Einstein’s relativity is a subject I’ve been interested in for years and years because it flies in the face of normal, every day experiences and every day “common sense”, yet it’s real. Time actually does pass by at different rates for objects travelling at different speeds relative to each other and for objects in different areas of gravity. I will not be explaining time dilation affects in this article though. This article is a very specific, side-topic of relativity. In particular, it’s about what relativity tells us we’d experience inside a closed box that was launched upward, or in free floating space, or in orbit (hint; it’s the same in all 3 scenarios).
If you want a relatively full (pardon the pun), layman’s explanation of relativity, I highly recommend Einstein’s book “Relativity: The Special and the General Theory”. It’s written for the layman and is a surprisingly simple read. There’s one chapter with tons of math that you can completely skip. The math chapter is NOT necessary to understand the fundamentals of relativity. The math is necessary only if you plan on writing relativity software or doing your own calculations for whatever reason. It’s NOT necessary to understand the theory and no other chapters have any math in them at all (except maybe things like 2 + 3… it doesn’t get any more complicated than that in the non-math chapters). I have a link to Amazon to the right which probably has a link to the book if you’d like to get it.
Why this article? This is a topic that comes up frequently in discussions of relativity and rather than explain it over and over, I figured I might as well write it once and then refer people to the write up.
Let’s get started:
Here’s the scenario: You’re in an elevator with no view of what’s going on outside your little container. You’re slammed down against the floor for a few seconds with extreme force, then suddenly, you’re weightless. What just happened? And, what’s going to happen? What will you experience? Let’s add two more variable (or take two away, depending on your viewpoint): Let’s assume there’s no atmosphere outside your elevator (you have plenty of air inside though). Let’s also say your elevator shaft goes all the way through the center of the Earth. It’s a mag-lev elevator with no moving parts and no touching parts, so no friction against the sides of the shaft. Both ends of the shaft are open (on both sides of the Earth). For you nit-pickers out there, we’ll also say it goes through the poles (north and south) and to simplify it even more for you extremist nit-pickers, we’ll say the Earth is not rotating and it is sufficiently removed from all the mass of the universe (no sun, no moon, no galaxies for billions of light years… fair enough?)
Here are some common (and wrong) responses:
- I’ll feel the speed of traveling upwards until I reach the apex (top) of the trajectory, then I’ll be weightless for just a very short moment, then I’ll fall and I’ll feel the extreme speed of falling. I’ll know when I’m at the top because I can easily feel it.
- I’ll be stuck to the bottom of the elevator all the way up, until I reach the top of the trajectory. I’ll feel it slowing down until I reach the top. Then, once the elevator changes direction, I’ll be pushed up against the ceiling on the way down and the force of me against the ceiling will increase as my downward speed increases.
Here’s what actually happens and what you’d feel:
First, the initial part of you being pushed against the floor. This is caused by an upward acceleration. You’d feel this acceleration as long as the acceleration were being applied… or more precisely, you’d feel the compression of your body against the elevator floor, caused by the elevator going upward and the inertial of the mass of your body resisting the change.
At the very moment the acceleration was turned off, you’d immediately experience weightlessness. Your upward speed is dependent on how strong the acceleration was and for how long it was applied. If it was strong enough and long enough, you could be moving upward for quite some time and distance (perhaps even hours). All you would know is that you’re weightless. You won’t know how fast you were traveling relative to the Earth. You would simply be “weightless”. You wouldn’t know whether you were moving up or down or were just floating in empty space.
When you reached the apex (the top) of your toss up, both you AND the elevator would start moving back towards the Earth, rather than away from it, but since both you AND the elevator do this at the same rate at the same time, there’s nothing inside the elevator to give you a hint that you’ve changed direction relative to the surface of the Earth. And, in fact, from one relativistic point of view, you haven’t “changed direction”. Unless you look out the window, there’s no way you’d be able to tell from your own senses alone, and in this hypothetical scenario, there are no windows, so all you’d know is that you’d just feel weightless.
On the way down, there’s no difference in your experience as on the way up, nor any difference in the transition from “up” to “down”. You’re not pushed up against the ceiling or the floor. Think about why: For that to happen, the elevator and you would have to be “falling” at different rates. Either you’d be pushing against the elevator or the elevator would be pushing against you and that would ONLY happen if objects fell at different rates. From Galileo’s famous experiment of dropping objects from the leaning tower of Pisa, and from the more accurate experiments of the astronauts on the moon dropping a brick and a feather in the vacuum of the moon, all objects fall at the same rate. Since you and the elevator fall at the same rate, neither of you would (or could) be pushing against the other. You’re both in free fall on the way up and and the way down. Your experience inside the elevator is that of weightlessness.
But, what about “Tidal Forces”?
Yes! There are “tidal” forces. You can look up tidal forces in Wikipedia or you can read about them in Einstein’s book I mentioned above. These are very small in this scenario and you would certainly not “feel” them, though, if you knew what you were doing, you could pull the change out of your pocket and do an experiment inside the elevator to detect these tiny forces, but as a matter of human experience and “feeling” them, that would not happen. In essence, all that you’d notice is objects inside the elevator would appear to “orbit” the center of the space inside the elevator, about once every 90 minutes or so. I won’t explain the internal “orbits” here (perhaps in another post).
Falling through the bottomless shaft:
By now, the main point of this article has been made, that you’d experience weightlessness for 100% of the trip as long as there’s no immediate acceleration applied to you. But, now that the point’s been made, let’s stress the point and go further and have some more fun with this…
As you fall back down to Earth and fall below the surface, into your bottomless elevator shaft, you’d still experience nothing unusual. As far as you’re concerned, you’re still weightless because you and the elevator are still falling at the same rate. Your speed relative to the shaft will increase all the way to the center of the Earth, but your rate of increase in speed will be decreasing as soon as you fall below the surface of the Earth. This is because as you get deeper, there’s more mass “above” you and less and less mass “below” you. The mass of the Earth above you is pulling you towards it, countering the the shrinking mass of the Earth below you, until you reach the center. At the center of the Earth, you have an equal amount of mass above you in all directions. At this point ALL directions are “up”. All of the mass of the earth is pulling you at equal rates in all directions, canceling all of it out. If you stopped at the center of the Earth, you’d be weightless. But, let’s continue. In our scenario, you’ve been falling for about 22.5 minutes by the time you reached the center. Now, the only thing keeping you moving is your own momentum. Gravity is no longer forcing you in the direction you’re going. You’re moving simply because you “are”. (any object in motion, remains in motion, unless acted upon by an external force). You’re now going “up” towards the opposite side of the Earth. But, since you’ve now crossed the center of the Earth, you’re putting more and more of the Earth’s mass behind you and less and less of it in front of you. That means the Earths gravity of that mass is pulling you towards the center again, even though there’s plenty in front of you pulling you up, there’s more behind you, pulling you towards the center and it’s winning. Your speed towards the other opening is decreasing. The rate of decrease is increasing, until you reach the opening that you’re traveling towards. You’ll shoot up directly out of the shaft and all the Earth’s mass is now behind you, still pulling you. Your rate of decrease stops, but your momentum still carries you upwards and gravity is still decelerating you, until you reach the other top of your trajectory and it starts all over again. This process will continue without end. You will never stop experiencing weightlessness. You are essentially in orbit, but instead of around the Earth, you’re in orbit through the Earth.
This is the classic elevator example that Einstein explains in his book “Relativity: The Special and the General Theory”. This is my own explanation, but it’s not much different from Einstein’s. Einstein’s point is that gravity and acceleration should be considered the same phenomenon. My point of this article is simpler… To explain that there’s no special human experience that can determine the speed or the apex in this scenario.
I’ll probably be writing up some more articles on relativity in the future (or, in the past, depending on your inertial frame of reference! 😉