Energy conservation and the real foundations of physics, for the bright philosopher

An Indian mystic recently asked: "Do you folks still believe that energy is conserved absolutely? Doesn't the modern Feynmann path version of quantum  mechanics show that there is some probability of energy NOT being conserved, opening the door to MANY possibilities?"

My reply: 

In the 1970s, Feynmann proposed a new formulation of quantum Field theory (QFT), different from the CANONICAL QFT which won the Nobel prize for him, for Schwinger and Tomonaga.. for work in the 1950s. The new formulation was called "Feynamann path." It is described clearly in Weinberg's authoritative text on Quantum Field Theory.which gives equal time to Canonical QFT and Feynmann path.

Originally, Feynmann felt that all of physics could be represented by computing the probability amplitudes of POSSIBLE graphs of particles (their creations and annihilations) over space-time. This did not work. My own teacher in this field, Julian Schwinger, pursued a DIFFERENT approach, the "functional integral approach", which calculated probability amplitudes for possible states of continuous FIELDS over space time. We saw the story, evident in Weinberg's book, as "Schwinger won." More precisely, Feynmann REFORMULATED Feynmann path as a system to calculate probability amplitudes for states of FIELDS over space-times. In the book, you will see an integral over space time, up in an exponent, of iS(fields(xμ,t)). No more point particles.

And so, no need to ask whether particles conserve their energy from one moment to the next. They are not particles anyway. 

But one may still ask whether the probability is nonzero for a path which starts with one level of energy and ends with another. This is a rather technical issue. 

I would prefer the Everett/Wheeler/Deutsch version of QFT, which is just as mainstream and credible now as either the canonical or (modernized) feynmann path version. Many philosophies of quantum mechanics are FAR LESS grounded in empirical reality (in experience!) than the two in Weinberg's book, but I would claim that the Everett/Wheeler/Deutsch version is MORE grounded in experiment. Why? For a simple reason: the Deutsch version is the main foundation of modern Quantum Information Science and Technology (QuiST), which has probed what QFT as such REALLY tells us with high precision, more than others. Every time you hear of people mumbling stuff about "qubits", you should give credit to Deutsch's seminal papers proving theorems about the Universal Quantum Turing machine. As I recall, the Fermi prize honoring the discovery of QuIST elaborated on three people -- Deutsch, the real progenitor, Bennett (applying such ideas to communications) and Shor who developed a specific algorithm for use in a Deutsch machine. 

The Deutsch version says that the entire dynamics of the cosmos (multiverse) is governed exactly by the modern QFT "Schrodinger equation", dΨ/dt = iHΨ, where  Ψ (space,t) at any time is a continuous wave function describing the state of the multiverse at any time t, and H is the "Hamiltonian operator," the same operator H used in the old canonical version of QFT. H is also called "the energy operator." it is conserved exactly and absolutely, in any multiverse governed by this Schrodinger equation. 

Of course, this is not the final answer to everything. There will always be edges of uncertainty and new questions. 

The two most obvious cavdeats are:

 (1) Could energy conservation be violated AT THE MOMENT of observation? For example, Stapp refers to Von Neumann's discussion of "process one" and "process two" . One of these Stapp associates with the modern quantum Schrodinger equation, but the other he associates with a kind of deus ex machina Copenhagen measurement operator. Everett's seminal PhD thesis, formulating this multiverse view of reality, argued that quantum measurement is the EMERGENT OUTCOME of the Schrodinger equation, operating statistically on macroscopic measurement objects and observers totally governed by that Schrodinger equation underneath. 

In my 2008 paper in IJTP (where Feynmann published many of his breakthrough papers), I explained why the old Copenhagen theory of measurement could NOT be explained that way, and is not in fact consistent with Everett's idea. (https://link.springer.com/content/pdf/10.1007/s10773-008-9719-9.pdf is not behind a pay wall.) 

(This was a wee bit more rigorous than what some call "informal proof," but this was a physics journal, not a mathematics journal. Maybe I should have also published a more formal theorem/proof somewhere, but my time was unbelievably oversubscribed in those days.) I also spelled out the rules for a different way of modeling macroscopic measurement devices which IS consistent with the Schrodinger equations, and is consistent with all experiments trying to test whether the old rules and new rules are right. (But we need more experiments at high precision to nail this down.)

(2)  David Deutsch himself, being an honest creative thinker, has not restricted himself to just ONE POSSIBLE theory of how the cosmos works. In my own paper for the Stapp Festschrifft (one of three linked to at www.werbos.com/religions.htm), I express roughly equal support for THREE types of theory for how the Cosmos works -- Einsteinian realism, Fock space realism (for which Everett/Wheeler/Deutsch without observers is a subset), and "cosmic Mind Idealism," the idea that the cosmos in the end is really more like a great mind than a great machine. Deutsch too has explored such ideas, as Penrose has at times said he was trying to understand. (I first met him at a neural network workshop organized by Pribram, which he visited in hopes of learning more about that kind of mathematics. But he has been distracted by other things since then.) 

In physics, as in so many other areas, a deeply intelligent strategy for the way ahead would entail MANY steps, and not assume that the next big step we need should be seen as the ultimate answer to everything. Nor should we be such rigid cowards that we take no big steps at all. In my view, the most important next big step would be WITHIN the Everett/Wheeler/Deutsch paradigm, using experiments in QuIST, to show that Everett was RIGHT in his PhD thesis, 

that a CORRECTED version of the observation models used in quantum optics, CONSISTENT with Everett's theory, fits experiment better than the old ones.

Strictly speaking, a new solid experiment was reported this week (that I saw), which does appear to demonstrate that 

the changes I asked for in my IJTP paper DO disprove the old Copenhagen model: https://www.facebook.com/paul.werbos/posts/3221743347856060

Ironically, it was not in quantum optics but in EWT, the realm of electroweak theory, which is the modern EXTENSION 

of the Hamiltonian/Lagrangian used in quantum optics!!! (Weinberg's book is authoritative, in part because he got his own Nobel prize for EWT.) But lots of new work in quantum optics is still essential to solidifying this big step forwards. 

I have ideas about what is true beyond that, but if we cannot take a baby step successfully, it is silly to debate more difficult issues. Certainly a valid model of dark matter and energy, and what we need to understand PSI, is many steps ahead -- visible as a mountain may be visible in the distance. For now, they are still parallel threads, if in fact we humans DO make progress and not just kill off our entire species.

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Indian mystic asked a further question about this:

Not sure if it makes any sense to talk about "state of the entire cosmos" and "wave function of the multiverse". I think science should stick to whats actually measurable.

Probably someone said that to Maxwell, when he modelled electromagnetism as the behavior or two or four basic vector fields, E(x,t) and H(x,t) over all space and time with only four differential equations, intended to describe everything in that realm. Can it make sense to formulate a theory of what happens at every point in the whole universe? How COULD that possibly make sense? There are many versions of machine learning in which that would NOT make sense, and their designs could never learn something like this. (I sometimes think of such folks as the DC policy Ai geniuses.) 

But it turns out that there is a simple symmetry principle, relativity, which VASTLY amplifies the information content of this theory, such that Maxwell's Laws actually are very powerful in making predictions of LOTS of testable phenomena. The ratio of successful predictions over number of parameters or terms in the model (including the symmetry principle as part of the model, basically just one more equation in the modern version) is ENORMOUS. 

The same goes for the Everett/Wheeler/Deutsch version of QUANTUM electrodynamics (QED), the modern generalization of Maxwell's Laws. (Or premodern, if you count EWT as the modern one. Here is an analogy: we usually still use Newton's Laws for predicting the effect of gravity on earth or even most solar system space work; it is rare that we need to pat for the extra precision we get form going to general relativity, in our local neighborhood. In the same way, QED is the foundation of what we do (almost always) in modern electronics, photonics and even QuIST and understanding the mundane brain. BUT: QED still needs some upgrades, in my view.) 

 

And when we talk of theoretical models which deal with actual measurements, we do have energy-time uncertainty relation, quantum tunnelling, and also virtual particles. 

We need enough precision to make actual predictions.  The modern Schrodinger equation, WITH the modern Hamiltonian operator H (spelled out in a lot of papers, including ones I link to at www.werbos.,com/religions.htm), is not really enough, because we ALSO need models of how the observation objects (like counters and polarizers) INTERACT with that universal wave function. We DO have models of that, which work well in simple experiments, but for trickier experiments we have COMPETING models of those solid state objects, and we do need to test them.

That is not about PSI. PSI is important, but depends on more advanced physics beyond QED, 

I remember someone once said to Dean Radin "Can;t you explain PSI by QED?" as I rec all, he was VERY emphatic (as am I) that NO, you can't. It is a bit more advanced than that. Vitiello has at times hinted that moving from QED to EWT might be enough, but I don't see that solving the problems. All the way to dark matter and dark energy, or further. But the existence of dark matter and dark energy is not speculative any more, and we know they have a lot of the needed properties. (A vast connected ocean of energy and matter, like the kind of ocean which can sustain the evolution of life.) 

Best of luck... and thanks for asking useful, solid  questions.