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The common explanation of why you can't lift yourself off the ground by pulling your feet up with your hands, or in more cliched terms "pull yourself up by your own bootstraps", is that if you consider your whole body as a system, the pull of your hands on your feet is just an internal force, so it can't pull your body off the ground.

But what about this thought experiment: let's say you say cross-legged with only your feet on the ground. Then you place your hands under your feet, so that only your hands are on the ground. Then you rapidly slide your hands way from under your feet and bearing your hands up. What would happen? Well, if your hands were 1 cm thick, then, the moment you removed your hands from under your feet, your feet would be 1 cm off the ground. So wouldn't you have managed to successfully lift yourself off the ground, if only for a moment before you crash back down?

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  • $\begingroup$ Stand on a board and drive a wedge underneath it and thus raise yourself up. But this isn't bootstrapping and neither is your example. For another example of "lifting yourself up", Google "Gravity Edge" (I still have one of these things...) $\endgroup$ – Alfred Centauri Sep 25 '13 at 0:41
  • $\begingroup$ @AlfredCentauri But do you agree that if you drive a wedge under you, and then rapidly remove the wedge from under you and pull it up, for a moment you and the wedge will both be entirely off the ground? $\endgroup$ – user30100 Sep 25 '13 at 0:48
  • $\begingroup$ Related: physics.stackexchange.com/q/68629/2451 and links therein. $\endgroup$ – Qmechanic Sep 25 '13 at 0:49
  • $\begingroup$ @user30100, you seem to have entirely missed the point of my comment. Whether you force your hands or a wedge between your feet and the ground, you have used the ground in some way to lift yourself up against gravity. Don't forget, the ground is applying a force upward to your body. If it weren't, you would freely fall, under the influence of the Earth's gravity, towards the Earth's center. For genuine bootstrapping, one could not push against the ground. $\endgroup$ – Alfred Centauri Sep 25 '13 at 2:40
  • $\begingroup$ @AlfredCentauri Yes, putting your hands under your feet requires using the ground. But I'm talking about the part that comes after that: removing your hands from under your feet and bringing them up. Doesn't that second action involve raising the center of mass of your body without being acted on by force that's external to your body? And doesn't the common argument against bootstrapping say that you can't raise the center of mass of your body using internal forces? $\endgroup$ – user30100 Sep 25 '13 at 3:10
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Let's consider this thought experiment. Let's go to a very light planet where $g$ is only a 1000th of what it is on earth. Lets get a very light ladder. This makes the thought experiment easier to imagine. The kind of ladder that makes an "A" shape so you don't have to lean it against anything. The ladder is so light that its mass is negligible compared to yours. Now you climb up the ladder and put your feet on one of the top rungs.

Now remember we feel almost weightless and the ladder is almost massless. Therefore we are able to pull the ladder out from under our feet to above our heads. Now we are certainly off the ground, and we will float for a while. The reason we are off the ground is because we climbed up a ladder. I fail to see how this is the same as pulling ourselves up by our bootstraps. Even if the ladder was considered part of your body, we still just climbed up the ladder.

Now lets think about your experiment. It's the exact same thing except the ladder is your hands. But since its the same thing as climbing up a ladder, it's really more like climbing up a ladder than pulling yourself up by your bootstraps. Does this make sense? Tell me if some part of the argument doesn't make sense.

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You could say that once I have raised the ladder over my head, I have lifted myself, since before the ladder-body system was touching that ground and now it is not.

However, this is not a fair definition of lifting yourself. For example, you could lift yourself in this sense by simply pulling your knees toward you chest so quickly that your feet leave the ground, but no one would call this lifting yourself because it would really seem like you are going down.

Also, if you tried to extend your feet again, you would find that your feet would hit the ground before becoming fully extended. Thus if your body could return to the same configuration it would actually be lower than it was originally. Comparing the minimum distance of the body off the ground between two configurations is misleading because some configuration can more easily have a large minimum distance from the ground.

A more sensible definition of pulling yourself up by your bootstraps would be if you could keep your body rigid while pulling on your bootstraps, but still cause an upward motion. We could even loosen this and say that you can move your body but you have to return to the same configuration.

It would be convenient if there were a way to compare the height of a body in two different configurations. So if I am a certain distance form the ground when my knees are pulled up to my chest, how far off the ground will I be when I extend my feet? It turns out there is a way to compare positions of two objects in different configurations. It is called the center of mass. If you have an object in any configuration you can calculate its center of mass. This center of mass is independent of configuration: the object can rearrange itself all it wants, but the center of mass you calculate won't change (if it isn't interacting with anything else).

Now it is sufficient for me to show that it is impossible to raise my center of mass by pulling on my bootstraps, for if I could raise my center of mass somehow, then I could return to my initial configuration and I would be higher off the ground, thus legitimately raising myself according to our more stringent definition.

However newton's laws say it is impossible for me to raise my center of mass by applying a force to myself, since only external forces can cause me to accelerate.

So it is impossible to pull yourself up by your bootstraps in the sense I described. You might say, "But it is possible to pull yourself up by your bootstraps in the sense I said." You would be right, but the statement is really as powerful. You are giving a way for someone to get there feet of the ground. The other statement is that the center of mass of any isolated system is always constant.

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  • $\begingroup$ Your ladder example doesn't make sense. Forget how you got to the top of the ladder. Suppose you were always on the top of the ladder. And then at some point, you pull the ladder up, raising the you-and-ladder system off the ground. Now please tell me how your thought experiment differs in any way from the example of pulling your feet up off of the ground. What's the difference between you standing on a ladder, and your legs (and the rest of you) standing on your feet? If you could pull a ladder up once you're on the top of it, then you could pull your feet up, since you're on top of them. $\endgroup$ – user30100 Sep 25 '13 at 3:16
  • $\begingroup$ I'm glad you agree that the two thought experiments are the same. That is one of the points I was trying to convince you of. I'm afraid I totally missed the source of your confusion at first but I think I found it now. I will try to edit my answer. $\endgroup$ – Brian Moths Sep 25 '13 at 3:31
  • $\begingroup$ To be clear, all I agreed to is that your ladder thought experiment is the same as the example of lifting yourself up by pulling up your feet. $\endgroup$ – user30100 Sep 25 '13 at 3:37
  • $\begingroup$ So you think it IS possible to pull yourself up by the bootstraps, while lowering other parts of your body in such a way that your center of mass stays the same, but your entire body leaves the ground? $\endgroup$ – user30100 Sep 25 '13 at 4:34
  • $\begingroup$ yes. I think that is possible. $\endgroup$ – Brian Moths Sep 25 '13 at 12:29

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