No longer a worry (Image: Michael Skolund/Workbook/Getty)

GAMBLERS already had enough to think about without factoring the end of time into their calculations. But a year after a group of cosmologists argued that they should, another team says time need not end after all.

It all started with this thought experiment. In a back room in a Las Vegas casino, you are handed a fair coin to flip. You will not be allowed to see the outcome, and the moment the coin lands you will fall into a deep sleep. If the coin lands heads up, the dealer will wake you 1 minute later; tails, in 1 hour. Upon waking, you will have no idea how long you have just slept.

The dealer smiles: would you like to bet on heads or tails? Knowing it’s a fair coin, you assume your odds are 50/50, so you choose tails. But the house has an advantage. The dealer knows you will almost certainly lose, because she is factoring in something you haven’t: that we live in a multiverse.


The idea that our universe is just one of many crops up in a number of physicists’ best theories, including inflation. It posits that different parts of space are always ballooning into separate universes, so that our observable universe is just a tiny island in an exponentially growing multiverse.

In any infinite multiverse, everything that can happen, will happen – an infinite number of times. That has created a major headache for cosmologists, who want to use probabilities to make predictions, such as the strength of the mysterious dark energy that is accelerating the expansion of our own universe. How can we say that anything is more or less probable than anything else?

One procedure physicists are fond of is to draw a cut-off at some finite time, count up the number of events – say, heads and tails – that occur in the multiverse before the cut-off time, and use that as a representative sample.

It seems reasonable, but when tackling the casino experiment, something strange happens. Wherever the cut-off is drawn, it slices through some of the gamblers’ naps, making it appear as if those gamblers simply never woke up. The longer the nap, the more likely it is to be cut off, so if you do awaken, it’s more likely that you have taken a shorter nap – that is, that you flipped heads. So even though the odds seemed to be 50/50 when the coins were first flipped, heads becomes more probable than tails once you and the other gamblers wake up.

“This thought experiment was unbelievably perplexing at first, because it seemed like probabilities were changing from one instant to the next without any explanation,” says Alan Guth of the Massachusetts Institute of Technology, who along with Vitaly Vanchurin of Stanford University in California, came up with the conundrum two years ago.

Last year, Raphael Bousso at the University of California, Berkeley, and colleagues devised an explanation that was effective, if unsettling. The changing probabilities were behaving as if time ends at the cut-off, they said, because time really does end at the cut-off. That’s why the initial 50/50 odds change when you wake up from your nap.

Upon waking, you have new information: you know that time didn’t end. That now means it is more likely that you only slept for a minute than for an hour. After all, time could end at any minute, and an hour has an extra 59 of those to spare. Heads wins.

The idea that time must end for the probabilities to make sense has been bugging Guth and Vanchurin for the last year. Now they say they have developed a mathematical explanation for the multiverse that saves the fourth dimension (arxiv.org/abs/1108.0665).

The essence of the argument is that you don’t need any new information, in this case the fact that you woke up, to understand why the odds are no longer 50/50. In a multiverse that grows exponentially, where each new generation of universes is far larger than the last, younger universes always outnumber older ones. Waking up, you will either be in a universe in which 1 minute has passed (heads), or in a universe in which 1 hour has passed (tails). “The experiment sets up a 59-minute ambiguity in the age of the universe,” Guth says. “You should always bet on the younger one.”

Waking up in the casino, you will either be in a universe in which 1 minute has passed, or 1 hour

But Bousso doesn’t feel safe just yet: “Nature has often seemed crazy as we discovered how far removed its workings are from our everyday intuition. The end of time may sound crazy, but it is by far the simplest interpretation.” Whether or not time is going to end, there’s a lesson to take from the debate: should you wake up in Las Vegas, bet heads.