Is the universe finite or infinite?

[twofish-quant]

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.

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.

The scientific "validity" of a theory could be several things, depending on the purpose of the theory.

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

http://en.wikipedia.org/wiki/Validity_(statistics)

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

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.

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.

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.

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?

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

Each one probably involves thousands of individual facts.

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.

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.

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?

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]

I think the terminology is off. Without any sort of experiment data, it's not a theory, it's a hypothesis.

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.

"Valid theories" are not expected to fail, but "well posed hypotheses" can.

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.

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.

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.

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.

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.

In the case of cosmology, m is twelve and n is in the tens (maybe hundreds) of thousands.

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).

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

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.

Also, I'm not *intentionally* trying to change arguments. Communications is difficult.

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

 

[twofish-quant]

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

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.

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

Well, I realize you don't agree with Popper, but I haven't seen much in the way of justification for your position.

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.

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.

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.

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.

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.

But when we see that the spectrum is thermal, suddenly the amount of independent information there drops drastically.

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

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

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

Well I'm afraid that is a perfectly absurd mode of discourse.

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.

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.

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]

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.

No one disagrees with that, and I have no idea why you think Popper would.

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.

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!

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.

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.

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.

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]

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

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

 

[twofish-quant]

That's what you don't get about Popper.

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

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.

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.

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 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.

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.

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.

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.

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.

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.

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.

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.

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]

... your job is to make the observations fit the premises.

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

 

[phinds]

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

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 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.

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

 

[Drakkith]

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.

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?

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

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

 

[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

Please allow me to make a clarification, I realize my wording sounds like nonsense but when I said "space" I meant "anything created by the big bang" and the farthest known element from that bang would demarc "space" and the "void" but I realize the word space is confusing :-)

 

[Whovian]

Please allow me to make a clarification, I realize my wording sounds like nonsense but when I said "space" I meant "anything created by the big bang" and the farthest known element from that bang would demarc "space" and the "void" but I realize the word space is confusing :-)

There is no void in any sense that space is expanding into. The Big Bang happened everywhere.

 

[Eric333]

There is no void in any sense that space is expanding into. The Big Bang happened everywhere.

Everywhere? In basic terms, it was a central node that exploded right? Then the elements of that explosion expanded outward (and is still doing so). What is 1 inch beyond the boundary of that ever expanding explosion?

 

[Whovian]

In basic terms, it was a central node that exploded right?

Nope. Again, it sort of occurred everywhere. In basic terms, it was an incredibly dense stuff everywhere, and space sort of started expanding, decreasing the density of this incredibly dense stuff and bringing any two points further apart. Sorry if this doesn't sound too rigorous, it's an imperfect wording, but suffices.

 

[Pesj]

Eric, you must not understand the expansion as an outward movement within three dimensions. If so we would observe empty space (no stars or galaxies) "inwards" and "outwards" and the galaxies would lie in a plane or disc in the other directions. This is not the case the universe is evenly filled with galaxies in all directions. The expansion is an ever increasing distance between non-gravitationally bound objects. There is no spatial point an inch beyond the big bang at any time. At least not located in what we usually define as the universe.

 

[Drakkith]

Everywhere? In basic terms, it was a central node that exploded right? Then the elements of that explosion expanded outward (and is still doing so). What is 1 inch beyond the boundary of that ever expanding explosion?

This is why I hate the term "Big Bang". It just screams "explosion in space". Instead of an explosion, imagine the universe running backwards in time. Everything gets closer to everything else until the entire universe, ALL of it, is extremely dense and extremely hot. This is the earliest period that we can make good theories about. At this point in time, the universe was still infinite in size and there is still no center. As time passed the universe expanded, meaning that the distance between all objects not bound increased with time, until we get to our present day universe. Have you ever heard of the raisin bread analogy?

 

[twofish-quant]

This is why I hate the term "Big Bang". It just screams "explosion in space". Instead of an explosion, imagine the universe running backwards in time.

I actually like the term. A "bang" is a loud noise and much of the data we are looking at involves essentially looking at the "sound of the universe".

One term that I've used in talking about the CMB which I think is accurate is the "wall of fire".

Everything gets closer to everything else until the entire universe, ALL of it, is extremely dense and extremely hot.

The other thing that I think is useful is not to think about the entire universe. One thing to imagine is to take a camera and "zoom in" to our part observable universe and then just think of that. There is a part of the universe that you can't see, but it helps not to think of that.

One other point is that much of what we think of as the big bang, isn't that dense and isn't that hot. One reason I like talking about the "wall of fire" is that the temperatures and density at CMB separation are typical of those that we see when we deal with ordinary fire.

At this point in time, the universe was still infinite in size and there is still no center.

This is why the "zoom lens" picture makes sense to me. Imagine a picture with you at the center that goes out several tens of billions of light years. By thinking about *part* of the universe rather than the whole thing, I'm thinking about a finite bit that my mind can comprehend.

 

[thomasdeflo]

the universe is finite

Following the holographic principle, the universe is finite:

http://thomasdeflo.heliohost.org/studies.html

 

[phinds]

... At this point in time, the universe was still infinite in size

No, it was only infinite in size THEN if it is infinite in size NOW and we don't know that it is.

 

[Mohd Abdullah]

My personal answer will be like this, the universe is neither finite nor infinite.

 

[Arifz]

Can you explain more please? What do you mean?

 

[phinds]

My personal answer will be like this, the universe is neither finite nor infinite.

Which is nonsensical.

 

[Drakkith]

No, it was only infinite in size THEN if it is infinite in size NOW and we don't know that it is.

Of course my slobbery friend!

 

[phinds]

Of course my slobbery friend!

Gad, you are slowing down. Two weeks to kibitz ?

 

[BruceW]

they haven't ruled out an FLRW universe with non-zero curvature yet! In other words, the universe is not necessarily infinite. It is simply large enough that we have a 'fairly flat' universe. 'fairly flat' meaning that most cosmological models predict that the most likely curved universes would be very curved compared to ours. Also, our universe is within experimental error of zero curvature. So in this sense, the universe is 'flat'. There are also chaotic inflation models that do not require a big bang. I guess these are less standard.

 

[Drakkith]

Gad, you are slowing down. Two weeks to kibitz ?

Quiet you, or I'll stuff you back in your kennel!

 

[Chronos]

In theory, if the universe is exactly flat, it is probably spatially infinite. Observationally, it is so close to being exactly flat it is impossible to draw any conclusion - other than it is huge [what a shock]. I doubt we will ever be able to conclusively prove one way or another.