In yesterday’s NYT article on time travel:
But what about killing your grandfather? In a well-ordered universe, that would be a paradox and shouldn’t be able to happen, everybody agrees.
That was the challenge that Dr. Joe Polchinski, now at the Kavli Institute for Theoretical Physics in Santa Barbara, Calif., issued to Dr. Thorne and his colleagues after their paper was published.
Being a good physicist, Dr. Polchinski phrased the problem in terms of billiard balls. A billiard ball, he suggested, could roll into one end of a time machine, come back out the other end a little earlier and collide with its earlier self, thereby preventing itself from entering the time machine to begin with.
Dr. Thorne and two students, Fernando Echeverria and Gunnar Klinkhammer, concluded after months of mathematical struggle that there was a logically consistent solution to the billiard matricide that Dr. Polchinski had set up. The ball would come back out of the time machine and deliver only a glancing blow to itself, altering its path just enough so that it would still hit the time machine. When it came back out, it would be aimed just so as to deflect itself rather than hitting full on. And so it would go like a movie with a circular plot.
In other words, it’s not a paradox if you go back in time and save your grandfather. And, added Dr. Polchinski, “It’s not a paradox if you try to shoot your grandfather and miss.”
“The conclusion is somewhat satisfying,” Dr. Thorne wrote in his book “Black Holes and Time Warps: Einstein’s Outrageous Legacy.” “It suggests that the laws of physics might accommodate themselves to time machines fairly nicely.”
Dr. Polchinski agreed. “I was making the point that the grandfather paradox had nothing to do with free will, and they found a nifty resolution,” he said in an e-mail message, adding, nevertheless, that his intuition still tells him time machines would lead to paradoxes.
It’s not just intuition. It’s that the paradox is still there: even though the billiard ball didn’t stop itself from entering a time machine, it stopped itself from entering the same time machine. Why do the shoot-your-grandfather paradox folks only consider the most extreme version, in which your grandfather is dead? The fact is that before you entered the time machine, your parent was born of a grandfather without a wound; after you entered & exited the time machine & shot your grandfather, your parent was born of a different grandfather — a grandfather with a wound. Likewise the billiard ball has now had two entrances into the time machine: one clean, and one with a glancing blow that made some impact on the time machine itself — a dent to a minor transferance of energy.
Well, I should read the paper. Maybe they address this! But it seems like this resolution — you don’t actually hit your grandfather, billiard ball (2) doesn’t knock billiard ball (1) completely off its course — resolves nothing. (And it took them months of mathematical struggle to come up with it?) I can only see the shoot-but-miss solution working in two possible ways: (1) the shooting has one and only one possible effect: hitting and killing your grandfather. All the other effects on the world that shooting a gun normally has do not exist. This is logically absurd. Or, (2) It would only work if in the travel to the past you actually can effect absolutely no change whatsoever. But wouldn’t Heisenberg’s uncertainty principle dictate that even if you are present only as an observer you carry the potential to effect change? What if you’re observing something previously unobserved?
I’m assuming that these paradoxes & their potential resolutions exist because the time machine goes in & out of the same universe. If it leaves one universe (Time Stream 1, TS1) and enters another (TS2) or creates another with its entry, then these paradoxes don’t exist. Kill away. But this theory has always struck me as unsatisfying …
Will have to discuss this with physics- and math-minded scientists.