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Our planet, space and the Chinese is something that has has bothered children all over the world for many years. Even adults sometimes think about these things. The question of whether the Great Wall of China is viewable from the moon is one of those things, and the question of the jumping Chinese is another. Why don't we investigate this last question once and for all ?

Let's do the math, without the physics. We could use Newton's laws in order to calculate the forces involved, but that would only give us a number that would be hard to interpret. Let's just try to do an estimate that we then can translate into something we can relate to instead. 

Assume that one billion people would be participating this event. That would be hard enough to synchronize, but theoretically another billion jumpers would be able to squeeze in on that side of earth. We don't want people interfering on the other side of the earth, mind you. It's a factor 2, which we can account for later, if needed. Anyhow, one billion people, each weighing 60 kg (~130 lbs), would have the weight of 6 ·1010 kg. Earth has the mass 6 ·1024 kg

The earth weighs  6 ·1024 / 6 ·1010  = 1014 times more than one billion people. That is 100,000,000,000,000 times more. This number is of course hard to comprehend, but it gives a hint that there would be no noticeable effect on Earth at all. 

Let's scale this down to something we can relate to: a housefly. We all know how it is when a fly lands on you. If you're lucky, you feel an itch, but often you feel nothing. The ordinary housefly does not make a noticeable impact on you; it does not make you stumble or lose your balance. A housefly weighs about 40 mg, 40 thousands of a gram, or 4 ·10-2 g, or 4 ·10-5 kg. Something weighing a factor 1014 times more would therefore weigh 4 ·10-5 kg x 1014 = 4 ·109 kg, or 4 million kilograms. Lead weighs 11 350 kg/m3, which means that it would take 4  · 109 kg / 11350 kg/m3 = 352 400 m3 of lead to come up in this weight. This corresponds to a cube of lead with the side 3√( 352 400) = 70 meters (76 yards or 230 feet). This is the side of the cube of lead that our imaginary fly would land upon. 

So, we therefore conclude that:

The effect that one billion people would have on earth, is the same as a housefly would have on a lead cube with sides 70 meters long.

We realize that increasing the amount of people would have little impact. Just add one fly for each billion people. It wouldn't matter at all, would it? Earth would not notice our effort.

While the excellent analyses above stand on their own, I should point out that an experiment of this nature was actually carried out in Britain in 2001.1 Schoolchildren across the country all jumped (from the ground, to avoid the distance problems of uneven chairs) at the same time, to determine what result (if any) there might be. While the Earth was not noticeably affected, researchers in Britain noted that local seismographs recorded the event, with the strength of (approximately) an earthquake of magnitude 2 on the Richter Scale. (Note: m_turner informs me helpfully that a M2 earthquake is equivalent to the energy release (roughly) of 1 ton of TNT.)

We might, therefore, attempt to scale up from the number of participating children in Britain (something around one million) to the number of Chinese. There remains the problem, however, of arc coverage and of coordination. In our case, we are looking at the local vibratory effects of the Jump, not the aggregate effect on the Earth's orbit/spin. This makes things harder; we would need to know the number of Chinese, where they were jumping in relation to each other, and how much they weighed! This is because of the effects of interference.

Assume the speed of sound in earth is speed s. This is the speed at which the vibrations from each Jump would propagate outwards from the spot of each Jumper. Now, if the jumpers are the correct distance apart, it is quite possible for the vibrations to meet when precisely out of phase with each other (that is, when the period of one wave is 180 degrees from the other). If this happens, physics tells us that for the zone of interaction where this condition occurs the net result will be zero - it will be as if no wave passed at all.

So, to really be sure, we'd need to know the average separation distance of the Jumpers' feet, the speed of sound s in their floors, and where (exactly) they were all standing. Otherwise, there is a very small but non-zero chance that when they jumped, they would cancel out each other at the surface point of measurement!

1: The reference is from Slashdot, posted September 7, 2001. Unfortunately, it was just a pointer to a Yahoo! news page which has expired; I'll endeavor to hunt down the original story.

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