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

ALAS, GRAVITY

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.

“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.” [https://en.wikipedia.org/wiki/Energy]

Space.com‘s Spaceman

^{1}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.[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 Space.com’s Expert Voices: Op-Ed & Insights.

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

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):

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