Detecting Earth in an Elevator: Thought Experiment

[Pera Mitic]

I have in mind thought experiment where physicist is in elevator falling towards the Earth. Question would be if he is not allowed to look outside, how would he detect the presence of the planet? Let's not take in consideration tidal forces and assume he is taking local measurements during small time intervals. And whole experiment is in vacuum. Is there a way he can detect Earth under these conditions before he crashes into it?

The way I see things, there are only two conceptually different ways that our physicist can detect the Earth. Either by taking a peek outside of the elevator, or by crashing. These are two different ways we can transfer/register information from one point in space to another.

Interesting thing is that first method has to do with constant velocity, and second with acceleration. Let’s notice one more thing. First method of information transfer has its maximum, speed of light. Should the second one have its maximum? Should there be maximal possible acceleration/force in nature? Why would non-inertial reference frames be any special compared to inertial, and don’t have the property of maximal information transfer?

 

[Ibix]

Depending on how you model a crash, the speed limit is either not relevant (if you consider the crash as the intersection of a pointlike elevator and the Earth then there is no extent to the collision so nowhere to transfer information) or is the speed of light, since both you and the elevator are held together by electromagnetic forces. The speed of light in an accelerating frame is a complicated thing, but it's always locally c. You can't muck around with causality just by accelerating.

Additionally, crashing doesn't tell you that you have hit a planet. A free falling elevator in deep space being struck by a wide flat-nosed rocket accelerating at 1g will react exactly the same as if it free fell onto the Earth. You need to look for tidal forces, or look out of a window, to tell the difference.

 

[Nugatory]

if he is not allowed to look outside, how would he detect the presence of the planet? Let's not take in consideration tidal forces and assume he is taking local measurements during small time intervals. And whole experiment is in vacuum. Is there a way he can detect Earth under these conditions before he crashes into it?

No. That's the point of the equivalence principle.

The way I see things, there are only two conceptually different ways that our physicist can detect the Earth. Either by taking a peek outside of the elevator

That doesn't work unless he sees specifically the surface of the Earth rushing towards him. If he sees anything else, he's not detecting the earth, he's observing that whatever he is looking at is accelerating away from him at 10 meters per second per second (assuming that he's looking at something at rest relative to the surface of the earth). This can be interpreted as evidence that what's he's looking at is subject to a force that he's not as easily as evidence that he is free-falling in the gravitational field of the Earth that he can't see.

Interesting thing is that first method has to do with constant velocity, and second with acceleration. Let’s notice one more thing. First method of information transfer has its maximum, speed of light. Should the second one have its maximum? Should there be maximal possible acceleration/force in nature?

It's hard to answer that until we have a clear quantitative definition of "information transfer" so that we can calculate its maximum. However, I will note that:
1) The external observation also depends on acceleration. If you look outside the elevator and see only things at rest relative to you, as opposed to accelerating relative to you, you have no reason to infer the existence of any forces or gravitational effects.
2) For a given acceleration (or deceleration, in the case of the elevator smashing into the earth) the force is proportional to the mass as well as the change of speed, so the force can be made arbitrarily large even though the change in speed is limited. Thus, there's no reason to expect a speed limit to lead to a force limit. (There are some issues with the definition of "speed" here as well).

Why would inertial reference frames be any special compared to non-inertial, and don’t have the property of maximal information transfer?

Inertial frames are special because the laws of physics are especially simple and mathematically tractable when you use an inertial frame to assign coordinates (when you are "in an inertial frame" to use more natural but somewhat sloppy terminology). Thus, we teach physics and solve problems using inertial frames (possibly augmented with a "fictitious force") because it's the easiest way of understanding the physics and using it to solve problems. Other approaches work just fine, but are more work and often contribute no new physical insight.

 

[Dale]

This thread is closed due to personal speculation which has been deleted