Star Trek part 2:  Mr. Scott's formula for transwarp teleportation

In the new 2009 move Star Trek, a possibly too young engineer Montgomery Scott is manning a small ground station on a frozen and hostile planet within sight of Vulcan, where both the older Spock and the young Kirk are separately marooned and find each other.  Mr. Scott, or Scotty as he is known, is certain he was assigned there as punishment for having argued with his admiral professor that it would be possible to teleport someone far across the galaxy and onto a ship traveling at warp, and incidentally for having attempted the feat with the admiral's pet dog, which vanished.  The older Spock reassures him that indeed what he proposed is entirely possible, based on an equation which Scotty himself will eventually develop.  Spock then shows Scotty that equation, and uses it to teleport Scotty and Kirk from that station to the warp-driven Enterprise.

As he looks at the equation, Scotty comments that he would never have thought to treat space as that which is moving; that is, he does not believe he ever would have developed that equation on his own.  The question is, does it matter that Spock gave Scotty the equation, which now Scotty will be able to publish to prove his theory, but which no one will ever actually discover or create in real time?  It is an object of a predestination paradox, something that exists in the past because it was brought from the future, but has no origin in time.

This type of grandfather paradox happened previously in Star Trek, when in Star Trek IV:  The Voyage Home Mr. Scott gave to Dr. Nichols the formula for transparent aluminum, which "he might have invented".  There were certainly ramifications of that, but ultimately it did not destroy the future.  It is sufficient that Spock would know the formula when he traveled to the past, and so could give it to Scotty; that that formula is now never "invented" is not a problem for time--directly.

It does, however, raise two concerns.

The first is that the equation will be "discovered" sooner.  This scientific and technological advance will have become the basis for other advances, at least some of which will be found sooner, some by different researchers from their original discoverers.  Time, though, depends on an event still over a century in the future, a moment when Spock, using the most advanced ship Vulcan could provide, will be mere seconds too late to save Romulus and instead will be pulled into a temporal vortex.  Very slight advances in technology now might mean that Spock will save Romulus--and in saving Romulus, undo the time travel event creating this history.

The other concern is more difficult to express; it is about Montgomery Scott himself.  Anyone who has reasoned his way through a difficult theory or discovery knows that this work changes you.  It builds your thought processes and prepares you to tackle similar problems more easily in the future, in a way that gaining an understanding from someone else's explanation does not.  If Scotty has just been handed the answer to the single most difficult question he ever solved, he is the poorer for it, and might not be as sharp an engineer thereafter as he was.

On the other hand, it might not be so serious.  After all, Spock did not leave Scotty with the equation; Scotty perhaps got no more than a hint to put him back on track to something he may still take years to unravel.  We might be fine.  Technological advances might already be behind schedule if the interferences with history have altered events enough.  We do not know that this will have more impact in this history than it had in the other.

Of course, we also lose Vulcan, and the advanced technology generated by its famed science academy.  Next time we will consider the impact of the loss of the Federation's most respected planetary member.