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The force we feel when standing on the Earth is electromagnetic in nature. We are accelerated upwards without a coordinate acceleration following due to the curvature of spacetime (that would be the case in a uniformly accelerated rocket in flat spacetime). You could see the difference between an accelerated rocket in flat spacetime and an accelerated rocket standing still in a gravitational field by examining the tidal forces. The tidal effects are absent in the rocket accelerating through flat spacetime.

Gravity is not a force and the only locally acting forces we effectively feel are the three basic forces of nature, mostly the EM force. But the tidal force is a true gravitational effect and has the capability to drive particles away from each other or towards each other. It is a non-local force though, as two points are involved. So can we say that the only real force-like quality of gravity is the non-local tidal effect?

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  • $\begingroup$ @PM2Ring Oh, yes. I mean a rocket accelerating uniformly through flat spacetime. The Weyl tensor can make you decide if you are at rest in a gravitational field or accelerating in a rocket. Only in first order, they are equivalent. $\endgroup$
    – Il Guercio
    Commented Apr 5 at 23:13
  • $\begingroup$ @PM2Ring But I stated in the answer that tidal forces are absent in the rocket. $\endgroup$
    – Il Guercio
    Commented Apr 6 at 0:23
  • $\begingroup$ @PM2Ring Oh, I meant the question, of course. Sorry, my fault! An accelerating rocket in empty, flat spacetime (or a rotating body, for that matter) is, in first order, equivalent to a rocket standing still in a gravitational field. Still, if you consider tidal effects you can discern in which of the two you find yourself. Because the Weyl tensor is zero in flat spacetime but not in the field around a mass. Don't I say that in the question above? So the equivalence principle holds in first order only. $\endgroup$
    – Il Guercio
    Commented Apr 6 at 3:17
  • $\begingroup$ @PM2Ring The tidal effects are only absent in the rocket that accelerates through flat spacetime. But in a rocket that hovers above a planet, they are present. But the effects are very small in most cases indeed. So in most cases, the equivalence principle holds very well in first order, as the second-order effects are tiny. $\endgroup$
    – Il Guercio
    Commented Apr 6 at 10:20
  • $\begingroup$ @PM2Ring Oh! I see what you mean now! I indeed didn't say which one. Gotchya! Thanks. I have made an edit. $\endgroup$
    – Il Guercio
    Commented Apr 6 at 10:22

2 Answers 2

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The tidal force is electromagnetic as well.

Suppose you are falling into a black hole and being spaghettified by the tidal force. If we turned off the electromagnetic force your atoms would just drift apart like a cloud of dust with no forces acting between them. The reason you feel yourself being stretched vertically and compressed laterally is due to the EM forces between atoms, just as the force you feel standing on Earth is an EM force.

In general the only time you feel a force is when the atoms in your body are being deflected away from a geodesic trajectory by the EM force. That happens when the EM force resists your fall towards the centre of the Earth, and when the EM force resists your deformation by tidal forces.

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    $\begingroup$ Yes, but the tidal force is the only real gravitational force driving particles away from each other or towards each other. The other three forces are local forces, while the tidal force is non-local. $\endgroup$
    – Il Guercio
    Commented Apr 5 at 23:15
  • $\begingroup$ So, locally you don't feel gravity as a force (only when you accelerate by means of EM you feel the EM force), but globally it can act as a force driving particles away from each other (or towards each other). Of course, the EM force can counter this force by pulling the particles together or pushing them away from each other. If only gravity existed particles would move towards each other or or from each other because of the tidal force. $\endgroup$
    – Il Guercio
    Commented Apr 6 at 0:29
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The force that keeps you from falling into the Earth is mainly Pauli force. By itself, electromagnetic force would cause condensed matter to collapse. It is true that electromagnetic tension is a crucial part of holding the structure of solid matter together, but the compressive strength is provided by Pauli repulsion.

A sensible physical definition of force is "that which a force gauge measures". Since you can measure gravity and Pauli forces with a force gauge, these should be considered forces. It is not bad to extend the definition to include short-range nuclear bosonic forces, but to then claim that only these and electromagnetism deserve to be called forces denys physical reality.

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    $\begingroup$ I'm pretty sure it's mostly the electromagnetic force that keeps you from falling into the earth; Pauli forces only come into play when dealing with degenerate matter as in neutron stars. I don't think you would survive conditions such that Pauli forces are significant. $\endgroup$
    – Hearth
    Commented Apr 6 at 2:07
  • $\begingroup$ @Heath No. Electromagnetism by itself can only compress neutral matter. $\endgroup$
    – John Doty
    Commented Apr 6 at 12:40
  • $\begingroup$ On small enough scales, nothing is neutral; the electron cloud of one atom will repel the electron cloud of an adjacent atom. $\endgroup$
    – Hearth
    Commented Apr 6 at 13:45
  • $\begingroup$ @Hearth If you take a bound, neutral arrangement of classical charged particles and compress it to half its size, the electromagnetic binding energy doubles. So, without the exclusion principle, condensed matter should collapse spontaneously. $\endgroup$
    – John Doty
    Commented Apr 6 at 23:29

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