The Holy Grail of modern physics is a so-called theory of everything, a unified field theory, a theory which unifies all known “forces.” That is, unifies all the fundamental interactions of nature. The three “quantum” interactions (electromagnetism, weak, strong) and gravitation.

A conventional sequence of theories depicts final unification as occurring at the Planck energy (density) level.

…

electroweak unificationoccurs at around 100 GeV,grand unificationis predicted to occur at 1016 GeV, andunification of the GUT force with gravityis expected at thePlanck energy, roughly 1019 GeV.Electroweak unification is a

broken symmetry: the electromagnetic and weak forces appear distinct at low energies because the particles carrying the weak force, the W and Z bosons, have non-zero masses of 80.4 GeV/c2 and 91.2 GeV/c2, whereas the photon, which carries the electromagnetic force, is massless.At higher energies Ws and Zs can be created easily and the unified nature [symmetry?] of the force becomes apparent.

A recent Symmetry Magazine article (below) was inspiration for this post. I’ve encountered the topic – unification of forces at high enough energies – many times before. But this latest article, while an experimental milestone, struck me as quite particle oriented, not helping advance visualization based on quantum field theory (QFT).[1]

The premise of Grand Unified Theory models is merging of gauge interactions at extreme energies, energy densities possibly in the quite early universe.

A Grand Unified Theory (GUT) is a model in particle physics in which, at high energies, the three gauge interactions of the Standard Model comprising the electromagnetic, weak, and strong forces are merged into a single force. Although this unified force has not been directly observed, the many GUT models theorize its existence.

If unification of these three interactions is possible, it raises the possibility that there was a grand unification epoch in the very early universe in which these three fundamental interactions were not yet distinct.

I like to imagine that at high enough energies, all localized vibrations – excitations in the various fields associated with “particles” – become a mash-up of energy transformations. Where direct vs. conventional mediated interactions alter hallmark designations. Unfettered field interactions.[2]

• Symmetry Magazine (A joint Fermilab/SLAC publication) > “LHC creates matter from light” by Sarah Charley (August 24, 2020) – Scientists on an experiment at the Large Hadron Collider see **massive W particles emerging from collisions with electromagnetic fields**. How can this happen?

The

Large Hadron Colliderplays with Albert Einstein’s famous equation, E = mc², to transform matter into energy and then back into different forms of matter. But on rare occasions, it can skip the first step andcollide pure energy—in the form of electromagnetic waves.Last year, the ATLAS experiment at the LHC observed two photons, particles of light, ricocheting off one another and producing two new photons. This year, they’ve taken that research a step further and discovered

photons merging and transforming into something even more interesting: W bosons, particles that carry the weak force, which governs nuclear decay.This research doesn’t just illustrate the central concept governing processes inside the LHC: that energy and matter are two sides of the same coin. It also confirms that

at high enough energies, forces that seem separate in our everyday lives – electromagnetism and the weak force – are united.

If you try to replicate this photon-colliding experiment at home by crossing the beams of two laser pointers, you won’t be able to create new, massive particles. Instead, you’ll see the two beams combine to form an even brighter beam of light.“If you go back and look at Maxwell’s equations for classical electromagnetism, you’ll see that two colliding waves sum up to a bigger wave,” says Simone Pagan Griso, a researcher at the US Department of Energy’s Lawrence Berkeley National Laboratory. “We only see these two phenomena recently observed by ATLAS when we

put together Maxwell’s equations with special relativity and quantum mechanicsin the so-called theory of quantum electrodynamics.”Inside CERN’s accelerator complex, protons are accelerated close to the speed of light. Their normally rounded forms squish along the direction of motion as special relativity supersedes the classical laws of motion for processes taking place at the LHC. The two incoming protons see each other as compressed pancakes accompanied by an

equally squeezed electromagnetic field(protons are charged, and all charged particles have an electromagnetic field). The energy of the LHC combined with the length contraction boosts the strength of the protons’ electromagnetic fields by a factor of 7500.

When two protons graze each other, their squished electromagnetic fields intersect. These fields skip the classical “amplify” etiquette that applies at low energies and instead follow the rules outlined by quantum electrodynamics. Through these new laws, the two fields can merge and become the “E” in E=mc².The LHC is one of the few places on Earth that can produce and collide energetic photons, and it’s the only place where scientists have seen two energetic photons merging and transforming into massive W bosons.

Just as photons carry the electromagnetic force, the W and Z bosons carry the weak force.

The reason photons can collide and produce W bosons in the LHC is that at the highest energies, those forces combine to make the electroweak force.

[1] And as to whether current QFT is incomplete – only a mathematical model of effective field theories. And the question as to whether unification requires additional dimensions and/or fields and interactions. Wiki notes:

Yet GUTs [Grand Unified Theories] are clearly not the final answer; both the current standard model and all proposed GUTs are quantum field theories which require

the problematic technique of renormalizationto yield sensible answers. This is usually regarded as a sign that these are onlyeffective field theories, omitting crucial phenomena relevant only at very high energies.

Is there a limit to probing those energies?

• YouTube > Sabine Hossenfelder > “Does nature have a minimal length?” (Feb 2, 2020)

The Planck length seems to be setting a limit to how small a structure can be so that we can still measure it. That’s because to measure small structures, we need to compress more energy into small volumes of space. That’s basically what we do with particle accelerators.

Higher energy allows us to find out what happens on shorter distances. But if you stuff too much energy into a small volume, you will make a black hole.

[2] As Wiki notes, extreme energy GUT models characterize such a state by a single unified coupling constant with yet several (so-called) force carriers. That is, in such a state, “particles” (excited fields) experience a single interaction strength while still mediated separately?

GUT models predict that at even higher energy, the strong interaction and the electroweak interaction will unify into

a single electronuclear interaction. This interaction is characterized by one larger gauge symmetry and thus several force carriers, but one unified coupling constant.

[3] Sometimes the tone of theories of everything strikes me as casting perfection onto the universe akin to that of ancient celestial spheres. A mathematical perfection or symmetry. Yet the universe need not play by any such vision. Perfection a quixotic quest.

]]>*Just a note before you go,A vision to be learnedTraveling near the speed of lightIt’s easy to get …*

Imagining how things would look when traveling near the speed of light is an interesting exercise. Using a freeware video game developed by MIT Game Lab (2012), this visualization (below) by The Action Lab is particularly interesting. An exploration of the various effects:

- Doppler effect
- Searchlight effect
- Time dilation
- Lorentz transformation
- Runtime effect (reference?)

“A Slower Speed of Light” hopefully corrects common misunderstandings – something that benefits contemporary physics classes.

OpenRelativity is a toolkit designed for use with the proprietary Unity game engine. It was developed by MIT Game Lab during the development of

A Slower Speed of Light. The toolkit allows for the accurate simulation of a 3D environment when light is slowed down.

A Slower Speed of Light was developed in hopes of being used as an educational tool to explain special relativity in an easy-to-understand fashion.The game is meant to be used as an interactive learning tool for those interested in physics.[1]

I get confused by the perspective blend of inertial and quasi-accelerating frames of reference: walking at the same speed but the speed of light getting slower and slower. As noted [1], relativistic effects are indeed why the game becomes increasingly difficult, more challenging.

• YouTube > The Action Lab > “Slowing the Speed of Light Down to 2 m/s [walking speed] – What Special Relativity Feels Like” (August 13, 2020). “When we start walking, we start to see relativistic effects that include time dilation and length contraction, and also doppler shifting.”

Description*: “In this video I show you what it would look like to slow the speed of light down to around walking speed. So with just walking around town you would experience relativistic effects. I talk about time dilation and length contraction and what it would look like to have it happen to you. Get the simulation created by MIT here.”*

The Action Lab • Pinned by The Action Lab

The Action Lab (August 13, 2020)

Interesting note:Even Einstein was mistaken on length contraction.He had said that a sphere would look like an ellipsoid. However, Penrose later proved that a sphere would still be spherical, although rotated.Notice in the simulation how the spheres are the only objects that don’t look distorted when moving at near light speeds!

From transcript:

[Re

doppler shift] So what that means is that normally light that we can’t see, like infrared light, as we walk towards it, it gets shifted more towards the red end of the spectrum instead of the infrared part of the spectrum; so, it moves up in frequency, and since it moves up in frequency, it becomes visible light to us.… and also the effect is stronger – the brightness increases. that’s because as we’re walking towards it we’re actually hitting more photons along the way than we normally would, so basically it increases

the intensity as we’re walking towards it.Space and time are always connected. if you’re completely at rest – not moving, all of your movement is going through time and not through space. so you’re at rest but you’re still moving forward through time. but

if you start to move forward through space, then that means your movement through time has to decrease. so the faster you move through space, the slower your movement through time is going to be.Now of course this time dilation is only relative to somebody watching you do that movement. but

you yourself always experience time at the same rate. but how it portrays itself to you as thefirst person view– as the person who’s walking at close to speed of light speeds – is that it seems like you’re going faster, so you can get more movement through space in a given time.In this simulation, as i start to walk so as i approach the speed of light, things get stretched out. now the easiest way to see this is i’m going to turn off the doppler effect. collect my last orb, so now the speed of light is really close to my walking speed, so the relativistic effects are really strong here. so notice as i start to walk, now notice how far away the cliffs seem like they get, so the

length gets stretched out. but i just told you that when you go closer to the speeds of light length actually contracts.now this is a really confusing point and a lot of people have gotten this wrong.For the most part length contraction does not appear as something being squished, but it actually appears as something being stretched out and lengthened, and also

rotated a little bit. even though length contraction is occurring, this is not what you would see.what you would see is completely different than what you would measure as length, and that’s because the photons in your line of sight in the direction of your travel are leaving the thing thatyou’re seeing at different points in the past.So, for example, if you’re looking at something, you see it being stretched out because the [slower?] photons from the back of it take longer to get there than the front [faster photons?] of it, and so it actually appears as though the thing is being stretched out.

[1] Wiki:

In

A Slower Speed of Light, the player controls the ghost of a young child who was killed in an unspecified accident. The child wants to “become one with light”, but the speed of light is too fast for the child. This is solved through the use ofmagic orbswhich, as each are collected,slow down the speed of light, until by the end it is at walking speed. These orbs are spread throughout the level. At the beginning of the game, walking around and collecting these orbs is easy; however, as the game progresses,the effects of special relativitybecome apparent. This gradually increases the difficulty of the game.As the game progresses and light becomes slower, the effects of special relativity start to become more apparent. These effects include the

Doppler effect(red/blue-shifting of visible light and the shifting of ultraviolet and infrared into the visible spectrum), thesearchlight effect(increased brightness in the direction of travel),time dilation(difference between the passage of time perceived by the player and the outside world), theLorentz transformation(the perceived warping of the environment at near-light speeds), and theruntime effect(seeing objects in the past because of the speed of light). These effects combine as the game progresses to increase the difficulty and challenge the player.

Some commentary on the realism of this simulation – the optics of moving close to the speed of light:

• Stack Exchange > Physics > How realistic is the game “A slower speed of light”?

And the inherent limitations of OpenRelativity, as noted:

• Visualizing relativity: The OpenRelativity project (2015).

[2] A NASA cartoon about near-light-speed travel:

• YouTube > NASA Goddard > “NASA’s Guide to Near-light-speed Travel” (August 14, 2020)

• Biggest ideas in the universe – Sean Carroll chats concepts > The Biggest Ideas in the Universe | 6. Spacetime (Apr 28, 2020)

]]>A recent Nature article (below) was inspiration for this post. I’ve been encountering the use of topology in physics for some time. Typically the mathematics is elusive, but the notions are compelling.

Wiki > Topology

A continuous deformation (a type of homeomorphism) of a mug into a doughnut (torus) and a cow into a sphere.

In mathematics,

topology… is concerned withthe properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling and bending, but not tearing or gluing.Intuitively, two spaces are homeomorphic if one can be deformed into the other without cutting or gluing.

A traditional joke is that a topologist cannot distinguish a coffee mug from a doughnut, since a sufficiently pliable doughnut could be reshaped to a coffee cup by creating a dimple and progressively enlarging it, while shrinking the hole into a handle.

Homeomorphismcan be considered the most basic topological equivalence. Another is homotopy equivalence. This is harder to describe without getting technical, but the essential notion is that two objects are homotopy equivalent if they both result from “squishing” some larger object.

Topology is relevant to physics in areas such as condensed matter physics, quantum field theory and physical cosmology.A

topological quantum field theory(or topological field theory or TQFT) is a quantum field theory that computes topological invariants.

Although TQFTs were invented by physicists, they are also of mathematical interest, being related to, among other things,knot theory, the theory of four-manifolds in algebraic topology, and to the theory of moduli spaces in algebraic geometry.The topological classification of Calabi-Yau manifolds has important implications in

string theory, as different manifolds can sustain different kinds of strings.In cosmology, topology can be used to describe

the overall shape of the universe. This area of research is commonly known asspacetime topology.

Nature > News Q&A > “The mathematician who helped to reshape physics” by Davide Castelvecchi (August 4, 2020) – Barry Simon [who is at the California Institute of Technology in Pasadena] linked a phenomenon that had shocked physicists to topology, the branch of mathematics that studies shapes.

]]>In recent years, physics has been swept by ideas from a branch of mathematics called topology. Topology is the study of objects that deform continuously without tearing, for example through stretching or twisting. But it is now proving crucial to understanding

the shapes of quantum wavesformed by the electrons inside matter. These waves can form shapes such as vortices, knots and braids that give materials a variety of exotic properties. In 1983, Barry Simon was the first person to make the link between strange phenomena in materials and topology.German physicist Klaus von Klitzing won a Nobel prize for the [Hall] effect’s discovery in 1985. But it took several breakthroughs by theoretical physicists to begin to understand the phenomenon. And it took Simon — a mathematical physicist who uses mathematical tools to solve theoretical problems that emerge from nature — alongside collaborators, to recognize that equations created to describe the quantum Hall effect were a manifestation of topology. It was topology that was making the material’s resistance robust to small changes, allowing it to change in only discrete jumps [due to the topological effect, called a winding number].

All hail vector spaces!

Imagine walking into an elementary school classroom and finding kids talking about quantum states. Depicting quantum interactions using diagrams and bra-ket manipulatives, for wave functions. Someday, eh.

While we may never achieve Ernest Rutherford‘s notion of a quantum theory so simple that we can explain it to an untutored barmaid, science communicators and teachers and even well-known physicists have introduced the subject to younger and younger students. Certainly while we all hunker down at home, online resources for exploring the topic are readily available.

When I taught middle school mathematics, the “algebra for all” movement was already underway. I was part of a new program which taught algebra to all 8th graders. Of course with mixed results. Sometimes grappling with “math is hard” and “I’m not good at math” attitudes.[1]

In the end, however, mastery of algebra was evident when students not only talked the vocabulary but used it appropriately, their notational expressions matching their explanation.

So, yesterday, a YouTube video by “rebel” physicist Sabine Hossenfelder caught my attention: “Understanding Quantum Mechanics: It’s not so difficult!” In just 8 minutes, she unpacks the notational framework of quantum mechanics. And then points to the essential mathematical area of study – linear algebra – and online resources.

What is a vector, what is a matrix, what is an eigenvalue, what is a linear transformation?

And there’s the connection with the legacy of “algebra for all” – that algebra’s not so difficult – and quantum literacy.

• YouTube > Sabine Hossenfelder > “Understanding Quantum Mechanics: It’s not so difficult!” (July 18, 2020).

(caption) In this video I explain the most important and omnipresent ingredients of quantum mechanics: what is the

wave-functionand how do you calculate with it. Much of what makes quantum mechanics difficult is really not the mathematics. In fact, quantum mechanics is one of the easier theories of physics.The mathematics is mostly just linear algebra: vectors, matrices, linear transformations, and so on. You’ve learned most of it in school already! However, the math of quantum mechanics looks funny because physicists use aweird notation, called the bra-ket notation. I tell you how this works, what it’s good for, and how to calculate with it.

Not all physicists touch on the mathematics of quantum theory for the general public. Such books by famous physicists might, at best, have some references in appendices or footnotes for key mathematical stuff.

Other physicists, like Sean Carroll, have been routinely using wave function notation in online public chats and lectures. Even the “1 over square root of 2” coefficient in simple examples.[2]

One of the lessons that was driven home when I was an aerospace engineer was that every specialty, every major program, came with jargon (and lots of acronyms), reflecting compact communications between members of that work environment and customer space. Understanding physics discourse is similar.

What interests me most about Hossenfelder’s presentation is commentary about the mathematical model and reality. That’s where some literacy can help. A better conversation about the necessary simplification in building a model.[3] A better interplay of “the two cultures” in going forward. A better narrative for public policy.

I like the term “measurement update” regarding the (so-called) measurement problem (or wave-function collapse).

Quantum mechanics is pretty much just linear algebra. What makes it difficult is not the mathematics.

What makes it difficult is how to interpret the mathematics.The trouble is, you cannot directly observe the wave-function. But you cannot just get rid of it either; you need it to calculate probabilities. But themeasurement updatehas to be done instantaneously [hmm] and therefore it does not seem to be a physical process.So is the wave-function real?Or is it not? Physicists have debated this back and forth for more than 100 years.[4]

[1] But algebraic concepts were introduced prior to the 8th grade. Most of my 6th graders, for example, learned the basics of equations (within a broader context of problem solving.) Typically with better results than in 8th grade.

And I remember, as a videographer in 2001, witnessing students in a 3rd grade class processing mathematical equations – translating verbal and visual descriptions into mathematical relations. All of them free of any educational rubrics (such as “new math”), fearless in their joy of grasping the language of numbers and expressions. Something which many of their elders (even parents) approached with dread.

Of course, in 6th grade, success depended on a solid grasp of arithmetic. Multiplication tables, for example. And waiting for the bell to ring at the end of class was a good time to call out multiplication challenges.

Another key skill for success was the ability to parse verbal and written descriptions of problems. Word problems. I saw this issue even before I started teaching, while observing high school math classes. The challenge of extracting the relevant information and encoding it into mathematical statements. In middle school, for example, translating various words into addition, subtraction, multiplication, or division; and the corresponding symbols for these operations.

So, a teacher’s toolkit embraced pictures, diagrams, manipulatives, etc. To address how the ways we learn best vary from person to person. There’s no “one size fits all” approach.

And it all had to be in a safe and low stress learning environment. Stress (including food insecurity) tends to compromise learning.

[2] For example, YouTube > “The Biggest Ideas in the Universe | 8. Entanglement” (May 12, 2020).

[3] A model is a “**reduction of reality**,” which makes “some claim about how our world works.” Without simplification, the chance of getting even close to the target reality or solving the equations becomes problematical. And solutions which match measurement bolster the credibility of the model, with predictions that are “good enough.”

Reference: “The Heisenberg Uncertainty Principle of Social Science Modeling” by Ben Klemens (July 7, 2020).

[4] Additional excerpts from transcript:

]]>The mathematics of quantum mechanics looks more intimidating than it really is. To see how it works, let us have a look at

how physicists write wave-functions. The wave-function, to remind you, is what we use in quantum mechanics to describe everything. There’s a wave-function for electrons, a wave-function for atoms, a wave-function for Schrödinger’s cat, and so on.The wave-function is a vector, just like the ones we learned about in school.Now, the wave-function in quantum mechanics is … not a vector in the space we see around us, but a vector in an abstract mathematical thing called a

Hilbert-space. One of the most important differences between the wave-function and vectors that describe directions in space is that the coefficients in quantum mechanics are not real numbers but complex numbers,

In quantum mechanics, we do not write vectors with arrows. Instead we write them with these funny brackets.Why? Well, for one because it’s convention. But it’s also a convenient way to keep track of whether a vector is a row or a column vector. The ones we talked about so far are column-vectors. If you have a row-vector instead, you draw the bracket on the other side.This notation was the idea of Paul Dirac and is called the

bra-ket notation. The left side, the row vector, is the “bra” and the right side, the column vector, is the “ket”. You can use this notation for example to write a scalar product conveniently as a “bra-ket”. The scalar product between two vectors is the sum over the products of the coefficients.Now, in quantum mechanics,

all the vectors describe probabilities. And usually you chose the basis in your space so that the basis vectors correspond to possible measurement outcomes. The probability of a particular measurement outcome is then the absolute square of the scalar product with the basis-vector that corresponds to the outcome. Since the basis vectors are those which have only zero entries except for one entry which is equal to one, the scalar product of a wave-function with a basis vector is just the coefficient that corresponds to the one non-zero entry.And the probability is then the absolute square of that coefficient.The whole issue with the measurement in quantum mechanics is now that once you do a measurement, and you have

projected the wave-function onto one of the basis vectors, then its length will no longer be equal to 1 because the probability of getting this particular measurement outcome may have been smaller than 1. But once you have measured the state, it is with probability one in one of the basis states.So then you have to choose the measurement outcome that you actually found and stretch the length of the vector back to 1. This is what is called the “measurement update.”

So, today I’m celebrating the Moon. The ancient mythology and modern physics of its stabilizing influence.

Both the Moon’s natural prominence in the earthly sky and its regular cycle of phases as seen from Earth have provided cultural references and influences for human societies and cultures since time immemorial.

After enjoying the full moon for July 4th, today this phys.org article reminded me about the role our Moon has played in Earth’s evolution, perhaps even critical to life as we know it.

Phys.org > “Higher concentration of metal in Moon’s craters provides new insights to its origin” by USC (July 1, 2020).

Life on Earth would not be possible without the Moon; it keeps our planet’s axis of rotation stable, which controls seasons and regulates our climate. However, there has been considerable debate over how the Moon was formed.

So, I searched for additional articles (below) on the claim that life on Earth would not be possible without the Moon. My impression is that life probably would have evolved, but not necessarily as we know it or in the same timeframe.

• Scientific American > “Without the Moon, Would There Be Life on Earth?” by Bruce Dorminey (April 21, 2009).

… four billion years ago a cooling Earth already had an ocean, but remained barren. The moon was perhaps half as distant as it is now, and as a result, the ocean tides were much more extreme.

… the moon is currently receding from Earth at a rate of 1.5 inches (3.8 centimeters) per year. As it does, Earth’s own spin rate is slowing. And, in the process, roughly 1020 joules of gravitational energy is shed into the oceans annually.

Molecular biologist Richard Lathe of Pieta Research, a biotech consultancy in Edinburgh, Scotland, contends that some 3.9 billion years ago,

fast tidal cycling caused by the influence of our moon enabled the formation of precursor nucleic acids.

• Phys.org > “Did we need the moon for life?” by Fraser Cain (Nov 23, 2015).

When the moon was closer, the power of its gravity to pull the Earth’s water around was more ferocious. But what impact has this gravity had on our world and its life?

Do we need the moon to make the magic happen?

Turns out, we might owe our very existence to it because its pull of gravity might have set our plate tectonics in motion.Without plate tectonics, our planet might be more like Venus, toasty and dead.It raises the level of the world’s oceans towards the equator. Without this gravity, the oceans would redistribute, raising levels at the poles. It has also slowed Earth’s rotation on its axis.

Shortly after its formation, the Earth turned once every 6 hours. Without that moon to slow us down, we’d have much more severe weather.

It stabilizes the Earth’s rotation on its axis.It’s possible that the Earth might have rolled over on its axis on a regular basis, causing a complete redistribution of the Earth’s water. Astronomers think this happened on Mars, because it never had a large moon to stabilize it.But the biggest impact that the moon has on life is through

tides. That regular movement of water that exposes the land at the edge of the ocean, and then covers it again just a few hours later. This could have encouraged life to adapt and move from the oceans to land.

• Space.com > “Moonless Earth Could Potentially Still Support Life, Study Finds” by Nola Taylor Redd (August 9, 2011).

… new simulations show that, even without a moon, the tilt of Earth’s axis — known as its obliquity — would vary only about 10 degrees.

The influence of other planets in the solar system could have kept a moonless Earth stable.The stabilizing effect that our large moon has on Earth’s rotation therefore may not be as crucial for life as previously believed, according to a paper by Jason Barnes of the University of Idaho and colleagues which was presented at a recent meeting of the American Astronomical Society.

The new research also suggests that moons are not needed for other planets in the universe to be potentially habitable.

• NASA > Facts About The Moon.

The Moon’s presence helps stabilize our planet’s wobble, which helps

stabilize our climate.

• Inside Science > “What Would Happen If There Were No Moon?” by Marsha Lewis, Contributing Producer (Dec 2, 2015).

]]>Nights would be much, much darker. The next brightest object in the night sky is Venus. But it still wouldn’t be enough to light up the sky. A full moon is nearly two thousand times brighter than Venus is at its brightest.

Without the moon, a day on earth would only last six to twelve hours.

There could be more than a thousand days in one year!That’s because the Earth’s rotation slows down over time thanks to the gravitational force — or pull of the moon — and without it, days would go by in a blink.A moonless earth would also change the size of ocean tides — making them about one-third as high as they are now.

Without a moon the tilt of our earth’s axis would vary over time. This could create some

very wild weather. Right now, thanks to our moon, our axis stays tilted at twenty-three point five degrees. But without the moon the earth might tilt too far over or hardly tilt at all leading to no seasons or even extreme seasons.

Without the moon helping to keep the earth on a steady tilt, scientists have even imagined that life on earth may not have evolved the way we know it.

These demonstrations illustrate the limits of everyday experience and provide interesting historical lessons.

• Physics World > “The legend of the leaning tower” by Robert P Crease (04 Feb 2003).

So why do falling-body experiments continue to be so popular? They were, for example, voted into the top 10 “most beautiful experiments” of all time in my recent poll of Physics World readers (September 2002 pp1920). I think the answer is related to the fact that, as

everyday experiencesuggests, heavier bodies do fall faster than light ones.

Here’s a more recent article on testing the strong equivalence principle (SEP) – in a gravitational field heavy and light objects fall at the same rate.[2] Another shout-out for research using X-ray data.

The same thing happens with you and Earth. When you jump, you fall back toward the planet very quickly. But the planet falls toward you as well — very slowly, due to your own low gravity, but at the exact same rate as a feather or a hammer would if you ignore air resistance.

• Space.com > “Einstein’s core idea about gravity just passed an extreme, whirling test in deep space” by Rafi Letzter (June 17, 2020) – Once again, physicists have confirmed one of Albert Einstein’s core ideas about gravity — this time with the help of a neutron star flashing across space.

“At some level, the majority of physicists believe that Einstein’s theory of gravity, called general relativity, is correct. However, that belief is mainly based on observations of phenomena taking place in regions of space with weak gravity, while Einstein’s theory of gravity is meant to explain phenomena taking place near really strong gravitational fields,” Morsink[1] told Live Science. “Neutron stars and black holes are the objects that have the strongest known gravitational fields, so any test of gravity that involves these objects really test the heart of Einstein’s gravity theory.”

[1] Astrophysicist Sharon Morsink, University of Alberta, Canada.

[2] As Wiki says, more specifically:

The

strong equivalence principlesuggests the laws of gravitation are independent of velocity and location. In particular,• The gravitational motion of a small test body depends only on its initial position in spacetime and velocity, and not on its constitution.

• The outcome of any local experiment (gravitational or not) in a freely falling laboratory is independent of the velocity of the laboratory and its location in spacetime.

The strong equivalence principle suggests that gravity is entirely geometrical by nature(that is, the metric alone determines the effect of gravity) and does not have any extra fields associated with it. If an observer measures a patch of space to be flat, then the strong equivalence principle suggests that it is absolutely equivalent to any other patch of flat space elsewhere in the universe.Einstein’s theory of general relativity(including the cosmological constant) is thought to be the only theory of gravity that satisfies the strong equivalence principle.

While already following this Big Science project [1], with construction underway (for the next 3 years), I felt that a specific post was appropriate. The **Deep Underground Neutrino Experiment** (DUNE) is a massive worldwide collaboration between countries, organizations, and over a 1000 scientists. All hail neutrinos! [2]

I spent some time yesterday pondering **neutrino oscillation**. Measuring how these particles change their identities is one of DUNE’s research objectives. Recently I viewed some YouTube videos (noted below) by **Fermilab**‘s Don Lincoln on this topic – helping to clarify how neutrino mass and flavor are sort of superpositions – a mixed vs. pure state.

• Symmetry Magazine > “DUNE moves to the next stage with a blast” by Lauren Biron and Leah Hesla (June 24, 2020) – Construction workers have carried out the first underground blasting for the **Long-Baseline Neutrino Facility**, which will provide the space, infrastructure and particle beam for the international **Deep Underground Neutrino Experiment**.

On June 23, construction company Kiewit Alberici Joint Venture set off explosives 3650 feet beneath the surface in Lead,

South Dakota, to begin creating space for the international Deep Underground Neutrino Experiment, hosted by theDepartment of Energy’s Fermilab.The blast is the start of underground excavation activity for the experiment, known as DUNE, and the infrastructure that powers and houses it, called the Long-Baseline Neutrino Facility, or LBNF.

Wiki:

The Deep Underground Neutrino Experiment (DUNE) is a neutrino experiment under construction, with a near detector at Fermilab and a far detector at the Sanford Underground Research Facility that will observe neutrinos produced at Fermilab. It will fire an intense beam of trillions of neutrinos from a production facility at Fermilab (in Illinois) over a distance of 1,300 kilometers (810 mi) to an instrumented 70-kiloton volume of liquid argon located deep underground at the Sanford Lab in South Dakota. The neutrinos will travel in a straight line through the Earth, reaching about 30 kilometers (19 mi) underground near the mid-point; the far detector itself will be 1.5 kilometers (4,850 ft) under the surface). About 870,000 tons of rock will be excavated to create the caverns for the far detectors. More than 1,000 collaborators work on the project.

The

Deep Underground Neutrino Experimentis an international flagship experiment to unlockthe mysteries of neutrinos. DUNE will be installed in theLong-Baseline Neutrino Facility, under construction in the United States. DUNE scientists will paint a clearer picture of the universe and how it works.The U.S. Department of Energy’s Fermilab is the host laboratory for DUNE, in partnership with funding agencies and more than 1,000 scientists from all over the globe. They contribute expertise and components, which provide economic benefits to each of the partner institutions and countries. DUNE consists of

massive neutrino detectors, at Fermilab inIllinoisand Sanford Underground Research Facility inSouth Dakota. LBNF produces the world’s most intense neutrino beam and provides the infrastructure.The PIP-II particle accelerator at Fermilab powers the neutrino beam.

• YouTube > Fermilab > Don lincoln > “Subatomic Stories **#10**: Understand neutrino oscillations like the pros” (June 11, 2020).

• Episode #11 (June 17, 2020) is on the Heisenberg uncertainty principle [3], but the Q&A part has some questions about neutrinos. [4]

• YouTube > Fermilab > Don lincoln > “Subatomic Stories **#12**: What scientists know about neutrino masses” (June 24, 2020).

This Fermilab page lists some of the essential questions about the neutrino:

- How much does a neutrino
**weigh**? - Which neutrino is the
**lightest**? - How many
**flavors**of neutrinos are there? - Are neutrinos their own
**antiparticles**? - Are all neutrinos
**left-handed**? - Do neutrinos violate the
**symmetries**of physics? - Where do the most energetic neutrinos
**come from**?

In his videos (noted above), Don Lincoln presents some tables about neutrino flavors (electron, muon, and tau) and masses (ν1, ν2, and ν3). There’s no one-to-one correspondence: “… mass and flavor neutrinos do not overlap perfectly.” This Fermilab page summarizes two mass scenarios:

ν1 ~< ν2 < ν3

ν3 < ν1 ~< ν2

Scientists can check whether neutrinos come in the normal or inverted mass ordering with experiments that look at

how neutrinos change over long distances. If things are “normal,” certain neutrino oscillations (changes between flavors) should happen at a higher rate than in the inverted world.The best measurement of that mass difference comes from looking at the energies of

neutrinos that come from reactors, usually carrying energies of a few million electronvolts, that are about 200 kilometers away from their source.Scientists have been able to pin down the large mass difference very well, too. The best measurement of that mass difference comes from looking at the energies of

neutrinos that come from accelerator sources. Those neutrinos have on the order of a billion or a few billion electronvolts, and the detectors are typically located 300 to 800 kilometers away from the source.Each neutrino of

a specific flavor is actually a combination of neutrinos of different masses. As a result, each neutrino of a specific mass has a certain chance [probability] of interacting as a particular flavor. For example,ν1 is very likely to interact as an electron neutrino.Neutrino oscillations are characterized by “

mixing parameters,” which dictate how the mass states add up to form the particular flavor states. (Mixing parameters also look at the differences between the squares of the three mass states.)The probability that the neutrino flavor at the point of interaction is different from the flavor at the point of creation depends on the speeds at which the three mass neutrinos move. This fact tells scientists both that neutrinos have mass and that those masses are different, because

if neutrinos were massless, they would all travel at the speed of light.In the simplest explanation for neutrino flavor change, the three neutrino flavors are quantum mechanical combinations of three neutrino mass states. This means that

neutrinos travel as a combination of the three mass states rather than as a single, static flavor.… we still don’t know the absolute mass of the neutrino. What we do know is that the three known types of neutrinos have different masses and that the sum of all three of those types is still

less than one millionth the mass of an electron.Neutrinos are the lightest of the massive fundamental particles in the

Standard Model. We know that neutrinos have mass because we have observed them change from one flavor into another, a process that can happen only if the neutrinos have mass. Interestingly, that process also requires the different flavors to have different masses. But unfortunately, the flavor change process depends only on the masses of the different flavors being different; it cannot tell us anything about the actual mass of the neutrino.

The charged leptons and quarks acquire their masses through interactions with the Higgs boson, but that isn’t necessarily the case for neutrinos. It also isn’t ruled out completely.One theory predicts that the neutrino has a very heavy partner that exists for a very brief time, and that heavy partner interacts with the Higgs boson to produce the light neutrinos we observe. Through the Higgs mechanism, then, the light neutrino mass would be ina “seesaw” relationshipwith the heavy partner mass –as the mass of the partner goes up, the mass of the light neutrino goes down. But this seesaw relationship has not yet been experimentally verified.

This University of California @ Irvine page notes that:

The probability of a neutrino changing type is related to the distance travelled by the neutrino from its point of production to its point of detection.

As a general rule, neutrinos travelling greater distances will exhibit greater depletion from oscillation.Moreover, the oscillation probability varies smoothly over increasing distance.

So, I do not recall seeing any particlular analogies for modeling neutrino oscillation. For mere mortals. Hopefully in lectures somewhere. Currently my best idea was to review visualizations for **coupled ocillators**, e.g., two coupled pendulums. And then consider a neutrino as sort of a coupled Majorana (particle-antiparticle) pair, with masses (ν1, ν2, ν3) as three modes, and “neutrino” oscillation as transitions between (or superpositions of) those modes. The mode with highest interaction corresponds to the highest mass (energy).

The search for sterile neutrinos is an active area of particle physics.

Do neutrinos and antineutrinos differ only in their chirality? Or do exotic right-handed neutrinos and left-handed antineutrinos exist as separate particles from the common left-handed neutrinos and right-handed antineutrinos?

• YouTube > Dan Russell, Penn State University, Graduate Program in Acoustics > “Coupled Pendulum” (Nov 8, 2014).

Another interesting visualization by Dan Russell is a two degree-of-freedom (2-DOF) mass-spring system (two identical masses connected by three identical springs), which exhibits two natural modes and a third coupled interaction.

• Mode 1 = coupling spring static (no cycle of stretching / compression) – like two identical 1-DOF systems in phase (equivalent to one mass with 2 springs but lower frequency by square root of 2). No nodes. Lowest system energy.

• Mode 2 = two masses move in opposite directions; coupling spring cycled in stretching / compression. (One node.) Higher system energy.

• Mode 3 = displaced (perturbed) interaction where one mass is moved from equilibrium position before releasing both; oscillators cycle in trading energy. Highest system energy.

His animation of a 3-DOF mass-spring system has 3 natural modes.

The future of (particle) physics?

Online videos > Fermilab > PIP-II: the new heart of Fermilab

[1] And, keeping things real, massive Big Science projects pose safety and enviromental issues during constrcution and operation, as noted in this article:

Nature > “Italian physicists to stand trial for conditions in underground lab” by Nicola Nosengo (May 16, 2019) – The Gran Sasso National Laboratories have seen no major accidents so far, but prosecutors charge that environmental controls were lax.

[2] And neutrinos play a role in multi-messenger astronomy.

[3] And regarding the **uncertainty principle**, Lincoln’s explanation corrects what many of us are taught in high school or college about its meaning. All hail the wave function!

Now if you want to have some knowledge of both the position and momentum of the particle, you need to change the

wave functionfrom an infinite sine wave to something more localized. To do that, you can simply start adding up the wave functions of particles whose momentum is well known, but for whom the position is not known. You start with a single wave, but then you add a series of waves that have a wavelength that are slightly different than the initial one. The cumulative wave function [Fourier Transform], which is the sum of more and more different wavelengths slowly morphs from being a sine wave to beinga wave function that is more localized.And in order to localize the wave function, you need to add all the wavelengths, which means you have no information about the wavelength and therefore the velocity. Because wavefunctions are built of mixes of wavelengths,

the more you focus the position, the broader range of wavelengths is needed. The more you restrict the wavelength, the less information you have about the position. That’s the real reason for the Heisenberg Uncertainty principle.In the case of virtual [vs. real] particles, the electrons exist for only a very short time. That means that both the energy and momentum could differ from the average and the result is that you could have electrons with a range of masses – even cases where the square of the mass is negative. Virtual particles break a lot of the rules and are super confusing when you first encounter them.

[4] From Q&A of Episode #11 (June 17, 2020) on the Heisenberg uncertainty principle:

• **Where do neutrinos get their mass from?**

The short answer is that we don’t know. They could get their mass from interactions with the Higgs field, but we aren’t sure about that. Neutrinos are so much less massive than other particles, that it’s possible that they get their mass from another mechanism.

• **Can a neutrino could pass through a neutron star?**

]]>The answer is basically no, or at least mostly so. The probability that a neutrino will interact depends on energy and the density of the material it is travelling through.

For a

high energy neutrinoof a hundred billion electron volts of energy, the neutrino will travel less than a tenth of a millimeter before interacting.For

low energy neutrinos, they can penetrate much farther, but we’re still talking a distance of about a meter or so.

Very low energy muon neutrinosdon’t have enough energy to make muons, so they bounce around inside the star essentially forever and eventually find their way out.The neutrino that would penetrate a neutron star most easily would have to an be

electron neutrino with a few million electron volts of energy. In principle, they could encounter a proton and make a neutron. The density of protons inside neutron stars is very poorly known, but if you take reasonable numbers, then a very low energy electron neutrino might travel as far as a kilometer before finding a rare proton and turning it into a neutron.

Force-less physics? No, I do NOT mean that the language of forces (electromagnetism, strong, weak, gravity) does not apply to our everyday experience or to physical descriptions. But only to a point, yes, as maybe counterproductive to deeper understanding. To getting beyond the Standard Model [7]. To understanding how the wave function is an approximation. And taking quantum field theory (QFT) really seriously.

QFT is hard, a combination of the hardest and most important physics. Lots of infinite quantities. Hilbert spaces. Normalizing. Best way to describe nature at its deepest level. – my note from Sean Carroll’s YouTube video The Biggest Ideas in the Universe | 9. Fields

It’s really all about energy. And how that contoured energy emerges in terms of forces. [1]

So, if the best analogies (or metaphors) for explaining “forces” are tossing objects back & forth, then something’s still “fishy” about quantum theory.

Subatomic forces at the quantum level are best understood as a cloud of force-carrying particles jumping from one object to another. – Don Lincoln [2]

In one case, for **repulsion**, analogies use scenarios of standard objects thrown back & forth between “agents” (people, automata, etc.) on a slippery surface. Thrown = emitted. Caught = absorbed. The actions and reactions cause the agents to move apart. Throwing pushes the thrower away; catching pushes the catcher away. So, the agents move away from each other. [Find a video of an actual demonstration?]

In the other case, for **attraction**, analogies use scenarios of peculiar objects thrown back & forth. Objects that carry momentum in a contrary direction.[3] Objects like boomerangs. For example, agent #1 throws a boomerang in the opposite direction to agent #2, but it loops back toward and around agent #2, who catches the boomerang as it’s going back toward agent #1. Throwing pushes the thrower toward; catching pushes the catcher toward. So, the agents move toward each other.

Moving up a level of understanding, Feynman’s sum over all (possible) paths of exchanged (virtual) particles results in a net metaphorical hill or valley of action/reaction energy between the agents. Hill = repulsion. Valley = attraction. At least in this case, for the electromagnetic (EM) force, there’s only one type of photon rather than standard and boomerang types. [Find a visualization of that?]

Can we do without swarms of force-carrying particles?

Can’t we at least imagine some visualizations involving fluids and pressure gradient differences?

Sure, there are limits to any analogy. A point where any metaphor becomes a counterproductive rabbit hole. But can’t we do better? There’s just something so lacking in analogies presented by physicists. (Perhaps that’s why quantum theory is incomplete as well?)

I’m surprised that veteran physicists and seasoned science communicators can’t do better. I expected more in the last 50 years. Perhaps there’s just no practical reason to pursue better visualizations. After all, in practice everything works just fine. Calculations to 12 decimal places! Technology advances. Career-wise, not much incentive to speculate, more motivation to compute or advance exotic mathematical frameworks.

But there’re problems. Nags that quantum theory is incomplete. Unsolved problems in physics.

So, in **quantum electrodynamics** (QED) and **quantum chromodynamics** (QCD), there’re so-called matter particles and “force carrying” particles (bosons). Feyman diagrams are visual ways of organizing the complex math. Physicists recognize that particle exchange really is about field interactions. But visualization goes no further.

Interaction between vacuum energy (of so-called empty space) and field energy is left as “**the dance of quantum activity** that includes virtual quarks … in **the hubbub of virtual activity that surrounds all particles**.” [6]

Feynman diagrams are shorthand accounting. Virtual “force particle” exchange is just a visual way of accounting for a more complex way in which energy density – field potential, is shaped. And contoured energy density sort of sounds like fluid dynamics, eh.

But when I think of sum over all paths, I think of interactions of expansive, extended vibrations in spacetime, not particle paths. Like waves moving in all directions (vs. moving along paths). As Carroll says in his YouTube video The Biggest Ideas in the Universe | 8. Entanglement: “Some smushy spherical disturbance, going off in all different directions.”

And when I think of (matter) fields, I think of interacting excitations. Extended in space and time. Superimposed excitations. Entangled excitations. And the energy in spacetime contoured by “charge.” Contoured so that net gradients between excitations may be characterized as repulsive or attractive.

[1] In the sense that we tend to identify forces with the (spatial) derivatives of (field) potential.

As I’ve written elsewhere:

Metaphorically, consider a stream or pond with an outflow point in the bed or bottom. That point does not (symmetrically) pull or push water. What it does is create localized [pressure] gradients in the flow of water. An object caught in those gradients is moved, as if a force is pulling / pushing it. The outflow point does not have a property of attraction (or repulsion).

Or, as Wilczek wrote: “… charge … creates a disturbance in the Grid” – a space-filling medium aboil with virtual particles – what we normally perceive as empty space.

Ordinary matter is a secondary manifestation of the Grid, tracing its level of excitation.

In Wilczek’s view, mass arises because the Grid is permeated with a not-yet-understood property that “slows down” some of the interactions in the field, just as electrons are slowed down in a superconducting medium. In the medium known as the Grid, we perceive that slowed-down quality as mass.

[2] Regarding analogies (vs. impenetrable math) on how “force” particles cause attraction and repulsion, this Fermilab video probably has the clearest visualizations you’ll find.

YouTube > Fermilab > Don Lincoln > “Subatomic Stories: Forces the Feynman way” (May 6, 2020).

Subatomic forces at the quantum level are best understood as a cloud of force-carrying particles jumping from one object to another. In Episode 5 of Subatomic Stories, Fermilab’s Dr. Don Lincoln gives a brief explanation of this phenomenon, including two analogies for how this complicated mathematics can be understood.

[3] Or imagine in electromagnetism (EM) that somehow an opposite charge causes the virtual photon to behave as if it (the exchanged particle) has negative mass.

[4] So, mass might be considered some type of “charge.” In a metric field. Then EM and gravity are about charge. Or, “charge” is some type of energy; and then EM and gravity are about energy density.

[5] Also, if an electron and positron share the same (electron) field and are reverse excitations in some sense; and “collisions” typically result in annihilation with emission of photons … it may be simpler to visualize wave forms being flipped / nulled (and kinetic surplus carried off as real photons) than swarms of (virtual) photons disappearing. In any case, an interesting experiment might be to detect any time-lag between proximty and emission of radiation.

And as to why there are only two types of EM charge … symmetry?

But the metric field is really the (spacetime) vacuum and effectively neutral. Paired virtual particles of opposite charge may emerge into fields, but the vacuum itself is not characterized by contrary excitations. So, as to whether spacetime geometry can be “reversed” …

[6] Quanta Magazine > “What Goes On in a Proton? Quark Math Still Conflicts With Experiments” by Charlie Wood (May 6, 2020).

A humble electron, for instance, can briefly emit and then absorb a photon. During that photon’s short life, it can split into a pair of matter-antimatter particles, each of which can engage in further

acrobatics, ad infinitum. As long as each individual event ends quickly, quantum mechanics allowsthe combined flurry of “virtual” activity to continue indefinitely.

[7] The “Physics preamble” of this “LHC the Guide: faq” CERN Brochure (January 2008) contains a helpful recap of the **Standard Model**.

]]>Please note that when speaking about particle collisions in the accelerator, the word ‘interaction’ is a synonym of ‘collision’.

This is a topic which I’ve followed for decades. A holy grail of physics: room temperature superconductivity. The physics of Cooper pairs: what makes two electrons pair up when their charge actually makes them repel each other?

SciTechDaily > “Breakthrough in Understanding the Physics of High-Temperature Superconductivity” by Helmholtz-Zentrum Dresden-Rossendorf (May 12, 2020).

How do electrons form pairs in high-temperature superconductors such as cuprates?

In superconductivity, electrons combine to create “Cooper pairs,” which enables them to move through the material in pairs without any interaction with their environment. But what makes two electrons pair up when their charge actually makes them repel each other?

For conventional superconductors, there is a physical explanation: … One electron distorts the crystal lattice, which then attracts the second electron. For cuprates, however, it has so far been unclear which mechanism acts in the place of lattice vibrations.

At this point “

Higgs oscillations” enter the stage: In high-energy physics, they explain why elementary particles have mass. But they also occur in superconductors, where they can be excited by strong laser pulses. They represent the oscillations of the order parameter –the measure of a material’s superconductive state, in other words, the density of the Cooper pairs.

So, “Higgs oscillations” = oscillations in the density of the Cooper pairs? Such oscillation can be induced via cyclic high-energy laser pulses. Like using your legs to continuously maintain a swing, eh.

]]>[Image caption] By applying a strong terahertz pulse (frequency ω), they stimulated and continuously maintained Higgs oscillations in the material (2ω). Driving the system resonant to the Eigenfrequency of the Higgs oscillations in turn leads to the generation of characteristic terahertz light with tripled frequency (3ω). Credit: HZDR / Juniks

Today my post celebrates another science communicator, Fraser Cain, and his YouTube channel by the same name. This week, I noticed his video “**Two Supermassive Black Holes Orbiting Each Other. Stephen Hawking Was Right!**” (May 11, 2020). Well-done visualization.

His channel description says:

Space and astronomy news from Fraser Cain, publisher of

Universe Todayand co-host of Astronomy Cast.If you’re a fan of space, sci-fi and pop culture, you’ll love our Guide to Space. These short videos come out every Monday and Thursday and answer a burning question that astronomy fans want to know. We talk about black holes, galaxies, the Universe, and the search for aliens.

Cain teamed up with a science teacher for the book **The Universe Today Ultimate Guide to Viewing the Cosmos: Everything You Need to Know to Become an Amateur Astronomer** (published October 23, 2018), a resource for viewing the Night Sky.

David Dickinson is an Earth science teacher, freelance science writer, retired USAF veteran and backyard astronomer. He currently writes and ponders the universe as he travels the world with his wife.

Fraser Cain is the publisher of Universe Today. He’s also the co-host of Astronomy Cast with Dr. Pamela Gay. He lives in Courtenay, British Columbia.

Wiki: Binary black hole (BBH).

And here’re some more questions about black hole systems.

So, most, if not all, black holes spin; and around them are spinning accretion disks of matter which feed those black holes. How fast is the spin in each case?

Or, how fast can matter fall into a black hole? That’s the question addressed in this article (below). The geometric alignment of a black hole system is important.

Royal Astronomical Society > “Matter falling into a black hole at 30 percent of the speed of light” (2018).

A UK team of astronomers report the first detection of matter falling into a black hole at 30% of the speed of light, located in the centre of the billion-light year distant galaxy PG211+143. The team, led by Professor Ken Pounds of the

University of Leicester, used data from theEuropean Space Agency’s X-ray observatory XMM-Newtonto observe the black hole. Their results appear in a new paper in Monthly Notices of the Royal Astronomical Society.Until now it has been unclear how

misaligned rotationmight affect the in-fall of gas. This is particularly relevant to the feeding of supermassive black holes since matter (interstellar gas clouds or even isolated stars) can fall in from any direction.

YouTube > Uni of Leicester > “**Computer simulation predicts matter plunging into a black hole at extreme velocity**” (Sep 17, 2018).

X-rays are so cool, eh.

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