What If Physics IS NOT Describing Reality

PBS Space Time produces some very good videos on the foundations of quantum mechanics (QM), so let me comment on their video What If Physics IS NOT Describing Reality to provide (crucial) missing information. This comment pertains only to the first 9 min of the video, i.e., it has nothing to do with “entropic uncertainty,” so you don’t have to watch more than that before reading my comment. After reading my comment, hopefully, you will appreciate that the physics of the quantum reconstruction program (defined below) is well-grounded in reality.

In 1996, Rovelli challenged physicists [1] to derive the formalism of QM from “physical principles and postulates” like Einstein derived the Lorentz transformations of special relativity (SR) from the relativity principle and light postulate. There were many takers for the challenge, one of which was Zeilinger and his Foundational Principle of QM in 1999 [2]. Hardy followed with “Quantum Theory from Five Reasonable Axioms” in 2001 and there were many others en route to “the first fully rigorous, complete reconstructions” by Chiribella, D’Ariano & Perinotti [3] and Masanes & Mueller [4] in 2010-11 (with many more thereafter). This axiomatic reconstruction of QM based on information-theoretic principles (quantum reconstruction program) has succeeded in rendering QM a “principle theory” exactly like SR per Rovelli’s challenge.

[We spell all of this out for the “general reader” in our book, “Einstein’s Entanglement: Bell Inequalities, Relativity, and the Qubit” Oxford UP (2024), this comment is just a summary.]

A “principle theory” per Einstein is one whose formalism follows from an empirically discovered fact [5]. SR is a principle theory because its kinematics (Lorentz transformations) follow from an empirically discovered fact called the light postulate, i.e., everyone measures the same value for the speed of light c, regardless of their relative motions. Since c is a constant of Nature according to Maxwell’s electromagnetism, the relativity principle — the laws of physics (to include their constants of Nature) are the same in all inertial reference frames — says it must be the same in all inertial reference frames. And, since inertial reference frames are related by uniform relative motions (boosts), the relativity principle tells us the light postulate must obtain, whence the Lorentz transformations of SR.

Likewise, the quantum reconstruction program has shown that the kinematics of QM (finite-dimensional Hilbert space) follows from an empirically discovered fact called “Information Invariance & Continuity”:

The total information of one bit is invariant under a continuous change between different complete sets of mutually complementary measurements.

which Brukner & Zeilinger extended from Zeilinger’s Foundational Principle in 2009 [6]. In layman’s terms that simply means everyone measures the same value for Planck’s constant h, regardless of their relative spatial orientations (let me call that the “Planck postulate”). Since h is a constant of Nature per Planck’s radiation law, and inertial reference frames are related by different spatial orientations (rotations), that empirically discovered fact can be justified with the relativity principle exactly like the light postulate of SR.

Quantum superposition is one consequence of the Planck postulate and that leads to ‘average-only’ conservation, which is responsible for the Bell-inequality-violating correlations of quantum entanglement. However, once you understand how ‘average-only’ conservation follows from quantum superposition, which follows from the Planck postulate, which follows from the relativity principle and Planck’s radiation law, there is nothing mysterious about the Bell-inequality-violating correlations of QM. Here is how those correlations make perfect sense using spin-1/2 (as shown in the video).

Suppose you send a vertical spin-up electron to Stern-Gerlach (SG) magnets oriented at 60 deg relative to the vertical (Figure 1, a la the video where they sent the vertical spin-up electrons to horizontal SG magnets).

Figure 1

Since spin is a form of angular momentum, classical mechanics says the amount of the vertical +1 angular momentum that you should measure at 60 deg is +1*cos(60) = 1/2 (in units of ##\hbar##/2, Figure 2).

Figure 2

But, the SG measurement of electron spin constitutes a measurement of h, so everyone has to get the same ##\pm##1 for a spin measurement in any SG spatial orientation, which means you can’t get what you expect from common sense classical mechanics. Instead, QM says the measurement of a vertical spin up electron at 60 deg will produce +1 with a probability of 0.75 and it will produce -1 with a probability of 0.25, so the average is (+1 + 1 + 1 – 1)/4 = 1/2. In other words, QM says you get the common sense classical result on ‘average only’ because of the observer-independence of h. [This is the source of indeterminacy in QM.] This explains the result shown in the video. That is, QM says the measurement of a vertical spin-up electron at 90 deg will produce +1 with a probability of 0.50 and it will produce -1 with a probability of 0.50, so the average is (+1 + 1 – 1 – 1)/4 = 0 = +1*cos(90).

Now suppose Alice and Bob are measuring the spin singlet state (the two spins are anti-aligned when measured in the same direction, as shown in the video) and Alice obtains +1 vertically and Bob measures his particle at 120 deg relative to Alice (Figures 3 and 4). If Bob had measured vertically he would have obtained -1, so at 120 deg Alice says he should get 1/2 per our single particle example.

Figure 3

Figure 4

But of course, Bob must measure the same value for h that Alice does, so he can’t get the fractional value of h Alice says he should (otherwise, Alice would be in a preferred reference frame). Instead, his outcomes at 120 deg correspond to Alice’s +1 outcomes vertically average to 1/2 just like the single-particle case. And, of course, the data are symmetric so Bob can partition the results according to his ##\pm##1 outcomes and show that Alice’s results satisfy the conservation of spin angular momentum on ‘average only’ when they are in different reference frames (making different measurements). So, Alice partitions the data per her ##\pm##1 outcomes (Figures 5 and 7) and says Bob’s results must be averaged to satisfy conservation of spin angular momentum, while Bob’s partition (Figures 6 and 7) says Alice’s outcomes must be averaged (Answering Mermin’s challenge with conservation per no preferred reference frame).

Figure 5

Figure 6

Figure 7

This should remind you immediately of an analogous situation in SR. There when Alice and Bob occupy different reference frames via relative motion, they partition spacetime events per their surfaces of simultaneity and show clearly that each other’s meter sticks are short. Consider the following events:

• Event 1: 20-year-old Joe and 20-year-old Sara meet.
• Event 2: 20-year-old Bob and 17.5-year-old Alice meet.
• Event 3: 22-year-old Bob and 20-year-old Kim meet.

Figure 8

There are three sisters (Sara, Kim, and Alice) in one reference frame moving at 0.6c relative to the reference frame of two brothers (Joe and Bob). The boys are the same age in their reference frame and the girls are the same age in their reference frame. This establishes simultaneity for each set, i.e., events are simultaneous for the boys if the events occur when the boys are the same age, e.g., Events 1 and 2 (Figure 8). Likewise for the girls, e.g., Events 1 and 3 (Figure 9). [Time differences are exaggerated for effect.]

Figure 9

According to Bob’s partition (Figure 8), the distance between Sara and Alice is 1000km while Alice says it’s 1250km. Clearly, Bob’s partition of the data shows Alice’s meter sticks are short. But, according to Alice’s partition (Figure 9), the distance between Joe and Bob is 800km while Bob says it’s 1000km. Clearly, Alice’s partition of the data shows Bob’s meter sticks are short.

In other words, the mystery of Bell-inequality-violating correlations from quantum entanglement resides in ‘average-only’ conservation that results from “no preferred reference frame” (NPRF) giving the observer-independence of h (NPRF + h). And, the mystery of length contraction resides in the relativity of simultaneity that results from “no preferred reference frame” giving the observer-independence of c (NPRF + c).

So, whose meter sticks are short? This question arises from the (wrong) constructive perspective, there is no causal mechanism for shortening meter sticks in SR. Length contraction is not a dynamical effect, it is a kinematic fact due to the light postulate, as justified by the relativity principle.

Likewise, who has to average their data to conserve spin angular momentum? This question arises in the (wrong) constructive perspective, there is no non-local, superdeterministic, or retro causal mechanism responsible for the Bell-inequality-violating correlations of QM. ‘Average-only’ conservation is not a dynamical effect, it is a kinematic fact due to the Planck postulate, as justified by the relativity principle.

Quantum information theorists have shown that you can think about QM as a principle theory, just like SR. This principle explanation of the Bell-inequality-violating correlations does not require non-local, superdeterministic, or retro causal mechanisms, exactly as the principle explanation of length contraction does not require the luminiferous aether. However, the physics of the quantum reconstruction program is clearly describing reality.

References

1. C. Rovelli, “Relational Quantum Mechanics,” International Journal of Theoretical Physics 35, 1637–1678 (1996).
2. A. Zeilinger, “A Foundational Principle for Quantum Mechanics,” Foundations of Physics 29(4), 631–643 (1999).
3. G. Chiribella, G. D’Ariano, and P. Perinotti, “Probabilistic theories with purification,” Physical Review A 81, 062348 (2010).
4. L. Masanes and M. Mueller, “A derivation of quantum theory from physical requirements,” New Journal of Physics 13, 063001 (2011).
5. A. Einstein, “What is the Theory of Relativity?” London Times, 53–54 (1919).
6. C. Brukner and A. Zeilinger, “Information Invariance and Quantum Probabilities,” Foundations of Physics 39(7), 677–689 (2009).