[As an intermediate post for Demystifying series]
[Draft 7-22-2024, 8-4-2024]

Here’s a possible story which helps demystify quantum field theory. A personal visualization, which stays within the bounds of spacetime and avoids needless paradoxes [1].

There are two key concepts to my sketch:

1. The first is the Grid, as characterized by Frank Wilczek.
2. The second is a quantum’s tail.

The Grid defines a cosmic superconducting landscape in which quanta can extend in spacetime essentially without limit, without loss of energy or waveform integrity, unless they interact with or are confined by other quanta within fields.

A quantum’s indefinite tail provides a context for superposition and entanglement. So-called waveform collapse and distant correlation of quantum state.

Yes, there are issues as to the viability of these two concepts. Later I’ll try to summarize any commentary that I’ve found so far.

This post lays out the second idea, namely, a quantum’s tail.

A quantum’s tail

The two photons of the RTO experiment [8] are entangled in a single two-body quantum state whose extent is represented by the dashed line and solid line of Figures 9.2 and 9.3. This two-quantum system acts like a single unified quantum. It could stretch across our galaxy, yet it’s a single object that can reconfigure itself, i.e. “collapse,” instantaneously. It might seem spooky, but this is the physically realistic interpretation of the experiments. – Hobson, Art. Tales of the Quantum: Understanding Physics’ Most Fundamental Theory (p. 183). Oxford University Press. Kindle Edition.

Quantum so-called discontinuities

A realistic interpretation of quantum physics entails that spatially extended quanta really can alter their entire configuration instantly. – Hobson, Art. Tales of the Quantum: Understanding Physics’ Most Fundamental Theory (p. 183). Oxford University Press. Kindle Edition.

In exploring how to tell a story which gets beyond the tropes of quantum physics – which finds a better visual model, there’s a dilemma: two core all-or-nothing “collapse” or “jump” situations (that usually are assumed to be instantaneous):

• the collapse of a superposition.
• correlated concord of quanta across indefinite distance.

The first case has to do with what some physicists call the wavefunction update; the second, with entanglement.

Historically, we’re talking about (various versions of) the double-slit experiment and the so-called “measurement problem” [5]. And “spooky action at a distance.”

How does the notion of quanta (e.g., photons) as wavepackets extended in spacetime view these situations? In each case, we’re talking about quanta which can range in “size” from the microscopic to macroscopic. From atomic to cosmic scales. From the extremely low to the extremely high ends of the electromagnetic (EM) spectrum. [1] [As discussed in my lecture “How big is a photon?“]

• Big Think > “What is a quantum particle really like? It’s not what you think” by Don Lincoln (September 19, 2023) – “It is completely reasonable to think of subatomic particles like electrons and photons as wave packets, …”

Quantum all-or-nothing packets

Quanta are “single units” – unified packets (bundles) of energy, excitations in (continuous) quantum fields. The double-slit experiment and beam splitters do not split photons (or electrons). Superpositions resolve as wholes – there are no halfsies [2]. Extended spatial wavepackets typically resolve at an atomic “point” in measurement devices.

As mentioned before (Chapters 2, 5, and 6), the instantaneous, or discontinuous, or digital, nature of quantum jumps arises from the unity of the spatially extended quantum. The entire extended quantum must change everywhere, all at the same instant. – Tales of the Quantum: Understanding Physics’ Most Fundamental Theory by Art Hobson

Entangled photons share (or are) the same quantum state. Even over vast distances. An interaction with one (measurement) resolves the other’s outcome. While popsci characterizations often use words like “connection” or “link,” these terms offer no sensible model (sans speculation about higher dimensions outside spacetime).

So, let’s try a hypothetical, and see where that might lead. While I’m not sure whether to visualize wavepackets as cosine linear superpositions or hybrid gaussian-cosine waveforms (or something similar), such forms have tails. Can these tails ever go to zero? [3]

[And there’s the question of dispersive or non-dispersive forms. See TBS references below.]

Quantum tail analogy (tension)

Objective: Visualize localized wavepacket collapse, within context of stress–energy–momentum tensor in relativity theory.

Schweitzer [Peter Schweitzer, a theoretical physicist at the University of Connecticut] has spent most of his career thinking about the gravitational side of the proton. Specifically, he’s interested in a matrix of properties of the proton called the energy-momentum tensor. “The energy-momentum tensor knows everything there is to be known about the particle,” he said. [7]

How can we visualize extended quanta – spread-out wavepackets – interacting with a photon-screen’s atoms at particle-like impact points? Hobson uses a balloon analogy.

In a typical double-slit experiment with light, the pattern (and hence the pre-impact photon) is a few centimeters wide [6].

Imagine that the photon is a large balloon settling down on a bed of nails [atoms]. The interaction – the bang – is going to occur at only a single nail [atom]. This does not imply that, before the bang, the balloon was present only at that single nail [atom]. – Hobson, Art. Tales of the Quantum: Understanding Physics’ Most Fundamental Theory (p. 84). Oxford University Press. Kindle Edition.

As mentioned before, you should imagine the electron as a large balloon and the detection screen as a bed of nails: the electron extends over many nails but the interaction is going to occur at only one of them. – Ibid. pp. 133-134.

Popping a soap bubble (or balloon) with a prick is a dramatic unified all-or-nothing interaction [4] – because the bubble’s thin (film) surface is under (essentially) uniform tension (as a minimal surface, with a difference in outside and inside pressure).

Entangled bubbles? Might merged bubbles be a useful analogy for entanglement? As to how coupled surfaces superimpose.

Quantum tails

• Wolfram > “Wavepacket for a Free Particle” by Andrés Santos (January 2009) – In general, the wavefunction of a free particle is a superposition of infinitely many harmonic waves.

If I understand correctly, there’s a problem with quantum tails – the strength of the quantum field – going to zero. If the matching wavefunction range (numerical value of Ψ) converges to zero. Because that means that the probability (Ψ squared) of that quantum being somewhere in spacetime is zero.

So, while quantum tails may become negligible (asymptotic), they cannot be ignored. How is that possible?

While fantastical, perhaps there’s a basis in superfluids. Flow with no energy loss. For example, Frank Wilczek’s Grid, which he characterizes as a cosmic superconductor. And in superfluids perhaps there’s no truncation of waveforms (sans interaction) …

So, …

TBS

Notes

[1] Compare for example, Wiki’s articled on Hegerfeldt’s theorem with:

Recall from Chapter 5 that de Broglie pointed out that each quantum “fills all space,” and Hegerfeldt proved the same result more rigorously by showing that quanta cannot be localized within any finite-size region. In other words, the size of every quantum (provided it’s not restricted by external forces [interactions]) is infinite.” – Tales of the Quantum: Understanding Physics’ Most Fundamental Theory by Art Hobson

[2] As in the famous (and all too frequently cited) “Schrödinger’s cat” thought experiment, the outcome, while indeterminate, still is a live cat or a dead cat. There is no half-alive cat.

Also compare:

… although each quantum is spatially extended (because it’s part of the extended EM field), it always behaves as a single unit. Any alterations in a quantum extend instantaneously to the entire quantum, even if it’s spread out over many kilometers. You can’t alter part of a quantum because it doesn’t have “parts”; it’s a single thing. – Hobson, Art. Tales of the Quantum: Understanding Physics’ Most Fundamental Theory (p. 79). Oxford University Press. Kindle Edition.

Hobson also wrote that:

(quote from Abstract below) But analysis of interferometry experiments using entangled photon pairs shows that entangled states differ surprisingly from simple superposition states. –

Quantum Engineering
Research Article
Open Access
Entanglement and the Measurement Problem
Art Hobson
First published: 24 March 2022
https://doi.org/10.1155/2022/5889159
Citations: 5

[3] I’ve explored these forms in my post on wavepackets, for example. Visuals by notable physicists (as noted in my posts) are limited. Mostly one or two dimensional. Typically looking like composite sine or cosine packets. With truncated tails. But many descriptions are vague – that quanta are fuzzy blobs and such. Yet, interfere like waves.

Hobson described a zero tail as “absolute localization (zero probability of finding the electron outside some finite region).”

… absolute localization is inconsistent with the states of elementary quanta. … The infinitely long exponential tails that Nauenberg is willing to ignore because their probability “becomes negligible” are important matters of principle. Such tails, whether exponential or not, must exist. –

American Journal of Physics
Comment on “There are no particles, there are only fields,” by Art Hobson [Am. J. Phys. 81, 211–223 (2013)]
Response to M. S. de Bianchi and M. Nauenberg
Art Hobson
Department of Physics, University of Arkansas, Fayetteville, Arkansas 72701
(Received 30 April 2012; accepted 10 June 2013) [http://dx.doi.org/10.1119/1.4811783]

Notes and Discussions (Am. J. Phys., Vol. 81, No. 9, September 2013)

[4] Typically; but, yes, there are ways to handle (or probe) a bubble without popping it. Which, as an analogy, introduces the notion of hard and soft interactions (measurements) – “pricks” – of quanta. Particularly, as to interactions which preserve (some degree of) entanglement.

[Google search: How do you poke a bubble without it popping?]

• How Stuff Works > Science > “Why Do Bubbles Pop?” by Allison Troutner (Mar 12, 2024) – When a bubble is poked, a hole forms and surface tension causes the molecules to shrink so quickly that the bubble flattens or bursts and the water escapes as tiny droplets.

The release of bubbles from carbonated (or sparkling) – fizzy – beverages is another example of change in stress in a pressurized mixed liquid.

• Let’s talk science > “The Chemistry of Pop” by Patrick Clarke (September 23, 2019)

[5] Re demystifying the so-called measurement problem of the double-slit experiment, note Hobson, Ibid. p. 188, where he distinguishes between a quantum superposition and mixture:

• a superposed quantum (in two states simultaneously) is a single unified (coherent) object (across / through both slits).
• a mixed quantum – a decoherred (incoherent) quantum “has definite [but indeterminate] properties associated with either one or the other of two states” (randomly through only one slit).

The crucial point is that detections, or measurements, occur when a macroscopic detector entangles with a quantum. – Hobson, Ibid. p. 187

[6] Regarding the size of photons, try this experiment:

If you followed my suggestion in Chapter 4 and performed a single-slit experiment using your thumb and forefinger as a narrow slit, a well-lit surface as the light source, and your retina as the screen, you have already observed directly a macroscopic phenomenon arising from a fundamental quantum principle: the wave nature of each photon. … The experiment demonstrates millimeter-wide photons. – Hobson, Ibid. p. 155.

[7] Here’s an article about research on “the shape of space-time surrounding a proton” – twisting shear forces and pressure changes. Which someday might explain “why quarks bind themselves into protons at all.”

• Quanta Magazine > “Swirling Forces, Crushing Pressures Measured in the Proton” by Charlie Wood (March 14, 2024) – New experiments – exploring the distribution of subatomic energies, forces and pressures – show [shear] forces push one way near the proton’s center and the opposite way near its surface.

Over decades, researchers have meticulously mapped out the electromagnetic influence of the positively charged particle. But in the new research, the Jefferson Lab physicists are instead mapping the proton’s gravitational influence — namely, the distribution of energies, pressures and shear stresses throughout, which bend the space-time fabric in and around the particle.

Schweitzer [Peter Schweitzer, a theoretical physicist at the University of Connecticut] has spent most of his career thinking about the gravitational side of the proton. Specifically, he’s interested in a matrix of properties of the proton called the energy-momentum tensor. “The energy-momentum tensor knows everything there is to be known about the particle,” he said.

The new approach measures the region of space-time that’s significantly curved by the proton.

But protons are made from the lightest members of the quark family. And lightweight quarks can also be thought of as lengthy waves extending beyond the proton’s surface. This picture suggests that the binding of the proton may come about not through the internal pulling of elastic bands but through some external interaction between these wavy, drawn-out quarks.

[8] Note re Art Hobson’s extensive use of the term “RTO experiment” in his book and other articles, without explaining what “RTO” means (as a acronym):

“RTO” likely refers to “J. G Rarity, P. R. Tapster, and Z. Ou” – as in “Rarity–Tapster interferometer.” It also happens to be about photon “Reflection / Transmission / Observation” discussed in his book’s Introduction – The Tale of the Quantum in the Window.

Related posts

• Demystifying QFT – Grid as superconductor
• Wavepackets and uncertainty principle
• QFT – fields and wave packets
• Knotty fields – quantum-topology-knot theory