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Why Did Stephen Hawking Give Up on a Theory of Everything?

Daniel Díaz and Ola Hössjer continue their discussion of the fine tuning of the universal constants of nature with Robert J. Marks

In a continuing conversation with Swedish mathematician Ola Hössjer and Colombian biostatistician Daniel Díaz on the fine-tuning of the universe — and Earth — for life, Walter Bradley Center director Robert J. Marks asks them about why a Theory of Everything eludes us and about the life-permitting interval — the narrow window for life that the constants of the universe permit. This is the second part of Episode 3, “The universe is so fine-tuned!” (September 16, 2021). Earlier portions, with transcripts and notes, are listed below.

This portion begins at 12:36 min. A partial transcript, Show Notes, and Additional Resources follow.

Robert J. Marks: In truth, there’s a lot of fundamental constants — the electric charge of an electron, the weak force, the strong force. There looks to be tens, maybe hundreds of different constants that we can look at … And look at the consequences of what would happen if it varied. Is it a fine tuned thing or is there a lot of wiggle room there?

Daniel Díaz: There are basically four fundamental forces, the electromagnetic force, the gravitational force, the weak, and the strong force. Th unification of those four forces is that what is called a Theory of Everything in physics. That theory does not exist yet, basically because gravitation is very stubborn and it refuses to be placed in the same category or in the same model as the others.

Gravity, a fundamental force, doesn’t join the Theory of Everything Club:

(Note that, toward the end, we are told that the graviton, gravity’s particle, is theoretical and unobservable.)

Robert J. Marks: In fact, I think it was Stephen Hawking who gave up pursuing the Theory of Everything. He appealed to Gödel: No matter what you did, there would be stuff that was true in the universe that you still needed to prove …

Note: Mathematical logician Kurt Gödel (1906–1978) is best known for eliminating the idea that there is a simple Answer to Everything: “In an exceptionally elegant essay, science writer Ashutosh Jogalekar (no stranger to controversy) talks about the huge difference Kurt Gödel (1906–1978) made by eliminating the idea that some single, simple explanation would put an end to all questioning about the nature of the universe in favor of some simple materialism.” – Mind Matters News

Robert J. Marks: So are there numerous constants that are finely tuned?

Daniel Díaz: That’s what we want to observe. So what follows is that we develop the theoretical way to measure those qualities for the cosmological and particle model.

What we expect is to find that some of them — maybe most of them — are going to be finely tuned. But again, if there is only one that is finely tuned, then that would be enough to say that the universe is finely tuned.

Note: At Forbes, astrophysicist Ethan Siegel has said that “It takes 26 fundamental constants to give us our universe, but they still don’t give everything” (August 22, 2015)

Robert J. Marks: But again, Stephen Hawking also said that nothing is ever proved in physics, you just accumulate evidence. So if you have one that is not finely tuned, that’s evidence. But if you have a bunch of them that are required to be finely tuned, that’s really evidence that something is going on. And as Fred Hoyle (1915–2001) said, somebody has been monkeying with the universe, so very interesting.

Ola, one of the terms that you use in your papers is LPI. What’s an LPI? What does it mean? And how do we measure it?

Ola Hössjer: LPI is a life-permitting interval for a certain constant of nature or cosmological constant. It could also be a life-permitting interval for a ratio between two constants of nature. In episodes One and Two [linked below], we talked about the universe being fine tuned. It requires two things. First of all, we need to find this life permitting interval, an independent specification. And then we need to find the probability that, if the universe were generated by chance, what would be the probability that these constants or ratios ended up within life-permitting intervals?

Note: Here’s an example of a ratio: “The fine-structure constant, or the strength of the electromagnetic interaction. In terms of some of the physical constants we’re more familiar with, this is a ratio of the elementary charge (of, say, an electron) squared to Planck’s constant and the speed of light.” – Ethan Siegel, Forbes

If that probability is small, then we say that that the constant or ratio is fine tuned. As Daniel said, it’s enough to find that one constant of nature is fine tuned in order for the universe to be fine tuned because then it’s also very unlikely that the universe was generated by chance.

Robert J. Marks: We talked before about the difference between just looking at the intervals and looking at the probability that an event falls within that interval. Can you give me some examples of constants of nature and the probability that an event lies within the life permitting interval?

Ola Hössjer: Yes. In our joint paper, we give a couple of examples. And the first example, that’s really a ratio or two constants of nature. It’s the ratio of the constant of gravity that Daniel talked about and Hubble’s Constant squared. Hubble’s Constant is related to the constant that explains how fast the universe is expanding.

Note: “The Hubble Constant is the unit of measurement used to describe the expansion of the universe. The cosmos has been getting bigger since the Big Bang kick-started the growth about 13.82 billion years ago. The universe, in fact, is getting faster in its acceleration as it gets bigger.” – Space.com

Robert J. Marks: Let me ask you this, why don’t you take the ratio of constants as opposed to the constants? I mean, couldn’t you kind of cook the books by looking at different ratios and seeing that they were fine tuned? What’s the reason behind taking these ratios?

Ola Hössjer: Well, sometimes the ratio is more fine tuned than each of the two constants themselves. It could be that they must have a certain ratio in order for life to exist. We can think of it as a balance between different forces, the balance is more important than the actual strength of the two forces.

Robert J. Marks: I see. So maybe the life permitting interval for one of these constants would not be as meaningful as with another one, because there’s an interplay between those two constants?

Ola Hössjer: Exactly. Sometimes the life permitting interval of the ratio could be smaller than the life permitting interval of each of the constants by itself. And in this case, theoretical physicists have come up with an equation that relates the ratio between the constants of gravity and Hubble’s Constant squared with the critical density of the universe (inverse) when the universe was very young. So that critical density is highly fine tuned. There are some other constants as well but this is sort of constant that comes up in that equation that says that the critical density of the universe is closely related to the ratio between the constant of gravity and Hubble’s Constant squared.

Robert J. Marks: I just thought of an example of this in my field of electrical engineering. There’s something called a voltage divider where the percent of a voltage that is bled off is just a function of the ratio between the two resistors. Therefore, talking about the sensitivity of a single resistor doesn’t make sense. You have to talk about the ratio of two.

Ola Hössjer: Yeah. And that example, which relates the ratio between the constant of gravity and the square of Hubble’s Constant, relates that to the inverse of the critical density of the universe. That’s called the Friedmann equation. And well-known physicist Paul Davies has estimated that the life permitting interval of that ratio between these two constants of nature has a relative size of 10-60. This is the length of the interval divided by its midpoint.

It’s more meaningful to talk about the relative size because it’s dimension-less, it’s not dependent on the unit we use to measure the constant of gravity or the Hubble’s Constant squared. So the relative size of the life permitting interval is 10-60. We can think of 1% as 10-2 or .1% as 10-3. So 10-60 is extremely small.

The important thing is not the size and not even the relative size per se, even though it’s dimensionless, it’s the probability that we assign to this life permitting interval. And that probability depends a little bit on how we choose the normal distribution, the distribution of the ratio between these two constants of nature. And it can be done in a few slightly different ways, but they all end up with probabilities that are about 74% of this relative size.

So if this relative size was 10-60, the probability is 0.74 × 10-60. And another approach is 50% instead of 74%. But the take home message is that the probability is all the same order as the relative size of the life permitting interval.

Robert J. Marks: Oh my goodness, 10-60… Now, putting that into perspective, I think I’ve heard that there are 1080 atoms in the universe. And so 10 10-60 is really, really big. It’s a million, million, million, million, million, million, million, million, million, million… becomes a tongue twister after a while. So it’s a really, really humongous number.

Ola Hössjer: It’s really amazingly large. And then we have another closely related example that also gives a highly fine tuned ratio. And then we still have the constant of gravity in the numerator of that ratio, but then we have something that is a contribution from vacuum energy to the cosmological constant that Daniel talked about. And then physicists have come up with very small number for the relative size of the life permitting interval of that ratio as well… Depending on the theory used, some authors come up with a relative size of that life permitting interval that is 10-50 or even 10-100.

Robert J. Marks: Now that’s the interval, not the probability.

Ola Hössjer: Yeah, and then the probability is of the same order as the relative size of the interval. So, it’s like a half of the relative size or 75% of the relative size of the life permitting interval, depending what approach we use for computing the probability. We chose the prior distribution or the ratio of these two constants but we could do it in different ways.

But at the end of the day, we come up with very similar numbers for the probability of ending up within this life permitting interval, which is of the same order as the relative size of this life permitting interval. The contribution of vacuum energy to the cosmological constant and its relative size was 10-50 or 10-100. And the probability of ending up in that interval is of the same order, regardless of which maximum entropy approach we use.

Next: Is life from outer space a viable science hypothesis?


Here are all of the instalments, in order, of the discussion between Robert J. Marks, Ola Hössjer, and Daniel Díaz on the fine tuning of the universe for life:

The first episode:

Ours is a finely tuned — and No Free Lunch — universe. Mathematician Ola Hössjer and biostatistician Daniel Díaz explain to Walter Bradley Center director Robert J. Marks why nature works so seamlessly. A “life-permitting interval” makes it all possible — but is that really an accident?

and

Fine-tuning? How Bayesian statistics could help break a deadlock: Bayesian statistics are used, for example, in spam filter technology, identifying probable spam by examining vast masses of previous messages. The frequentist approach assesses the probability of future events but the Bayesian approach assesses the probability of events that have already occurred.

The second episode:

Life is so wonderfully finely tuned that it’s frightening. A mathematician who uses statistical methods to model the fine tuning of molecular machines and systems in cells reflects… Every single cell is like a city that cannot function without a complex network of services that must all work together to maintain life.

Can there be a general theory for fine-tuning? If you make a bowl of alphabet soup and the letters arrange themselves and say, good morning, that is specified. What are the probabilities? Ola Hössjer sees the beauty of mathematics in the fact that seemingly unrelated features in cosmology and biology can be modeled using similar concepts.

The third episode

Was the universe created for life forms to live in? How would we know? We can begin by looking at the fundamental constants that underlie the universe. The constants of the universe — gravitational constant, entropy, and cosmological constant — must be finely tuned for life to exist.

Why did Stephen Hawking give up on a Theory of Everything? Daniel Díaz and Ola Hössjer continue their discussion of the fine tuning of the universal constants of nature with Robert J. Marks. The probability, they calculate, that the fine tuning of our universe is simply random is down to 10 to the minus sixty — a very small number.

The fourth and final episode

Is life from outer space a viable science hypothesis? Currently, panspermia has been rated as “plausible but not convincing.” Marks, Hössjer, and Diaz discuss the issues. Famous atheist scientists have favored panspermia because there is no plausible purely natural explanation for life on Earth that would make it unnecessary.

Could advanced aliens have fine-tuned Earth for life? That’s a surprisingly popular thesis, considering how hard it is to account for life without assuming a creator. As Robert Marks, Ola Hössjer, and Daniel Díaz discuss, some prominent atheists/agnostics have chosen to substitute advanced extraterrestrials for God.

Our universe survived a firing squad and it’s just an accident? According to the Weak Anthropic Principle, if things weren’t the way they are, we wouldn’t be here and that’s all there is to it. Given the odds, a philosopher likens the Weak Anthropic Principle to surviving a firing squad and concluding, incuriously, well… that’s just the way things are.

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 1000th power of universes would only permit 3,322 different paths. Infinity is required but unprovable.

and

If extraterrestrials didn’t fine tune Earth, maybe there is a God. In the face of a grab bag of ideas like creation by ETs or countless universes (some run by cats), why does the idea of a Creator seem far out? Traditional philosophers, not committed to a religion, have thought that deism (and theism) are rational, science-based conclusions, based on fine tuning.

You may also wish to read: No Free Lunches: Robert J. Marks: What the Big Bang teaches us about nothing. Bernoulli is right and Keynes is Wrong. Critics of Bernoulli don’t appreciate the definition of “knowing nothing.” The concept of “knowing nothing” can be tricky.

Show Notes

  • 01:09 | Introducing Dr. Daniel Díaz and Dr. Ola Hössjer
  • 01:53 | Wiggle room
  • 06:06 | More gravity, more weight?
  • 07:37 | Other examples of universal constants
  • 12:36 | Are these numerous constants fine-tuned?
  • 13:38 | LPI
  • 24:02 | Are there any constants which are not fine-tuned?

Additional Resources

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Why Did Stephen Hawking Give Up on a Theory of Everything?