Assignment 4. Mechanical Supertasks

For submission

Recall that a collection of bodies used in the slow supertask can spontaneously eject a mass in the reversed supertask scenario.

1. Once the masses are set up, must a body be ejected?

2. If a body is ejected, what speeds can it take?

3. Consider two sets of masses of the slow supertasks back to back as shown. Describe two different things that may happen.

For discussion

Not for submission

A. The configuration of bodies accelerating the spaceship can be collapsed from a two-dimensional arrangement to a one-dimensional arrangement. Can the same collapse be carried out for the case of the forward transfer machine? If so, what happens to the colliding bodies at the end of the supertask?

B. The physical assumptions used in the simple collision supertasks here are incompatible with quantum theory and relativity theory. What significance does that have for the analysis?

C. Energy and momentum conservation are violated in these supertasks. Does that mean that the relative consistency proofs fail?

D. Collisions with accumulation points cannot be treated consistently in this simple collision mechanics. Does that mean that the relative consistency proofs here fail?

E. Can you think of another case of a relative consistency proof?

F. Why is "clockwise" rotation in the familiar clockwise direction?