Does information paradox in the Many Worlds interpretation cause a problem?

Question

I'm taking a philosophy of time travel class. In one of the lectures, the teacher was discussing problems with the Many Worlds interpretation. He talked about how since anything that can possibly happen happens in some timeline, in one timeline there is a person that comes out of what appears to be a timemachine with the complete works of Shakespeare. This person didn't actually come from the future, but he and the works of Shakespeare were created due to random quantum fluctuations. He gives the book to Shakespeare, who publishes it as his own. Later in the same timeline, someone reads his work and creates what he thinks is a timemachine to go back and give Shakespeare his complete works. He gets into this machine and disappears. My teacher says this is a problem because it is indistinguishable from a genuine information paradox. My questions are:

1) Is this really a problem? Even though it looks like an information paradox, it doesn't seems to be one. Instead of the book coming from nowhere, it came from random fluctuations.

2) This question's more weird: Even if it were a paradox, would it matter to people in the other universes or would it not be a problem for them? Since people in one timeline can't observe another timeline, would the paradox be isolated and not actually affect any other universe or am I confused about what a paradox would mean?

This isn't super important, I'm just curious. I'm also not sure this is even the right place to ask these questions. Anyway, thanks for your thoughts.

Answer 1

Who needs a time machine, or quantum mechanics? All you need is randomness of some sort, which quantum mechanics happens to have. If you're content to consider simple coin-flips as random, you have the same problem.

Imagine: in the 16th century, William Shakespeare had a really boring decade. He was so incredibly bored that he took up mathematics, which he discovered he had a talent for. His mathematical inventions were:

• to invent base-6 notation as a way of keeping track of numbers up to 36 = 6 × 6 on his two hands;
• to realise that 36 different numbers are enough to represent the letters A-Z, word breaks, and several punctuation marks besides;
• to make the logical jump that if he rolled a six-sided die millions and millions of times, some of the time he might come up with long tracts of meaningful text.

William followed this up with playing dice for a lark, to see what would happen. You would not believe the incredible streak of luck that he had. He rolled a six sided die uncountably many times, and every single roll led to an intelligible bit of writing. It so happened that by playing dice, he wrote all of his plays and poems. And so after all, Shakespeare was a charlatan: he had no talent for writing; he was just an extremely lucky mathematical genius. And he took his shameful secret to his grave, just barely holding onto his sanity, fearful that his luck would run out. This explains how a sixteenth century playwright would anticipate so much of nineteenth and twentieth century sensibility and philosophy (which the dice put into the mouths of his fools and villains: lucky for him, given his cultural context).

This is totally absurd, but it is possible. The problem is that the probability that totally random events (such as dice rolls or the spontaneous aggregation of what appears to be a time-traveller with the complete works of Shakespeare) have some chance of producing events like this. In fact, the die-rolls theory is more likely, because the original version you were told also has to randomly produce a healthy living person who is also completely sane, apart from being convinced that they are a time-traveller.

Is the complete works of Shakespeare information? To us it is, who have the cultural context and the physical means to interpret it, more or less easily. What makes it information is that it has structure which is unlikely to come about by chance: it is pertinent, and therefore presumed to be purposeful. Its improbability is the crux of the so-called paradox: having acknowledged that it is an improbable event for it to come about by chance, we do not have to marvel that there is some probability (vanishingly small) that it could come about by chance.

Answer 2

Your teacher is wrong. Firstly, note that the presence or absence of a problem has nothing whatsoever to do with the MWI - what is being described could happen in this universe, without recourse to the MWI, it would just be astronomically improbable. However, if this series of events were truly a paradox, it would have to be strictly impossible, and so the problem would be present or absent whether the series of events is astronomically improbable as is the case without MWI or whether it the series of events is virtually certain to occur as is the case when we consider all possible worlds in the multiverse in MWI. Thus, we can entirely disentangle the MWI from this question.

Now, the resolution of the apparent paradox is hinted at in the question you ask in point 2). An information paradox occurs if we can reliably communicate information back in time. By assumption, the series of events we describe doesn't constitute that - it occurs purely by random chance.

To see this more clearly, suppose instead that in the year 2000 I walked into a door (could be a door to a funky contraption that looks like a time machine, or it could just be a regular door to a library) carrying the complete works of Shakespeare (I don't even dematerialise as I walk through, I continue and exit on the other side just fine), and in the year 1999 I walked out of a door carrying the complete works of Shakespeare (once again I had walked in normally, no magic materialisation happening here either). Has an information paradox occurred in this scenario? Have I transmitted the works of Shakespeare back in time?

"Of course not," you say, "but the situations are fundamentally different - the alleged time-traveller I described dematerialised in the future, and materialised in the past." But, so what? The dematerialisation/materialisation events are far more improbable than the walking in/walking out of a door events, but they are not fundamentally any different - both are due to random fluctuations and in both cases the works of Shakespeare were present at a future time and present at a past time, one is just far more likely to occur than the other. But clearly, in the second case we would not suggest that any information has been transmitted back in time.

The apparent contradiction stems from our thinking that just because certain random fluctuations are possible in our universe they are properly "caused" by the laws of our universe. That is not to say that events in a universe with probabilistic laws are totally randomly caused - we have compelling evidence that they follow particular, albeit probabilistic, laws. Rather, you can think of a series events having two causal elements - reliable, definite, physical laws, which determine a probability distribution of series of possible events, and then a random element that selects from this distribution.

For information to be transmitted reliably from event A to event B, event A must through the physical laws affect the probability distribution element of B's cause in a way that makes it highly likely for that information to emerge at event B. This is clearly not what is happening in either case above.

Event A - which in the first case is the dematerialisation of the alleged time-traveller in the future with the complete works of Shakespeare, and in the second case is me walking in to a door with the complete works of Shakespeare - has, as per the physical laws of our universe (relativity, quantum mechanics, etc.), no bearing whatsoever on the probability distribution element of the cause of event B - which in the first case is the materialisation of the alleged time-traveller in the past with the complete works of Shakespeare, and in the second case is me walking out of a door with the complete works of Shakespeare.

These just happen for unrelated reasons - in the first case, sheer random chance causes the highly improbable materialisation event to occur, and in the second case some unrelated set of causes (having to do with me being a perennial bookworm) lying strictly in the past of event B shape the probability distribution, making it likely for me to walk out of the door with the complete works of Shakespeare. In either case, no information is transferred from event A to event B, and there is no information paradox.

Answer 3

I seems to me that your teacher is wrong.

The case of Shakespeare with a real time machine is described in the Wikipedia article on the bootstrap paradox - http://en.wikipedia.org/wiki/Bootstrap_paradox

The case with the real time machine seems to be distinguishable from your teacher's since with a real time machine there is a causal loop; in particular the time traveler causes Shakespeare to publish his writings.

In your teacher's case there does not seem to exist a causal link between the disappearing man in the future and the appearing quantum fluke man in the past.

I would love to hear your teacher's explanation.