Why is Inertia not included as one of the fundamental interactions, yet gravity is included as one of the four known interactions, and there is an equivalence established between gravity and inertia.
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2$\begingroup$ I think you should tell us more about what you mean when you say "there is an equivalence established between gravity and inertia". That statement is a little vague, and vagueness causes agita on these pages. $\endgroup$– garypCommented May 2, 2018 at 12:55
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$\begingroup$ Considering inertia as an interaction between an object and the rest of the universe is at the core of Mach's principle: en.wikipedia.org/wiki/Mach%27s_principle. This is a confusing topic with many subtleties. $\endgroup$– Stéphane RollandinCommented May 2, 2018 at 14:12
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3 Answers
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Gravitation can, in certain very important cases, be regarded as a force between bodies, an interaction. We can't do this, can we, for inertia (even though we acknowledge the equivalence of gravitational and inertial mass)?
answered May 2, 2018 at 11:32
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$\begingroup$ Can you be specific and quote some "very important cases" where gravitation can "be regarded as a force". Why can't inertia also be mediated by a force quantum ? $\endgroup$– M. IlkiwCommented May 2, 2018 at 15:47
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$\begingroup$ (1) [Q]uote some "very important cases" where gravitation can "be regarded as a force": apple dropping? solar system? rotation of galaxies? (2) Why can't inertia also be mediated by a force quantum ? Is there evidence that it can or a well-developed theory in which it can? At this stage I must admit that I, like a fool, rushed in where angels fear to tread. I await (like you, perhaps) a much more profound answer than my superficial response. $\endgroup$ Commented May 2, 2018 at 16:03
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Inertia and gravity are same at fundamental level and therefore, if gravity is a fundamental interaction, then so is inertia even though we may not recognize it that way.
Inertia - A body due to its mass (energy), creates a dip of space around it. That dip makes a force be required to make a change in state of the body. Hence causes inertia.
Gravity - Same dip (curve) due to mass (energy) of the body manifests as gravity for other bodies.
So, their origin is same and that is curving of space.
Inertia is nothing but gravity of the body acting on itself against any change of state. Therefore gravitational and inertial mass are same.
My view is that gravity and inertia are same phenomena. They are two sides of same coin.
Curving of space by mass/energy of a body manifests as gravity for other bodies.
Same curving of space manifests as inertia of the body, when we try to change its state of rest, or uniform motion.
gravity is measure of coupling strength of a mass to a known gravitational field.
Inertia is measure of coupling strength of a mass to its own gravitational field.
I would be happy if someone busts this view conceptually, or mathematically.
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One can say that the Higgs field is responsible from the inertia since the mass is the quantity of the inertia and Higgs gives the masses of the particles. So, inertia can be interpreted as an interaction where the Higgs field is involved.
This is indeed consistent since for instant photon is massless, meaning that it has no inertia, and as a matter of fact, photon does not interact with Higgs boson.
Of course Higgs boson, being responsible for inertia, is not a gauge boson, it does not give a phase difference to the particles but still it is an interaction and the cause of inertia in the first place.
However, gravity interacts with all kinds of energy even it is not interacting with the Higgs boson, i.e., doesn't have a mass/inertia.
So, inertia and gravity are not equivalent. But of course they are interacting.
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$\begingroup$ The Higgs mechanism is not responsible for mass in general. This is a common confusion. The Higgs mechanism is required to explain some of the mass of some particles, but it is in no way the cause of all mass / inertia everywhere. $\endgroup$ Commented Nov 5, 2019 at 19:38
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$\begingroup$ I didn't claim that the Higgs mechanism is the cause of inertia or the only source. Even if, in principle, the masses of the leptons and quarks are not necessarily from Higgs's VEV, the Standard Model does predict that all the mass of the known fundamental particles originates from the Higgs mechanism. Of course not necessarily... However, even if we consider Higgs mechanism giving the masses of only the electroweak bosons, it can still be interpreted as an interaction responsible for inertia (even if it might not be the only one). $\endgroup$ Commented Nov 9, 2019 at 22:41