New Scientist’s executive editor Richard Webb, a “recovering particle physicist,” offers a look at the current state of the idea that there might be an infinity of universes out there. Why believe it? Mainly, it turns out, to avoid believing something else:

Gods and their intelligent designs are less in the mainstream of scientific thought now, yet similar ideas about an optimal universe still trickle through cosmology. That is principally down to some mysterious numbers that determine its workings. Tot them all up in the standard models of particle physics and cosmology, and you end up with about 30 constants of nature – numbers like the strengths of the fundamental forces and the masses of elementary particles that our theories can’t explain, but are just “there”.

Change many of these constants, and nothing happens. “But with others, it’s drastic, not to say lethal,” says cosmologist Paul Davies at Arizona State University. Alter the relative strengths of gravity and electromagnetism just a little, say, and stars and galaxies can’t form. Flip the tiny difference in the proton and neutron’s masses to make the proton heavier, and you don’t even get stable atoms.

“Changing these numbers would probably preclude any life in the universe,” says Davies. It isn’t a big leap to say it looks like the knobs have been twiddled – as if the universe were somehow fine-tuned for our existence

. Richard Webb, “Why is the universe just right for life? Blame the multiverse” at New Scientist (November 17, 2021)

Other cosmologists, like Carlo Rovelli, say no because we don’t know what a universe based on different principles that actually worked would be like. We can easily see why, if our universe departed from its program, it could just twinkle out of existence. But we can’t know that universes formed on other principles would not work.

Some cosmologists accuse those with doubts of just wanting to think we are special, much as some chimpanzee behaviorists accuse humans of thinking that we are not just bipedal apes. The trouble with such accusations is that they are irrelevant. Just as humans might actually be unique in intellect, our universe might actually be the only one.

Many people assume that the idea that ours is the only universe must be a religious one. Webb quotes cosmologist Paul Davies: “‘You have to decide if the origin of the universe is a natural, or a supernatural, event,’” says Davies. “‘If it is a natural event, you wouldn’t expect it to happen just once.’”

Perhaps not. But we can just as easily theorize that a Divine Mind created an infinity of universes. Perhaps ours is one of the few that was “chosen” to produce life. True, one could just as easily simplify cosmology by positing that natural laws randomly produce countless universes, a handful of which may work. But what, exactly, are those laws? Because they are outside our universe, we must take them on faith.

The problem with the multiverse doesn’t lie in issues around a role for God. The problem opponents cite is that there is no serious evidence for any universe other than our own. Acceptance of theories without evidence (perhaps to evade a logic problem of some kind) is bad for science in principle.

Although popular science magazines might imply that physics is pointing us to the reality of a multiverse, there is much opposition from within the discipline. Prominent proponents of the multiverse have included well-known cosmologists such as Max Tegmark and Alexander Vilenkin, Brian Greene and Neil Turok, Alan Guth and Stephen Hawking, as discussed in online science magazines. But opponents include theoretical physicist Sabine Hossenfelder (“Why the multiverse is religion, not science”), cosmologist Paul Davies (“it also leads to a fake universe with fake physics”, which undermines arguments from physics) and cosmologist George Ellis (“beyond the domain of science”). Well-known science writer John Horgan considers the idea “bad for science” and mathematician Peter Woit thinks that it “has left conventional science completely behind.”

A mathematical argument against the multiverse

In any event, as computer engineering prof Robert J. Marks notes, even if we allow for an infinite sum of universes, simple mathematical reasoning shows why just anything can’t happen:

In a nutshell, the reason is that some infinities are bigger than other infinities. (And this is not a claim like infinity plus one is bigger than infinity. Infinity plus one is still infinity.) …

The number of points on a line segment from, say zero to one, is a bigger infinity than the number of counting numbers {1,2,3,…}. We can label the infinite number of universes in the multiverse as universe #1, #2, #3, etc. Because they can be counted, this infinity is said to be countably infinite. This looks to be the smallest infinity. (“Smallest infinity” sounds like an oxymoron but isn’t.) And, no, true infinity is not the same as the symbol ∞. In mathematics, ∞ typically means “increasing without bound.” And no matter how high you count, you still have infinity to go.

The number of points on a line segment — the bigger infinity — can be referred to a “continuous infinity.” The points on a line are too many to count. They can’t be ordered as points 1,2,3, etc. Given any point on a line, for example, there is no closest point. No matter how close a point is chosen to a given point, there will be a closer third point midway between the first two points.

This situation is not true for the countably infinite. Given any number, say 112, the numbers 111 and 113 are the closest numbers. Not so with the set of numbers on the line segment from zero to one. Consider the midpoint ½ =0.5. Is 0.501 the closest number to 0.5? No. 0.5001 is closer and 0.50001 even closer. This can go on forever, getting closer and closer. But there is no closest number to 0.5.

How does this apply to claims that there is an infinite number of universes where — as a result — anything can happen? If there is a countably infinite number of possibilities (e.g. we have three eyes in one universe, two in another), then the infinity of universes must be continuous in order to include all possibility combinations. (The proof is here.)

The universes in the multiverse cannot therefore be counted but would correspond rather to a smear on the number line. Such a multiverse is inconceivable. It also begs the question of where our universe, counted by us as universe #1 in the multiverse, fits in this uncountable continuum.

Such observations are fun, but stories about a multiverse look more and more to be fairy tales. There is no experimental proof of parallel universes and many, including me, feel the infinite multiverse hypothesis is a fantasy built on soft sand by imaginative minds and speculative mathematics. No physical proof exists.

Robert J. Marks, “Why Just Anything Can’t Happen Via Infinite Universes” at Mind Matters News (October 28, 2021)

Of course, a proponent of the multiverse might well retort that the fact that we can’t conceive of a multiverse doesn’t rule it out. No, but it does raise the question of why the multiverse is considered a serious theory is science. Perhaps the concept of a multiverse is doing something — for example, countering religious objections to a meaningless universe that depend on fine-tuning — that has itself, in atheist Peter Woit’s words, “ left conventional science completely behind.” It does so at a considerable cost in rational thinking.

You may also wish to read: In an infinity of universes, countless ones are run by cats… Daniel Díaz notes that most of the talk about the multiverse started to appear once it was realized that there was fine-tuning in nature. Robert J. Marks points out that even 10 to the 1000^th power of universes would only permit 3,322 different paths. Infinity is required but unprovable.