This video about Einstein’s general [vs. special] relativity equations is interesting. Not that I can grasp a higher-dimensional hypergraph, a geodesic ball of a Riemannian manifold, etc. [1] But that the derivation starts from some first principles and obtains Einstein’s formulation – an alternate approach..

Also, this struck me for the non-vacuum derivation – “that particles can be treated as **localized topological obstructions**.” (Akin to my comments about so-called particles as “knots.”)

• YouTube > The Last Theory > “How to derive general relativity from Wolfram Physics with Jonathan Gorard” (Sep 21, 2023) and hosted by Mark Jeffery – The structure of space-time in the presence of matter falls out of the hypergraph.

DESCRIPTION

One of the most compelling results to come out of the

Wolfram Physicsis Jonathan’s derivation of the Einstein equations from the hypergraph.Whenever I hear anyone criticize the Wolfram model for bearing no relation to reality, I tell them this: Jonathan Gorard has proved that general relativity can be derived from the hypergraph.

In this excerpt from our conversation, Jonathan describes how making just three reasonable assumptions –

• causal invariance

• asymptotic dimension preservation

• weak ergodicity– allowed him to derive the vacuum Einstein equations from the Wolfram model.

In other words, the structure of space-time in the absence of matter more or less falls out of the hypergraph.

And making one further assumption – that particles can be treated as localized topological obstructions – allowed Jonathan to derive the non-vacuum Einstein equations from the Wolfram model.

In other words, the structure of space-time in the presence of matter, too, falls out of the hypergraph.

It’s difficult to overstate the importance of this result.

At the very least, we can say that the Wolfram model is consistent with general relativity.

To state it more strongly: we no longer need to take general relativity as a given; instead, we can derive it from Wolfram Physics.

**Notes**

[1] I have a general appreciation of the stress-energy tensor, but hardly these terms / concepts:

• Hausdorff dimension

• Geodesic balls, tubes & cones

• Ricci scalar curvature

• Ricci curvature tensor

• Einstein equations

• Einstein–Hilbert action

• Relativistic Lagrangian density

• Causal graph

• Tensor rank

• Trace

**Related posts**

This video about Einstein’s general [vs. special] relativity equations is interesting. Not that I can grasp a higher-dimensional hypergraph, a geodesic ball of a Riemannian manifold, etc. [1] But that the derivation starts from some first principles and obtains Einstein’s formulation – an alternate approach..

Also, this struck me for the non-vacuum derivation – “that particles can be treated as **localized topological obstructions**.” (Akin to my comments about so-called particles as “knots.”)

• YouTube > The Last Theory > “How to derive general relativity from Wolfram Physics with Jonathan Gorard” (Sep 21, 2023) and hosted by Mark Jeffery – The structure of space-time in the presence of matter falls out of the hypergraph.

DESCRIPTION

One of the most compelling results to come out of the

Wolfram Physicsis Jonathan’s derivation of the Einstein equations from the hypergraph.Whenever I hear anyone criticize the Wolfram model for bearing no relation to reality, I tell them this: Jonathan Gorard has proved that general relativity can be derived from the hypergraph.

In this excerpt from our conversation, Jonathan describes how making just three reasonable assumptions –

• causal invariance

• asymptotic dimension preservation

• weak ergodicity– allowed him to derive the vacuum Einstein equations from the Wolfram model.

In other words, the structure of space-time in the absence of matter more or less falls out of the hypergraph.

And making one further assumption – that particles can be treated as localized topological obstructions – allowed Jonathan to derive the non-vacuum Einstein equations from the Wolfram model.

In other words, the structure of space-time in the presence of matter, too, falls out of the hypergraph.

It’s difficult to overstate the importance of this result.

At the very least, we can say that the Wolfram model is consistent with general relativity.

To state it more strongly: we no longer need to take general relativity as a given; instead, we can derive it from Wolfram Physics.

**Notes**

[1] I have a general appreciation of the stress-energy tensor, but hardly these terms / concepts:

• Hausdorff dimension

• Geodesic balls, tubes & cones

• Ricci scalar curvature

• Ricci curvature tensor

• Einstein equations

• Einstein–Hilbert action

• Relativistic Lagrangian density

• Causal graph

• Tensor rank

• Trace

**Related posts**

Here’s a recent article by Fermilab’s Don Lincoln which updates his (included) Jan 14, 2016, YouTube video on Quantum Field Theory. One refreshing part of the article is a visualization of a wave packet (similar to those in my post above) – which resolves the so-called “wave-particle duality” – and this outright declaration:

For example, an object like an electron has a wavelength, but it doesn’t extend off to infinity. Instead, the amplitude (or height) of the wave has a location where it is maximized, and then it decreases at distances farther from the maximum. The result is what is called a wave packet. …

It is completely reasonable to think of subatomic particles like electrons and photons as wave packets, …

There are places where Lincoln still uses *legacy phrases* based on intrinsic properties. Like when he writes: “subatomic entities, like electrons and photons, **possess** both wave and particle characteristics” or “subatomic objects **have** both wave and particle properties.” Rather than saying **exhibit** such properties (or that their **interactions exhibit** such properties).

• Big Think > “What is a quantum particle really like? It’s not what you think” by Don Lincoln (September 19, 2023) – Imagine tuning forks, not tiny-ball models (not even fuzzy ones).

]]>… [so-called] particle interactions are a heady mix of

vibrating and interacting fields.According to this theory, an electron is nothing more than

a wave packet in the electron field. The meaning of the wave packet is the same as in traditional quantum mechanics — that is, if you square the wave function (representing the wave packet), the outcome is the probability of detecting an electron at that location.

This article references a useful NASA visualization of galactic motion with and without (so-called) dark matter.

Terms: (in)elastic collision, lower mass limit

• Space.com > “We still don’t know what dark matter is, but here’s what it’s not” by Monisha Ravisetti (August 21, 2023) – “It’s all about mindset in science, where a null result can be as impactful as a positive result.” – Daniel Jardin (Northwestern University), member of Super Cryogenic Dark Matter Search (SuperCDMS) collaboration.

“

There are roughly 1 billion dark matter particles passing through you every second, but they interact so rarely that you can’t tell,” Jardin said. “We’re looking for a 1 in a billion billion billion billion chance of interaction.”

• YouTube > NASA Goddard > “Mystery of Galaxy’s Missing Dark Matter Deepens” (Jun 17, 2021) – The mystery of why NGC 1052-DF2 is missing most of its dark matter still persists.

]]>The article below is NOT about two-photon physics as in matter creation (image).

Wiki > A **Feynman diagram** for photon–photon scattering: one photon scatters from the transient vacuum charge fluctuations of the other.

From quantum electrodynamics it can be found that photons cannot couple directly to each other and a fermionic field according to the Landau-Yang theorem since they carry no charge and … a photon can, within the bounds of the uncertainty principle, fluctuate into a virtual charged fermion–antifermion pair, to either of which the other photon can couple.

See also: Wiki > Matter creation > Photon pair production

The article IS about shaping electromagnetic pulses (of radio frequencies) … an interesting perspective on interactions in the photon (EM) field.

So, how do researchers manipulate photons so that they can “collide” – interacte in new ways?

What’s a time reflection? (Temporal re-ordering: the wave’s “trailing edge prior to reflection is now at the front. … the reflected wave maintains its shape but is stretched out in time.”)

How do you engineer a material with time variations of their electromagnetic properties?

Well, by sending broadband signals (wavepackets) into a strip of metal filled with (super fast) electronic switches that are connected to reservoir capacitors – controlling impedance (effectively the refractive index) along the strip. “This causes a portion of that wave to reverse and its frequency transforms into another one.”

In this case, the two microwave photons are (apparently) “a signal consisting of two unequally strong peaks.”

• Phys.org > “No longer ships passing in the night: These electromagnetic waves had head-on collisions” by CUNY Advanced Science Research Center (August 14, 2023) – Typically, when two electromagnetic waves cross paths, they move right through each other without interacting.

While photons would be expected to go through each other without any interaction, by triggering a time interface the scientists were able to demonstrate strong photon-photon interactions and control the nature of the collision.

“This newest work shows that we can use abrupt temporal changes in tailored metamaterials – known as time interfaces – to make waves collide as if they were massive objects. We were also able to control whether the waves exchanged, gained or lost energy during these collisions.” [Andrea Alù, Distinguished Professor and Einstein Professor of Physics at The City University of New York Graduate Center and founding director of the CUNY ASRC Photonics Initiative.]

**Notes**

[1] From an early 2023 news cycle … lots of hype.

• Physics World > “Physicists perform first measurement of ‘time reflection’ in microwaves” (Mar 17, 2023)

]]>The material in question consists of a 6m-long strip of metal serving as a microwave waveguide that snakes back and forth 20 times to form a device some 30 cm^2. Thirty capacitive circuits are positioned at regular intervals along the length of the strip, but separated from it by switches. The idea is to inject a train of microwave pulses and then switch all the circuits on or off at the same time while the pulses are in transit along the strip – causing a sudden change in the metamaterial’s effective refractive index and impedance. That sudden change temporally reflects the microwave signal.

As noted above: “If you try to replicate this [LHC] 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.”

So, do photons interact with each other? Can “matter” be created directly from the photon (electromagnetic) field? Evidently only at extreme photon energies and densities. Like in pulsars.

The first step to achieving laboratory photon–photon “collision” is to do the math, simulate the conditions.

• Phys.org > “Let there be matter: Simulating the creation of matter from photon–photon collisions” by Osaka University (August 10, 2023) – A team led by researchers at Osaka University has simulated conditions that enable photon–photon collisions, solely by using lasers.

]]>“Our simulations demonstrate that, when interacting with the intense electromagnetic fields of the laser, dense plasma can self-organize to form a

photon–photon collider,” explains Dr. Sugimoto, lead author of the study. “This collider contains adense population of gamma rays, ten times denser than the density of electrons in the plasma andwhose energy is a million times greater than the energy of the photons in the laser.”

Photon–photon collisions in the collider produce electron–positron pairs, and the positrons are accelerated by a plasma electric field created by the laser. This results in a positron beam.

Quantum phenomena in mechanical systems? How does that work? Nanofabrication. And ultra-low quantum decoherence. For 7.7 milliseconds.

• Phys.org > “A quantum leap in mechanical oscillator technology” by Ecole Polytechnique Federale de Lausanne (August 11, 2023) – By coupling mechanical oscillators (optomechanical systems) to light photons, scientists have been able to cool them down to their lowest energy level (close to the quantum limit), “squeeze them” to reduce their vibrations even further, and entangle them with each other.

]]>In order to efficiently operate optomechanical systems in the quantum regime, scientists face a dilemma. On one hand, the mechanical oscillators must be properly isolated from their environment to minimize energy loss; on the other hand, they must be well-coupled to other physical systems such as electromagnetic resonators to control them.

Black hole mergers produce detectible gravitational-wave “chirps.”

Here’s an interesting overview of formation of black holes, detection of collisions (mergers), and modeling the expansion of the universe.

• Space.com > “Gravitational waves show black holes prefer certain masses before they collide” by Keith Cooper published (August 14, 2023) – A preference for “universal masses” 9 and 16 times the mass of our Sun have been identified in the gravitational-wave events detected so far.

]]>A larger sample of

gravitational-wave eventsmay be coming soon. A new observing run involving LIGO, Virgo and KAGRA that will last 20 months has recently begun, and the aim is to discover another 300 events. We will know soon enough whether the new results enhance the peaks in the distribution around the universal masses and the gap between them.

Credit: J. Sommerfeldt/Technical University of Braunschweig

“Punching” emptiness … the interaction of localized energy densities …

Success in “hitting” a target depends on its effective surface area – the **cross section** presented to an impinging projectile. For example, in archery, hitting a target edgeways is harder than frontways.

Cross sectional models are critical to analysis of photon-scattering experiments which explore atomic structure. Modeling interactions between photons and bound electrons, and between photons and the “empty” field around nuclei.

This article is about modeling the practical, real effects of the quantum vacuum.

• Physics.aps.org > “Quantum Deflection Unraveled” by Ryan Wilkinson (August 8, 2023) – Improved calculations of a quantum phenomenon called Delbrück scattering resolve a long-standing discrepancy between theory and experiment.

The sky owes its color to a process known as Rayleigh scattering, in which light bounces off [is scattered via interactions with] electrons bound to atoms. Quantum physics permits an analogous effect, dubbed Delbrück scattering, whereby photons deflect from [interactions with] the electrostatic field around atomic nuclei.

According to quantum theory, empty space is not actually empty but teeming with particle–antiparticle pairs that flit in and out of existence.

Delbrück scattering occurs when photons interact with such [virtual] pairs in the electrostatic field of a nucleus.

**References**

• Wiki > Cross section (physics) – Quantum scattering, Scattering of light

]]>In physics, the cross section is a measure of the probability that a specific process will take place [occur] when some kind of radiant excitation (e.g. a particle beam, sound wave, light, or an X-ray) intersects a localized phenomenon (e.g. a particle or density fluctuation). … In a way, it can be thought of as the size of the object that the excitation must hit in order for the process to occur, but more exactly, it is a parameter of a stochastic process.

It is not uncommon for the actual cross-sectional area of a scattering object to be much larger or smaller than the [geometric] cross section relative to some physical process.

This graphic illustrates a proton moving at nearly the speed of light toward the viewer with its spin aligned along the horizontal direction (large arrow). The two views of concentric circles at the bottom show the spatial distributions of the momentum of up quarks (left) and down quarks (right) within this proton (white is high; violet is low). Credit: Brookhaven National Laboratory

The interplay of theory and experiment in “imaging” a proton.

How are quarks and the gluons distributed within the proton? Do up and down quarks contribute equally to a proton’s spin? Do gluons contribute to spin?

**Terms**: quantum chromodynamics (QCD), lattice QCD, energy-momentum distributions, polarized protons.

• Phys.org > “Calculations reveal high-resolution view of quarks inside protons” by Brookhaven National Laboratory (August 2, 2023) –

]]>A collaboration of nuclear theorists at the U.S. Department of Energy’s (DOE) Brookhaven National Laboratory, Argonne National Laboratory, Temple University, Adam Mickiewicz University of Poland, and the University of Bonn, Germany, has used supercomputers to predict the spatial distributions of charges, momentum, and other properties of “up” and “down” quarks within protons. The results, just published in Physical Review D, revealed key differences in the characteristics of the up and down quarks.

… [accelerator] scatterings give scientists access to the

Generalized Parton Distribution(GPD) of the proton – parton being the collective name for quarks and gluons. If youpicture the proton as a bag filled with marblesrepresenting quarks and gluons, the GPD provides a description of how the energy-momentum and other characteristics of these marbles are distributed within the bag … the likelihood of finding a marble with a specific energy-momentum at a particular position inside the bag.According to their calculations, the scientists concluded that up and down quarks can account for less than 70% of the proton’s total spin.