Re: Would a time traveller create a massive explosion?

What a great question.  Clearly you have been spending a lot of time 
laying in bed thinking when you could have been sleeping.

There are several assumptions in your question that we don't have any 
data to support either way.  The first assumption is that a person 
traveling through time would appear instantenously.  Perhaps the time 
traveler would just fade in gradually, one molecule at a time.  But, 
let's go with your assumption for the sake of discussion.

As an object moves into a space previously occupied by air, if it moves 
into that space gradually, the air molecules have time to shift and move 
out of the way.  As the object moves into a space more quickly, the air 
molecules that are displaced bunch up, creating a localized higher 
pressure area.  Whenever a material, such as a loudspeaker cone, 
vibrates, it alternately creates localized high and low pressure waves as 
the air tries to move along with the speaker cone.  Air molecules near 
the solid object try and communicate to molecules farther away that they 
need to move out of the way.  The information between adjacient air 
molecules is transmitted at the speed of sound, roughly 700 miles per 
hour.

Let's think of the air molecules as if they were a row of dominos.  When 
the first one tips over, it knocks the next one over, and so forth until 
the dominos have all fallen down.  The dominos fall at a characteristic 
rate, determined by their size and the effects of gravity.

When an object moves fast enough, air molecules are not able to transmit 
information to other air molecules fast enough to let them know to move 
out of the way.  Let's say that instead of tipping over the first domino, 
a train comes plowing through the row.  It smashes into the first 
domino.  The first domino doesn't have time to tip over before the train 
smashes into the second domino, followed by the third.  Pretty soon you 
have a row of dominos smashed up against the front of the train.

A fast moving object in air will build up a pile of air molecules on the 
front of the object.  That pile of air molecules is essentially a region 
of high pressure that we call a sonic boom.  The number of air molecules 
involved in a particular sonic boom will depend upon the size of the 
object and the speed it is traveling.  An F-16 fighter jet traveling at 
twice the speed of sound will not produce as large a sonic boom as the 
space shuttle traveling at 25 times the speed of sound.  Likewise an F-16 
traveling at just above the speed of sound should not creat as loud a 
sonic boom as one traveling two times the speed of sound since less air 
is displaced per unit of time.

The sound from an explosion is also largely a sonic boom.  In a chemical 
explosion a solid occupying a certain space is suddenly converted into a 
gas occupying essentially the same space.  It is similar to having gas 
compressed at perhaps a million pounds per square inch and the vessel 
containing the gas suddenly disappears.  The gas from the explosion is at 
a very high pressure, and as the gas expands, it produces a sonic boom in 
proportion to the velocity and size of the explosive.  An explosive with 
a higher velocity will produce a higher pitched cracking sound, compared 
with the lower pitch from a lower velocity explosive.  The size of the 
sonic boom, however, is still largely a function of the size of the 
explosion, rather than just the velocity of the explosive.

So, going back to your question, let's say that an object the size of a 
person suddenly appears in a location previously occupied by an equal 
volume of air.  As you suggest, the air will be suddenly displaced by 30 
cm or so and should create a pretty good shock wave.  However, let's 
consider the amount of air displaced.  Say we send a 220 pound guy back 
through time.  If this guy has a mass density of about 1 g/cc (same as 
water), his body occupies a volume of 100 liters or about 0.1 cubic 
meter.  From http://wahiduddin.net/calc/
density_altitude.htm we find that 
the density of air is approximately 1.2250 kg/m3.

The volume of air displaced by our time traveler will be approximately 
0.1 cubic meter or about 0.1223 kg of air.  We should be able to simulate 
the shock wave produced by displacing that amount of air by using an 
explosive that produces approximately the same amount of gas (0.1 cubic 
meter of gas).  Since a chemical explosive essentially converts solid to 
gas, then a chemical explosive weighing 0.12 kg should produce a similar 
shock wave as produced by out time traveler.  The explosion is probably 
similar to a good size hand grenade.

So, even if our time traveler appears in an instant, the size of the 
shock wave he produces is still proportional to his size, rather than 
infinite in size.  The time traveler, however, will have the outside of 
his body subjected to the other side of the shock wave, which should be 
rather unpleasant for him, unfortunately.  It would almost certainly pop 
his ear drums and could leave him badly damaged.  So, our time traveler 
may have something more to worry about than suddenly surprising granny 
and have her beat him with her umbrella.

Great question.  Of course something else to worry about is whether there 
are other types of shock waves generated by traveling through time.  But 
that is beyond my expertise.