AN IDENTICAL copy of you is also reading this story. This twin is the same in every way, living on an Earth and in a universe that looks exactly like our own. And there may be an infinite number of them. Such doppelgängers could be a natural consequence of our present conception of the universe. Now, some physicists say they could pose a serious problem for quantum mechanics. But a possible fix may also be in sight, and it could help tie abstract quantum concepts to concrete physical causes.
In the uncertain, fuzzy world of quantum mechanics, particles do not have fixed properties until they are observed. Instead, objects that obey quantum rules exist in a “superposition” of all their possible states simultaneously. Schrödinger’s famous cat, for example, is both alive and dead until we take a peek inside the booby-trapped box in which it has been placed.
Because the probability that the cat will be found alive is based on a quantum event – the decay of a radioactive substance within the box – it can be calculated using a principle called the Born rule. The rule is used to transform the vague “wave function” of a quantum state, which is essentially a mixture of all possible outcomes, into concrete probabilities of particular observations (in this case, the cat being alive or dead). But this staple of quantum mechanics fails when it is applied to the universe at large, says Don Page at the University of Alberta in Edmonton, Canada.
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At issue is the possibility that there could be a multiplicity of copies of any particular experiment floating about the universe, just as there could be a multiplicity of yous. There could even be an infinite number of them if, as is thought, the early universe underwent a period of exponential growth, called inflation. Although this period ended very soon after the big bang in our observable region of space, inflation may have continued elsewhere, giving rise to a “multiverse”, an infinite space containing infinite copies of our Earth. “In an infinite universe, every possible thing would happen, and it would happen an infinite number of times,” says cosmologist of Tufts University in Medford, Massachusetts.
Missing ingredient
Crucially, says Page, all of these copies pose a problem for the Born rule: it’s unclear how to calculate the probability of different outcomes for a given experiment without first adding some extra ingredient that accounts for the multitude of copies (). “You can’t just plug in the Born rule and get answers that make sense,” he says (see “Identity crisis”).
of the University of California, Davis, has dubbed the problem the “Born rule crisis”. The shortcoming means we could not, in theory, calculate the probability of the outcome of any new measurement of the universe, such as the mass of the neutrino. “It’s a deep failure of something, either of quantum theory or the multiverse,” Albrecht says. “If you’re a cosmologist, you should be worried,” he adds.
“It’s a deep failure of something, either of quantum theory or the multiverse”
Others, like physicist at the University of California, Santa Barbara, are not convinced there is a crisis. He says adjustments for missing information are fairly routine in quantum physics and should not require an overhaul of the theory.
A deeper problem, he says, is that we still don’t understand what quantum probabilities really mean. “Quantum mechanics is now 100 or so years old, but it is still deeply mysterious,” he says. “Because the concepts are so divorced from human experience, we’re still not sure we’re thinking of them in the right way.”
Probability is treated differently in the two main interpretations of quantum mechanics. In the traditional view, observing a quantum system yields just one outcome. This view, called the Copenhagen interpretation, is a bit baffling. An initial superposition of states in a given system collapses into just one state upon being measured. Exactly why this change happens, or how the system “chooses” to be in one state or another, is unclear.
An alternative, proposed by physicist Hugh Everett in the 1950s, suggests the initial mix of states never collapses. Instead, making a measurement splits our universe into parallel versions that exist in an abstract quantum realm, and all possible outcomes occur somewhere. If a system is a mix of two equally probable states, the universe splits into two when the system is observed. But what if Schrödinger’s cat is, say, 70 per cent more likely to be found alive? Does that mean the universe with the live cat would somehow be “more real” than the one in which the cat died?
at the University of California, Santa Cruz, Max Tegmark of the Massachusetts Institute of Technology, and David Layzer of Harvard University, suspect the key to clearing this confusion could lie in the multiverse, and in tying quantum probabilities to real physical observers.
Without using the Born rule, they calculate the probabilities linked to an experiment with an infinite number of identical copies throughout the multiverse ().
Imagine a quantum version of an experiment in which someone reaches into a bag containing 70 red balls and 30 blue balls. If there are an infinite number of such bags and ball-pickers, the probabilities associated with the experiment simply equate to the relative numbers of observers who find each kind of ball, says the team – in this case, 70 per cent red and 30 per cent blue. The situation is identical to one in which the same single experiment is repeated an infinite number of times. “Once you consider the combined system of all of these experiments, the probabilities come from counting up the observers and not from using the Born rule,” Aguirre says.
Framed in this way, the Copenhagen and Everett interpretations look the same. The universe, filled with its infinite copies of ball-pickers, would still split into many different quantum versions in the Everett scheme. Each would have a different set of outcomes for the balls – in one version, person 1 might get a red ball and person 2 a blue, and so on up to 100 balls, for example, while in another quantum version, it might start with persons 1 and 2 both pulling out red balls. But if you counted all the balls in each quantum version, the final ratio between red and blue balls would be the same as that in every other quantum version.
That suggests that you only have to consider one quantum version of the universe, just as in the Copenhagen interpretation. Tegmark says this resolves the conundrum of how the many-worlds interpretation deals with probabilities – some do not have to be “less real” than others, as previously suggested. “All those many worlds that Everett invented are out there,” he says.
“I think this is an important advance,” says Vilenkin. “They showed that the mathematics really works out. It kind of clears up the foundations of quantum mechanics.”
Identity crisis
Not knowing who you are is not just the cause of existential angst – it could also be the source of quantum uncertainty.
The outcomes of quantum experiments cannot be predicted exactly. Instead, a principle called the Born rule calculates the probability of each possible outcome.
The Born rule can’t cope, however, if there are multiple doppelgängers running the same experiment elsewhere around the universe. It seems to need an extra ingredient, like a measure of the distribution of these doppelgängers, to work out the probability of outcomes in a given experiment.
A team led by Anthony Aguirre of the University of California, Santa Cruz, has tackled this problem without resorting to the Born rule (see main story).
They say an infinite number of doppelgängers, or copies, performing the experiment is equivalent to one observer doing the experiment an infinite number of times. This picture ties the abstract Born rule to something concrete – the existence of multiple, identical observers; a possibility that could arise if our universe is large.
In their scheme, some of these copies would get one outcome in a quantum experiment and others another outcome, with the relative numbers agreeing with the Born rule. So instead of a single observer who doesn’t know the outcome of an experiment ahead of time, in this picture multiple observers get different outcomes, and quantum uncertainty “comes from the fact that you don’t know which observer you are”, Aguirre says.
But the probabilistic nature of quantum mechanics is still a mystery. “At this stage, I would say it is a matter of taste whether it’s ‘better’ to have uncertainty from the existence of inaccessible copies or uncertainty that’s intrinsic to quantum mechanics,” says Mark Srednicki of the University of California, Santa Barbara.
