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]

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

**Possible conceptual framework**

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

entanglement

Research objective: Demystify the historical tropes of quantum mechanics

point particle

wave-particle duality

uncertainty principle

spin

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.”

]]>[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.]

Here’re some articles on advanced microscopy research, including quantum microscopy by coincidence.

Not included (as yet) below is an article about nano fab of crystal lattices – direct deposition of individual atoms at lattice sites vs. more conventional doping (impurity) techniques.

1 . Studying ultrafast **molecular dynamics**

- Observing molecular processes that occur on timescales faster than a millionth of a billionth of a second
- Imaging changes in bond lengths and angles between individual atoms while electrons shift position
- Collecting spectral signals at the femtosecond timescale

• Phys.org > “Ultrafast X-ray spectroscopy: Watching molecules relax in real time” by Rachel Berkowitz, Lawrence Berkeley National Laboratory (May 24, 2023) – Examining how a molecule responds to light on extremely fast timescales allows researchers to track how electrons move during a chemical reaction.

(image caption)

D-scan measurement. The pulse reconstructed in (D) from the measurement shown in (A) has a pulse duration of 5 fs and relative peak-power of 76% which proves the good degree of compression. (B) shows the D-scan retrieved by the software (Sphere Ultrafast Photonics). (C) shows the spectrum (red) and its spectral phase (blue). Credit: Science (2023). DOI: 10.1126/science.adg4421(video visualization caption)

The angles between atoms inan excited methane moleculechange as the molecule relaxes, distorting its shape and redistributing the absorbed energy. Credit: Diptarka Hait/Berkeley LabDesigning the next generation of efficient energy conversion devices for powering our electronics and heating our homes requires a detailed understanding of how molecules move and vibrate while undergoing

light-induced chemical reactions.Researchers at the

Department of Energy’s Lawrence Berkeley National Laboratory(Berkeley Lab) have nowvisualized the distortions of chemical bonds in a methane molecule after it absorbs light, loses an electron, and then relaxes. Their study provides insights into how molecules react to light, which can ultimately be useful for developing new methods to control chemical reactions.Examining how a molecule responds to light on extremely fast timescales allows researchers

to track how electrons move during a chemical reaction. “The big question ishow a molecule dissipates energy without breaking apart,” said Enrico Ridente, a physicist at Berkeley Lab and lead author on the Science paper reporting the work. This means examininghow excess energy is redistributed in a molecule that has been excited by light, as the electrons and nuclei move about while the molecule relaxes to an equilibrium state.The researchers used the Cori and Perlmutter systems at the National Energy Research Scientific Computing Center (NERSC), a DOE Office of Science user facility at Berkeley Lab, to perform calculations that confirmed their measurements of the molecule’s movements.

“We can now explain how the molecule distorts after losing an electron and how the energies of the electrons respond to these changes,” said Diptarka Hait, a graduate student at Berkeley Lab and the lead theoretical author of the study.

2. Nanotechnology | Nanophysics | Nanomaterials

- Optical
**metrology**on an atomic scale - Application of
**AI deep learning**to picophotonics, the science of light-matter interactions on the picometer scale

• Phys.org > “Topologically structured light detects the position of nano-objects with atomic resolution” by Ingrid Fadelli, Phys.org (May 19, 2023) – …

(image caption)

Mr. Cheng-Hung Chi, PhD student at the University of Southampton, usessuperoscillatory lightto detect the position of anano-wirewith atomic resolution. Credit: University of SouthamptonOptical imaging and

metrologytechniques are key tools for research rooted in biology, medicine andnanotechnology. While these techniques have recently become increasingly advanced, the resolutions they achieve are still significantly lower than those attained by methods using focused beams of electrons, such as atomic-scale transmission electron spectroscopy and cryo-electron tomography.In the team’s proof-of-principle experiments, their

optical localization metrology methodperformed remarkably well, resolving the position of the suspended nanowire witha subatomic precision of 92 pm(i.e., around λ/5,300), while the nanowire naturally thermally oscillated with amplitude of ∼150 pm.For reference, a silicon atom is 220pm in diameter.“We are now working on

detecting picometer movements with a high frame rate, so we can shoot a video featuring the real dynamics of Brownian motion of a nanoscale object,” Zheludev [Nicolay I. Zheludev] added.

3. New microscopy technique, dubbed **quantum microscopy by coincidence** (QMC)

How does this work?

I’ve not encountered this perspective before: that a biphoton effectively has half the wavelength of single (classical) photon. The research teams’ apparatus apparently uses spontaneous parametric down-conversion, although SPDC is not mentioned (just references to signal & idler photons). “… a computer … builds an image of the cell based on the information carried by the signal photon.”

- A paper (“Quantum Microscopy of Cells at the Heisenberg Limit”) in the journal
*Nature Communications*(April 28, 2023) - “Because a
**biphoton**[two entangled photons] has double the momentum of a photon, its wavelength is half that of the individual photons [which results in increased resolution.].” - “… one of the paired [entangled] photons passes through the object being imaged and the other does not. … Amazingly, the paired photons remain entangled as a
**biphoton**behaving at half the wavelength despite the presence of the object and their separate pathways.”

• Caltech > News > “Quantum Entanglement of Photons Doubles Microscope Resolution” by Emily Velasco (May 1, 2023) – Using a “spooky” phenomenon of quantum physics, Caltech researchers have discovered a way to double the resolution of light microscopes.

[Shorter and shorter wavelengths of

laser lightcarry more energy …] So, once you get down to light with a wavelength small enough to image tiny things, the light carries so much energy that it will damage the items being imaged, especially living things such as cells.QMC gets around this limit by using

biphotonsthat carry the lower energy of longer-wavelength photons while having the shorter wavelength of higher-energy photons.“Cells don’t like UV light,” Wang [Lihong Wang, Bren Professor of Medical Engineering and Electrical Engineering, Caltech] says. “But if we can use 400-nanometer light to image the cell and achieve the effect of 200-nm light, which is UV, the cells will be happy, and we’re getting the resolution of UV.”

Wang’s lab was not the first to work on this kind of

biphoton imaging, but it was the first to create a viable system using the concept. “We developed what we believe a rigorous theory as well as a faster and more accurate entanglement-measurement method.We reached microscopic resolution and imaged cells.”Wang says future research could enable entanglement of even more photons [“multiphotons”], although he notes that each extra photon further reduces the probability of a successful entanglement, which, as mentioned above, is already as low as a one-in-a-million chance.

- Big Think > “Plants perform quantum mechanics feats that scientists can only do at ultra-cold temperatures” by Elizabeth Fernandez (May 27, 2023) – The paths of excitons in plant chromophores resemble those seen within a Bose-Einstein condensate.

“Chromophores … can pass energy between them in the form of excitons to a reaction center where energy can be used, kind of like a group of people passing a ball to a goal,” Anna Schouten, the study’s lead author, explained to Big Think.

[1] Wiki > Chromophore

A chromophore is the part of a molecule responsible for its color. … The chromophore is a region in the molecule where the energy difference between two separate molecular orbitals falls within the range of the visible spectrum. Visible light that hits the chromophore can thus be absorbed by exciting an electron from its ground state into an excited state.

See also Wiki > Chlorophyll – *Chlorophyll molecules are arranged in and around photosystems that are embedded in the thylakoid membranes of chloroplasts.*

And Wiki > Resonance energy transfer – *a mechanism describing energy transfer between two light-sensitive molecules (chromophores).*

[2] Wiki > Exciton (electron-hole pairs as integer-spin particles)

When a molecule absorbs a quantum of energy that corresponds to a transition from one molecular orbital to another molecular orbital, the resulting electronic excited state is also properly described as an exciton. … Molecular excitons have several interesting properties, one of which is energy transfer … whereby if a molecular exciton has proper energetic matching to a second molecule’s spectral absorbance, then an exciton may transfer (hop) from one molecule to another.

[(Wiki) Creative Commons Attribution-Share Alike 3.0 Unported license]

]]>- A quandary over preserving the “absoluteness” of any observed quantum event

Alice & Bob et al. measure quantum states & wonder about predicting outcomes.

- Visualization of quantum fields (quantum field theory & topology)

In continuous quantum fields, localized disturbances (excitations) interact and exchange energy between fields – as real outcomes.

- A quandary over properties of excitations (wiggles, wave pulses / packets) and superpositions

“We suppress dimensions in order to make sense of things.”

- An unsettling quantum vacuum

Modeling interactions of excitations with vacuum states of quantum fields gets weird.

Here’s a rundown of the “the basic arcana of quantum foundations” and the so-called “measurement problem” in quantum physics. A provocative title at least. Using a coin toss metaphor. No visualizations.

But this article does mention superpositions and wave functions. And so-called “collapse” theories. Information theory. The “many worlds” interpretation (as a “perspectival” theory).

And Alice & Bob (each in their own lab) plus Charlie & Daniela viewing Alice & Bob from the “outside.” (I’m not sure how time is correlated in such a system: “Charlie, for example, treats Alice, her lab and the measurement she makes as one [macroscopic] system that is subject to deterministic, reversible evolution.”)

And spacetime relativity.

So, there’s the question of the “absoluteness of observed events” – whether quantum measurements (of something specific in a specific way for a specific quantum system) are the same for everyone.

Does the discussion conflate “observer” (introducing the notion of choice) with “measurement”? As noted elsewhere, “the universe is always looking,” all the time [1] and outcomes agree just fine. But the discussion here is about OUR ability to predict outcomes.

Any progress in perspective? Or rethink? I still prefer using the phrase wave function “update” vs. “collapse” (and follow experiments which explore whether that really is instantaneous).

There’s no relational quantum theory here (the question of quantum properties as relational vs. intrinsic). No consideration of topology – the topology of: quantum fields, quanta, quantum interactions. And no caution that (mathematical) wavefunctions are simplifications of reality anyway – the article does not address the debate over reality of the wave function.

- Scientific American > “Quantum Theory’s ‘Measurement Problem’ May Be a Poison Pill for Objective Reality” by Anil Ananthaswamy [2] (May 22, 2023) – Solving a notorious quantum quandary could require abandoning some of science’s most cherished assumptions about the physical world.

[Image caption] A core mystery of quantum physics hints that objective reality is illusory – or that the quantum world is even weirder than expected.

At the heart of this bizarreness is what’s called the measurement problem. Standard quantum mechanics accounts for what happens when you measure a quantum system: essentially,

the measurement causes the system’s multiple possible states to randomly “collapse” into one definite state. But this accounting doesn’t define what constitutes a measurement – hence, the measurement problem.In a recent preprint, the trio [Ormrod, Venkatesh, and Barrett] proved a theorem that shows why certain theories – such as quantum mechanics – have a measurement problem in the first place and how one might develop alternative theories to sidestep it, thus preserving the “absoluteness” of any observed event.

[Nicholas Ormrod, University of Oxford] Ormrod says. “If we ever can recover absoluteness, then we’re going to have to give up on some physical principle that we really care about. … Holding on to absoluteness of observed events, it turns out, could mean that the quantum world is even weirder [nuanced] than we know it to be.

…

The article recaps three important properties of perspectival theories, and concludes that “all BIL theories have a measurement problem.”

- Bell nonlocality (B) – entangled, correlated “particle” pairs (as a single inseparable state; so, please avoid the term “linked,” eh).
- Preservation of information (I) – via wave function determinism [while coherent].
- Local dynamics (L) – no faking Bell nonlocality [inter-regional causal affects bound by the speed of light].

Dynamical separability is “kind of an assumption of reductionism,” Ormrod says. … it may be that the dynamics of a [coherent] system are similarly holistic [relational], adding another kind of nonlocality to the universe.

The problem is that no one yet knows how to construct a theory that rejects dynamical separability – assuming it’s even possible to construct – while holding on to the other properties such as preservation of information and Bell nonlocality.

In the end, only experiments will point the way toward the correct theory, …

Visualizing quantum fields is hard. I applaud those who take up the challenge. Here’s Nick Lucid’s latest one.

- 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.

Time codes:

05:33 What is a Quantum Field?

07:50 Quantum Fields Visualized

… the purpose of quantum field theory. It is to predict how these [so-called] particles will interact.

It’s about particle interactions.If there are no particle interactions, quantum field theory is kind of useless.Every point in space has an existence value, essentially.

And you can see that each of those points are wiggling. Every point is wiggling. Sure. That’s sort of the quantum uncertainty going on here, right?

If there is a large enough disturbance, a full disturbance in this field, we perceive that disturbance as a particle. Okay?

There would be a disturbance at an individual point in a continuous space. Okay. … What you see is a spike in a surface. Which might be called a wave, if you will.

Yes, we would treat the spike that moves around as a

wave pulse.It’s just a disturbance in the electron field, for example. In this case, electric charge is represented by color: red for positive and purple for negative. And quantum spin orientation is represented by the vertical direction: up for spin up and down for spin down. It’s a representation. They’re not really going up and down.

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.Something we do in physics is we suppress dimensions in order to make sense of things. It’s very common.

So, visualizations of excitations in fields tend to be oscillations of some type. Perhaps involving higher dimensions. With a confined (point-like) topology but extended in spacetime (so, not mere points).

And interacting within their corresponding field(s) and perhaps the roiling quantum vacuum as well. So, a particular property is relational, inseparable from that dynamic context. Restless. Not fixed. Superposed.

But interactions tune that context, to field contours. As, for example, with alignment to magnetic fields (long underrated compared to electromagnetic fields in classical physics). Superpositions change.

- 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.

And it’s not like the fields occupy different places in space. They all occupy all space. Correct.

Yes, they’re all coexisting.

They all coexist and overlap each other [cf. Wilczek’s Grid]. Right.

Which allows particle interactions to happen because then energy can be exchanged between fields [cf. tuning forks metaphor]. If you have an electron and a positron come together at the same spot, what you get is anti-matter annihilation.

Okay. Which is how that works. Sure.

They just cancel each other out. They just cancel each other out because they have opposite values and it essentially turns the quantum field to a zero value or what we would call the vacuum state of the field.

And by doing that, by assigning existence to every point in space, you’re essentially assigning all possible properties for those particles, for those things we perceive as particles into that spot. All the information is there.

Hmm.

RESONANCE

A striking aspect of quantum fields is that feeding enough energy into them – “you can slap a field and make some particles” (Paul Sutter) – always generates (according to the Standard Model) identical so-called particles. For some events, lots and lots of them. Hence, analogies to modal resonances, standing waves (e.g., realized “notes” from plucked musical strings). For the photon field, tiny, low-power laser diodes produce lots of photons.

• Classroom physics > Standing Waves, Oscillators, Resonance Mode Shapes

My 2-1-2022 comment for “A particle by any other name?” discusses resonance:

As waves or field vibrations, quantum particles “are localized, resonant excitations of these fields.” Sort of natural frequencies (resonances) in spacetime energy.

Everyday examples of resonance include musical instruments and wineglasses. Macro-scale phenomenon. Classical physics.

• Wiki > Resonance

Resonance phenomena occur with all types of vibrations or waves: there is mechanical resonance, acoustic resonance, electromagnetic resonance, nuclear magnetic resonance (NMR), electron spin resonance (ESR) and resonance of quantum wave functions.

But resonance underlies atomic and molecular behavior as well. Our existence depends on such quantum interactions – “in such varied settings, from everyday life down to the smallest scales.”

As physicist Paul Sutter said, “you can slap a field and make some particles.”

• “Reality is fields” comment (May 8, 2017)

- Quanta Magazine > “How the Physics of Resonance Shapes Reality” by Ben Brubaker, Contributing Writer (January 26, 2022) – The same phenomenon by which an opera singer can shatter a wineglass also underlies the very existence of subatomic particles.

Almost anytime physicists announce that they’ve discovered a new particle, whether it’s the Higgs boson or the recently bagged double-charm tetraquark, what they’ve actually spotted is a small bump rising from an otherwise smooth curve on a plot. Such a bump is the unmistakable signature of “resonance,” one of the most ubiquitous phenomena in nature.

Electrons bound to atoms are a little like sound waves trapped inside flutes. As for the atomic nuclei, further advances in the 1930s showed that many kinds of atomic nuclei only exist in the universe today because of resonance.

The frequencies at which quantum fields prefer to vibrate stem from fundamental constants whose origins remain obscure; these frequencies in turn determine the masses of the corresponding particles.

Blast the vacuum of empty space hard enough at the right frequency, and out will pop a bunch of particles.In this sense, resonance is responsible for the very existence of particles.

TOPOLOGY

And as to quantum topology? Like for spinors (fermions). Mostly silence on that topic – while we just do the calculations, eh. Any visualization possible? – without overwhelming our “eyes and brain.”

So, how is the quantum vacuum modeled in quantum field theory? As virtual, mathematical interactions … or as real interplay between fields and excitations?

- 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.

And so what the standard model tells us is that different particles, different fields interact in different ways. That make sense. And we do the calculations using things like Feynman diagrams.

Time codes

10:26 Feynman Diagrams Explained

12:20 Virtual Particles Explained

13:50 How to use Feynman Diagrams

15:05 Quantum Electrodynamics

An excellent introduction to Feyman diagrams – “to represent that [particle interactions] and be able to calculate what’s going to happen with quantum fields.”

(from transcript)

The jiggly spots is the vacuum state of the quantum field. What if we can pretend that those wiggles and jiggles are particles? Because if they’re not necessarily zero, but they’re not like a whole occupation of a spot … So they’re not actual particles, but maybe we can pretend they’re particles, something that we now call virtual particles. They’re not actually particles, but we can pretend that they are. If we do that, then we can start to simplify the math a little bit.Something you might have noticed in those diagrams is that there’s really only one type of vertex.

Every single one of these vertexes has two straight lines and a wiggly line. That’s all that can exist in what we call quantum electrodynamics, which is a type of quantum field theory.

So here’s one scenario. You’ve got an electron and a positron coming together, annihilating and making a photon.

But if I turn [rotate the vertex] this [2nd scenario] … Now, we’ve got an electron coming in, an electron going out, and a photon going out. So now we have an electron emitting a photon and changing direction.

Then [3rd scenario] here we have an electron absorbing a photon and then changing direction. But still an electron. But still an electron. Both the arrows are pointed up in time. Yep.

What we have here [4th scenario]? A photon coming in and dividing into an electron and a positron. Exactly. Ya. See? This is how you read these diagrams.

WHAT QUANTUM FIELD THEORY SAYS ABOUT THE REAL WORLD

His failure, Feynman admitted, was to understand what the math was saying. It provided numbers: predictions of quantities that could be tested against experiments, and which invariably survived those tests. But Feynman couldn’t figure out what these numbers and equations were really about: what they said about the ‘real world’. — Ball, Philip. Beyond Weird (pp. 6-7). University of Chicago Press. Kindle Edition.

[1] Re “the universe is always looking,” see, for example, Quotes > Philip Ball.

And measurements (which do not require any observer) are about interactions, quantized transactions of energy.

[2] **Anil Ananthaswamy** is author of The Edge of Physics (Houghton Mifflin Harcourt, 2010), The Man Who Wasn’t There (Dutton, 2015), and Through Two Doors at Once: The Elegant Experiment That Captures the Enigma of Our Quantum Reality (Dutton, 2018).

Recent Articles by Anil Ananthaswamy

- Is Our Universe a Hologram? Physicists Debate Famous Idea on Its 25th Anniversary
- Astronomers Might See Dark Matter by Staring into the Void
- Astronomers Gear Up to Grapple with the High-Tension Cosmos

- Quantum reality, quantum worlds – new book explores quantum foundations
- 2022 Nobel Prize – ‘spooky action’ pioneers
- A particle by any other name?
- QFT – fields and wave packets
- Feynman’s legacy — quantum originality