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GR: Chicken or egg redux

One of the major sources of confusion I’ve encountered in reading about modern physics is the discussion of gravity. No surprise, eh.

Classical mechanics includes both Newtonian and relativistic mechanics. In Newtonian physics, gravity is an attractive force, which acts at a distance between all objects; and can be represented as a universal gravitational field.

In General Relativity, gravity is the curvature of spacetime, a geometry which always “attracts” (unless in Planck world) somehow. “In particular, the curvature of spacetime is directly related to the energy and momentum of whatever matter and radiation are present.”

“Matter tells space-time how to curve, and curved space tells matter how to move.” — John Wheeler, as quoted in Einstein: His Life and Universe by Walter Isaacson.

But that’s not the end of the story, by any means. Newtonian physics emerges from General Relativity: GR “represents classical mechanics in its most developed and most accurate form.” In a Venn diagram, General Relativity encloses Newtonian physics.

In quantum mechanics and quantum field theory (basically if you’re a quantum field theoretical physicist), gravity should “pop out” of the field equations. In other words, the curvature of spacetime should emerge from quantum gravity theory. In a Venn diagram, a unified theory encloses classical mechanics. So, there’re gravity waves and gravitons as the “force carriers” for gravity. [1]

Quotes from Carroll’s book TBS.

The “deeper” understanding (in theory) should always allow us to “smooth out” the math (with shortcuts and approximations) and get the simpler equations, which permit practical applications and predictions in the macro world.

For example, although the wave function is probabilistic, the (aggregate) wave function of a moving baseball collapses to the position and velocity we expect when catching or hitting the ball. Newtonian mechanics works just fine in our everyday world. Newtonian language works just fine in our everyday world.

And the same thing applies to GR and the curvature of space. All those 3D visualizations of gravity wells as an analogy to some higher spacetime dimensionality where particles (and aggregates) curve spacetime and then follow that geometric texture.

Anyway, in the books and other articles, there’s often conflation of languages, mixing of the languages used in the different domains. Maybe it’s hard to be 100% consistent, eh.

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[1] But I do not even understand how photons — as force carriers — mediate EM interactions so as to produce the classical equations and behaviors at a macroscopic (aggregate) level. My only guess is that the statistical behavior of a dense “fluid” of (virtual) photons in the field around electromagnetic objects resolves to a net divergent / convergent force (transfer of momentum), a cumulative effect. In other words, much like how we can describe systems of gas using properties like temperature, pressure, and volume — the fine-structure constant reflects an (aggregate) property of that “fluid.” So, what is the density of virtual photons in an EM field? An infinitude? More absurd math?

Force carriers do not obey the Pauli exclusion principle. Photons do not interact with each other (although lately the literature may indicate otherwise in Planck world).

This is not a question about the interaction when an electron emits a (real) photon, where such “recoil” may be visualized in a Feynman diagram. It’s about an electron’s static Coulomb field, a “force” field which obeys the inverse square law and extends to infinity (as permitted for mass-less carriers; otherwise any net outflow of momentum would result in the electron “evaporating,” eh). “The relative strength of the electromagnetic interaction between two charged particles, such as an electron and a proton, is given by the fine-structure constant.” Back in Planck world, again.

2-2-2014 Notes


A “cosmic tango” — Einstein: His Life and Universe by Walter Isaacson

“Gravity is geometry” — James Hartle, as quoted in Einstein: His Life and Universe by Walter Isaacson

“Matter tells space-time how to curve, and curved space tells matter how to move.” — John Wheeler, as quoted in Einstein: His Life and Universe by Walter Isaacson

Since E = mc^2, energy curves space as well, perhaps even at the Planck level.

If gravity results from a 4-d curved space (e.g., 3-sphere), then space might have some type of dimensional structure, perhaps appropriate to structural dynamics. One standard 2-d analogy or illustration of space-time distortion is an embedding diagram.

Our everyday, colloquial experience with gravity, weight, etc., is that things move when pushed or pulled. So, gravity pulls us down, in that perspective. Some type of force. Since it’s everywhere we roam, some type of (invisible) force field. A ride on a “vomit comet” is quite fascinating, as a result.

Being in a curved space-time geometry is something else. In this perspective, we’re always sort of falling, just propped up by other matter, which in turn is always falling in another frame of reference, maybe ad infinitum. On geodesics. Perhaps gravity, as a dimensional property of curved space, is most efficient from an energy point of view.

But there’s more, of course. Stellar events with massive changes in mass (or energy) can, according to General Relativity, create gravity waves. And gravity waves propagate (no faster than the speed of light) as a field. So, we hypothesize gravitons.

6 thoughts on “GR: Chicken or egg redux

  1. “It is not uncommon to hear that energy is ‘equivalent’ to mass. It would be more accurate to state that every energy has an inertia and gravity equivalent, and because mass is a form of energy, then mass too has inertia and gravity associated with it.” []

  2.‘s Spaceman1 on March 2, 2016, discussed why in a quantum world “we can’t figure out a way to describe gravity without swearing.” There’s also a video.

    The infinities are too much to handle. We can’t find clever ways to package them up. We can’t forget about them and pretend they don’t exist. We can’t patch over them with known measurements. The math is too complicated. There are simply too many possible configurations of both the interactions and the underlying space-time. We can’t make the math simple enough to solve; our mathematical models lose their predictive power. They break down.

    [1] Paul Sutter is an astrophysicist at The Ohio State University and the chief scientist at COSI science center. Sutter is also host of Ask a Spaceman, RealSpace and COSI Science Now. He contributed this article to’s Expert Voices: Op-Ed & Insights.

  3. Today, this article “Vomit Comet: Training Flights for Astronauts” reminded me of Chapter 6 “Inertia” in Lederman’s book on symmetry:

    Frictionless motion, and the concept of an ideal vacuum, however, was too great a conceptual leap at the time of the Greek philosophers. … The Greeks lived in a world dominated by friction; inertia was too hard to notice. They could not separate the concept of friction from the concept of pure and distilled, or idealized, motion. — Lederman, Leon M.; Hill, Christopher T. Symmetry and the Beautiful Universe (p. 120). Prometheus Books. Kindle Edition.

    More people than ever have a feel for inertia due to modern speedy transportation — especially how our bodies react in cars, to everyday acceleration, turning, and braking. But I sometimes think that generations of scientists raised in space might help advance physics, having lived in a world dominated by inertia.

    See also “OK Go Releases First Zero-G Music Video” (February 12, 2016):

    The video, which you can watch on OK Go’s Facebook page, begins with a few lines of white text on a black background. “What you are about to see is real,” the text reads. “We shot this in zero gravity, in an actual plane, in the sky. There are no wires or green screen.”

    See also “Kids with Disabilities Float Like Astronauts in Gleeful Flight” (August 25, 2017):

    The kids also participated in science experiments and demonstrations to illustrate the effects of microgravity on physical systems. The demos included things like lighting a candle, mixing liquids of different densities, playing ping-pong with bubbles of water and using a fidget spinner.

  4. Sean Carroll’s Mindscape Podcast with Carlo Rovelli “Episode 2: Carlo Rovelli on Quantum Mechanics, Spacetime, and Reality” (July 10, 2018) is an excellent dialog on current theories of gravity like string theory and loop quantum gravity.

    In particular, I found the characterization / clarification of the notion of spacetime fascinating.

    CR: And in fact, generally, it is presented in books by saying, “Well, [the] gravitational field is nothing else than spacetime.” But I like better to think of it the other way around. Spacetime, [is] nothing else than gravitational field. It’s the same thing, right? When you understand that those things are the same, you can say it two different ways.

    SC: So Einstein is saying that gravity is not a thing that lives in spacetime, it’s a manifestation of the nature of spacetime itself.

    CR: Exactly, it’s not one additional thing that lives in spacetime, it’s a manifestation of Newtonian space and time. This clear background that Newton told us is there, is actually there, but is the gravitational field. It’s same thing as the gravitational field. Which means it can move, it can stretch, it can bend. And Einstein wrote the equation for that. And this is a gravitational wave, the black hole sort of things. So that’s one ingredient.

    CR: And why points lose their meaning in quantum gravity is because the gravitational field is also space. The gravitational field doesn’t live in space, but is space itself. So in the moment in which you look at the quantum properties of the gravitational field, you’re also looking at the quantum property of spacetime, of space. And one, a bit modern way of viewing what he was doing, is the following. If you try to pinpoint the position of a particle, in arbitrary small precision, you can, but because of quantum mechanics, the velocity of the particle becomes very indeterminate. But the velocity is also the momentum and the momentum is also the energy, so you have a very large energy, so to say, and a very large energy, because of gravity, energy is also mass, is MC squared, so it’s like having a large mass and if you have a large mass in a small area, you create a black hole. So when you try to zoom in a point very, too small, automatically you create a little black hole. And if you work out the numbers, you look at a scale and that’s a minimal scale you can look at, right?

  5. This article “What Is Gravity?” by Charlie Wood (August 21, 2019) is a good historical recap of our understanding of gravity.

    The classical notion of space (and gravity) as one smooth fabric clashes with the quantum picture of the universe as a collection of sharp little pieces. How to extend the reigning Standard Model of particle physics, which spans all known particles as well as the other three fundamental forces (electromagnetism, the weak force, and the strong force), to cover space and gravity at the particle level remains one of the deepest mysteries in modern physics.

  6. Charlie Wood continues his discussion of gravity in this August 27, 2019, article “What Is Quantum Gravity?” A useful overview of the search for a universal 10^n and 10^-n “gravitational rulebook.” And whether space is a fundamental or emergent cosmic aspect (similar to research on “the problem of time”).

    Planets and stars are really collections of atoms, which, in turn, are made up of electrons and bundles of quarks. Those particles hang together or break apart by swapping other types of particles, giving rise to forces of attraction and repulsion.

    Electric and magnetic forces, for example, come from objects exchanging particles known as virtual photons. For example, the force sticking a magnet to the fridge can be described as a smooth, classical magnetic field, but the field’s fine details depend on the quantum particles that create it. Of the universe’s four fundamental forces (gravity, electromagnetism, and the strong and weak nuclear forces), only gravity lacks the “quantum” description. As a result, no one knows for sure (although there are plenty of ideas) where gravitational fields come from or how individual particles act inside them.

    … when physicists try to calculate the curvature of space around an electron, slight as it may be, the math becomes impossible.

    In the late 1940s physicists developed a technique, called renormalization, for dealing with the vagaries of quantum mechanics, which allow an electron to spice up a boring trip in an infinite variety of ways. It may, for instance, shoot off a photon. That photon can split into an electron and its antimatter twin, the positron. Those pairs can then shoot off more photons, which can split into more twins, and so on. While a perfect calculation would require counting up the infinite variety of electron road trips, renormalization let physicists gather the unruly possibilities into a few measurable numbers, like the electron charge and mass. They couldn’t predict these values, but they could plug in results from experiments and use them to make other predictions, like where the electron is going.

    Renormalization stops working when theoretical gravity particles, called gravitons, enter the scene. Gravitons also have their own energy, which creates more warping of space and more gravitons, which create more warping, and more gravitons, and so on, generally resulting in a giant mathematical mess. Even when physicists try to pile some of the infinities together to measure experimentally, they end up drowning in an infinite number of piles.

    In practice, this failure to deal with curvature around particles grows fatal in situations where lots of mass and energy twist space so tightly that even electrons and their ilk can’t help but take notice — such as the case with black holes. But any particles very near — or worse, inside — the pits of space-time certainly know the rules of engagement, even if physicists don’t. [Engelhardt said, “my instinct would be to look at the cosmos rather than to look at particle colliders.”]

    Theorists discovered in the late 1990s that descriptions of a simple, box-like universe including gravity were mathematically equivalent to a picture of a flat universe with only quantum physics (and no gravity). [See this YouTube PBS Space Time channel video “The Holographic Universe Explained” – note 1].

    the relationship between space and particles might be something like the one between room temperature and air molecules. Physicists once thought of heat as a fluid that flowed from a warm room to a cool room, but the discovery of molecules revealed that what we sense as temperature “emerges” from the average speed of air molecules. Space (and equivalently, gravity) may similarly represent our large-scale experience of some small-scale phenomenon. “Within string theory, there are pretty good indications at this point that space is actually emergent,” Engelhardt [a theoretical physicist at MIT] said.

    [1] Video description: “We live in a universe with 3 dimensions of space and one of time. Up, down, left, right, forward, back, past, future. 3+1 dimensions. Or so our primitive Pleistocene-evolved brains find it useful to believe. And we cling to this intuition, even as physics shows us that this view of reality may be only a very narrow perception. One of the most startling possibilities is that our 3+1 dimensional universe may better described as resulting from a spacetime one dimension lower – like a hologram projected from a surface infinitely far away.”

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