If equivalence principle was not true could we have almost inertial reference frames near the earth? Specially, is it was possible for a person in a train to know that if it is standing still or it is moving by constant velocity? (I mean wrongness of equivalence be apparent and could be seen easily: for some matters $m_g/m_i=1$ and for some matters $m_g/m_i=2$)
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$\begingroup$ Inertial (as in the thing measured by force-meters pushing on the object) and gravitational (as in the thing measured by accelerometers on the surface of the object) masses are already not equal, see for example this question and many other related ones. Does that answer the question? Remember that equivalence just states that a person in a closed box can't tell if they're sitting on a planet or accelerating upwards at one $g$. $\endgroup$controlgroup– controlgroup2025-11-05 02:45:50 +00:00Commented Nov 5 at 2:45
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$\begingroup$ @controlgroup I do not agree with that statement. The equivalence principle is well tested experimentally. Inertial and gravitational masses do appear to be the same. $\endgroup$Dale– Dale2025-11-05 03:07:48 +00:00Commented Nov 5 at 3:07
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$\begingroup$ @Dale I mean in the sense that the amount of gravity a thing seems to produce is not necessarily equal to the inverse of the amount of acceleration it undergoes under a certain force. Yes, all things accelerate at the same rate under gravity. $\endgroup$controlgroup– controlgroup2025-11-05 03:09:08 +00:00Commented Nov 5 at 3:09
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$\begingroup$ @controlgroup oh, you mean “active” gravitational mass and I always think of “passive” gravitational mass $\endgroup$Dale– Dale2025-11-05 03:19:39 +00:00Commented Nov 5 at 3:19
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If equivalence principle was not true could we have almost inertial reference frames near the earth?
Yes. This would be a small change to Newtonian gravity. Essentially it would be similar to Coulomb’s law with two exceptions. First, it would be tied to a new electromagnetically neutral “charge” which is always positive, the passive gravitational mass. Second, the force would always be attractive, never repulsive.
Those two changes have some far reaching consequences. And they contradict observations. But they are logically consistent.
is it was possible for a person in a train to know that if it is standing still or it is moving by constant velocity?
Inertial frames would be those of Newtonian mechanics. I.e. to identify one would require knowing the gravitational force on an object and correcting for it. Luckily, gravitational forces could be measured.
This would allow the determination of gravitational acceleration, but would not give information about velocity.
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$\begingroup$ Could you please answer second part of the problem which we say here again: if we have $m_g/m_i=1$ for some materials and $m_g/m_i=2$ for others, could we design an experiment which tells use if our train is moving or is standing still? $\endgroup$moshtaba– moshtaba2025-11-05 07:39:32 +00:00Commented Nov 5 at 7:39
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$\begingroup$ @moshtaba I have edited the answer to clarify $\endgroup$Dale– Dale2025-11-05 12:08:48 +00:00Commented Nov 5 at 12:08