# Einstein's quantum elevator in a vacuum

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?

• 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. – G. Smith Nov 20 at 19:15
• Right. So the concept of free-fall becomes irrelevant at a certain point – Wookie Nov 21 at 11:59
• Who carries the measuring tapes, and how do they communicate their results? Some of the concepts lose their meanings in these 'independent' system arrangements... – Philip Oakley Nov 26 at 10:37
• @PhilipOakley - are you pointing out that it would be hard to realize the gravitational force on the objects separately as they would influence each other? – Wookie Nov 26 at 14:11
• @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. – Philip Oakley Nov 26 at 15:46

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.

https://en.wikipedia.org/wiki/Free_fall

• 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. – Jeff Learman Nov 26 at 17:48
• @Wookie why the deselect? – Árpád Szendrei Dec 7 at 16:23
• @ÁrpádSzendrei - ah so sorry, my nephew must have got at the computer. I will undo. Your answer was perfectly useful – Wookie Dec 8 at 16:45

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.

• This seems like a detail according to the original question, but it is absolutely true! – DarioP Nov 27 at 9:35
• Increase scale to make the greater Einstein be as great as our sun and you can see it with more strength. – kokbira Nov 28 at 15:38
• @Jeff Learman - would there be a minimum speed of falling that would allow them to escape each others gravitation? – Wookie Dec 2 at 12:48
• @Wookie - Yes, if they had something to jump from. The escape velocity for each of them would depend on the total mass and his distance from the barycenter. But if they're all just falling from an initial static setup, they would get closer together as they fell toward the ground, regardless of how fast they all fell towards the ground. – Jeff Learman Dec 3 at 13:28

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.

• In my opinion this point is excellent – Wookie Dec 8 at 17:29

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.

• Yes, that is true if mechanics were operating – Wookie Dec 8 at 17:26