Yeah, I don’t think this paper is going to convert you. As my other comment on this thread will attest, I consider TI pretty much a failed project, so maybe I’m not the best person to defend it. Still, here’s my most charitable attempt to answer MichaelHoward’s questions on behalf of TI.
Would John Cramer’s transactional interpretation require more complexity (at the level of the fundamental laws, rather than the amount of stuff in the universe) than the many worlds interpretation?
TI has a claim to be less complex than MWI in one respect. Relativistic versions of the Schrodinger equation have both advanced (waves propagating backwards in time) and retarded (waves propagating forward in time) solutions. A relativistic version of MWI would presumably ignore the advanced solutions by fiat (or based on some “principle of causality”, which I think just amounts to fiat). Specifying this condition adds to the complexity of the theory. TI doesn’t require this specification, since the interpretation incorporates both advanced and retarded solutions. Another advantage of TI is that it does not require specification of a preferred basis.
What about MWI’s main claim to simplicity, the lack of any collapse postulate or hidden variables? The original TI involved the “selection” of one transaction out of many in accord with the Born rule, and this might be regarded as tantamount to collapse. A new version of the TI developed by Ruth Kastner (called the PTI, or possibilist transactional interpretation), defended in the linked paper, goes modal realist, and declares that all possible transactions are real, but only one is actual. I don’t know what to make of this claim. I don’t understand how “actualization” is any better than “collapse”. Simply declaring the other branches to be real doesn’t help if you still need to appeal to a mysterious selection procedure, even if the selection procedure only determines what is actual rather than what is real. Perhaps it is possible to make sense of actualization in a non-mysterious manner, separating it from collapse, but I haven’t seen evidence of this. The paper says at one point, “Such actualized transactions will furthermore naturally line up with decoherence arguments, since decoherence… is fundamentally based on the nature of absorbers available to emitted particles.” I don’t understand this claim.
Of course, Cramer and Kastner claim that MWI’s advantage in this regard is illusory, a product of disregarding the Born rule. Any attempt to account for the full formalism of quantum theory (unitary evolution + the Born rule) will have to involve some component like their actualization procedure. This ignores Deutsch and Wallace’s attempts to ground the Born rule in assumptions about rational decision-making, which I think are promising (although I know you, Eliezer, disagree).
Roughly what proportion of the physics community backs it?
A very very small proportion, I’m fairly sure.
Is it a non-differentiable (or even discontinuous) phenomenon? Does it violate CPT symmetry? Does it violate Liouville’s Theorem (has a many-to-one mapping from initial conditions to outcomes)? Can it represent a non-linear or non-unitary evolution?
All of this depends on how you interpret the “actualization” step in the PTI account. I take it that it’s not meant to be a dynamical process like objective collapse, in which case the dynamics have a claim to being continuous, time-reversible, unitary, etc. I should note that thinking of a retro-causal interpretation in terms of our usual dynamical systems framework (talking about the “evolution of the quantum state”, for instance), can be misleading. These theories explicitly reject the idea that explanatory priority implies temporal priority.
Could it propagate an influence faster than light?
Well, depends on what you mean. Influence transmission is restricted within light cones, but since this transmission can be either backwards or forwards in time, you can get phenomena which, from a temporally chauvinistic point of view, appear to involve FTL transmission.
Yeah, I don’t think this paper is going to convert you. As my other comment on this thread will attest, I consider TI pretty much a failed project, so maybe I’m not the best person to defend it. Still, here’s my most charitable attempt to answer MichaelHoward’s questions on behalf of TI.
TI has a claim to be less complex than MWI in one respect. Relativistic versions of the Schrodinger equation have both advanced (waves propagating backwards in time) and retarded (waves propagating forward in time) solutions. A relativistic version of MWI would presumably ignore the advanced solutions by fiat (or based on some “principle of causality”, which I think just amounts to fiat). Specifying this condition adds to the complexity of the theory. TI doesn’t require this specification, since the interpretation incorporates both advanced and retarded solutions. Another advantage of TI is that it does not require specification of a preferred basis.
What about MWI’s main claim to simplicity, the lack of any collapse postulate or hidden variables? The original TI involved the “selection” of one transaction out of many in accord with the Born rule, and this might be regarded as tantamount to collapse. A new version of the TI developed by Ruth Kastner (called the PTI, or possibilist transactional interpretation), defended in the linked paper, goes modal realist, and declares that all possible transactions are real, but only one is actual. I don’t know what to make of this claim. I don’t understand how “actualization” is any better than “collapse”. Simply declaring the other branches to be real doesn’t help if you still need to appeal to a mysterious selection procedure, even if the selection procedure only determines what is actual rather than what is real. Perhaps it is possible to make sense of actualization in a non-mysterious manner, separating it from collapse, but I haven’t seen evidence of this. The paper says at one point, “Such actualized transactions will furthermore naturally line up with decoherence arguments, since decoherence… is fundamentally based on the nature of absorbers available to emitted particles.” I don’t understand this claim.
Of course, Cramer and Kastner claim that MWI’s advantage in this regard is illusory, a product of disregarding the Born rule. Any attempt to account for the full formalism of quantum theory (unitary evolution + the Born rule) will have to involve some component like their actualization procedure. This ignores Deutsch and Wallace’s attempts to ground the Born rule in assumptions about rational decision-making, which I think are promising (although I know you, Eliezer, disagree).
A very very small proportion, I’m fairly sure.
All of this depends on how you interpret the “actualization” step in the PTI account. I take it that it’s not meant to be a dynamical process like objective collapse, in which case the dynamics have a claim to being continuous, time-reversible, unitary, etc. I should note that thinking of a retro-causal interpretation in terms of our usual dynamical systems framework (talking about the “evolution of the quantum state”, for instance), can be misleading. These theories explicitly reject the idea that explanatory priority implies temporal priority.
Well, depends on what you mean. Influence transmission is restricted within light cones, but since this transmission can be either backwards or forwards in time, you can get phenomena which, from a temporally chauvinistic point of view, appear to involve FTL transmission.