# Anthropic Principle and Infinitely Minute Variations

1. Jan 14, 2014

### QuestionMarks

Let's assume as per the anthropic principle, for the mere sake of argument alone, that the physical constants of the universe are indeed biased towards life and that any significant change would eradicate the possibility of any form of conscious life. For the sake of argument as well, let's please ignore discussion on whether this is philosophically relevant or merely tautology.

What I do want to zero in on is the idea that a change "by any small amount" would invalidate possible life. If indeed only a small change would do this, I could see this as significant, but isn't the idea of "small" here arbitrary and, itself, anthropic?

An example to demonstrate using imaginary constants. Let's say:

Constant A has a value of 10^-30. Assume if we were to change it by even 10^-40, this would eliminate the possibility of conscious life of any kind. Indeed, we might consider this a "small" change (by human or relative terms), but what about a change by 10^-41? 10^-42? And so on to 10^-(infinity)? Isn't it more useful then to define the range by which a constant could be changed and still maintain conscious life? And why could there not then be an infinite number of variations (of increasingly small changes) to that constant which still support life? It would seem to follow then that there are an infinite number of possible combinations without conscious life, but also an infinite number of combinations having it.

All in all, it doesn't seem like we can say there exists a "narrow range" for life to form (regardless of how "small" a variance might effect this) and that this is a big oversight in such arguments. Am I missing some way to limit the variance possible to any such constant that's important?

Last edited: Jan 14, 2014
2. Jan 14, 2014

### Chronos

Some of the physical constants of the universe are extremely sensitive to change. For example, a change in the fine structure constant of about 3 parts in 10 thousand would preclude stars from synthesizing carbon. This would have consequences for carbon based life forms. Even tighter bounds exist for certain other constants. The ratio of matter to antimatter in the primordial universe was 1 part in a billion off from being exactly even. Had it been exactly 50-50, all matter would have been annihilated and nothing would have remained to form stars, etc. Had it been off by 2 parts in a billion, the universe would have already collapsed into a singularity.

Personally, I find all this a lot less mysterious than it sounds. We are here, as most would agree, so all of these bad things that could have happened did not happen. If you tossed a dice with a trillion sides and rolled the number 314,159,262, would you view that as an unfathomable mystery and a sure sign of intelligent design, or shrug it off as 'it is what it is'? Could you be persuaded to believe the dice actually rolled all the other numbers and you just happen to live in the one universe where it came up 314,159,262? It seems a tad eccentric to deduce the universe is fine tuned for life. The truth is, life is fine tuned for the universe.

Last edited: Jan 14, 2014
3. Jan 14, 2014

### QuestionMarks

Chronos, thanks for the explanation. I'm aware though of this general line of reasoning and looking at demystifying it from a different angle though.

What I was considering was that, even if the values are constrained to a certain range, there should be an infinite number of possible variations even within this range because you could vary the value by smaller and smaller decimal places without exceeding either boundary.

For instance, let's say our boundry is between 1 and -1. I could then start with 1 and come up with the values:

1 - 0.1
1 - 0.01
1 - 0.001
1- 0.0001
...and so construct an infinite number of values that still fits that range.

Thus when we ask "Why is our universe this way rather than that way?" and think that this way is special because the constants are constrained to a small range, we are not recognizing that said range still includes an infinite set, and thus doesn't seem all that special. I was wondering if there's something I was missing in that reasoning.

Sorry if my original post did not portray this well.

4. Jan 14, 2014

### Chronos

I agree. While some individual properties of the universe are tightly constrained, the parameter space is actually quite large. I forget which one it is, but, I recall reading once that one particular property of the early universe was constrained to like one part in a septillion, which I found interesting. In a multiverse sense, it is quite silly to claim this is the only universe that could support life when in fact an infinite number of such universes are mathematically possible. I have my doubts about there being innumerable universes with wildly different properties.

A theory of everything [TOE], in principle, would have the universe emerging from a single, mysterious first cause. We have already determined a hierarchy of structure in the fundamental forces of the universe - gravity, nuclear strong force and electroweak force. We even have an idea of energy levels at which each of these forces broke free and assumed it own identity. Assuming there was only one force in the beginning, all other forces are emergent, and their hierarchy and properties predetermined by whatever conditions existed at the beginning of time. Can we expect initial conditions always be similar? That is literally the million dollar question in physics [think Nobel prize]. I think it must be as simple and uniform as CMB temperature anisotropies. On that basis, the answer could be we live in the only universe possible arising from perfectly simple initial conditions. I expect to be folded, spindled, stapled and mutilated for not offering a mathematically rigorous proof.

5. Jan 14, 2014

### QuestionMarks

Chronos, I thought that was a pretty lucid reply and was interested in some of why you thought that way. I messaged you so as to allow the thread to stay on topic.

6. Jan 15, 2014

### Chalnoth

No.

The whole "first cause" thing is a misnomer that really has nothing to do with the way physics works. Cause and effect are human constructs that are applied after the fact, and are largely a way for humans to make sense of our macroscopic world with increasing entropy. These concepts really don't have anything to do with the realities of quantum mechanics or general relativity, and the idea that a unification of the two could somehow resurrect the notion of cause and effect is extremely unlikely.

Just to take an example, if we had the full and complete wavefunction of the universe across one time-slicing of the universe, then as long as fundamental physics is unitary (which seems likely), that wavefunction at that specific point in time is all you need to exactly determine the state of the universe at any other point in time.

How can you have a sensible "first cause" if this is the case? Any time slicing of the universe can be said to "cause" any other time slicing you want, because any time slicing fully determines every other possible time slicing.

That's a pipe dream.

7. Jan 15, 2014

### Chalnoth

A bit of quibbling about semantics first:

That's not really the anthropic principle. The anthropic principle generally takes one of two forms, the strong and weak.

The strong anthropic principle states that the universe must be such that it can harbor life. I don't think we need to discuss this.

The weak anthropic principle states that intelligent observers will only be able to observe conditions that allow them to exist. This is definitely a tautology (like much of mathematics), and it's a tautology that might help us to make sense of our own universe. It is, in short, a selection effect.

The statement that the physical constants of our low-energy physics need to be very specific for intelligent observers to exist is the statement that our universe is finely-tuned. This usually takes the form where we might expect some parameter that describes our low-energy physical laws lies between 0 and 1. If so, then we might reasonably expect a parameter value of 0.2353 or 0.7236. But we would think it very strange indeed if the value turned out to be 0.00000000000012, unless there were some physical process that would set it to that value. A universe where certain parameters take on values like that is a finely-tuned universe.

The anthropic principle might help us to make sense of why certain aspects of our universe appear to be finely-tuned, or it might turn out that there is some as-yet-unknown physical process which dramatically reduces the available parameter space (in the example above, of an imaginary constant of $1.2 \times 10^{-13}$, what if there were some physical process that limited the possible range of this value to between $1.1 \times 10^{-13}$ and $1.3 \times 10^{-13}$. If there were some physical process, then it would turn out that this parameter value wasn't finely tuned after all.

8. Jan 15, 2014

### skydivephil

You say "dramatically reduces the available parameter space " but how do we know what the parameter space is in the first place? Surely we have no idea whether its big or small.

9. Jan 15, 2014

### julcab12

... I always had a hard time making a clear sense of fine-tuning. Why/How can such parameters had preferred strength or state? I could say that some unknown physical process is at play or even preventing it, or non-equilibrium explanation by Boltsman Or perhaps the many-world interpretation, unstable differing decays and behavior of matter/antimatter, CP violation and so on(other attempts),. But it fell short somehow on my intuition as a satisfactory explanation because each time i went on that path it often led me to ad-hoc reasoning and circular.

In terms, i ended up on some sort of preferred morphological directional limits in relation to regularities of the universe which we valued as constant. Maybe i'm just rooting more on local solutions rather than adding some variables(multiverse/etc).

10. Jan 15, 2014

### QuestionMarks

Cause and effect certainly has some peculiarities with the arrival of QM, but I believe you are stretching them too far. If you procured the wavefunction of the universe at any given point, I give that you could evolve it into all further possible states. What you could not do is, as you say, "exactly determine the state of the universe at any other point in time." You are, of course, limited to the probability of each state within that manifold (and we should not merely assume the "most likely" one). Regardless of whether you want to call it probabilistic determinism or the effects of measurements, some sense of our logic system is still relevant. Unless of course you take the many-worlds interpretation of QM where every possible state has an actual reality "somewhere," and we are arbitrarily in one of those, but this is by no means consensus. Maybe we will find that logic does need a drastic change, but so far it remains arguably our best tool, and we haven't given up on "history" yet.

Regardless, this conjecture is off-tracking the thread. I was curious about some of the views mentioned as well (and thus messaged Chronos), but if we banter about the implications and interpretations of QM (which is not a settled matter within the community), then we will never get to discussing the OP fully.

11. Jan 15, 2014

### QuestionMarks

I knew someone would quibble me some semantics, hah!
I'm aware of this, though perhaps I should have been even more specific in the OP so as to steer the post quicker and closer to my question.

As I have previously mentioned, I am not talking about the (strong) anthropic principle's general validity, exploring its meaning, or worrying whether we call it anthropic or fine-tuning. What you said in the last paragraph is a bit more relevant when talking about parameter space.

However, I have a very narrow focus for my questioning and am considering that for any parameter space regardless of how small, there should exist a infinite set of possible values that satisfy this parameter space. Considering this then, claiming that any parameter space is "small" seems a bit of a bias based on how we generally look at numbers. We could only then, at best, say that the infinite number of values satisfying the parameter space is a smaller infinity than the infinite values not satisfying it.

Another way to look at it, is to redraw the number line over that parameter space with smaller increments. As the increments are smaller, the parameter space blows up, and things look less finely tuned. The only way to keep it small would then be to compare the size of the increment to other constants (some perhaps orders of magnitude bigger), but I'm not sure if that is really a sensible way to preserve any "specialness."

12. Jan 15, 2014

### Chalnoth

A multiverse isn't adding new variables. In general, the multiverse concept tends to reduce the number of assumptions in the theory.

The smart money is on the correct explanation being a combination of new understanding of physical processes which reduce the available parameter space, and there being a prolific universe which explores many different parameters for low-energy physical laws.

13. Jan 15, 2014

### Chalnoth

Not if the allowable parameter values are actually discrete, as opposed to a range of floating-point numbers. This would be the case, for example, if universes could only exist in a somewhat stable state if they are in local minimum of a potential. This potential might have a large number of such local minima, but possibly not the infinite number that a range of floating point numbers might have.

Even with continuous parameter ranges, it is reasonable to talk about parameter space volume. There is, unfortunately, no non-arbitrary way to do this. But it would still seem odd if, as far as we knew, our universe could lie in any point in a large volume, but happens to lie in a location that has rather special significance (e.g. near an edge or a point of symmetry). You could produce a naive likelihood of this by comparing the volume of the parameter space that is this close or closer to any edge or point of symmetry in the space against the volume of the rest of the space.

14. Jan 15, 2014

### QuestionMarks

What reasons do we currently have to assume this though? I though this was an attractive way out as well but ended up feeling it more convenient than actually justifiable.

I'm not sure I follow, but set theory has also baffled me before. It seems like what you're saying is that, indeed, one infinity can be larger than another? If so, this I noted and agreed with, so perhaps the question is indeed whether finding yourself next to that edge or point does have any significance? Back to philosophy then... Shouldn't we say though that there is only philosophical implications to this if there are only a few (or really, one) way to be close to that edge, and that if there are many ways to be close to the edge then it is tautology (as we would necessarily have to be close to the edge to perceive it so, and so there is nothing "special")?

15. Jan 15, 2014

### Chalnoth

Well, for one, what little we know of quantum gravity seems to suggest that space-time may exist only in discrete steps. If true, then the number of degrees of freedom is a finite (if large) number.

Well, yes. Certainly some infinities are larger than other infinities. Otherwise we couldn't write down such things as:

$$\lim_{x \rightarrow \infty} {x^2 - 1 \over 2x^2 + 1} = {1 \over 2}$$

That said, in this case, we don't even have to be talking about infinities. Even if you can divide a volume up into an uncountably infinite number of points, you can still talk about that volume in finite terms.

For example: what fraction of the volume of a 1cm radius sphere is within 1mm of its surface?

16. Jan 15, 2014

### QuestionMarks

Assuming that could constrain all our constants to discrete steps, then yes. I think I was ignoring this because, from here, it moves the explanatory exploration of the universe to a different (potential) undesirable. We could then of course ask why this restraint (in steps) rather than that (conceivable) one? I might argue that we'd be butting heads with the principle of sufficient reason here, but perhaps it's best to remain silent until quantum gravity has (or will not have) had its say.

I see what you're saying now, though I think to talk about its significance, it might be easier to discuss as probability. For instance, we could say there is a higher likelihood of finding ourselves anywhere else in the sphere (universe with no life) than to the edge (a universe with life). This then seemingly must go back to the tautological question of whether that's significant that we happen to find ourselves near the edge. I suppose the only difference here is that we could repose that question with the considerations that, assuming the variables involved are allowed to be continuous and there is any parameter space at all, "small" can still allot for an infinite variation. To me, that doesn't seem significant or "special," but I'm not sure I can pose a rigid argument for this.

17. Jan 15, 2014

### Chalnoth

This is just the basic question of model selection. Presumably any fully-specified fundamental model (we don't have any such model yet, at least not developed to this point) would provide the set of possible values.

In fact, this might potentially be one mechanism to experimentally test for a fundamental model: imagine we have some model of the universe that permits values of some constant to be 0.1663, 0.2314, or 0.3114 (due to some complicated dynamics or some such), then measuring a value of 0.2044 for this parameter would demonstrate that model was false.

If, on the other hand, the fundamental model permitted millions of different values of the parameter to within any conceivable experimental accuracy we might ever develop, then we just can't use this tool to confirm or falsify that model.

Well, when doing anything like this we really have to think of the parameter space where intelligent observers are possible as being a selection effect: we can only reasonably examine values within this space.

In the analogy I used above, for instance, the 1cm sphere would be the parameter space that obeys both the constraints that life is possible and our current knowledge of physical laws is satisfied. If we happened to inhabit a weird location within that space (e.g., near a point of symmetry), then a reasonable conclusion is that we're not understanding the constraints properly, that there are constraints from physical laws that we don't yet understand.

I'm not sure that any clear amount of fine tuning remains after adjusting for the selection effect that is the weak anthropic principle.

18. Jan 15, 2014

### QuestionMarks

I suppose I was adding unnecessary complexity by trying to allow for some argument that a set having an infinite variety of values that satisfy life was "more" tautological (in the weak anthropic sense) than a set with a finite many ways to satisfy life. Unless there were indeed "only one way to do it," then I'd presume it's a tautology either way, and the "extent" of which doesn't have too much significance.

Still, in the same breath of typing that, I imagine a universe where there were two possible combinations only of the constants that would form life, and that gives me pause. This would seem significant, though the only implications I could draw would be that there, similarly, were at least two universes, or we don't actually have the full picture. So I guess it still remains the same scenario.

I've never been the biggest fan of the multiverse, but it sure does seem inescapable. I suppose the question of recent consensus has migrated more towards if and what constraints could be put on something like a multiverse (and I'm including the varied ways to get one in that, such as inflation, many-worlds, etc.). Without giving up on the principal of sufficient reason at some point (where we ask why this rather than that) or arbitrarily valuing something as a reason for those constraints (such as life, simplicity, low-energy, etc.), I don't see how to not let it run rampant though. But I suppose we've exhausted a lot of the line of thought here, and this paragraph is a matter for a whole different discussion.

19. Jan 17, 2014

### julcab12

OT. It does gave some positive interpretation on quantum field theory mainly the behavior of particle-quantum superposition due to excitation of the field. But i'm a bit concern of the value given i.e jitters in the field = variety sets of physical realities/possible states. So rather than headin in the direction of many world interpretation within a sets of dimensions. My intuition tells me that there is something going on in that field w/out the need of such large factor/s(sets of finite/infinite dimension). Although it is clear that particle do behave like each state should be in term equal to a diverse set of reality.

I still suspect constraints in time that may possibly affect the 'projection' of the field that causes it to appear that way. Maybe it's suggesting a different interpretation that cancels out other projected state within our locality and what is left is our UNIverse.

20. Jan 17, 2014

### Chalnoth

This is putting the cart before the horse. You're basically saying, "This conclusion makes me uncomfortable, so I don't think it's true." To see that the many worlds interpretation is the simplest possible, you basically need to examine two things:
1. Quantum mechanics describes the universe we experience. That is, those "jitters in the field" are, at a base level, precisely what we see when we experience the world around us.
2. Quantum mechanics does not allow all components of the wavefunction to interact with one another. To a high degree of accuracy, as a quantum system evolves, parts of the wavefunction evolve forward in time as if the other parts of the wavefunction did not exist.

Combine one and two, and you have the many worlds interpretation. To get out of it, you have to make up new assumptions, such as the assumption that the part of the wave function we observe is the only one there is.