21 Jun '03 19:271 edit

(I got the idea for this one while racing cars on my bicycle this morning.)

StarValleyWy, physicist, interrupts the idyllic stupor of RHP one day, shouting incoherently about how Einstein is a fraud. After being calmed down, he explains that he has constructed a machine that could, in theory, propel one to any arbitrarily large velocity. He explains:

The machine as it is consists of a straight 80-mile stretch of highway, at one end of which is placed a flatbed truck 60 miles in length, such that it covers all but the last 20 miles of the highway. On top of this truck is another, placed so that the ends are flush, 40 miles in length. On top of this is a truck 20 miles in length placed in the same manner. At a signal, the bottom truck starts moving at 20 mph with respect to the road. The second moves at 20 mph wrt the bottom truck. The third moves at 20 mph wrt the truck below it. After one hour, the bottom truck has traveled to the end of the road. The second truck has traveled to the end of the first truck, and to the end of the road. The third truck has traveled to the end of the second, and thus to the end of the road. Thus, while each truck used energy necessary only to propel it at 20 mph, the top truck traveled 60 miles in one hour, for an average speed of 60 mph. Enlarging distances and adding arbitrarily many trucks could clearly propel the top truck at any velocity desired, namely one faster than light. Thus Mr. Einstein was a fraud.

There is one seemingly tiny flaw. What is it?

StarValleyWy, physicist, interrupts the idyllic stupor of RHP one day, shouting incoherently about how Einstein is a fraud. After being calmed down, he explains that he has constructed a machine that could, in theory, propel one to any arbitrarily large velocity. He explains:

The machine as it is consists of a straight 80-mile stretch of highway, at one end of which is placed a flatbed truck 60 miles in length, such that it covers all but the last 20 miles of the highway. On top of this truck is another, placed so that the ends are flush, 40 miles in length. On top of this is a truck 20 miles in length placed in the same manner. At a signal, the bottom truck starts moving at 20 mph with respect to the road. The second moves at 20 mph wrt the bottom truck. The third moves at 20 mph wrt the truck below it. After one hour, the bottom truck has traveled to the end of the road. The second truck has traveled to the end of the first truck, and to the end of the road. The third truck has traveled to the end of the second, and thus to the end of the road. Thus, while each truck used energy necessary only to propel it at 20 mph, the top truck traveled 60 miles in one hour, for an average speed of 60 mph. Enlarging distances and adding arbitrarily many trucks could clearly propel the top truck at any velocity desired, namely one faster than light. Thus Mr. Einstein was a fraud.

There is one seemingly tiny flaw. What is it?