[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:

- The first is the Grid, as characterized by Frank Wilczek.
- 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.

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, butthis 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.

A

realistic interpretation of quantum physicsentails 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, …”

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.]

**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.

• 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

[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 tailsthat 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 forefingeras 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 thatthe binding of the proton may come aboutnot through the internal pulling of elastic bands butthrough 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 “**R**eflection / **T**ransmission / **O**bservation” discussed in his book’s Introduction – The Tale of the Quantum in the Window.

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:

- The first is the Grid, as characterized by Frank Wilczek.
- 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 first idea, namely, the Grid.

The Grid [that ur-stuff that underlies physical reality] fills space and time. Every fragment of Grid – each space-time element – has the same basic properties as every other fragment. The Grid is alive with quantum activity. Quantum activity has special characteristics. It is spontaneous and unpredictable. And to observe quantum activity, you must disturb it. The Grid also contains enduring, material components. The cosmos is a multilayered, multicolored superconductor. The Grid contains a metric field that gives space-time rigidity and causes gravity. The Grid weighs, with a universal density. – Wilczek, Frank. The Lightness of Being: Mass, Ether, and the Unification of Forces (p. 111). Basic Books. Kindle Edition.

Figure 8.1 Grid, old and new. a.

A grid is often used to describe how various things are distributed in space. b. The Grid, which underlies our most successful world-model, … – Wilczek, Frank. The Lightness of Being: Mass, Ether, and the Unification of Forces (p. 74). Basic Books. Kindle Edition.

One of the best analogies for Wilczek’s Grid (which he uses himself, as noted above) is a Geographic Information System’s **multilayered data model**, as discussed in this article:

• TechnoFAQ.org > “Thoughts on the Future of GIS. What Will Change in 50 years?” by Lucy Benton (July 5, 2017)

Thus we come to suspect that the entity we call

empty space is an exotic kind of superconductor. – Ibid. p. 96.Even though the conceptual and mathematical parallels run very deep,

Grid superconductivity differs from conventional superconductivityin four main ways: … – Ibid. p. 213.

The primary ingredient of reality is alive with quantum activity. … The primary ingredient of reality also contains enduring material components. These make

the cosmos a multilayered, multicolored superconductor.I will use the word Grid for the

primary world-stuff. That word has several advantages [vs. ether, space-time, quantum field]:We’re accustomed to using mathematical grids to position layers of structure, … – Ibid. p. 74.

Ordinary matter is a secondary manifestation of the Grid, tracing its level of excitation. – Ibid. p. 75. [2]

So the recent astronomical discovery that Grid weighs – that the entity we perceive as

empty space has a universal, nonzero density– crowns the case for its physical reality. – Ibid. pp. 104-105.

We’ve seen that not only can two quanta be entangled with each other, but

a single quantum can be entangled with the quantum vacuum.– Hobson, Art. Tales of the Quantum: Understanding Physics’ Most Fundamental Theory (p. 181). Oxford University Press. Kindle Edition.

**Objective**: Visualize layered Grid interplay with spacetime geometry, within context of stress–energy–momentum tensor in relativity theory.

Layered (stratified) systems are common in fluid dynamics, e.g., for plasma, gas, water. Macroscopic stellar and planetary atmospheres, oceans. Where there are gradients, due to density, temperature, …

As a physical model, stratification introduces the notion of **shear** (stress) between layers. And perhaps conceptually as quantum **curvature** and inertia. [3]

[1] As a counterpoint to statements like this:

• New Scientist > “How quantum entanglement really works and why we accept its weirdness” by Michael Brooks (22 May 2024) – Subatomic particles can appear to instantly influence one another, no matter how far apart they are. These days, that isn’t a source of mystery – it’s a fact of the universe and a resource for new technologies

“

These quantum correlations seem to appear somehow from outside space-time, in the sense that there is no story in space and time that explains them,” says Nicolas Gisin at the University of Geneva, Switzerland.

[2] Here’s a quote from one of Wilczek anecdotes about Feynman.

Feynman told me that when he realized that his theory of photons and electrons is mathematically equivalent to the usual theory, it crushed his deepest hopes. He had hoped that by formulating his theory directly in terms of paths of particles in space-time – Feynman graphs –

he would avoid the field concept and construct something essentially new. For a while, he thought he had. – Wilczek, Frank. The Lightness of Being: Mass, Ether, and the Unification of Forces (p. 84). Basic Books. Kindle Edition.

[3] 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.

Drafts of two lectures are now available.

This post is about my ongoing physics research project. To tell a story (perhaps literally) which conceptually unpacks quantum field theory. That is, to develop a framework which:

- Visualizes Wilczek‘s Grid (discussed in other posts).
- Demystifies the historical tropes of quantum mechanics.

Perhaps these tasks are underway elsewhere. While visualization has advanced over the decades, I’ve not encountered any systematic elucidation. Just mainly lots of math. An occasional analogy or wave form. And Big Science and table-top physics are focused on new so-called particles or new types of interactions. Or refining values of key parameters. All of which is vital, but not a compelling narrative.

These fields are actually three dimensional, but if I showed you a three dimensional version of this, your eyes and brain would just be overwhelmed and it wouldn’t be useful. – Nick Lucid [1]

“*Demystifying quantum mechanics*” preserves the wonder and weirdness of quantum physics. In fact, for me, such demystification makes quantum physics even more mind-boggling – further revealing the limits of our conceptualizations and models. [5]

I’d like to see progress beyond the “frozen” tropes that still pervade technical discussions and general perceptions. For example, in one sense, over the last 100 years or so, it’s progress for the term “*wave-particle duality*” to have garnered wider recognition. Yet, in another sense, it’s become a catch phrase which sidesteps any more nuanced understanding (as well as fostered popular philosophical allusions). [A note here will cite current examples.]

This project really requires a team. But finding collaborators is problematical. Those with a passion for quantum physics, with skillsets in mathematical physics and visualization (including evocative analogies), and having some distance from academic pressure – to work on telling a story rather than publishing noteworthy papers.

So, I’ll start with a story: a parable by Wilczek (although he may not have called it that) and a tale framed as a remembrance of a journey toward new physics.

- Introduction
- Prologue – a parable of the Grid
- Beyond all gloss – a quantum story
- Quantum physics beyond remembrances
- Notes

*Intelligent deepwater fish – or super-dolphins – figure out “swimming” in a medium*

Suppose some species of deepwater fish, that never break the surface, evolved to become more intelligent, and started to do theoretical physics.

Eventually the fish-physicists would realize that they could get a nicer version of mechanics by assuming that they lived in a medium – call it water – [which] complicates the appearance of things. In this way, they’d realize that what they hitherto regarded as “nothingness,” their ever-present environment, is actually a material medium.

And then they might be inspired to do experiments to try to make ripples in the medium, to find its atoms, and so forth.

Well, we’re like those fish. Human-physicists have discovered that we can get nicer, simpler accounts of how particles behave by assuming that we’re embedded in a medium, whose presence complicates the appearance of things.

– Physics history, Earth: Frank Wilczek, “

What is Space?” (2009)

At this elevation, the landscape looked wonderful. The day was clear, clean. Inside the observatory, Tau was shielded from the not so delightful aspects of the site. Like reduced atmospheric oxygen, gusty cold, and higher radiation.

Tau was waiting for results of his latest simulations. Even supercomputers took awhile.

The conference room was one of his favorite places, with expansive windows and multispectral overlays. Presently unoccupied, Tau was reflecting on being there. Something serendipitous, in a way.

Some of the solar and dish arrays were visible outside. And the more recent upgrades which kept the place operational. The site was witness to a long arc of physics. Of understanding quanta. In the past many people saw the solar panels as collecting particles and the dishes waves. An alchemy of the sky’s electromagnetic spectrum. But that didn’t really matter if you just did the math. Visualization was mostly a never-mind.

*Leave the stage of everyday …go behind the scenes,beyond all gloss …until there’s just the lower bound*

*What remains?What only can be imagined …perhaps modeled mathematically*

*What are the words (or poetry)to frame such a construct,it’s structure and topology?*

*How does the everyday emerge*from that matrix effectively?

Research objective: visualizing the Grid (inspired by theoretical physicist Frank Wilczek)

The journey: the mundane –> mysterious –> mundane redux

As discussed my post (and comments) “How stiff is space-time?” – here’s Wilczek’s depiction of the multilayer *Grid*.

The primary ingredient of reality is alive with quantum activity. … The primary ingredient of reality also contains enduring material components. These make the cosmos

a multilayered, multicolored superconductor.I will use the word

Gridfor theprimary world-stuff. That word has several advantages [vs. ether, space-time, quantum field]: We’re accustomed to using mathematical grids to position layers of structure, … – Wilczek, Frank. The Lightness of Being: Mass, Ether, and the Unification of Forces (p. 74). Basic Books. Kindle Edition.

10^n and 10^-n

energy / contours of energy

dimensions

fluids

fluid dynamics

diffusion equations

energy spectrum

fields

gradients

wave forms

superposition

wavepackets

confinement (boundary conditions, dampening)

What’s actually happening [re quanta] is a combination of (1) fundamentally smooth functions, (2) differential equations, (3) boundary conditions, and (4) what we care about [which factors in dissipation]. – Sean Carroll [2]

interactions

• Quanta Magazine > “Entanglement Made Simple” by Frank Wilczek (April 28, 2016) – An aura of glamorous mystery attaches to the concept of quantum entanglement, but …

Research objective: Demystify the historical tropes of quantum mechanics

As quantum field theorist

Steven Weinbergputs it, “The basic ingredients of nature are fields; particles are derivative phenomena.” – “Tales of the Quantum: Understanding Physics’ Most Fundamental Theory” by Art Hobson

Regarding wave–particle duality, you’ll see that the successes of quantum field theory – the theory that unites quantum physics with Einstein’s ideas about space and time as stated in his special theory of relativity – has convinced such leading quantum theorists as

Steven WeinbergandFrank Wilczekthat the universe is made of waves in fields rather than particles in empty space; both the scientific consensus and the evidence now point in that direction. – Ibid.

Philip Ball is an excellent science / physics communicator, but this recent article (below) presents a legacy framework. It does not even mention the context of current quantum field theory, as discussed by physicists like Steven Weinberg and Frank Wilczek, as well as the demystification (and clarification) which Art Hobson offers in his book *Tales of the Quantum* (particularly regarding the double-slit experiment).

But Ball’s brief historical recap hopefully puts to rest the notion of “morphing” – the “flawed classical analogy” that quanta are like shape-shifters, with different forms for different occasions. That neither classical term – *wave* or *particle* – suffices (yet, without any mention of *wavepacket*, eh).

However, he does not mention that even atoms (and molecules) exhibit interference in double-slit experiments.

Nor does he mention the role of entanglement:

So

entanglement and nonlocality are ubiquitous within atoms, which is why an atom behaves in so many ways likea single unified quantum; it can, for example, interfere with itself. Every highly entangled system is similar to individual atoms in the sense thatthe entangled system behaves in the unified, “all or nothing” manner of single quanta. – Hobson, Art. Ibid. (p. 181)

• Chemistry World > “A common misunderstanding about wave-particle duality” by Philip Ball (13 June 2024) – Instead of treating quantum particles as shape-shifters, we should think in terms of probability distributions

The meaning and the significance of wave-particle duality is widely misunderstood, as some of the reporting of the latest work shows.

… there is no reason to say that quantum entities are ever really waves. Rather, the probabilities of where we will observe them in an experiment can be conveniently determined by the calculus of the Schrödinger equation, …

Confined in a well [so-called particle in a box], an atom’s wavefunction is tightly confined: it looks [interacts] like a discrete particle.

When the optical lattice is turned off, the atoms are free to wander – and the Schrödinger equation predicts that their wavefunctions spread in all directions. This doesn’t mean that the atoms themselves are smeared out like waves; rather, what spreads is the probability distribution of them being found subsequently in a given location. That is just what the researchers see: they image the atoms’ later positions, and find that the histograms of these positions over many repeated experiments on the same system reveal a distribution that evolves in time just as the Schrödinger equation predicts.

force (charge, mass)

singularity

collision

Context: interactions with the Grid and so-called mass / charge states; and the topology of “flavors,” etc.

- the neutrino
- mathematical models and infinities
- why sum over all paths works (with finesse) [3]
- …

[1] Regarding our ability to visualize higher dimensions …

My post “Reckoning quanta, quantum events” cites Nick Lucid’s discussion of quantum fields.

• YouTube > The Science Asylum > “What Are Particles? Do They ACTUALLY Exist?!” by Nick Lucid (May 1, 2023) – Somewhere between 1926 and 1950, we gave up the concept of particles in favor of quantum fields. In this video, I explain the motivations for that to a non-physicist: my wife.

[2] Carroll’s post also is an example of the use of an occasional analogy (violin strings) or wave form (but not wave pulse / packet).

• Preposterous Universe (Sean Carroll) > “Thanksgiving” (November 23, 2023) – A frequently misunderstood (or misinterpreted) feature of nature is the relationship between discrete (measurable) “quanta” – individual excitations of quantized fields (“particles”) or the energy levels of atoms – and smooth and continuous mathematical models of reality.

[3] See these comments for my post “Reckoning quanta, quantum events“

• May 24, 2023 > “… the equation [Feynman path integral], although it graces the pages of thousands of physics publications, is more of a philosophy than a rigorous recipe. … it does not tell researchers exactly how to carry out the sum. … they face deep confusion about which possibilities should enter the sum.”

• May 25, 2023 > “Our work paves the way for experimentally exploring the fundamental problems of quantum theory in the formulation of path integrals.”

[4] Perhaps Tau’s observatory (on some planet) is a far future successor to the observatory noted in this Space.com article:

• Space.com > “The highest observatory on Earth sits atop Chile’s Andes Mountains — and it’s finally open” by Sharmila Kuthunur (May 1, 2024) – Establishing and constructing the telescope required broad collaboration, with both technical and political challenges.

The Japanese University of Tokyo Atacama Observatory, or TAO, which was first conceptualized 26 years ago to study the evolution of galaxies and exoplanets, is perched on top of a tall mountain in the Chilean Andes at 5,640 meters (18,500 feet) above sea level. The facility’s altitude surpasses even the Atacama Large Millimeter Array, which is at an elevation of 5,050 meters (16,570 feet).

TAO is located on the summit of Atacama’s Cerro Chajnantor mountain, whose name means “place of departure” in the now-extinct Kunza language of the indigenous Likan Antai community. The region’s high altitude, sparse atmosphere and perennially arid climate is deadly to humans, …

[5] *Demystification* in the sense also used by Fermilab’s Don Lincoln, as noted in my post Wavepackets and uncertainty principle:

• YouTube > Fermilab > “Demystifying the Heisenberg Uncertainty Principle” by Don Lincoln (Oct 16, 2023)

]]>[Preliminary 11-11-2023] [**“Quantum** **foundations**” series]

- Context
- First big idea:
*wave function* - Second big idea: wave function as
*sum of sines and cosines* - Third big idea:
*Fourier transform* - Fourth big idea:
*momentum of a wave*depends on its wavelength - macOS
*Grapher examples* - Conclusion
- Lincoln’s (Fermilab)
*video* - Notes
- Related posts

This post was inspired by Don Lincoln’s latest YouTube video (below).

Insights from quantum field theory (QFT) have helped me better understand strange aspects of quantum theory [1].

In particular, leaving behind notions of *point particles* and *wave-particle duality*, and just going with fields and *wavepackets* in those fields (and their interactions). As Don Lincoln noted, “*It’s perfectly reasonable to think of fundamental particles as wavepackets.*“

Wavepackets are superpositions of multiple frequencies (excitations, vibrations). Inherently superpositions. Mathematicaly, this amounts to *Fourier transforms*.

Wiki > If the packet is strongly localized, more frequencies are needed to allow the constructive superposition in the region of localization and destructive superposition outside the region.

So, Fermilab’s Don Lincoln’s latest YouTube video on the uncertainty principle caught my attention. Lincoln explains that the foundation of that principle predates Heisenberg’s formulation (1927) – grounded in the mathematics of Fourier (1807).

If you know where an electron is [its position], you have no idea how fast [its momentum] or even if it’s moving. That’s the gist.

It’s simple really. All it really says is that if you measure one variable well, you will measure the other one poorly. You can’t simultaneously measure both well.

Basically, where the wave function – actually the square of the wave function – is large, the particle is likely to be there. Conversely, where the square of the wave function is zero, the particle can’t be there at all. The width of the [squared] wave function gives you a sense of the range of possible locations where the particle can be, which is a way of saying the width is a measure of your uncertainty of the position of the particle.

Okay. So, what was Fourier’s insight? Basically, he realized that for any function that you can build it by adding together the right amounts of sine and cosine waves.

He begins with an example of how a square wave can be mathematically constructed by superimposing multiple sine waves of specific frequencies. Approximated as closely as desired (see my example below).

There likely are no true square waves in nature. Likewise fundamental so-called particles are not singular waveforms (single-mode plane vibrations) either.

Lincoln uses some visuals to make the connection between two graphs:

- the
**position space**plot – of the square wave, with position on the x axis - a
**W space**plot – with the number of wiggles on the x axis (how many different sine waves are added and how much amplitude each one contributes to the function series)

The information in a wave function series can be represented in two “spaces” and transformed from one to the other.

The x-axis of this second plot is kind of funny. It is basically the number of wiggles – the number of wavelengths – in a fixed distance. There was one, then three, then five, and so on.

For the purposes of this video, I’m going to write the number of wiggles as W, and it equals one over the wavelength. Wavelength is written as the Greek letter lambda. Shorter wavelength means higher W – that’s how it works.

So, now I need to make a super important point. These two graphs … represent exactly the same information. The two plots are effectively the same thing, but one records the shape of the function

in position space, while the other records the number and amount of waves, which we might callthe function in W space.

Lincoln then uses the **normal distribution** (aka bell curve) – vs. the square wave – as a more realistic function to advance his demonstration: “We can do a Fourier transform and find out what the shape of the curve will be in W space.”

It turns out that the Fourier transform of a normal distribution is also a normal distribution.

Now here is the most important point. It turns out that

the width of the normal distribution in W space is related to the width of the normal distribution position or x space. So, if you do the math, you find that Delta x times Delta W is equal to one over two times pi.

𝜟x𝜟W = 1/2π

So, what does that mean? It means that if Delta x gets small, then Delta W gets big and vice versa. They can’t both be small at the same time.

Lincoln then recaps some history in quantum mechanics: Louis De Broglie (1924) proposed that the momentum (p) of a wave = h/𝞴. So:

p = hW

𝜟p = h𝜟W or 𝜟p/h = 𝜟W

So, from above 𝜟x𝜟W = 𝜟x𝜟p/h = 1/2π or 𝜟x𝜟p = h/2π = h_bar

So, this looks a lot like the Heisenberg Uncertainty Principle, although it’s missing that one-half factor, which means that I haven’t derived the uncertainty principle here. It turns out that derivation is a little more complicated …

• Square wave Fourier series (movie)

• Gaussian 3D wavepacket (movie)

So, from the four big ideas, Lincoln concludes, “*you have everything you need to see where the Heisenberg Uncertainty Principle comes from.*“

Well, hmm, … So, I’d still like to see a realistic *visualization* of how a photon – as a **wavepacket** – results from an electron’s transition from a higher to lower energy state (whether that resolves the quantum topology or not):

An example which models how a spacetime modal transition in energy (a process which is not instantaneous) entails a superposition of many waves into a wavepacket – a sum of subtle frequency and/or phase differences, with constructive superposition in the region of localization and destructive superposition outside the region.

At that point, it’s reasonable that a superposition (extended in space) is connected to the Uncertainty Principle, because that sum of waves inherently has no single position or momentum – only a range. It’s a composite only characterizable by relational field interactions. And standard deviations.

Perhaps there’s a taste of this model with the Hydrogen spectral series and the 21 cm fine and hyperfine emission lines due to “spreading” from local field interactions and relativistic effects.

Anyway, a visualization in macOS Grapher is TBD, after looking at:

• Wiki > Uncertainty principle > Visualization and Wave mechanics interpretation

Adding together all of these plane waves comes at a cost, namely the momentum has become less precise, having become

a mixture of waves of many different momenta.

• YouTube > Fermilab > “Demystifying the Heisenberg Uncertainty Principle” by Don Lincoln (Oct 16, 2023)

**Description**

The

Heisenberg Uncertainty Principleis one of the most non-intuitive concepts in all of quantum mechanics. It says that it is impossible to precisely know both an objects location and its motion. Know one well and you must know the other poorly. The origins of this are deeply tied to thewave nature of matterand the connection between waves and momentum. In this video, Fermilab’s Dr. Don Lincoln sorts it all out.

Fourier transform square wave:

https://mathworld.wolfram.com/FourierSeriesSquareWave.html

Fourier transform gaussian:

https://mathworld.wolfram.com/FourierTransformGaussian.html

Additional Fourier transform explainer:

https://mriquestions.com/fourier-transform-ft.html

Wavelength, momentum, and wave number:

http://faculty.chas.uni.edu/~shand/Mod_Phys_Lecture_Notes/Chap6_Matter_Waves_Notes_s12.pdf

[1] So, perhaps a series of “demystifying” articles, eh.

- Demystifying point particles
- Demystifying wave-particle duality
- Demystifying quantum spin
- Demystifying the uncertainty principle
- Demystifying force (charge, mass)
- Demystifying singularities
- TBD

Can the mind-boggling, awe-inspiring scale of the universe improve the odds of our collective survival? An expanding overview effect?

“I believe our future depends powerfully on how well we understand this Cosmos in which we float like a mote of dust in the morning sky.” – Carl Sagan, Cosmos (1980)

Well, that hardly seems the case currently. With so much conflict from claims of exceptionalism and supremacy. And without viable alternatives for those attached to political and physical violence.

“Human beings have a demonstrated talent for self-deception when their emotions are stirred. … we’ve accumulated dangerous evolutionary baggage — propensities for aggression and ritual, submission to leaders, hostility to outsiders … Which aspects of our nature will prevail is uncertain, particularly when our visions and prospects are bound to one small part of the small planet Earth.” – Carl Sagan, Cosmos (1980)

So, an expanding vision. At a practical level. Win-win’s, rather than a winner’s might. Realizing a deeper, wider connection to others.

• Science Daily > “Awe-inspiring science can have a positive effect on mental wellbeing” by University of Warwick (October 5, 2023) – Psychologists have revealed a profound connection between the spirituality of science and positive wellbeing, much like the benefits traditionally associated with religion [such as feelings of awe and wonder].

This recent APOD (below) reminds us that in 1920: “*Many astronomers then believed that our Milky Way Galaxy was the entire universe.*” Modern images from the HST and JWST make the notion of an island universe peculiar.

Now, almost one hundred years later, it is difficult to fully appreciate how much our picture of the universe has changed in the span of a single human lifetime.

As far as the scientific community in 1917 was concerned, the universe was static and eternal, and consisted of a single galaxy, our Milky Way, surrounded by a vast, infinite, dark, and empty space.This is, after all, what you would guess by looking up at the night sky with your eyes, or with a small telescope, and at the time there was little reason to suspect otherwise. — Krauss, Lawrence. A Universe from Nothing: Why There Is Something Rather than Nothing (pp. 1-2). Atria Books (2012). Kindle Edition.

• NASA > APOD > “Edwin Hubble Discovers the Universe” (2023 October 6)

*Edwin Hubble Discovers the Universe*

**Image Credit & Copyright**: Courtesy Carnegie Institution for Science

**Explanation**

How big is our universe?

This question, among others, was debated by two leading astronomers in 1920 in what has since become known as astronomy’s Great Debate.

Many astronomers then believed that our Milky Way Galaxy was the entire universe.Many others, though, believed that our galaxy was just one of many.In the Great Debate, each argument was detailed, but no consensus was reached.

The answer came over three years later with the detected variation of single spot in the

Andromeda Nebula, as shown on the original glass discovery plate digitally reproduced here.When Edwin Hubble compared images, he noticed that this spot varied, and on October 6, 1923 wrote “VAR!” on the plate.

The best explanation, Hubble knew, was that this spot was the image of

a variable star that was very far away.So

M31 was really the Andromeda Galaxy– a galaxy possibly similar to our own.Annotated 100 years ago, the featured image may not be pretty, but the variable spot on it opened a window through which humanity gazed knowingly, for the first time, into a surprisingly vast cosmos.

As discussed elsewhere (e.g., in “QFT – How many fields are there?” and comments), in the Standard Model, “there is one field for each kind of particle.”

So, consider the positron – the “negative-energy solution” of the Dirac equation.

It’s likely that electrons and positrons (anti-electrons) are localized vibrations (excitations) in the same field. Just “reverse” excitations. For example, as noted by Ethan Siegel as “equal-and-opposite excitations of a quantum field.” (Cf. Don Lincoln’s QFT visualizations.)

While electrons and positrons can be separated using magnets, if all fundamental particles are “identical” wavepackets (cf. John Archibald Wheeler’s quip that “they [electrons] are all the same electron”), why would electrons and positrons interact differently in a gravitational field – to spacetime geometry? If geometry is geometry … on identical “mass” energy packets [1]. (Imagine a classroom physics demonstration in which electron and positron “balls” accelerate differently down an inclined plane, eh.)

Perhaps due to different wavepacket topologies? Or interactions with the quantum vacuum? [2]

Or some new physics? (Cf. “Beyond the Standard Model – sliver of reality?“)

Well, some physicists are checking, i.e., testing CPT symmetry. This article starts with an illustration of dropping objects from the Leaning Tower of Pisa.

But this experiment does *not* confirm that hyddrogen and antihydrogen atoms “fall” at the same rate.

“This is the first Leaning Tower of Pisa experiment with antimatter [magnetically trapped antihydrogen atoms],” says Tim Tharp, an associate professor at Marquette University, referring to Galileo’s fabled experiment dropping objects from the leaning tower to compare their rates of acceleration.

• Symmetry Magazine > “Antimatter falls down” by Sarah Charley (September 27, 2023) – Results from the ALPHA experiment (the Antimatter Factory at CERN) confirm that matter and antimatter react to gravity in a similar way.

Antimatter is identical to matter, except that some of its properties are flipped. For instance, electrons are negatively charged, but their antimatter counterparts, positrons, are positively charged.

Thus far, matter and antimatter seem to be either equal or mirror images of each other in all areas. “Antimatter is a very specific reflection of matter,” Tharp says. “Some things are the opposite, and some things are the same.”But one area that hadn’t been fully investigated is how antimatter interacts with gravity.

“We don’t know everything there is to know about gravity,” Tharp says. “We have this image that gravity warps spacetime. If antimatter fell the opposite way, that picture wouldn’t fit anymore. These results are a new, substantial piece.”

Even though ALPHA has shown that antimatter falls down, the precision is too low to know if antimatter and matter experience gravity with the same strength.

[1] Interact the same with the Higgs field.

[2] Or a possible twist? Wilczek noted that: “We have quantum fields that create left-handed particles, and separate quantum fields that create right-handed particles.” So, left / right handed electrons and positrons …

• Space.com > “Are we really made of ‘star stuff’ and what does that even mean? (video)” by Robert Lea (August 21, 2023) – These inspiring words from Carl Sagan apply to all life forms, not just us.

“The cosmos is within us. We are made ofstar stuff. We are a way for the universe to know itself.” – Carl Sagan

With this sentiment, Sagan, who passed away in 1996 at the age of 62, was talking about the cosmic origins of humanity.

And in a new video from the European Southern Observatory (ESO), part of the

Chasing Starlightseries, astrophysicist Suzanna Randall explains what this statement means and how it relates to the elements that comprise our bodies.As the astrophysicist points out, however, we maybe shouldn’t let this go to our heads too much. As an ego-cleanser, Randall concludes by adding: “Before you get too excited, cockroaches are also made up of star stuff.”

• YouTube > European Southern Observatory > “Are you made of starstuff?” (Aug 4, 2023)

]]>The building blocks of life were created by stars, which fuse atoms, creating heavier and heavier elements. When most massive stars explode as supernovae these elements are dispersed into space, enriching the surrounding gas, which in turn can form new stars and possibly planets.

Remember pet rocks? So, what if someone gave you a gift, claiming it was even better than a Moon rock or Mars pebble. Something almost magical. An expensive novelty item. As advertised on TV: *“Tangled Blocks” … go quantum! do Einstein spooky action! each block contains a particle entangled with one in the other block.*

This post was inspired by a YouTube video on entanglement. More on that below. But that presentation reminded me that there are degrees of entanglement. And the limits of analogies sans any mathematical framework. And current entanglement-measurement methods.

While AI’s still much in the news regarding chatbots (large language models), more traditional AI neural networks are used for a lot of scientific research. Even “quantumness.”

• Phys.org > “Using AI to accurately quantify the amount of entanglement in a system” by Bob Yirk, Phys.org (August 1, 2023)

An international team of physicists has found that deep-learning AI technology can accurately quantify the amount of entanglement in a given system – prior research has shown that the degree of “quantumness” of a given system can be described by a single number. In their paper, published in the journal Science Advances, the group describes their technique and how well it worked when tested in a real-world environment.

Over the past several years, as scientists have learned more about entanglement, they have found that in order for it to be useful in applications, designers of such systems need a way to determine the degree of its entanglement. And that presents a problem, of course, because measuring a quantum state destroys it.

To get around this problem, physicists have developed what is described as quantum tomography, where multiple copies of a state are made and each is measured. This technique can ensure 100% accuracy, but it is exhaustive and requires considerable computing power. Another approach involves making educated guesses using limited information about a system’s state. This involves a trade-off between precision and resource use. In this new effort, the research team brought a new tool to the problem: deep-learning neural networks.

So, in this YouTube video (below), physicist Katie Mack [**The End of Everything: (Astrophysically Speaking)**] presents an analogy for quantum entanglement. Explaining what entanglement is about using the familiar macroscopic pair-of-coins model.

Well, while her analogy explains the weirdness, the visualization begs certain questions:

1 . How do you know those two particular “coins” are entangled? – both initially when provided to Alice & Bob and after traveling for 10 years.

Can we produce a single entangled pair on demand? For typical entanglement-measurement methods, there’s only a probability of entanglement for any pair of “particles” (like one in a million).

Can we transfer entangled quantum states on demand?

2 . What does the (often used) term “connection” (rather than “apparent connection” or correlation) imply?

Is this misleading? (Same question for the term “link.”)

Is “shared (quantum) state” too technical a characterization? (For which that “state” remains undisturbed until a measurement – disentanglement – decoherence.)

3 . To what degree is the “system” of the coins entangled?

Evidently, entanglement need not be 100% (or only apply to certain degrees of freedom, in this case side value). [1]

4 . In real-world examples (like entangled photons or electrons), aren’t groups (ensembles) of “particles” involved? And extensive post-hoc analysis of measurements?

There’s a probability of entanglement.

• YouTube > Perimeter Institute for Theoretical Physics > “Quantum 101 Episode 5: Quantum Entanglement Explained” (Aug 1, 2023) – Quantum entanglement allows physicists to create connections between particles that seem to violate our understanding of space and time.

Description

Quantum entanglement is one of the most intriguing and perplexing phenomena in quantum physics. It allows physicists to create connections between particles that seem to violate our understanding of space and time.

This video discusses what quantum entanglement really is, and the experiments that help us understand it. The results of these experiments have applications in new technologies that will forever change our world.

Join Katie Mack, Perimeter Institute’s Hawking Chair in Cosmology and Science Communication, over 10 short forays into the weird, wonderful world of quantum science.

(from transcript)

[As an analogy for two entangled particles prepared in a lab to have opposite (indeterminate) spins: “You can’t know ahead of time if it’s spin up or spin down. All you know is that when you measure it, the other particle will be the opposite.”]

But what if we could do some magic trick to entangle these coins? Sort of.

One comes up, heads, the other will come up tails. No matter how far apart they are.

Let’s say I give this coin to Alice and this one to Bob just before they set off on rocket ships going in opposite directions. Alice and Bob are each under strict instructions not to flip their coins until they’ve been traveling for ten years.

When the time is up, they each flip their coin and immediately send radio signals to each other with the answers.

But while those signals might take years to reach their destinations, the entanglement means that the moment Alice sees heads, she knows that Bob’s coin landed tails and vice versa.

Alice doesn’t have to wait for Bob’s radio signal to arrive to know what it will say. Alice’s coin had a 50/50 chance of coming up heads. But once it does, Bob’s coin is tails 100% of the time.

Because Bob’s signal is still traveling to her when she finds out the answer, it’s as if Alice has predicted the future.

This might sound impossible, but it’s exactly what quantum entanglement does to individual particles in experiments.

- But how does it work?
- How do the particles know what to do?
- Are they passing messages that we can’t see?
- And why can we entangle particles but not coins?
- And that is one of the most interesting and puzzling concepts of quantum mechanics.

[1] Re how much entanglement is contained in a quantum state

• Wiki > Quantum entanglement

As a measure of entanglement

Entropy provides one tool that can be used to quantify entanglement, although other entanglement measures exist. If the overall system is pure, the entropy of one subsystem can be used to measure its degree of entanglement with the other subsystems.

• Quantiki > Entanglement-measure

Entanglement measure quantifies how much entanglement is contained in a quantum state. Formally it is any nonnegative real function of a state which can not increase under local operations and classical communication (LOCC) (so called monotonicity), and is zero for separable states.

• Wiki > Quantum tomography – Quantum tomography or quantum state tomography is the process by which a quantum state is reconstructed using measurements on an ensemble of identical quantum states.

• Caltech > Science Exchange > “What Is Entanglement and Why Is It Important?” – Entanglement can also occur among hundreds, millions, and even more particles.

• Imaging at the molecular and atomic level

• 2022 Nobel Prize – ‘spooky action’ pioneers

• Spooky action vs. spooky communication

]]>So, for me, there’s always been a nagging shortfall of visualization for the major theories of modern physics: Relativity and Quantum theories. Successful theories indeed. But a focus on the mathematics, with some hand-waving surrounding implicit assumptions (or definitions), conveying a flawless formulation in popular presentations.

As discussed elsewhere, in Quantum Mechanics there’s the long-standing “*shut up & compute*” mantra. And legacy characterizations of particles and waves. Like, odd visualizations of huge radio telescope dishes collecting EM “particles.” Or, “force carrying” (fundamental) particles somehow producing attraction and repulsion.

In Relativity, there’s the mantra “*the speed of light (electromagnetic radiation) is the same (constant) in all inertial frames of reference*.” But the long-standing nag’s been how those frames are known to be inertial – sans any acceleration (even a tad) – as agreed upon between all observers.

Elsewhere the incompleteness of the Standard Model of physics has been discussed. And the quest to integrate relativity and quantum theories (a quantum theory of gravity, for example). A presentation below highlights how defects can still lurk in the metaphors and mathematics.

The first article below provides some historical background on how Einstein developed his theory of relativity. The second piece is a YouTube video which discusses an unresolved flaw (*internal inconsistency*) in the conceptual framework of relativity.

Here’s a useful recap of how we came to understand that electricity and magnetism are linked (rather than independent) phenomena. Some seminal experiments. By tinkerers.

• Big Think > “71 years earlier, this scientist beat Einstein to relativity” by Ethan Siegel (June 28, 2023) – Michael Faraday’s 1834 law of induction was the key experiment behind the eventual discovery of relativity. Einstein admitted it himself.

All of these phenomena [demonstrated by Faraday] could be encapsulated by a single physical rule, known today as Faraday’s law of induction.

In the first scenario, you move the magnet into a stationary, conducting coil. …

In the second scenario, where you instead keep the magnet stationary and move the conducting coil down onto the magnet, …

… experimentally, both of these setups [that seem so different on the surface] must be equivalent. In both scenarios, a magnet moves into a coil of wire at the same speed, where they produce the same electric currents of the same magnitude, intensity, and direction in the coils of wire.

And it was this realization, more than any other, that led Einstein to the principle of relativity.

The principle recognizes, first and foremost, that there is no such thing as a state of absolute rest. … Only relative motion within the system matters …

Here’s a provocative, historical perspective visualizing conceptual inconsistency in relativity (in line with my interest in a theory of space – see paper cited at end of video). Sort of a lesson in having your cake and eating it too (having absolute acceleration in a relativistic paradigm).

• YouTube > Dialect > “Why The Theory of Relativity Doesn’t Add Up (In Einstein’s Own Words)” (June 24, 2023)

Description: Relativity is as successful a theory as it is mind-bending – yet Einstein himself did not believe it was complete, and in a 1914 paper he critiqued its internal consistency at some length. … and so here we find ourselves compelled to ask the same question Einstein did over a century ago: is the theory of relativity truly consistent, and if not, what does this mean for its future?

Video chapters: *Intro, Of Axioms & Absolutes, Einstein Calls Out His Own Theory, Defining “Absolute” Acceleration, What are We Accelerating Relative to, Einstein’s Mistake, Where Do We Go from Here*.

The quest for “a more intuitive and concrete way of understanding the Theory’s formalism” sans mathematical abstraction

[from transcript file]

]]>For that reason in a 1914 paper entitled “on the relativity problem,” Einstein wrote that he felt special relativity suffered from the same

undeniable fundamental defectthat Newtonian physics did – that is, thatit relied on a notion of absolute acceleration in order to complete its formalism.For instance if you say you’re accelerating in a car, you’re implying that you’re accelerating relative to the ground. but if that ground were say actually the deck of a boat accelerating equally and oppositely over a body of water, then relative to someone on the shore you’d actually be at rest.

… the answer to this problem is to define absolute acceleration [non-inertial motion] as meaning acceleration

relative to an inertial frame.But of course inertial frames are defined via an absence of acceleration so this definition is horrifically circular!

[Nope, accelerometers don’t help. Invoking “the rest of the universe” as a frame is no help – the problem of locality ensues. Tensors are just a mathematical repackaging, eh.]

… and special relativity, of course, rejects both these possibilities, telling us that we can have neither absolutes nor ethers.

For the remainder of his life, Einstein would struggle to interpret the meaning of Relativity, changing his mind frequently about its implications and completely reversing his stances on topics such as the existence of the Ether or Mach’s principle.

Indeed, it’s easy to see that this defect comes about because we want to treat acceleration as absolutely real and yet at the same time persist in saying that all the components which go into making up acceleration – time, space, length, velocity – are all relative.

… for all the mystery surrounding what the Ether may or may not be, what our current theories most strongly suggest is the idea that we detect its presence every time we accelerate.[The Lorenzian Axiom (an answer to this question) … in and of itself feels pretty

arbitrary and jarring. Einstein’s Axiom … hardly feels any less arbitrary or jarring.Neither intuitive.]