How can two things that are different be equal? In a gravitational field there is actually gravity that push us down, but in the accelerated frame there is nothing that push us down.
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2Yeah, but what's gravity? – Jahan Claes Nov 20 '21 at 00:39
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4Einstein didn't say that acceleration and gravity are equal. He said that in a closed elevator where you are taking measurements (i.e., you can't see anything outside the elevator), it's impossible to distinguish between a 1 g acceleration and sitting on the ground on earth. – David White Nov 20 '21 at 00:52
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@DavidWhite And what that means? He after said gravity is an ilusion so he meant they are equal, or no? – Nov 20 '21 at 00:59
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1This might help - Why can't I do this to get infinite energy? – mmesser314 Nov 20 '21 at 01:43
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How can two things that are different be equal?
That is essentially what all of physics is about. From $F=ma$ to $E=mc^2$, pretty much all of physics is about finding equalities between seemingly different things. The fact that two things are different in no way prevents them from being equal. It just means that there is a connection of some sort, possibly a surprising one.
In a gravitational field there is actually gravity that push us down, but in the accelerated frame there is nothing that push us down.
In this case the connection is that gravitational mass and inertial mass are the same. When that is the case the gravitational force has the same form (locally) as a fictitious force: both are directly proportional to the mass. The differences between gravity and a fictitious force are only apparent non-locally, meaning over distances and times where tidal effects are noticeable.
Dale
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in the accelerated frame there is nothing that push us down.
Actually this is not true! Newton's laws only hold in inertial (non-accelerating) reference frames. To use $F=ma$ in an accelerating frame, one needs to include so-called fictitious forces. The name is somewhat unfortunate; it means that there is no force from the point of view of an inertial observer, but a fictitious force is experienced by an accelerating observer as if it were any other force. Anyway, in the reference frame of an elevator that is accelerating up with acceleration $g$, there is a fictitious force pushing down on observers in the elevator with magnitude $mg$. This is the same force that would be experienced by an observer sitting in an elevator that was at rest on the surface of the Earth, in the sense that no experiments done by an observer in the elevator (which do not interact with the outside environment of the elevator) can definitively decide whether the elevator was accelerating up or sitting on the Earth's surface.
There is a difference between gravitation and acceleration; they are not equivalent. The difference is tidal forces. In other words, if we look at the effect of a gravitational field over a large enough region of space that it is not approximately constant, then we can tell the difference between a gravitational field and uniform acceleration.
Andrew
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Einstein thought of it in a different way:
In a gravitational field (if we are not accelerating down), there is something pushing us up.
In the accelerated frame, there is something that pushes us up.
This image from researchgate.net shows the equivalence between the earth's gravitational field and a rocket accelerating at 'g'.
The arrow on the ball on the right shouldn't really be there, it's probably showing what happens to the ball from AE's point of view.
We could say instead that the ball remains stationary, but the floor of the rocket accelerates towards the ball and hits it.
John Hunter
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