires detailed calculations based on the detailed structure of whatever molecules are being used, and those calculations will be done with standard QM (with which RTI is **empirically equivalent**). A molecule that for example is subject to excitation by extraneous photons will be a source of loss of unitarity (leading to 'which-way information') even according to standard QM. It's just that standard QM won't be able to explain why.

Regarding hypothetical coupling constants that don't exist: the idea that one could imagine a large electromagnetic coupling constant that does not in fact exist in our world, and that this should be a refutation of a physical theory about our world, leads to absurdities. I can imagine a world in which real photons have large finite rest mass, thus 'refuting' the theory of relativity as it applies to our world, since then photons will fail to travel on null cones. Does this mean that relativity is wrong?

In any case, as is explicitly shown in Kastner/Cramer 2017 (https://arxiv.org/abs/1711.04501) , the basic coupling amplitude between fields is not the only arbiter of the non-unitary transition. Marchildon has overlooked transition amplitudes, which contribute to the probability that a measurement-type interaction will take place. This issue is explicitly discussed in the above paper, in the form of decay rates, which depend on both the coupling constant and specific transitions between atomic states. Thus, transition probabilities are crucial aspects of the (time-dependent) probability of a measurement transition, and contribute factors that greatly decrease the basic coupling probability of 1/137.

The same observation applies to the strong force coupling, in which the probability of non-unitarity is always greatly decreased by the relevant transition probabilities. Finally, the suggestion that the strong coupling constant might exceed unity in no way refutes the interpretation of RTI, since that only occurs for extreme separation between quarks, and could be seen as expressing a critical transition zone, beyond the limit of quark confinement, in which enormous energies have to be injected. In this extreme zone, you have to put in so much energy that you create new quarks, which corresponds very nicely to exceeding what would be a coupling of unity for a single quark.

In conclusion, I can find no substantive objections presented in Marchildon's discussion. I hope I've corrected the misunderstandings he expresses here.

Follow-up regarding the issue of a physically meaningful probability: the essential point is that the full physical probability of a non-unitary measurement transition is always given by the square of the [coupling constant times the transition amplitude] for the relevant transition. And this is always time-dependent (i.e. a decay rate applying to the emitting atom, taking into account the specific absorbing atoms present). This has all been shown explicitly and quantitatively in Kastner/Cramer 2017 referenced above (eqs (10) and (11), https://arxiv.org/pdf/1711.04501.pdf). Thus, absorption is indeed clearly and quantitatively defined in RTI--it's right there in the above equations--contrary to Marchildon's ongoing claims. Marchildon's focus only on part of the account (i.e. just the factor of the square of the coupling constant) has apparently led to confusion. Perhaps my discussion of the coupling constant separately, in heuristic terms, might have contributed to this confusion. But the quantitative and unambiguous account of absorption at the relativistic level is indeed there in eqs (10, 11), for anyone who wants to see it.