Is the universe finite or infinite?

twofish-quant

Sure, but that's different from saying that we must have observational confirmation *right now*. Also for someone that is demanding large amounts of experimental and testable evidence, he seems prone to making statements like "The multiverse idea is not provable either by observation, or as an implication of well established physics."

It also turns out to be less of a problem than it appears. What will happen if something isn't provable is that people will end up with different ideas, and in the end people will "agree to disagree." If you can't come up with a compelling argument as to what exists in the multiverse, then some people will think it's gumdrops and other people will think it's Coca-Cola, and in the end people will just give up fighting over it.

One thing that it sort of weird is that the citation that "The multiverse idea is not provable either by observation, or as an implication of well established physics." is a citation to someone that *isn't* a scientist, whereas the link to people that have tried to use the anthropic principle are to practicising theorists.

On the other hand, it's equally dangerous to limit what we define as "science" so strongly that it excludes natural phenomenon that are amenable to logical deduction, and limit "evidence" in a way that biases what can be studied. You end up with higher levels of non-sense.

If we reject Marxism and Freudian psychoanalysis as being outside the bounds of science, that's not very far from saying that science has nothing useful to say about human societies or the human mind, and that opens the door up to even worse silliness. One of the reason that I think Popper's statements that Marxism is unfalsifiable is wrong is that much of Marxism was falsified but it took several tens of million dead to do it. If we could have figured out that it wasn't going to work in 1925, then it would have saved us a lot of trouble. Past is past, but I do worry a lot about going to work and operating under economic assumptions that will prove disastrously wrong.

Science is hard.

Ken G

Of course they can be part of the same field, I already mentioned the "quintessence" idea. But the point is, simply making them part of the same field does not give any reason to synchronize the time when dark energy takes over with the time that life appears and with a brief period of measurable curvature. Even if it's one field, that's still two surprising coincidences associated with that field, not one. My point is that we already know one of those surprising properties to be true, but we should still expect the other surprise to not be true, hence the word "surprise."
Where did I say any such thing? Not at all, what I've said over and over is that no theory should ever be rejected for any reason other than it did not agree with experiment, or it can be replaced by something simpler and make the same predictions. What I also said is that a theory that creates a cosmic coincidence should be expected to fail. That means it is making a "risky prediction", that means it is a valid theory (but one that should still be expected to fail). I never said any theory that gives measurable curvature should be rejected prior to measuring the curvature, I said that a theory that finds it more likely that there will not be detectable curvature than that there will be is placed in a bad position if curvature is detected, expressly because we should then look instead for a theory that made the "risky prediction" that curvature should be detected. The problem with inflation is that it is not one theory, it is a factory of theories, so no matter what is observed, there is somewhere in that factory a version that gets it right. That's not the meaning of "risky predictions"!
I agree that it would be a useful paper to anticipate curvature detection and offer an explanation for the double-coincidence. Such a paper does make a risky prediction-- it says "this theory predicts a double coincidence, in a way that unifies the double coincidence into a single principle (rather than jury-rigging a generic model to get that outcome), so if that is what is observed, this theory should be considered the best way to understand it." Note that is not the same as saying "here I have a theory with enough free parameters to accomodate whether or not curvature is detected, so I can make either outcome seem natural with the appropriate parameter choice." That's not making a risky prediction, that's preparing for a rationalization.

To do that, logically, you have to start with my actual claims. It's best to stick to what I said and not dubious reconstructions.
Now it seems you are applying the practice of dubious reconstruction to Popper as well!

twofish-quant

I haven't done the math in detail, but if you assume that dark energy doesn't have a constant equation of state and that there is non-zero curvature, then the coincidence disappears. Depending on how the EOS evolves you can set thing up so that curvature is a generic feature of the universe, and they EOS evolves in such a what that it *doesn't* suddenly switch on.

But getting to the broader point about "how theorists really do theory." A lot of it involves "playing" with ideas. You stated an interesting principle which is that "all theories that create a cosmic coincidence should be rejected". OK. Let's accept that principle and see where that gets it. Can you tweak the EOS and curvature so that there *isn't* a coincidence?

If there isn't a reason then let's *invent* one. The problem with Popper's ideas of how science works is that a lot of good theory involves asking *what if*.

I'm asking if the math is such that the coincidences cancel each other out. So you assume that dark energy *always* evolves, and that cosmic curvature *always* exists. At which point you no longer have a coincidence because an observer will *usually* see dark energy and cosmic curvature

Therefore LCDM with zero curvature and constant DE should therefore be expected to fail because it creates a cosmic coincidence. If you change the model so that you have a non-zero curvature and a non-constant DE, then (and I need to check the math) the concidence disappears.

That makes zero sense. If a theory fails, then how can it be *valid*. If LCDM with zero curvature and constant DE is wrong, then it's wrong. if it's not wrong, then it's not wrong. If you argue for "no cosmic coincidence" then it's wrong.

But there is a *reason* for this.

The two big predictions of inflation that seem to hold true are the horizon problem and the CMB background fluctuations. *If* you believe that FTL signaling is impossible *and* you believe that the big bang is more or less accurate, then you *MUST* believe that something like inflation happened.

People have looked for alternative explanations that explain the horizon problem and those either involve some sort of faster than light signaling *or* complete rejection of the big bang.

If you reject FTL signalling *AND* you don't reject big bang completely, then this wipes out any non-inflationary theory that anyone has suggested in the last thirty years. At that point, what you can do is to create a "factory" for generating inflationary theories, and then you end up with several hundred different scenarios, and then you start looking for other things that allow you to cross out scenarios.

Now it's *possible* that we may have missed something, but the longer things go on without anyone able to suggest anything new, the more likely we are that we didn't miss anything, and if you have any ideas on how to deal with the horizon problem without inflation, I'm open to suggestions.

Also, if you can "parameterize" ignorance than that's good. The thing about LCDM is that it reduces our ignorance about the universe to 12 numbers. The good thing about the standard model is that it reduces our ignorance of the universe to 24 numbers. If you are in a situation were you can list "all possible theories that are not in contradiction to known facts" then you are in good shape.

And yet another reason why I think Popper is all wrong. If you can't explain then at least you can describe.

If you can get to the point where you can describe a situation with a number of parameters, you are doing really, really well. We can do this with the big bang. We *can't* do this with supernova or accretion disk jets or galaxy formation. (This is a problem since the early measurements of the universe *assumed* that type SNIa's have constant luminosity. We have *zero* theoretical reasons to explain why that is. Also a lot of the galaxy distances come across because of Tully-Fisher, and we don't know why that works.)

So if you are in a situation where you can describe the whole world with twenty parameters, you are doing really, really good.

Here's something to try. Try to come up with a model with ten numbers that can describe your day tomorrow, in which that anything that can happen is described by those ten numbers and anything that can't happen is outside the scope of those numbers.

It's actually quite hard.

This isn't about you.

If you didn't make the claim that "models with cosmic coincidences should be rejected" then you should have, because it's an interesting claim, that you can get a theory paper out of it.

A lot of what theorists to involves "playing" with ideas. You actually came up with an interesting idea, but rather than developing it, you are backing away from it, which seems odd. If you aren't going to develop the claim, then I will.

I'm trying to understand the universe. This involves creating ideas and throwing them at each other. If you aren't willing to develop a particular idea, then someone else needs to.

Something to remember is that the goal isn't to "win the argument" or to "be correct." The goal is to find truth. If I have a new idea and go to one of my colleagues, they are going to automatically and reflexively take the opposing side because that's how physics works.

One thing that happens in graduate school to a lot of students is that student argues with advisor. Advisor comes up with counterarguments. Student starts backing down, and then advisor takes student to task, because they could have used other arguments and shouldn't have backed down.

One other trick is that pretty much any adviser will do is to vehemently argue something that they don't really believe in. It's a useful trick because students will tend naturely to try to please their advisers by copying them, but if you are in a situation where you don't know what your adviser believes, that doesn't work. Just because someone strongly argues for proposition A doesn't mean that they are emotionally attached to it. They could just be playing with an idea.

twofish-quant

Also, I'm willing to wait X number of years for data on string theory. The trouble comes in when there are public policy issues where you can't wait and you can't falsify. Global warming comes to mind. There isn't a practical way of experimentally falsifying global warming without risking the destruction of the planet, but the fact that we can't practically *experimentally* falsify global warming doesn't make it "non-science."

The closest you can do without burning down the planet is to run "what-if" computer simulations that take known physical principles and extrapolate them to show that yes, if we don't do X and Y, the planet will be destroyed. But if this is philosophically *valid* to make statements about "alternative earths" then I don't see why statements about multiverses are inherently non-scientific.

It's also possible to take these ideas too far. For example, Imre Lakatos extended a lot of Popper's ideas, but he ultimately came to the conclusion that sociology and Darwinism were not science.

Ken G

And that's exactly what I'm talking about-- that's precisely the kind of alternative to standard inflation models that I referred to at the outset when I pointed out that curvature detection would constitute evidence for the the need of that kind of alternative! I'm glad we have finally reached agreement.First of all, you have changed my words once again. I said that a theory can be valid and expected to fail at the same time. And indeed, that is actually a very nice feature of a good candidate theory.

The scientific "validity" of a theory could be several things, depending on the purpose of the theory. Some theories are designed to help us build new technology, but these are highly mature theories, and these are only "valid" if they have a huge preponderence of evidence in their favor. There is little issue in determining which theories of this type are valid, they have become part of a trusted scientific analysis scheme. However, immature, or candidate, theories have a totally different criterion for being "valid", and this is the only place where we need input from philosophers like Popper to help us determine what our standard of "validity" should be.

The Popper insight here is that for a candidate theory to be a valid candidate theory, it must make "risky" predictions, which are (by definition) predictions that seem to have a high likelihood of failure-- so if they don't fail, it is grounds for graduating the candidate theory to a trusted theory. The quintessential example of this is special relativity, which predicts that in the Sagnac experiment, airplanes travelling different speeds between the same events should measure different elapsed times. That is a risky prediction for relativity to make, because no one in their right mind who was skeptical of relativity would expect that prediction to be successful. That is precisely what "falsifiability" means in Popper's scheme, not the caricature you imagine.
In either this thread, or the other we are debating, I pointed to the distinction between the inflation phenomenon (everything you just mentioned), and a particular theory of inflation (scalar potentials, slow roll, etc.). There is wide mainstream consensus that the inflation phenomenon is most likely necessary to understand our observations. What we are talking about here is specific elements of any particular theory, like eternal inflation and the multiverse, and whether these theories are numerous enough to "stack the deck" such that they are bound to succeed-- rather than facing legitimate risks of failure. If I roll a die, and have 6 different theories that predict each of the 6 outcomes, that's not a "risky" prediction, and so I cannot attribute "success" to the one that happens to prove true in that single case.

Sounds like something Adler or Freud or Marx might have said, word for word. This is exactly why Popper is not wrong.
I've no doubt. And the reason has a lot to do with the number of fundementally independent facts I need to explain about my day tomorrow. But in cosmology, just how many fundamentally independent facts do we need to explain? And how many variables will we allow ourselves to have to explain them? That's exactly why it is essential to be able to make risky predictions-- any attempt to predict n independent results with m parameters is going to be very risky indeed, if m << n, but presents no risks at all if n=m.

Please find the place where I said that quote. Then ask yourself: if you really had a logical position to stand on, why would it be so important for you to constantly change my argument?Actually I know all about graduate school. But I agree with your basic point-- a good argument involves sticking to one's guns, and so even though neither of us "pull our punches", the reason we are still involved in this discussion is we believe some mutual understanding can emerge between the lines of what appears to be a simple debate.
Yes, and they might find themselves arguing the opposite point tomorrow, or next year. They may even forget why! It's just the value of discourse.

twofish-quant

I think the terminology is off. Without any sort of experiment data, it's not a theory, it's a hypothesis. If it's hypothesis with strong predictive value, then it is a "well-posed" hypothesis.

It's important to get the definitions right. There is a big difference between a "valid theory" and a "well-posed hypothesis". "Valid theories" are not expected to fail, but "well posed hypotheses" can.

"Validity" has a specific meaning in science, which is rather different than the meaning in mathematics.

http://en.wikipedia.org/wiki/Validity_%28statistics%29

Disagree. I think that it is *good* for a theory to make risky predictions, but if you can't do it then you make the best with what you have. Also, there are useful models that *don't* make risky predictions or any predictions at all.

But this is a perfectly correct way of doing science. I know that there are six possible alternatives, I create a different model for each of the six scenarios, and once I know what the answer is, I eliminate five of them.

If I roll the dice, and it turns into a butterfly and flies away, then at that point I know that I'm outside of my initial model assumptions.

galaxy distributions
nucelosynthesis numbers
CMB radiation characteristics
observations of galactic evolution
observations of chemical evolution

Each one probably involves thousands of individual facts.

In the case of cosmology, m is twelve and n is in the tens (maybe hundreds) of thousands. If it turns out that we have to turn m from twelve to fifteen, it's not a big deal.

One problem that I have with the way that cosmology is taught is that it doesn't quite go through how much data we have.

You didn't. My point is that you should have.

Also, I'm not *intentionally* trying to change arguments. Communications is difficult. Also, "arguments by psychology" don't work that well.

Ken G

Who said anything about there not being any experimental data? I said if the theory is a good candidate theory, it makes predictions we would expect to fail (unless we are already inclined to accept the theory, in which case it is not a candidate theory any more). The classic example was general relativity, which certainly did have data to support it, but also made predictions that no one expected to be true unless they already favored the theory. That's the quintessential example of a good candidate theory, which with further verification graduated to a just-plain-old good theory. My use of the word "valid" in regard to a candidate theory is quite different from how the word would be used for a mature and well-accepted theory. I am saying "valid" in the sense of achieving the goals we have for a candidate theory, to wit, a theory that is consistent with what is already known, yet also makes risky predictions that we would tend to disbelieve if we were skeptical of the theory. That's a valid candidate theory, in that it meets our goals for it.

Well, I realize you don't agree with Popper, but I haven't seen much in the way of justification for your position. Popper, and I, are talking about trying to judge when a theory can be regarded as science, so the issue arises when an idea is still rather speculative. For mature theories that have already been tested in a wide array of legitimately falsifiable venues, and have had their domain of reliablity clearly spelled out,we have no issue and no need for Popper's falsifiability criterion. Popper would know that as well, only caricatures of his views would overlook that.

That is fine under only one circumstance-- after you eliminate five and settle on #6, you must be left with a theory that actually makes predictions that could, or even should, be wrong. That's arriving at a "good candidate theory." It doesn't matter much what path you took to get to it, it must have that attribute. But if, instead, you have 6 possible outcomes to a single experiment, and design 6 theories that explain each one, and settle on whichever worked, and then have exhausted any predictive potential of that theory because you have no new falsifiability for it, then you are not making a scientific theory, you are doing rationalization of your own view. It's a bit like studying the end of your nose instead of nature. That is what Popper was trying to say, and indeed did say, quite famously.

But that data is far from independent. Let's take for example the CMB. If we count all the bits of data that has been taken on the CMB, the result would be astronomical, no pun intended. But when we see that the spectrum is thermal, suddenly the amount of independent information there drops drastically. We have the temperature, and the fluctuation spectrum. Again, the fluctuation spectrum has a huge number of bits, but when you analyze them, you see a few humps, and those few humps are all that anyone is trying to fit with current cosmological models. So they are fitting one T, and several humps, and they are doing it with a few parameters. It's quite unclear how to tell if the degrees of freedom in the data are more than the parameters used, once you establish the basic idea that you have a thermal spectrum coming from recombination, and how that has "covered the tracks" of what came before. This is the fundamental distinction, alluded to above, between a general "phenomenon" (like a thermal fireball, or an era of inflation), versus a "theory" (which attempts to explain the phenomenon, not just rationalize it).

Well I'm afraid that is a perfectly absurd mode of discourse. I must have missed the section of logic that goes "proof by telling other people what they should have said, and then refuting it." Baloney.

I can accept that-- I withdraw any claim you are doing it on purpose.

twofish-quant

The technical term for "candidate theory" is "hypothesis." You can make up your own terminology, but it just gets confusing for everyone.

Again. "Valid" has a specific meaning among scientists. You can invent your own terminology, but it just makes things more confusing.

It works? Through a lot of trial and error we've come up with cultural practices that seem to be able to say meaningful things about the universe.

Then there is yet one more thing that I disagree with Popper with. Mature theories can be wrong. The amount of evidence to overturn a mature theory is higher, but they still can be wrong.

Disagree. I have a problem if I come up with one theory, and it can "explain" any outcome. However if I design six different theories, and then pick the one that works, that's fine. I don't see why it's necessary to create "new" falsifiability.

No it doesn't, because the fact that it's thermal is still "indepdendent."

It's actually quite clear. There are statistical tests that determine how far something is likely to produce a given curve "by chance."

It's not. I'm trying to illustrate how theoretical discourse works among physicists. Someone comes up with a good idea. Then you toss it against the wall to see if it breaks. You came up with an interesting idea. At that point, one of us argues for the idea. The other one argues against the idea (it doesn't matter who does it), and if it survives, then it might be interesting enough to share with other people.

Except that I'm not refuting it. I'm trying to explain why I don't agree the way that you are going about science. In the course of talking about things, you came up with an interesting idea. Rather than go and develop that idea, you gave it up. That's a shame.

My point is that this is not a good way of doing theory. If you come up with a thousand rules that prevent you from exploring ideas, that's not a good way of doing science. So far most of this discussion has been able metaphysics, and the discussion *shouldn't* be about philosophy, because if you are talking too much about philosophy, that's a sign that you aren't talking about physics.

Ken G

No one disagrees with that, and I have no idea why you think Popper would.That's what you don't get about Popper. If you design six theories, flexible enough to cover all possibilities, and one of them succeeds so you pick it, then you are doing rationalization of that outcome. What you are missing is any reason to think your theory got it right by anything but pure dumb luck. That's why Popper requires risky predictions. It's the same as if I asked a thousand people to come up with numerological schemes that follow some general prescription but include a range of possible parameters, to predict my birthday, and one of them succeeded. I'd have no reason at all to attach any importance whatever to that numerological scheme. But if I only asked one person, and they made the "risky prediction" that I was born a certain day, and sure enough I was, then I'd have to give their approach some attention!OK I think we crossed wires somehow there. I may have misinterpreted what you were saying-- I don't think we should reject any cosmological schemes that require cosmic coincidences, because it would simply mean that the scheme was incomplete. It could still be right! Indeed, a scheme that requires a cosmological coincidence is an excellent result if it is testable (like Kepler's ellipses), because it is then very easy to tell if it is on to something or not (it makes a "risky" prediction, that other orbits, by some cosmic coincidence, will also be ellipses). Even better would be a scheme that makes the same risky prediction, and offers a reason to think of it as something other than a coincidence (like Newton's inverse-square gravity). So we don't reject theories that look like they require coincidences, but we expect them to be wrong unless there is some deeper theory that we are missing. The greatest excitement of all is when a prediction that requires what seems to be a cosmic coincidence tests out successfully. Note this is rather the opposite of the spirit of the multiverse approach to cosmology, which is looking more and more like a factory that is rigged to make sure nothing ever seems like a cosmic coincidence, yet without pinning itself down to any risky predictions, so you have no chance of judging what is actually a good theory that points to some deeper truth we have been missing.
Popper's criteria are not rules to prevent you from exploring, they are rules to keep you from fooling yourself that you are exploring-- when you really aren't.

Eric333

there's probably some element of "space" that is expanding from the Big Bang, but the void which that space resides in (i.e., which it is expanding into) must be infinite.

Eric

Drakkith

Space is not expanding into any pre-existing space or void.

twofish-quant

I think that I do get Popper. I just disagree with him.

The reason is deductive logic. For example, I claim that because mints are green, the sky is blue. However, someone else can argue equally well that because mints are green, the sky is pink, or orange, or magenta. In order to make a scientific argument, I have to present a chain of logic that starts out with a set or premises, and logically to a conclusion, so that no one can question the conclusion if the premises are correct.

If I've done that, then there is something there more than "dumb luck."

And sometimes just presenting the change of logic is scientific progress. For example, accretion disk jets. We are pretty sure we know the premises (i.e. the scientific laws that operate with accretion disk jets). We know the result (i.e. accretion disk jets exist). What we don't have is the logical chain of reasoning that connects the rules with the result. Now if someone could present that chain of reasoning, that would be a scientific theory, not withstanding that it hasn't demonstrated anything new.

In the case of the early universe, there a lot more wiggle room because the premises are unclear, but as we know more, there will (hopefully) be less flexibility both in the premises and in the observations.

This is the problem with "God does it" arguments. I can argue that God created the sky blue. Fine, so why didn't he want pink skies? In some religions you can constraint the actions of God through motivational arguments (i.e. God loves you therefore...) But even that doesn't constrain things when it comes to the natural world. I don't see why a loving God would prefer blue skies over pink ones. Therefore why is the sky blue and not pink is a scientific question and not a theological one.

But if instead of matching one number with one number, you match one with fifty, then you have something useful. For example, you come up a formula someone correctly figures out your age *and* height, that would be useful, because you go from age to height.

The main job of theoretical physicists is to come up with logical chains, and sometimes you don't have the whole chain. The reason I brought this up is that the statement "reject any cosmological schemes that require a coincidence" is a perfectly good premise, and one thing that a theorist should do is to ask, assume this is true, then what logically follows. If you come up with something non-obvious (i.e. "rejecting cosmological schemes that require a coincidence" -> "cosmological constant numbers have been misinterpreted"), this is something that you want to share with people.

You shouldn't expect anything. The problem that I have with the way that you are thinking is that you are trying to do physics theory by assuming philosophical principles, and that it's a good way of going about things, not the least of which is that we will probably never agree on what those principles are. You say "Popper says this" and I say "so what, he's wrong" then what?

Science involves a lot of people, and the job of a theorist *isn't* to figure out if a theory is true or not. The job is to come up with logical chains and deductive facts, and then through them into the pot for people to make some use of.

And that's where the "anthropic project" has been useful. For example, one "deductive fact" which is non-obvious is that the existence of stable matter is very sensitive to dimensionality and the fine structure constant, whereas it's not sensitive to the cosmological constant. That's interesting.

But you can't tell the universe what to do. The "multiverse approach to cosmology" is no different than the approach scientists take to most problems, and it's what Thomas Kuhn calls 'ordinary science." You have a set of premises, and your job is to make the observations fit the premises. You'd *like* to make a "risky prediction" but you go into your model and it turns out that it doesn't make any predictions that aren't trivially wrong.

Doing "revolutionary science" requires the universe to cooperate, and you can't make the universe do that. As far what constitutes a good theory, there are heuristic criterion, and as for "deeper truths" if you take enough data and make enough models you'll stumble onto the truth by accident.

You can't *plan* to make risky predictions, because any predictions you can plan for aren't risky.

They don't do a good job of that.

There are some tricks that people use to deal with the psychology and cognitive bias aspects of doing science. One is to do what I was trying to do with with the "coincidence principle". You flip a coin, and then have one person advocate an idea and then someone else tear it down, and then you blow a whistle and have people switch places.

The other thing is to make heavy use of mathematics to make unambiguous predictions. We can disagree whether inflation is true, but it's got a mathematical model so it's not possible to dispute whether it lead to conclusion X or not.

And if you can't explain, at least you can classify and observe. It's an important fact that all supernova Ia have the same absolute magnitude. We have no clue why. Pointing out that supernova Ia is a statement and not a model, and if you think the only valid scientific inquiry involves making falsifiable models, it's not science which is an absurd conclusion.

Chronos

That is where MOND came from ... My apologies, I couldn't resist.

phinds

You completely misunderstand cosmology and the structure of the universe. The universe isn't expanding "into" anything. That idea is nonsense.

Alex-NL

On a related note: can Hawking radiation cross the "boundary" from what's beyond it into our visible bubble? Afaik the phase velocity of the Schrödinger wave isn't limited to c.

If so and if the magnitude of this effect could be measured, it could theoretically be possible to calculate the size of the universe beyond our visible bubble with the assumption that the universe has a roughly equal mass-energy density at very large scales.

phinds

If it were possible/meaningful to do so, don't your reckon someone would have DONE it by now?

Drakkith

What boundary? Hawking radiation is emitted from our side of the event horizon of a black hole. And what does the Schrodinger wave function have anything to do with this?

Phinds, down boy! Down! *waves a steak at Phinds* Go get the steak!