Well, no, because there are millions and billions and trillions of quantum events that could have resulted in his not being elected president -- over, to be sure, many, many, many years.

OTOH, there is a reason why SF stories tend to invoke the interpretation and then actually have many worlds based on human decisions.

I have a notion that if we could view alternate universes, they would be of only modest value for deciding what to do-- while they might help with avoiding some disasters, evaluating the effects of most decisions would be impossibly hard because so many non-obvious factors would go into the outcomes.

IANAP(hysicist), but I'd guess indexical uncertainty should give us at least a 1% chance Obama will lose the election. A dust speck jumping positions is wildly unlikely, but a discontinuous event isn't the only way the outcome can change. Over five months, enough small changes can add up to flip the outcome without any individually seeming abnormal.

A toy model: Drawing a number greater than 35 from a standard normal distribution has probability ~1e-268. But if we drew a standard normal every day up until the election and add them together, we'll end up with a number greater than 35 about 0.1% of the time. If we waited a year, it would be 3%. What's unthinkable in the short term becomes plausible in the medium term.

Of course, probability is in the mind, and there are many reasons to give Obama near-even odds besides indexical uncertainty.

Edit: Bad math.

Edited at 2012-06-28 01:23 am (UTC)

A lot of physical systems are chaotic, so a tiny difference in the initial conditions will cause a very different arrangement of particles some time in the future, even if the rough statistical properties of the system (air pressure, temperature etc.) will be more or less the same. So the dust in the car engine example might not be so much about the whole dust particle suddenly quantum tunneling into the engine, but instead a single air molecule moving differently some time in the past and leading to a slightly different arrangement of dust particles once the car rolls around. (Not a physicist, don't really know what I'm talking about, sorry.)

IAAP(hysicist), and this is correct. Scott simply failed to continue applying the butterfly effect.

Yeah, think this is the answer here. A different Everett branch is getting a *lot* of tiny pushes in randomly different directions, and in a chaotic system small differences being eventually amplified into big ones is the norm, not the exception. It's more like, the car is half a second later, as a result someone is greeted with "how are you" rather than "how was your day", and that sets off a different train of thought which results in a differently worded speech...

Part of the apparent disconnect is because descriptions like "2/3 chance" are overloaded, referring both to true probabilities (which have the MW implications you're describing) and confidences. If we had perfect information about the current state of the world (up to quantum limits) and a good enough computer model to accurately simulate it in exact detail, we could probably tell the winner of the election with 99+% confidence, this reflecting the true probability. But we've got very limited information and blunt-instrument predictive models, so we're stuck with a confidence of about the level of 2/3.

Heh. In my vocabulary, "true probabilities" refers to confidences, and squared amplitudes are a special case.

What ciphergoth replied. Probability is epistemic, first and foremost. But, I agree that (let me rephrase) 99+% of the many worlds* probably go one way or the other. While the butterfly effects might make Obama or Romney late to a rally, the attractors are too strong for that to be likely to make a difference. Only a fatal traffic accident, lightning strike, or comparably drastic Act Of Butterfly will do, for the most part, to throw the election.

(*) Substitute squared amplitude, or whatever your favorite interpretation dictates.

Also, what Oscar Cunningham and orthonormal said.

I don't know whether the probabilities are so extreme if you know where you are at the start, but they aren't if you don't, and in reality you don't. That is, you don't get to start from just one universe, you start from every universe that matches what you've observed so far. If the universe stopped branching today, the question would simply be whether you started out in a branch where Obama wins or in one where he doesn't.

Edited at 2012-06-28 07:56 am (UTC)

MW doesn't ground all probability in uncertainty.

Probability is uncertainty, so if you don't have perfect knowledge you can (and should) assign probabilities even in a deterministic universe. For instance, if I flip a coin and hide it under my hand, the probability I give for it being heads is 0.5, even though the result is already fixed. This describes my uncertainty; I have no information favouring heads over tails, or vice versa. No one is claiming that the coin has a 0.5 chance of flipping over due to quantum while under my hand. That event has a minuscule probability. If my friend had seen which way the coin landed (say heads) when it landed then she would assign a near 1 probability to heads.

In your example, you assign a 1/3 probability to an Obama win based on your limited knowledge (of poll results, campaign strategies, etc.). But this is just due to your limited knowledge. You would assign the same probability even if the laws of nature had turned out to be deterministic. However, we can imagine someone in the same position as my friend in the coin-flip example. They have full knowledge of the current state of affairs. They know the position of every particle on the planet, and for a sphere around us of radius (time to election)*(lightspeed). Then based on their knowledge (including the views of every voter, the intended strategies of the politicians, etc.) they can assign a probability to the event that Obama wins. In a deterministic universe this would be 0 or 1, but in a quantum universe they can't make a perfect prediction of what happens. MW says that as time passes the worlds split and our observer has indecical uncertainty about who which one she's in. Your post amounts to arguing that despite this randomness the probability she assigns is still roughly 0 or 1, and I'm inclined to agree with you. Although other commenters argue that chaos will amplify small changes, it seems like our observer would still have a very good guess of who was going to win. But even the quantum randomness made them uncertain, there's no reason why their probability for an Obama win would tend back to 1/3; the probability you gave based on your knowledge.

~Oscar_Cunningham

This.

Some things, like the 10^20th digit of pi, are things that you or I should treat probabilistically (since we can't reliably guess it with our current resources) but which will be the same in all Everett branches. Other things, like the hidden coin, will turn out the same in all branches starting from the one you currently occupy, but indexically you don't know the relevant fact about which one you occupy. And still other things are truly quantum-random from your current standpoint.

In the context of an election, there are some factors of each kind. Of course there are quantum-random ones like whether a candidate, in mid-debate, forgets the departments of government he plans to eliminate. (Although the chances that a particular candidate will have such a moment do depend on the candidate.)

Then there are hidden-coin indexically random events: perhaps Greece is still hiding even more massive debts than anyone at Intrade suspects, and a Eurozone collapse will swing the economy and the election in most of the branches from this point forward, but we just don't currently know whether we live in that branch or in one in which the damage is containable.

And finally, there are digit-of-pi factors which are subjectively random because we're not able to reason them out reliably, like our uncertainty about the effects of current policies on the economy for the next few months (because good macroeconomics is really difficult by human standards).

-orthonormal

Thanks. This and some of the other responses really help.

A large number of Everett branches are indeed not going to be distinguishable from each other by most humans (one atom in a reactor decays a few ms sooner or later, for instance); but a)there are vastly more branches than that (everything that could possibly happen does happen in at least one) and b)chaos - a change that is tiny to the point of undetectability NOW might have big effects LATER (and also might not).

I don't think your understanding is correct. It's not a case of running the universe forward from its current state and getting a result (we don't have that information), it’s a case of considering all universes that are indistinguishable from the current macroscopic state.

Now considering big bang theory if you trace time back far enough everything stems from QM differences on a microscopic scale. Now trace time forward. But as others correctly point out its not sudden QM fluctuations causing the futures to diverge it’s many small effects of chaotic systems (stemming from the original tiny differences in the initial states of the system) cascading over a long period of time.

So all those different universes (on the microscopic scale) that are indistinguishable (on the macroscopic scale based on our relative knowledge) really do exist and hence the probabilities based on our state of ignorance really do match the actual frequencies of QM universes.

Incidentally latest Betfair markets (the world's most accurate prediction market) have Romney as the big shortener.

Latest odds:

Obama 1.66
Romney 2.58

Obama currently has a 60% chance of winning.

"Incidentally latest Betfair markets (the world's most accurate prediction market) have Romney as the big shortener."

Can you link me to evidence that Betfair outperforms InTrade?

The trick in quantum mechanics is that you have to take EVERY path into account. When you say that there is a 2/3 chance of Obama winning the election, in QM this means that 1/3 of all possible decisions, including those at the subatomic level, result in his reelection. In the other 1/3 of ALL paths, Obama loses or the election is called off, for example, because the Earth quantum tunneled into being a black hole.

The problem, for me, about the alternate universes interpretation is that it implies there are lucky universes very unmuch like our own. For example, if you can rely on random air currents wafting you gently to the ground or buoying you to the desired level, you don't need elevators or airplanes. I'm not saying that these universes cannot exist, but they seem so unlikely, it would be nice to be able to do so.

The problem for Kripke, the 15 year old mathematician who first came up with the idea, was that too many people took him literally and came up with an awful lot of junk speculation based on a rather abstract idea. Parallel universes are interesting mathematically. They come up in doxastic and epistemic logic, but they aren't what most people think they are.

There are many processes with high Lyapunov's exponent (strong 'butterfly effect'). For example, bouncing of atoms off each other in gas.

Suppose a single atom is moved in alternative universe. It, basically, bounces off other atoms, and each bounce increases the difference. All of the brownian motion becomes different. The water drops in clouds form in different random locations. The turbulent flows have high Lyapunov's exponent as well, i.e. the disturbances increase in difference. In a week, all the random component of the weather is different. The election is somewhat affected by weather; but the probability does not need to be equal our ignorance-and-stupidity type of uncertainty about the outcome of election. I.e. you can be 66% certain that Obama would win the election in 99% of the universes if you assume effect of the weather and such to be strong enough over this time only in 2% of the worlds to significantly enough sway the election (1% of the time swaying it against Obama).

Knowing what I am talking about: I did cloud simulation for computer graphics, have experience with an RTS game engine that only sends the commands between the players, everyone running their own simulator, it diverges rapidly if there is a slightest difference in initial conditions. Have experience with entirely different game engine with entirely different mechanics diverging when playing back replays (recorded by recording the control input). The butterfly effect is incredibly robust.

More generally on MWI: the physical theories have to predict experimental data (or make a best guess whenever probabilistic). It does not suffice to just generate all possible and then say "somewhere here is your answer", that doesn't match the format for outputs. The picking of the answer - either deterministically, or making a best guess - is part of the theory. That is the fundamental distinction between prediction and explanation.

Science is similar to Solomonoff induction where the programs that output strings which *begin* with your data are considered, not just the programs that contain your data somewhere inside, it is a critically important point easily overlooked. Without that point, it simply doesn't work - you get some sort of bruteforce guesser as the shortest program, with zero predictive power.