How Many Universes are There?

Response to a Quora Question


Anil Mitra

Link to my Website

The QuestionStephen Hawking said in his last post before he died that the number of universes was finite. Why would he do such a thing? Does the fact that it is finite mean that no new universes will ever form again?

Disclaimer—the answer below first appeared on Quora. Their policy, which I presume is an agreement, is that they retain non-exclusive rights to answers by members. Changes made here but not made in the Quora answer are marked in differently colored font.

My view is that current physics warrants no conclusion at all as to the number of ‘universes’.

Before explaining why I think so, I will clarify the meaning of the term ‘universe’. If ‘universe’ means all that there is over all time and space then there is and can be only one universe. I will use the term ‘universe’ in just that sense. So what does it mean to talk of the plural, ‘universes’. In that use we are speaking of something rather like our empirical cosmos. So where the question uses the term ‘universe’ it refers to ‘cosmoses’. We could use a term like sub-universe, mini-verse, but I will use the term cosmos. I avoid the term multiverse altogether.

I should tell you a little about my background too. Though I’m an engineer, my interests are ‘omnivorous’. In physics, as a grad student in engineering, I took most of the graduate (PhD) level theoretical courses in physics—classical mechanics, quantum mechanics, electromagnetism with special relativity, and general relativity—in which I performed better than most (PhD) physics students. However, I have not used that experience professionally or to do research. I’m still keen on theoretical physics but I do not think of myself as an expert.

I will now explain my view.

At the end of this answer there are two quotes that show that Stephen Hawking held that theoretical models of the empirical universe are true of the entire universe—seen or empirical as well as unseen.

To hold that that is true one must assume that the entire universe is (a) like our empirical cosmos with regard to our physical laws and (b) is also described by models that describe our cosmos at least down to just after the big bang singularity.

While, as far as physics goes, it is speculative to talk of other cosmoses, because our models are only and strictly of the empirical, it is also speculative to say that there is no other cosmos.

For example, even if there is no time before the big bang on our models, it does not follow that there was no time at all. If our cosmos is finite on our models, it does not follow that the universe is finite. If the cosmos is infinite on our models, it still does not mean that the models capture or that the cosmos is the entire universe—for the universe may be even larger in magnitude and or dimension and the cosmos embedded in it. In that case, the cosmos may be almost observationally and structurally isolated from the rest of the universe (at present and since the big bang). Of course if the isolation is absolute then it makes no sense to talk of a larger or embedding universe but it is only in the models that the isolation is known to be absolute.

So the claim that there is only this universe is the result of (i) placing unwarranted faith in our models of the empirical cosmos and (ii) lack of imagination.

Some physicists and others assert that it is speculative metaphysics to claim or even talk of other cosmoses. On the basis of current physics, that is true (but not unwarranted if one does not pretend that it is more than speculation). On the other hand the claim that there is but one cosmos or just a few is just as speculative. It results from taking our theoretical models too seriously (and perhaps even personal investment in the models). This, by the way, has happened before in physics, e.g. toward the end of the nineteenth century just before the relativity and quantum revolutions..

The correct view from physics, according to the argument above, is that the extent of the ‘greater universe’ and the number of sub-universes is unknown.

Here are the quotes. It’s not necessary to read them to understand my argument above. Both quotes are rather long but not essential to my argument (there is more in the linked articles). Neither article is technical.

The first is from The Beginning of Time (a lecture by Hawking)—

The focussing of our past light cone implied that time must have a beginning, if the General Theory of relativity is correct. But one might raise the question, of whether General Relativity really is correct. It certainly agrees with all the observational tests that have been carried out. However these test General Relativity, only over fairly large distances. We know that General Relativity can not be quite correct on very small distances, because it is a classical theory. This means, it doesn't take into account, the Uncertainty Principle of Quantum Mechanics, which says that an object can not have both a well defined position, and a well defined speed: the more accurately one measures the position, the less accurately one can measure the speed, and vice versa. Therefore, to understand the very high-density stage, when the universe was very small, one needs a quantum theory of gravity, which will combine General Relativity with the Uncertainty Principle.

Many people hoped that quantum effects, would somehow smooth out the singularity of infinite density, and allow the universe to bounce, and continue back to a previous contracting phase. This would be rather like the earlier idea of galaxies missing each other, but the bounce would occur at a much higher density. However, I think that this is not what happens: quantum effects do not remove the singularity, and allow time to be continued back indefinitely. But it seems that quantum effects can remove the most objectionable feature, of singularities in classical General Relativity. This is that the classical theory, does not enable one to calculate what would come out of a singularity, because all the Laws of Physics would break down there. This would mean that science could not predict how the universe would have begun. Instead, one would have to appeal to an agency outside the universe. This may be why many religious leaders, were ready to accept the Big Bang, and the singularity theorems.

It seems that Quantum theory, on the other hand, can predict how the universe will begin. Quantum theory introduces a new idea, that of imaginary time. Imaginary time may sound like science fiction, and it has been brought into Doctor Who. But nevertheless, it is a genuine scientific concept. One can picture it in the following way. One can think of ordinary, real, time as a horizontal line. On the left, one has the past, and on the right, the future. But there's another kind of time in the vertical direction. This is called imaginary time, because it is not the kind of time we normally experience. But in a sense, it is just as real, as what we call real time.

The three directions in space, and the one direction of imaginary time, make up what is called a Euclidean space-time. I don't think anyone can picture a four dimensional curve space. But it is not too difficult to visualise a two dimensional surface, like a saddle, or the surface of a football.

In fact, James Hartle of the University of California Santa Barbara, and I have proposed that space and imaginary time together, are indeed finite in extent, but without boundary. They would be like the surface of the Earth, but with two more dimensions. The surface of the Earth is finite in extent, but it doesn't have any boundaries or edges. I have been round the world, and I didn't fall off.

The second quote is from Taming the multiverse: Stephen Hawking’s final theory about the big bang (Thomas Hertog - Wikipedia was a “key collaborator” of Stephen Hawking)—

Modern theories of the big bang predict that our local universe came into existence with a brief burst of inflation – in other words, a tiny fraction of a second after the big bang itself, the universe expanded at an exponential rate. It is widely believed, however, that once inflation starts, there are regions where it never stops. It is thought that quantum effects can keep inflation going forever in some regions of the universe so that globally, inflation is eternal. The observable part of our universe would then be just a hospitable pocket universe, a region in which inflation has ended and stars and galaxies formed.

“The usual theory of eternal inflation predicts that globally our universe is like an infinite fractal, with a mosaic of different pocket universes, separated by an inflating ocean,” said Hawking in an interview last autumn. “The local laws of physics and chemistry can differ from one pocket universe to another, which together would form a multiverse. But I have never been a fan of the multiverse. If the scale of different universes in the multiverse is large or infinite the theory can’t be tested. ”

In their new paper, Hawking and Hertog say this account of eternal inflation as a theory of the big bang is wrong. “The problem with the usual account of eternal inflation is that it assumes an existing background universe that evolves according to Einstein’s theory of general relativity and treats the quantum effects as small fluctuations around this,” said Hertog. “However, the dynamics of eternal inflation wipes out the separation between classical and quantum physics. As a consequence, Einstein’s theory breaks down in eternal inflation.”

“We predict that our universe, on the largest scales, is reasonably smooth and globally finite. So it is not a fractal structure,” said Hawking.

The theory of eternal inflation that Hawking and Hertog put forward is based on string theory: a branch of theoretical physics that attempts to reconcile gravity and general relativity with quantum physics, in part by describing the fundamental constituents of the universe as tiny vibrating strings. Their approach uses the string theory concept of holography, which postulates that the universe is a large and complex hologram: physical reality in certain 3D spaces can be mathematically reduced to 2D projections on a surface.

Hawking and Hertog developed a variation of this concept of holography to project out the time dimension in eternal inflation. This enabled them to describe eternal inflation without having to rely on Einstein’ theory. In the new theory, eternal inflation is reduced to a timeless state defined on a spatial surface at the beginning of time.

“When we trace the evolution of our universe backwards in time, at some point we arrive at the threshold of eternal inflation, where our familiar notion of time ceases to have any meaning,” said Hertog.

Hawking’s earlier ‘no boundary theory’ predicted that if you go back in time to the beginning of the universe, the universe shrinks and closes off like a sphere, but this new theory represents a step away from the earlier work. “Now we’re saying that there is a boundary in our past,” said Hertog.

Hertog and Hawking used their new theory to derive more reliable predictions about the global structure of the universe. They predicted the universe that emerges from eternal inflation on the past boundary is finite and far simpler than the infinite fractal structure predicted by the old theory of eternal inflation.

Their results, if confirmed by further work, would have far-reaching implications for the multiverse paradigm. “We are not down to a single, unique universe, but our findings imply a significant reduction of the multiverse, to a much smaller range of possible universes,” said Hawking.