# Cosmological Constants, Inference to the Best Explanation, and Many Universes

Scientists keep discovering the number 10^122 occurring in mathematical relationships in the natural world [hat tip: GeekPress]. The last time this happened, it was when 10^4 kept appearing in both electromagnetic and strong/weak nuclear contexts, and it turns out that it signaled a common relationship between the two. So scientists are concluding that the best explanation is some common, underlying factor that explains why the same ratio keeps coming up.

Now here's what I'm wondering. If we're just one universe among a huge number, and the constants in each universe are different, then we just happen to be the universe with these constants. So why assume some common explanation for why the constants are the ones we've got? Doesn't the multiple universe explanation make the search for a common explanation otiose? At least that's what you'll hear if you try to make an inference to the best explanation when the constants happen to be in the narrow range that allow for the development of life. So what's different about this inference to the best explanation when both arguments involve what cosmological constants we happen to find ourselves with?

I haven't read the article, but the way you've written it up, the 10^122 isn't a cosmological constant so much as it is a derivation of some as-yet-unknown relationship between real constants. The frequent and unexpected sightings of 10^122 indicate an underlying structure that we haven't found yet. Thus the search for that structure.

However, regarding the actual cosmological constants, no one seems to be looking for why they have that value and they don't seem to be related in any way that suggests an underlying structure. So that is consistent with the multi-universe idea.

Basically what I'm saying is that there's no contradiction here since the 10^122 isn't a cosmological constant.

But the many-universes response to the design argument claims that we have the constants we have because every set of constants occurs somewhere. That means a world with these constants that have this mathematical relationship will occur somewhere. When we discover that that's here, we shouldn't be surprised, given that every combination of constants occurs. It doesn't matter if the question is about a set of constants falling within a certain range or the ratio between a certain set of constants. In both cases, the fact is unsurprising in a multiverse without any further underlying explanation.

I'm not saying there's a contradiction. I'm just pointing out that we do issue a call for such an explanation, which means we don't find the multiverse explanation plausible.

That means a world with these constants that have this mathematical relationship will occur somewhere.

Untrue. If the laws of physics remains constant throught the multiverse (in some versions of the muliple-universe explanation this is the case), then it is by no means assured that every possible relationship can occur. Super-simple-example, for y = x^2, y will always be positive.

So if the Laws of Physics remain constant, then it makes sense to inquire about the recurring derived numbers since they tell us something interesting about the laws of physics that we didn't know before. Plus, plain curiousity is appropriate even in a world where the constants were determined randomly--we do have to live in this world after all, so it makes sense to learn about it, even if after a certain point, the "whys" become unanserable. (Similarly, I get *exteremly* frustrated by classmates who insist that because the Trinity is a mystery, therefore we shouldn't try to learn *anything* about the Trinity.)

I'm not talking about the laws of mathematics, either, so I'm not sure how your example is relevant. It's a law of mathematics that the square of any number is positive, and that would be true in every universe.

I'm not sure the view that the universes have the same constants is going to work in a response to the fine-tuning design argument. The original argument is that the narrow range of constants that allows for life is so surprising that we need an explanation of why the numbers should be in the range allowing for life. Then the designer is postulated as such an explanation. The many-universes response claims that if there are many universes, all with different sets of constants, then it's not surprising that one of the universes has a set of constants in the narrow range necessary for life. I don't see how such a response can be given if the constants are the same in every universe.

To be clear, I'm happy to ask why the constants have this interesting feature. I'm just not sure if those who respond to the fine-tuning argument with the many-universes response can consistently wonder the same thing.

I'm not talking about the laws of mathematics, either, so I'm not sure how your example is relevant. It's a law of mathematics that the square of any number is positive, and that would be true in every universe.

I was trying to use a shortcut so that I wouldn't have to type so much. Here's a real example: The law of gravity -- F = Gmm/r^2 Now the constant G may be variable across different universes, but let us assume that the law of gravity is otherwise constant across all uniververses, otherwise the fine-tuning argument has no traction. Now, with the exception of G, the rest of the equation is arrainged so that F must be a positive number. That is an interesting result, quite apart from what the value of G is.

Extrapolating into areas in which I no longer have expertise, it isn't hard to imagine a complex scientific formua that involves the force of gravity squared, C, and somehow involves 10^122. Again interesting because the gravity component must be positive even if G is negative. And note that C must be positive since it is a speed and thus is an absolute value. Now suppose that the 10^122 is the result of some sort of product and not of addition or subtration; now we know that whatever 10^122 represents *can't* be a negative number regardless of the values of G or C. Again, interesting and contradicts your supposition that all relationships between constants are possible.

I'm not sure the view that the universes have the same constants is going to work in a response to the fine-tuning design argument.

Not what I was trying to say at all. I'm saying that all universes have the same Laws, not constants. Thus gravity is F = Gmm/r^2 across all universes even though the valuse for G may vary. However, in no univerise is it the case that gravity is F = Gmm/r^5. Fine-tuning assumes this, otherwise the narrow band of life-supporting constants could be eaily widened by changing the laws of physics.

To be clear, I'm happy to ask why the constants have this interesting feature. I'm just not sure if those who respond to the fine-tuning argument with the many-universes response can consistently wonder the same thing.

I'm trying to argue that they can (even though I'm not one of them). First off, I need to again reiterate that the 10^122 isn't a constant, it's a derived relationship between real constants. Since those relationships are largely as-yet-unknown, and since those relationships are goverend by laws of physics (and not by the actual values of the constants, per-se), then the derived relationships are actually quite interesting since they tell us about the laws of physics which are constant across all universes. (admittedly, some hold that the laws of physics are different across universes too--this argument wouldn't work for them. But then again, it didn't look like you were talking about this group.)

The other reason for them to wonder about it is just plain natural curiosity. Since we have to live in this universe, it is appropriate to wonder about it, even if we *could have been* born in some other universe. Your line of reasoning seems to be that if the final "why" in a string of "whys" is unanswerable or random, then all of the previous "whys" can't be consistently asked. I find that line of reasoning to be flawed--there is plenty to discover in the initial "whys" even if the final "why" is opaque to us.

I don't think I'm supposing that all relationships between constants are possible. I'm supposing that there's a huge range of constants and that the range of relationships between them is thus also huge. I'm also supposing that the many-universes response to the fine-tuning design argument claims that all the possible relationships between constants will occur somewhere or other.

I wouldn't describe a whole bunch of different laws that take the form F=Gmm/r^2 as the same law. If G is different in each universe, then it's a different law. It just has the same mathematical form. I don't in fact think the fine-tuning argument assumes different law-forms are possible. I think all it assumes is different values for the constants are possible.

Your line of reasoning seems to be that if the final "why" in a string of "whys" is unanswerable or random, then all of the previous "whys" can't be consistently asked.

I don't think that's true. I think all I'm assuming is that if the final "why" is unanswerable or random in the way many-universes responses require, then it follows that this particular "why" is for the same reason no further explainable. The kind of answer I would expect from a question like this depends on having an answer to why the constants are what they are, and that's the explanation the many-universes model (at least as a response to the fine-tuning argument) says we shouldn't expect to find.

I wouldn't describe a whole bunch of different laws that take the form F=Gmm/r^2 as the same law. If G is different in each universe, then it's a different law. It just has the same mathematical form. I don't in fact think the fine-tuning argument assumes different law-forms are possible.

Hmmm...we seem to have a fundamentally different view of what the fine-tuning argument involves. The rest of our conflict seems to turn on this difference, so I'm thinking that we'll have to agree to disagree on this one.

Well, the way it's presented by the philosophers I've read is that if the constants are slightly different (even holding the rest of the equations constant) you'd have no possibility even of stars or even Helium forming, never mind rational life. I've never heard them mentioning wholly different equations, and in fact that would seem to me to hurt the argument, because different equations with different constants might give a better chance of getting the right combination than if you hold the equations fixed but vary only the constants.

Exactly how I understand it, and thus exactly my point. Wholly different equations hurt the fine-tuning argument.

However, keeping the form of the equations constant while allowing for "variable constants" means that you have something very interesting to investigate even allowing for totally random values for the constants. Thus the many-universes proponents have seomthing interesting to investigate because numbers like 10^122, while they might only reveal things about the constants, are likely to reveal something about the form of the equations, and if you're really lucky, might be reflective of ONLY the form, and not the constants at all.

Well, here's what I don't get about your argument. Suppose we find that 10^122 forms the relation between two seemingly-unrelated sets of constants. The ratio between G and some other constant is 10^122, and the ratio between c and some other constant is 10^122. If all four constants are what they are for no particular reason, then the fact that two of them form the same ratio as the other two seems interesting but in fact is not. It's just a result of being in the universe whether those two sets of random constants both happen to form the same ratio. That doesn't seem all that interesting to me.

It would be different if what you're calling the laws and what I'm calling the law-forms were to generate these ratios, but I don't think that's what they're talking about here. They're talking about mere ratios between constants, constants that are randomly-generated according to the many-universes response to the fine-tuning argument.

Now I have to go read the article...

OK. It's a login only article. Grrr...so the uninformed speculation continues...

At any rate, yes, the way I was interpreting it was that the "law-forms" were generating the constants.

So if 10^122 is simply a straight-up ratio between lots of different constants, then that is weird, but not terribly interesting. (So uninteresting that I would assume it not to be newsworthy. Nevertheless, I can see a reporter describing it that way out of ignorance or laziness.) But the way you wrote it up in the original post, it sounded like it was showing up in lots of different contexts similar to how 10^4 showed up in multiple contexts showing that those contexts are related. If 10^122 really is like 10^4, then it too is signalling some deeper relationship, and that is worth inquiring about, regardless of the particular values of the cosmological constants.

Side note: the reason why I call them the same law (what you call law forms), is that when I see "C", I don't think "3x10^8m/s", I think "the speed of light in a vacuum, whatever that speed happens to be". Basically, you're being more particularist than I am--my physics/math background has trained me to think as abstractly as possible when dealing with equations. We don't use the actual values of variables and constants until we are finally ready to solve the equation.

I guess it's not publicly available anymore. It was when I linked to it. So I can't go back and look at it either, I guess.

On the side note: I'm used to thinking of the laws of nature as whatever specific things vary from possible world to possible world, with the laws determining what happens in each world. Then on a many-universes model, you'll have different, spatiotemporally disconnected, parts of the actual world with different laws. The equations therefore don't specify everything that laws specify, so they're not the laws until the constants actually have values.

I guess I see it a bit differently. Since the "constants" don't remain the same across universes, they are actually variables (since they, you know, vary). This isn't a problem since we aren't varying a basic number, like "4", but rather values of things like "speed of light" or "mass of an electron". Therefore, "C" isn't a numbered constant, it's a variable that gets determined by the universe it is in.

Thus E=mc^2 has no constants (well, it has a "2" as an exponent, but I'm not counting that), it just has variables: energy, the mass of whatever you're measuring, and the speed of light for your universe. Thus the "Law" is the same in all universes, even if the values are different. After all, you wouldn't call it a different law becuase you measured a different mass, right?

We call them constants because in our experience, they never change, but when talking about multi-universe explanations, they do change and aren't constants in that context. As such, we should remember that these "constants" aren't really about the numbers so much as they are about what they measure (speed of light, or mass of an electron, or whatever).

Right, we're not disagreeing on the substance. It's just that philosophers use the term 'law' to refer to exactly the things that vary from universe to universe. If it's a theistic view, then God determines the laws. If there's some other process generating universes with different laws (or if it's uncaused), it's still laws that are varying. That's what the term has traditionally meant in philosophy, and that includes philosophers like Leibniz who also were good scientists in their own right. I suspect Newton used the term the same way, but I haven't read much of his stuff on this.

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