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Gravitation is the mutual attraction of masses, yet Einstein showed it is how spacetime is curved by mass and how mass moves in relation to this curvature. Why then do we still consider gravitation a "force"?

JDUdall
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2 Answers2

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The need for the concept of "fundamental force" comes from quantum mechanics, where a fundamental force is assigned a coupling constant that enters the quantum mechanically modeled interactions. Mainstream physics assumes a form of general relativity that is quantized, and quantization needs a coupling constant for the interaction with the space time of GR.

At present GR is not definitively quantized; an effective quantization of gravity(GR) is used in most cosmological model efforts. That is why the term "fundamental force" is used for gravity.

These are the coupling constants for all the mainstream "forces" that are used in quantum mechanical theoretical models.

funforc

anna v
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  • The trouble is that this has become disconnected from the real world, where "force" is what a force gauge measures. I have no problem with generalizing the concept to forces with microscopic range, but you should include the Pauli force, the force that resists the compression of condensed matter, easily seen in experiments and everyday life. – John Doty Jan 16 '23 at 14:11
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    No, the Pauli does not have the same function in the mainstream standard model of physics. It can be interpreted as a macroscopic type "force", but not as fundamental in the in the sense above. There is no coupling constant associated in the QFT. – anna v Jan 16 '23 at 15:56
  • That's what I mean by "disconnected". Of course it's fundamental: the phenomena are fundamental to physics, the abstractions are not. A physics that denies that an effect you can measure with a force gauge is a force has lost touch with the physical world. A force gauge doesn't measure coupling constants. – John Doty Jan 16 '23 at 16:02
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    In the language used by mainstream physics for the elementary particles QFT, it does by definition. – anna v Jan 16 '23 at 18:11
  • How did "mainstream physics" cease to be about the phenomena of the physical world? – John Doty Jan 16 '23 at 19:18
  • If you're honest about physics, you can't define away phenomena you don't wish to address. – John Doty Jan 16 '23 at 19:24
  • @JohnDoty I don't think anybody is defining phenomena away. The disagreement is how to categorize Pauli exclusion force. I was under the impression that it was an emergent property of the fundamental forces, and for that reason it's not categorized as fundamental, even if it is extremely important (solidity of matter and all that). – hegel5000 Jan 16 '23 at 23:41
  • @hegel5000 The phenomena are fundamental, they do not emerge from the abstractions of theory. Even in the theory, the Pauli force does not depend on any other force for its existence. – John Doty Jan 16 '23 at 23:47
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    @JohnDoty in order for physics to have a consistent mathematical theory, it has to define terms which can only come from the language we all use. In the quantum mechanical theories fundamental force is used in the sense I describe in my answer. One could invent new terms that have no meaning in everyday language, but that is not the way it has been done. – anna v Jan 17 '23 at 06:06
  • @annav Physics is not mathematics. Mathematics is merely a tool, and, indeed, not a fundamental one. The phenomena are in charge. It is critical for physics to respect the phenomena. Calling mathematical abstractions fundamental forces is upside down. You need a definition? A fundamental force is what a force gauge measures. That's a physical definition. – John Doty Jan 17 '23 at 12:58
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[gravity] is not really a force at all

This is true and it isn't, but beside the point anyway as we're best talking about fundamental interactions, not forces, so as to include decays. The weak interaction, for example, does exert forces, but they're so feeble it primarily matters because of the decays it causes.

Isn't the "true" fundamental interaction that between mass and spacetime?

@annav's answer already noted fundamental interactions are of quantum-mechanical significance. There are any number of reasons gravity must be quantum. Therefore, GR must emerge from the effects of gravitons. The most fundamental account of gravity is therefore in terms of how particle interactions affect the spacetime in which particle interactions are suited. (However, there's a bit more to being a fundamental interaction than having a particle-based - or to be more precise, field-based - explanation.)

Is this because some physicists don't really believe in GR?

Having said all that, even if the universe weren't quantum in the slightest, it still would make sense to consider gravity a fundamental interaction. Such a universe would have "classical" field theories for electromagnetism and gravity, and the latter would be GR or an alternative. It would be a gauge theory like EM, except based on diffeomorphism invariance rather than local $U(1)$. Field theories' Lagrangians' kinetic terms would use an alternative to partial derivatives that adds two kinds of term, those proportional to the EM field for EM, plus those proportional to Christoffel symbols for GR. See also here & here for further parallels.

J.G.
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