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Suppose that I put lots of big magnets around me, or say, that I charge myself up to a macroscopic charge. Now, suppose that there's a huge magnet in front of me (or a huge object with opposite charge). Will I feel the force attracting me (that is, the acceleration) while I don't try to resist to it and gets pulled to it, or would I feel it only if I try to resist and stay at the same place on the ground ?

Could it be that I feel the acceleration while I'm in air and gets attracted to the magnet AND also while I'm trying to resist hard to stay motionless on the ground?

Motivation: strong equivalence principle tells us that to be (locally) inertial is to free fall. To be locally inertial, is like to be at rest, that is, no force can ever be felt at rest. This is exactly what one notices if one experiments free falls: no force, just nothing. On the contrary, if one is on its chair (that is, getting accelerated upward), one feels some force. Could it be that electrostatic force also be integrated into a (parametrized) deformation of space time, which would mean that when one is getting accelerated to the magnet/charge (that is, not resisting it), one doesn't feel anything?

EDIT: The good question is the following one. Is there some constraints known on the distribution of charge density per unit of inertial mass, $\frac{q}{m_i}$ ? If such charge density was cosntant for all physical objects, then we would obtain a (0th order) strong equivalence principle for electromagnetism. If it is linear, one can imagine that there's a first order equivalence principle, and so on.

sure
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  • a though experiment involving gravity would make me think that one shouldn't feel the acceleration while getting accelerating toward a magnet or some charge. Imagine you're charged on your chair, and you have some big charge of opposite sign just ahead of your head. If the charge and their distance are well calibrated, there's a point where gravity "force" and electrostatic "force" will cancel exactly. At this point, you should experience free fall. Hence, you shouldn't feel anything. – sure Apr 12 '15 at 13:02

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I don't think so. The whole point about the equivalence principle, is that gravity is indistinguishable from inertia. It is rooted in the fact that gravitational and inertial mass are the same. See this answer.

This is not the case for the electromagnetic interaction. Two bodies with different charges but identical masses will not have the same acceleration under identical elecromagnetic fields. If you are left to accelerate in an electromagnetic field, the heaviest parts of your body will accelerate slower than lighter parts (assuming that they have the same charge). If you are left in free fall in an electromagnetic field and you take off your watch, the latter will very probably move away from you.

You can of course fine tune the charge distribution within your body (and your watch) to negate these effects, but you would have to know that they are there in the first place to do that. It kind of defeats the point.

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Steven Mathey
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  • I do agree that the charge is a real coupling constant because it is not necessarily proportional to inertial mass. That is, $\frac{q}{m_i}$ is not a constant. Yet, how could it be, imagining that I fine tune the charge distribution such that the charge density per unit of inertial mass is constant, that I feel both the force pulling me to the magnet or the force when I try resisting it? There's something weird here. – sure Apr 12 '15 at 13:15
  • I claim that one obtains different order of strong equivalence principle regarding the distribution of $\frac{q}{m_i} $.
    1. $\frac{q}{m_i} = c$ one obtains a "strong equivalence electrostatic principle",
    2. $\frac{q}{m_i} =$ linear in $q$ or $m_i$, one obtains a first order strong equivalence electrostatic principle,
    3. $\frac{q}{m_i} = $quadratic in $q$ or $m_i$, one obtains a second order strong equivalence electrostatic principle.

    The good question is, is there any constraint on $\frac{q}{m_i} $ ?

     – sure Apr 12 '15 at 13:20
  • I guess that you can make up any kind of equivalence principle. It feels very unnatural though. In order to do this, you would have to measure the electromagnetic field over all space and your body's local mass density and place charges in your body in just the right way. You can only do this by first making the difference in between electromagnetics and gravity. – Steven Mathey Apr 12 '15 at 14:36
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The only thing you can feel are relative stresses between different parts of your own body. If every single cell of your body (or whatever scale is small enough that you can treat it as rigid) had the same charge/mass ratio, then they would all undergo the same acceleration, there would be to tension or compression, and you wouldn't feel the effect of the field. The equivalence principle says that everything has the same "charge"/mass ratio, and so feels the same acceleration at the same point in spacetime. See Does large acceleration have to cause damage to the human body? and High speed does not kill. Does acceleration do it ? or jerk?.

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tparker
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