Gravity is a Force

Physicists are sharply divided over whether gravity is a force. Oh, they refer to it as a force all the time, such as saying it is one of the four fundamental forces, but then say it is a fictitious force.

The excellent video channel Veritasium has explanation of Why Gravity is NOT a Force.

It is like the people who say that centrifugal force is not a force, but centripetal forces is.

Gravity has been considered a force since Newton in the 1600s, so the opposite view requires explanation.

Actually, it is not so clear that Newton believed that gravity was a force. He was very much against action-at-a-distance:

Newton famously struggled to find out the cause of gravity.^[12] In a letter to Bentley, dated January 17 1692/3, he said:

You sometimes speak of Gravity as essential and inherent to Matter. Pray do not ascribe that Notion to me, for the Cause of Gravity is what I do not pretend to know, and therefore would take more Time to consider it. (Cohen 1978, p. 298)

In a subsequent letter to Bentley, dated February 25, 1692/3, he added:

It is inconceivable that inanimate Matter should, without the Mediation of something else, which is not material, operate upon, and affect other matter without mutual Contact…That Gravity should be innate, inherent and essential to Matter, so that one body may act upon another at a distance thro’ a Vacuum, without the Mediation of any thing else, by and through which their Action and Force may be conveyed from one to another, is to me so great an Absurdity that I believe no Man who has in philosophical Matters a competent Faculty of thinking can ever fall into it. Gravity must be caused by an Agent acting constantly according to certain laws; but whether this Agent be material or immaterial, I have left to the Consideration of my readers. (Cohen 1978, pp. 302-3)

Aristotle also denied that gravity was a force.

The Aristotelian explanation of gravity is that all bodies move toward their natural place.

There are two arguments that gravity is not a force. One says that you do not feel gravity in free fall. You feel it when you stand on the ground, but you are really feeling the force of the ground pushing you up.

The second is that general relativity teaches that gravity is just curvature of spacetime, not a force. This is a variation of Aristotle's argument.

A typical explanation:

“The one sentence statement of general relativity is that ‘gravity is the curvature of spacetime,’” explains Dr. Sean Carroll, assistant professor of physics at the University of Chicago. “Really, the differences come in understanding what that sentence means.”

Carroll says that origin of the theory of general relativity dates to 1905, when scientists, notably including Albert Einstein, realized that space and time are related characteristics of a four-dimensional existence. ...

However, within this new 4-D framework, says Carroll, Einstein could not understand gravity, and how it worked in spacetime. He decided that rather than being a force, like electromagnetism, gravity must be a property: a geometric curvature.

This stuff about Einstein believing that gravity is geometrical curvature is a modern invention. Yes, he used the equations for curvature, but did not subscribe to the geometric interpretation that is popular today.

General relativity differs very slightly from Newtonian gravity. It is silly to say one is a force and the other not. They are essentially the same.

My biggest quibble is with those who say electromagnetism is a force, but gravity is not. In modern physics, all of the four fundamental forces have geometrical interpretations, where the field strength is given by curvature. Test particles follow curvature, in all cases. Here is a recent paper explaining it. So if gravitational forces are fictitious because particles are just following curvature, then nothing else is a force either.

Those who deny that gravity is a force sometimes go one step farther, and deny causality. Eg, from the Stanford Encyclopedia:

Causation in Physics

What role, if any, do causal notions play in physics? On the one hand, it might appear intuitively obvious that physics aims to provide us with causal knowledge of the world and that causal claims are an integral part of physics. On the other hand, there is an influential philosophical tradition, dating back to Ernst Mach and to Bertrand Russell’s extremely influential article “On the Notion of Cause” (1912), denying the applicability or at least the usefulness of causal notions in physics. While this tradition is perhaps not as dominant today than it once was, there continues to be a lively and active philosophical debate on whether causal notions can play a legitimate role in physics and, if yes, what role that might be.

One part of this is that if you believe in determinism and the block universe, then the Big Bang caused everything, and nothing else had any influence.

I take the view that we have forces and causes. I am all in favor of the geometrical interpretation, but not to deny forces and causes.

While I think most physicists take a geometrical view, here is a new oddball paper:

A Puzzle About General Covariance and Gauge

Eleanor March, James Owen Weatherall

We consider two simple criteria for when a physical theory should be said to be "generally covariant", and we argue that these criteria are not met by Yang-Mills theory, even on geometric formulations of that theory. The reason, we show, is that the bundles encountered in Yang-Mills theory are not natural bundles; instead, they are gauge-natural.

Of course Yang-Mill (gauge) theories are generally convariant, as the theory is independent of any particular coordinates. If you change coordinates, then the equations of motion transform as you expect from vectors and tensors.

The paper makes the trivial point that if you change the coordinates, that does not necessarily tell you how to change the gauge. Yang-Mill theories are covariant over a change in coordinates and gauge.

These confusing arguments only obscure the fact that gravity, electromagnetism, strong, and weak forces all use the same geometrical constructions. Just the bundles are different. Gravity uses the tangent bundle on spacetime, while the other forces use U(1), SU(3), and SU(2) bundles. They are all covariant.

The Wikipedia article on general covariance says that Einstein popularized the term, but did not use it precisely. So I guess that is why some might think that it applies to general relativity, but not to other bundles.

Update: Here is a new paper explaining general covariance.

The free field then couples to the gauge field, producing an interaction term in the Lagrangian that is gauge-invariant. Neither the original electron field, nor the gauge field are gauge invariant, but the way they appear in the Lagrangian is through a gauge invariant term. One then proceeds to define gauge invariant things like the tensor field 𝐅:=d⁢𝐀 and claims that the physics of the theory is contained only in those objects.

Likewise, diffeomorphisms in GR are regarded as extra, unphysical degrees of freedom: the physics must be contained only in gauge-invariant quantities. This is in flagrant contrast with what experience tells us: in ‘real life’ things are constrained to fixed frames of reference, and one can measure ‘gauge-variant’ [8] quantities, such as the energy, proper time, the electric field, and so on.