The pollen and the electron: a study in randomness by Tejinder P. Singh

Dear James,

Greetings, and thanks so much for your very kind comments, appreciation, and evaluation. I am glad we agree that there is a possibility of an underlying determinism beneath quantum mechanics.

I will read your essay now. Thanks for pointing me to it.

Best wishes to you for this contest,

Tejinder

Dear Peter,

It is so nice to meet you again.

What I have shown is: There is a deterministic matrix dynamics at the Planck scale, from which quantum theory and its indeterminism are emergent, after coarse-graining over time scales much larger than Planck time. This implies that if one takes any set-up involving a quantum system measuring apparatus apparent wave function collapse, this can be mapped to a deterministic solution of the underlying Planck scale matrix dynamics. The apparent random wave function collapse comes about because we have ignored the change taking place in the d.o.f. that have been coarse-grained. There is a collapse, but it is not random: it *is* deterministic.

I am really sorry I am unable to comprehend the set-up you describe. Its beyond my reach, because it seems so sophisticated. But if it is a solution of qm, it can in principle always be mapped to the deterministic matrix dynamics.

Kind regards,

Tejinder

The determinism that underlies quantum indeterminism

And the story of John and his dog Bax Morn

John the wood-cutter lives in a hut in the forest with his faithful dog Bax Morn. The hut has two doors, left door and right door, and a call bell on the outside of the hut, in between the two doors.

Every morning John goes out to the woods to cut wood, and comes back in the evening at random times - sometimes a little early when the sun is still up, sometimes a little late, even after dark. But John has no watch nor clock, and in fact has no clue that time can be measured in hours and minutes.

When John rings the bell after returning, Bax Morn opens the left door on some days, and the right door on other days. Which door on which day, is completely random, and John can never predict which door might open on a given day. But he noticed that on the average both doors get opened equally often, over a month say.

Morn's behaviour puzzles and amuses John - such a random dog, he thinks. But he loves Morn, and never questions the dog's apparently random choice of the door. Still, he has this funny feeling after ringing the bell - he thinks of himself as a superposition of John the left and John the right, not knowing which way to go, as if his state has gotten entangled with the two doors. Until one of the doors opens, and his state collapses to John the left or John the right.

But Morn keeps a secret - he is a very smart dog, and the opposite of random. Morn understands time and its measure, and keeps a secret watch, which he never shows to John. For fun, Morn has made a rule. Left door to be opened if it is some minutes past an *even* hour like 4 pm or 6 pm. Right door to be opened after 5 pm or after 7 pm.

Quantum mechanics is like John and Morn. Since John does not know about the secret watch, he concludes that Morn's behaviour is random. The randomness is an apparent consequence of quantum theory being approximate, the approximation being the neglect of the watch.

But the watch is not a hidden variable. It can be detected by using more precise probes than qm uses. If John installs a CCTV camera inside the hut and observes Morn from outside, he will see Morn behaving deterministically, not randomly. [Please allow now for a John who knows the measure of time]. A more complete theory underlying qm includes the watch and the CCTV camera. It is a deterministic theory. The randomness of qm is removed because an extra parameter comes into play now: John's exact time of arrival back home. In qm, this time of arrival is of no consequence to the outcome of the measurement, and that is where the impression of randomness comes from. In the deeper theory, the time of arrival on successive days determines the outcome of the measurement.

Why must there be a deeper theory with a watch and a cctv camera? We explain that in the essay :-)

Tejinder

Dear Jochen,

Thanks so much for reading my essay, and asking deep questions, whic I try responding to.

With regard to nonlocality, I start by copy-pasting here a question that Markus Mueller asked me on his page, followed by my response there:

"Dear Tejinder,

thanks a lot for your kind words!

Let me ask you a question on your approach. If dynamics at the Planck scale is fully deterministic, and coarse-graining leads to quantum mechanics, then Bell's theorem implies that this dynamics must be non-local (as you also point out in your paper). But if it's non-local, an immediate worry would be that it leads to superluminal signalling. Is it clear that the coarse-graining in your model removes the possibility of signalling?

Best,

Markus

Thank you Marcus, for asking an important and interesting question. I try to explain what I mean by non-locality in this matrix dynamics, and why it does not imply superluminal signalling. In this dynamics at the Planck scale, there is no space-time. There is only a new notion of time - the Connes time. All processes take place in a Hilbert space, where there is no conventional notion of distance [space-time emerges subsequently, from this Hilbert space, after spontaneous localisation]. So, whereas Alice and Bob are two space-like separated observers from the viewpoint of a conventional Minkowski spacetime, who are making their respective measurements, the picture of the same set-up is very different in matrix dynamics. From the viewpont of this new dynamics, a correlated pair of say electron and positron in an entangled state are represented by operators evolving with time, but this evolution does not imply that the electron and positron are moving away from each other. We must not think of them as spatially separated. Also, one talks of simultaneity in Connes time, which plays the role of an absolute [reversible] time. When Alice makes a measurement on the electron, it simultaneously changes the state of the positron [simultaneous in Connes time]. But no travel or signalling is involved.

I explain this in some detail in this paper:

https://arxiv.org/abs/1903.05402

starting at the bottom of p. 26. Basically, there are two different ways of lookimg at an EPR event. One is the space-time-less matrix dynamics way [non-local but no signalling], and the conventional way..involves signalling. Quantum non-locality appears to violate relativity if we accept that QM needs space-time. But qm does not need spacetime - in fact spacetime is external to qm and must be removed so as to find a better description of qm. The matrix dynamics achieves that - because there is an absolute time, but no light-cones. Lorentz invariance is emergent.

"

Because there is no space-time in the matrix dynamics, there is no signalling. How does this interface with general relativity? The spontaneous localisation of macroscopic bodies gives rise to the emergence of space-time with its light cone structure, as well as Riemannian curvature.

I hope these remarks are useful. I will continue in the next post, to avoid making this one too long.

Tejinder

Continued..the locality for macroscopic systems here, which obey general relativity, holds to a great accuracy, but only in an approximate sense, not in an exact sense. I think one can say - just as you do - that the emergent stochasticity that keeps macroscopic objects classical - washes away signalling, on averaging. This is just as it happens in the GRW theory of spontaneous collapse.

Next, you say:

"Your theory, as I understand it, seems essentially classical at the most fundamental level. How, for instance, does the quantum speedup emerge from your dynamics? (This isn't intended as criticism, by the way; ultimately, nobody knows where the quantum speedup comes from---or with absolute certainty whether it exists at all!---but it seems to me that a theory such as yours, which postulates the emergence of quantum mechanics from more fundamental dynamics, might be able to shed some light on this question.) You mention that the 'predictable quantum computer' would lead to physical hypercomputation. Is then the loss of predictability in the coarse-graining process what brings this 'down' to the capacities of a quantum computer---i. e. becoming not a question of how computational power is gained in going to the quantum, but rather, how it is lost in the averaging?

"

Your point about hyper-computation is very nice, and the answer is : Yes.

I am not clear - my fault - what exactly is meant by quantum speed-up? Does it refer to the presence of quantum superposition in a quantum computer? We can discuss this further if you could kindly elaborate.

"Another point is that, as described, quantum theory seems to emerge as the statistical version of a more fundamental, deterministic theory. How does this evade the theorem that is commonly thought to make such a description impossible?"

The underlying theory is classical, but not in a trivial Newtonian sense. It is rather that: one takes the canonical c-number variables of a classical relativistic dynamics, including gravity, and converts them to operators. But quantum commutation relations are not imposed on them. Instead, the operators obey a Lagrangian dynamics that follows from an action principle, and the dynamics determines the evolution of the commutation relations.

Because the Lagrangian possesses a global unitary invariance, there results a novel conserved Noether charge, of great importance, not present in the conventional classical dynamics. This charge is responsible for the emergence of quantum theory after the underlying dynamics has been coarse-grained over time intervals much larger than Planck times. The indeterminism is only an apparent and illusory consequence of ignoring the coarse-grained degrees of freedom. There is no actual indeterminism. The coarse grained d.o.f. are not hidden variables...they can be accessed by probing Planck scales.

Hope these remarks are useful Jochen...thanks again,

Tejinder

Dear Lawrence,

It is good to meet you here again, and thanks so much for your kind comments.

In proposing a deterministic matrix dynamics at the Planck scale, I have followed in the footsteps of Stephen Adler. In his theory of trace dynamics, described in his book `Quantum theory as an emergent phenomenon' he proposed a deterministic matrix dynamics at the Planck scale. Here the matrix valued [equivalently operator valued] canonical variables obey Hamilton's equations of motion, obtained by starting from a Lagrangian dynamics. This is instead of the quantum theory's Heisenberg equations of motion, and now there are no quantum commutation relations.

I showed how to include gravity in trace dynamics, by using concepts from Connes' non-commutative geometry programme. From this theory, after coarse-graining over many Planck times, quantum theory and general relativity, as well as quantum indeterminism, emerge as low energy approximations.

As for Hawking radiation, there is no information loss paradox in my theory, because the full Hamiltonian at the Planck scale is not self-adjoint. It results in non-unitary evolution during black hole formation, and during evaporation, the correlations are hidden as Planck scale corrections to the thermal spectrum.

Thanks again for your kind interest,

Tejinder

Dear Raiyan Reza,

Thank you for your very kind comments.

And never label yourself as lowly because you are an undergrad. Every scientist was once an undergrad like you, and undergrads like you are the scientists of tomorrow.

My best wishes,

Tejinder