WHY is there a 1 in 2 chance of getting a tail when you flip a coin? It may seem like a simple question, but the humble coin toss is now at the heart of a lively row about the multiverse. At stake is the ability to calculate which, of an infinite number of parallel universes, is the one that we inhabit.
The debate comes in the wake of a paper posted online a couple of weeks ago by cosmologists and Daniel Phillips, both at the University of California, Davis. They argue that conventional probability theory, the tool we all use to quantify uncertainty in the real world, has no basis in reality (). Instead, all problems in probability are ultimately about quantum mechanics. 鈥淓very single time we use probability successfully, that use actually comes from quantum mechanics,鈥� says Albrecht.
This controversial claim traces back to the uncertainty principle, which says that it is impossible to know both a quantum particle鈥檚 exact position and its momentum.
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Albrecht and Phillips think particle collisions within gases and liquids amplify this uncertainty to the scale of everyday objects. This, they say, is what drives all events, including the outcome of a coin toss. Conventional probability 鈥� which says the outcome simply arises from two equally likely possibilities 鈥� is just a useful proxy for measuring the underlying quantum uncertainties.
鈥淨uantum uncertainty is what drives all events, including the outcome of a coin toss鈥�
In the case of a coin toss, quantum uncertainty in the position of neurotransmitter molecules in the nervous system of a coin flipper might translate into an uncertainty in the number of times a coin turns in the air before being caught, ultimately determining whether it is a head or a tail, the pair suggest.
In a back-of-the-envelope calculation that used estimates for coin size, speed and neurotransmitter uncertainty, the pair were able to show that this quantum sequence of events could give the same probability of throwing a head or a tail as the conventional calculation 鈥� one-half. They say this supports their argument that conventional probability is just shorthand for an underlying quantum reality.
But does any of this matter if the odds are ultimately the same? Yes, says Albrecht, because there is one use of conventional probability that cannot be traced back to a quantum origin: predicting the fate of the universe.
Physicists have long known how to make predictions about quantum objects, even though such entities do not have fixed properties until they are observed. Before that, they exist in a superposition of all possible states, which is described by an equation known as the wave function. A principle called the Born rule lets physicists extract a probability of observing a particular state from the wave function, and so allows them to predict a quantum object鈥檚 behaviour.
There is just one problem. The Born rule breaks down in some situations. The latest theories in cosmology say that our universe is just one part of a vast multiverse containing a large or even infinite number of other 鈥減ocket鈥� universes. Some of those universes will be exact copies of our own, right down to a duplicate you. The mathematics behind the Born rule can鈥檛 cope with this.
鈥淚n these situations, the quantum wave function can tell you nothing about which pocket you are in,鈥� says Albrecht. That鈥檚 a problem if we want to predict the properties of our universe, which will look identical to many others at a given point in time, but which can eventually evolve differently due to quantum uncertainty.
Until now, physicists seeking to predict the properties and behaviour of the multiverse have added a sprinkling of conventional probability to reflect the chance of us being in a particular universe. For example, in a multiverse with just two universes, you might add a 50-50 chance of being in either one, just as we instinctively assign the same odds to a coin toss.
Albrecht says that is wrong. Unlike a coin toss, these probabilities do not have a quantum origin. To explain the multiverse scenario, a new theory of probability is required. 鈥淚t is not an extension of our everyday experience of probability,鈥� he says. 鈥淚t is really a brand new thing.鈥�
The claim has sparked a range of responses from cosmology heavyweights. of the University of California, Santa Barbara, is waiting for the idea to be fleshed out. 鈥淭o make it really interesting, you have to go to the next step and say what the new method is going to be,鈥� he says.
of the University of Alberta, Canada, who was first to highlight the problem of applying the Born rule to the multiverse, says researchers are already in a pickle. 鈥淚f the Born rule doesn鈥檛 work, we need a replacement, but we can鈥檛 deduce one from concepts we already have.鈥�
of Tufts University in Medford, Massachusetts, doubts there is a replacement. 鈥淚f you know the wave function of the universe, you still have to decide which copy is you,鈥� he says. 鈥淚 think there is no way to do it.鈥� As a result, he is sanguine about continuing with conventional probability in multiverse calculations.
Albrecht admits that a single example of a system that can be described in purely conventional terms would lend support to this argument, but he says he hasn鈥檛 encountered one yet. 鈥淚鈥檝e been challenging people for a couple of years now,鈥� he says.
One that comes close is placing a bet on the value of the millionth digit of pi. It is easy to calculate this exactly 鈥� it is 5, as it happens 鈥� but if neither party knows that in advance, it becomes a probability problem, and conventional probability says there is a 1 in 10 chance of winning the bet.
Albrecht and Phillips say quantum effects come into play here too, through the choice of which digit to bet on, either as neural fluctuations, as with the coin flip, or as other uncertainty from a random number generator.
Page thinks that is a claim too far, though. 鈥淥ne could conceptually imagine a case where quantum mechanics is not relevant for choosing which digit we are talking about.鈥�
Our understanding of the multiverse is far from settled, says Srednicki. 鈥淭he multiverse is an unruly beast and we would like to tame it, but I don鈥檛 think anyone has drawn blood yet.鈥�
