And summing over universes with real values of lapse leads to the wildly fluctuating, physically nonsensical solution. He and Hartle analyzed the issue of the contour of integration in He and his colleagues argue that, in the minisuperspace case, only contours that pick up the good expansion history make sense.
Imaginary numbers pervade quantum mechanics. To team Hartle-Hawking, the critics are invoking a false notion of causality in demanding that lapse be real. According to Hertog, Hawking seldom mentioned the path integral formulation of the no-boundary wave function in his later years, partly because of the ambiguity around the choice of contour. He regarded the normalizable expansion history, which the path integral had merely helped uncover, as the solution to a more fundamental equation about the universe posed in the s by the physicists John Wheeler and Bryce DeWitt.
Wheeler and DeWitt — after mulling over the issue during a layover at Raleigh-Durham International — argued that the wave function of the universe, whatever it is, cannot depend on time, since there is no external clock by which to measure it.
And thus the amount of energy in the universe, when you add up the positive and negative contributions of matter and gravity, must stay at zero forever. The no-boundary wave function satisfies the Wheeler-DeWitt equation for minisuperspace.
In the final years of his life, to better understand the wave function more generally, Hawking and his collaborators started applying holography — a blockbuster new approach that treats space-time as a hologram. Hawking sought a holographic description of a shuttlecock-shaped universe, in which the geometry of the entire past would project off of the present.
But Turok sees this shift in emphasis as changing the rules. In backing away from the path integral formulation, he says, proponents of the no-boundary idea have made it ill-defined. For the past year, Turok and his Perimeter Institute colleagues Latham Boyle and Kieran Finn have been developing a new cosmological model that has much in common with the no-boundary proposal. But instead of one shuttlecock, it envisions two, arranged cork to cork in a sort of hourglass figure with time flowing in both directions.
While the model is not yet developed enough to make predictions, its charm lies in the way its lobes realize CPT symmetry, a seemingly fundamental mirror in nature that simultaneously reflects matter and antimatter, left and right, and forward and backward in time. Boyle, Finn and Turok take a stab at the singularity, but such an attempt is inherently speculative. Questions abound about how the various proposals intersect with anthropic reasoning and the infamous multiverse idea.
The no-boundary wave function, for instance, favors empty universes, whereas significant matter and energy are needed to power hugeness and complexity. Hawking argued that the vast spread of possible universes permitted by the wave function must all be realized in some larger multiverse, within which only complex universes like ours will have inhabitants capable of making observations. The recent debate concerns whether these complex, habitable universes will be smooth or wildly fluctuating.
An advantage of the tunneling proposal is that it favors matter- and energy-filled universes like ours without resorting to anthropic reasoning — though universes that tunnel into existence may have other problems. Or perhaps, instead of a South Pole-like non-beginning, the universe emerged from a singularity after all, demanding a different kind of wave function altogether.
Either way, the pursuit will continue. I mean, this is the super ultimate "why" question? So I'm going to talk about the mystery of existence, the puzzle of existence, where we are now in addressing it, and why you should care, and I hope you do care. The philosopher Arthur Schopenhauer said that those who don't wonder about the contingency of their existence, of the contingency of the world's existence, are mentally deficient.
That's a little harsh, but still. Laughter So this has been called the most sublime and awesome mystery, the deepest and most far-reaching question man can pose. It's obsessed great thinkers. Ludwig Wittgenstein, perhaps the greatest philosopher of the 20th century, was astonished that there should be a world at all. He wrote in his "Tractatus," Proposition 4. John Archibald Wheeler, one of the great physicists of the 20th century, the teacher of Richard Feynman, the coiner of the term "black hole," he said, "I want to know how come the quantum, how come the universe, how come existence?
And I've no doubt there are five Einsteins in the audience tonight. Any Einsteins? Show of hands? No Einsteins? So this question, why is there something rather than nothing, this sublime question, was posed rather late in intellectual history.
It was towards the end of the 17th century, the philosopher Leibniz who asked it, a very smart guy, Leibniz, who invented the calculus independently of Isaac Newton, at about the same time, but for Leibniz, who asked why is there something rather than nothing, this was not a great mystery. He either was or pretended to be an Orthodox Christian in his metaphysical outlook, and he said it's obvious why the world exists: because God created it.
And God created, indeed, out of nothing at all. That's how powerful God is. He doesn't need any preexisting materials to fashion a world out of.
He can make it out of sheer nothingness, creation ex nihilo. And by the way, this is what most Americans today believe. There is no mystery of existence for them. God made it. So let's put this in an equation. I don't have any slides so I'm going to mime my visuals, so use your imaginations.
Now that's the equation. And so maybe you don't believe in God. Maybe you're a scientific atheist or an unscientific atheist, and you don't believe in God, and you're not happy with it. God doesn't exist by logic alone unless you believe the ontological argument, and I hope you don't, because it's not a good argument.
So it's conceivable, if God were to exist, he might wonder, I'm eternal, I'm all-powerful, but where did I come from? Laughter Whence then am I? God speaks in a more formal English. Laughter And so one theory is that God was so bored with pondering the puzzle of His own existence that He created the world just to distract himself. But anyway, let's forget about God. And to a Buddhist, the world is just a whole lot of nothing.
It's just a big cosmic vacuity. And we think there's a lot of something out there but that's because we're enslaved by our desires. If we let our desires melt away, we'll see the world for what it truly is, a vacuity, nothingness, and we'll slip into this happy state of nirvana which has been defined as having just enough life to enjoy being dead.
So that's the Buddhist thinking. What are we going to put in that blank? Well, how about science? Science is our best guide to the nature of reality, and the most fundamental science is physics.
So maybe physics can fill this blank, and indeed, since about the late s or around , physicists have purported to give a purely scientific explanation of how a universe like ours could have popped into existence out of sheer nothingness, a quantum fluctuation out of the void.
Stephen Hawking is one of these physicists, more recently Alex Vilenkin, and the whole thing has been popularized by another very fine physicist and friend of mine, Lawrence Krauss, who wrote a book called "A Universe from Nothing," and Lawrence thinks that he's given — he's a militant atheist, by the way, so he's gotten God out of the picture.
The laws of quantum field theory, the state-of-the-art physics, can show how out of sheer nothingness, no space, no time, no matter, nothing, a little nugget of false vacuum can fluctuate into existence, and then, by the miracle of inflation, blow up into this huge and variegated cosmos we see around us. Okay, this is a really ingenious scenario.
It's very speculative. It's fascinating. But I've got a big problem with it, and the problem is this: It's a pseudo-religious point of view. Now, Lawrence thinks he's an atheist, but he's still in thrall to a religious worldview.
He sees physical laws as being like divine commands. The laws of quantum field theory for him are like fiat lux, "Let there be light. As Galileo taught us, one of the foundational features of modern physics is that objects can move, and tend to do so, without any need for an external cause or mover.
Roughly speaking, the same goes for the universe. Consider an issue that is inextricably tied to why the universe exists: has it existed forever, or did it come into existence at some particular moment, presumably the Big Bang? Nobody knows. If we were Pierre-Simon Laplace, who believed in the classical physics of Newton and scoffed at the idea that God would ever interfere in the workings of nature, the answer would be easy: the universe exists forever.
Time stretches from the infinite past to the infinite future. Of course you are always welcome to consider other theories, but in unmodified Newtonian physics the universe has no beginning. Then in along comes Einstein and his theory of general relativity. Space and time are subsumed into a four-dimensional spacetime, and spacetime is not absolute — it is dynamic, stretching and twisting in response to matter and energy. Not long thereafter, we learned that the universe is expanding, which led to the prediction of a Big Bang singularity in the past.
In classical general relativity, the Big Bang is the very first moment in the history of the universe. It is the beginning of time. Then in the s we stumbled across quantum mechanics.
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