If Einstein was in an elevator in free-fall in a vacuum and in his upturned hand was a miniature elevator containing a miniature Einstein who had a miniature elevator in his hand and so on in ever decreasing sizes until the last elevator is on the scale of the Planck length would all these objects theoretically fall at the same rate?
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3$\begingroup$ the last elevator is on the scale of the Planck length We have little idea how anything behaves between about $10^{-18}$ meters and $10^{-35}$ meters. That is a lot of orders of magnitude. $\endgroup$– G. SmithNov 20, 2019 at 19:15
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1$\begingroup$ Who carries the measuring tapes, and how do they communicate their results? Some of the concepts lose their meanings in these 'independent' system arrangements... $\endgroup$– Philip OakleyNov 26, 2019 at 10:37
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3$\begingroup$ @Wookie Actually it was about the lack of reference points in, and between, each of the elevators. So there is no 'clock' nor 'ruler' that can be trusted. "Free-fall" implicitly defines that you are holding the ruler, and the only watch is the pendulum clock on the wrist that holds the ruler. Plus some vain assumptions about the lift being 'glass'. Oh, and that mini-elevator being held, isn't actually elevating/lifting/lowering anything. so if we remove all the elevators and local attraction then by definition.. It becomes Zeno's Einsteins flying in formation. $\endgroup$– Philip OakleyNov 26, 2019 at 15:46
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5 Answers
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The answer is no, these objects would not "fall at the same rate," because all the Einsteins' masses would attract each other. All Einsteins would be accelerating toward their barycenter, and thus would fall at different rates with respect to any reference point, such as the ground they're falling towards or the barycenter of all the Einsteins.
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1$\begingroup$ This seems like a detail according to the original question, but it is absolutely true! $\endgroup$– DarioPNov 27, 2019 at 9:35
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2$\begingroup$ Increase scale to make the greater Einstein be as great as our sun and you can see it with more strength. $\endgroup$– kokbiraNov 28, 2019 at 15:38
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Mass of an object is an intrinsic property of the object itself, independent of the gravitational field.
Weight of the object depends on how it is moving and it has direction. Objects in freefall are weightless.
The answer to your question is yes, all the objects would be in freefall and feel weightless independent of their sizes.
What is the difference between weight and mass?
In a roughly uniform gravitational field, in the absence of any other forces, gravitation acts on each part of the body roughly equally, which results in the sensation of weightlessness, a condition that also occurs when the gravitational field is weak (such as when far away from any source of gravity). The experimental observation that all objects in free fall accelerate at the same rate, as noted by Galileo and then embodied in Newton's theory as the equality of gravitational and inertial masses, and later confirmed to high accuracy by modern forms of the Eötvös experiment, is the basis of the equivalence principle, from which basis Einstein's theory of general relativity initially took off.
answered Nov 20, 2019 at 17:31
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2$\begingroup$ You are answering a different question than was asked. The question is "fall at the same rate" not "be in freefall" and/or "feel weightless." So, your statement and analysis is correct, but doesn't answer the question. $\endgroup$ Nov 26, 2019 at 17:48
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$\begingroup$ @ÁrpádSzendrei - ah so sorry, my nephew must have got at the computer. I will undo. Your answer was perfectly useful $\endgroup$– WookieDec 8, 2019 at 16:45
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Not at all. Einstein elevator makes zero the acceleration, not the velocity. Fortunately, Einstein elevator lead us to a uniform aceleration. So we don’t need to deal with position and speed uncertainties
We only have plane waves moving down ar several speeds. Of course, Elevators might not remain in Alberts hand for so much time: smallers ones will be the first changing its relative position due to the well defined z position. No body said velocity were the same for all of them at anytime.
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First, we must define the "elevator". If it is a plain elevator, then all the Einsteins have the same velocity at t=0. If the elevator comes with a shaft, then velocities may vary between any two adjacent Einsteins.
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The gravity here is emergent not only from the body they are falling towards but also each other. They will fall on different paths due to the relative masses. The force of gravitational attraction is the same so the speed of movement in the vacuum is the same but they will not fall towards the massive body at the same rate. Individual objects on tiny scale may have some own motion so they are not in inertial frame. Answer is no. No objects will fall at same rate.
