Finite Big Bang, Infinite universe?

[danda22]

Who makes the claim the the Big Bang is a finite structure?

hmm ok i realize this has probably already been answered in full. but as far as i know all experts have claimed that the big bang was just one giant explosion. how is it possible. for something that is infinite. to explode? infinite.. encompassing all.. if it exploded... that is mind boggling... the big bang must of been finite. which therefore means that. the universe must also be finite.. even though it is increasing in size by the second

 

[Cuetek]

how is it possible. for something that is infinite. to explode? infinite.. encompassing all.. if it exploded... that is mind boggling... the big bang must of been finite. which therefore means that. the universe must also be finite.. even though it is increasing in size by the second

The definitive and probably final answer is, no one knows. Right now, it is debated that the universe may be finite but unbounded like a three-D equivalent of the surface of a sphere (some takers, but not so many lately) or infinite and homogeneous (a great deal of reasonably conditional concurrence).

Using math that conforms to the tenets of the cosmological principal and relativity, these two theses are considered the totality of the options to within what I imagine to be at least a 99% certainty among most physicists. Talk to anyone of them long enough about the inherent difficulty of conclusive data with respect to the presumptions of the cosmological principal, and that confidence level will generally drop to somewhere between 98% and 50% as evidenced by the progression of the first two-thirds of this thread.

As stated earlier in the thread, I feel that the current version of the Big Bang is an idealized model of how an expanding universe would behave if the cosmological principal were true. But the cosmological principle is more likely a coping mechanism to make the balance of the unobservable universe conform to what we can see of it, rather than a valid projection of the physical continuum. I feel that the expanding profile of the mutually receding galaxy groups (the evidence for the Big Bang) will ultimately prove to be both finite in extent and multiply manifest (other Big Bangs out there) just like every physical structure or behavior ever observed.

Every physical behavior or structure ever observed proved to be both finite in extent (finite rule) and multiply manifest (plurality principle). From quarks to molecules to flatworms to physicists to supernovae to galaxy clusters, whatever physical phenomenon you care to identify, you can find both it's spatial limits as well as other examples of it scattered about the universe. The same will almost certainly be determined to be the case for the phenomenon of the Big Bang, provided the species survives it's social adolescence long enough to develop the necessary technology.

-Mike

 

[marcus]

but as far as i know all experts have claimed that the big bang was just one giant explosion.

No expert has claimed that the big bang was just one giant explosion. Someone who said that would necessarily be ignorant, and not an expert.
The explosion idea is probably the most common mistake that uninformed people make.

The common misconceptions about the big bang were described in the Scientific American of March 2005 in an article by Lineweaver and Davis. The explosion misconception was one of those which they tried to kill off.

It would be good if you would read the SciAm article. I always keep a link to it in my sig. It is the princeton.edu link in small print at the end of the post. The Princeton astro department uses the article in their intro astro course.

 

[marcus]

Who makes the claim the the Big Bang is a finite structure?

I do.

-<[{( Crackpot Alert!)}]>-

Erm... labelling your post with "crackpot alert" is not a good start. Have your read the PF rules?

Cuetek later changed the word "crackpot" to "speculation". Whatever you call it, it is idiosyncratic and way off the mainstream to argue that the big bang had to be a finite volume.

Our first job is to understand the standard cosmo model and what it says. The standard model fits the data extremely well and you have to have some solid reasons to go against it.

There is nothing in the standard model which says that the state around the start of expansion had to be finite volume. Expansion could have begun with an infinite volume. It was not an explosion (that is a common pop-sci misconception).

The standard LCDM (lambda cold dark matter) allows for at least two cases---expansion could have begun with a finite volume (e.g. boundaryless like a 3D hypersphere) or it could have begun with an infinite volume (e.g. boundaryless like Euclidean 3D space).
Observationally it may be possible to distinguish between these two cases in the future, so we will be able to infer which. Meanwhile, until more precision data, two versions of LCDM.

 

[Cuetek]

Bringing up the crackpot comment for good measure, eh? Be that as it may.

The standard LCDM (lambda cold dark matter) allows for at least two cases---expansion could have begun with a finite volume (e.g. boundaryless like a 3D hypersphere) or it could have begun with an infinite volume (e.g. boundaryless like Euclidean 3D space).

Historically speaking, all cosmological explanations about the nature of the universe beyond observable space are found to be incorrect due to the discovery of unsuspected diversity that lies beyond. The sequence of those corrections as time goes by is as follows: What ever describes the universe as a complete model is corrected as only locally relevant by the discovery of further structural diversity at greater and greater scales. You may say what you like about how your idealized model may suffice under it's own presumptions, but don't be surprised when the universe diverges from your presumption.

Observationally it may be possible to distinguish between these two cases in the future, so we will be able to infer which. Meanwhile, until more precision data, two versions of LCDM.

If history is any indication, neither will prove to be more than a regional descriptor of a hierarchically diverse universe. Humans like to imagine some complete and sufficient description of the universe. That's a fools ploy. The universe always has more to offer beyond our current view. Taking that inevitability formally into consideration is the smart perspective. Expecting the conventional wisdom to change dramatically is always a better bet than thinking it to be pretty much accurate with only a few details to sort out. Those details tend to hide whole schools of thought.

Sure, the Big Bang will be the predominant effect for many thousands of times the diameter of the particle horizon. But if history holds true, the Big Bang will eventually dissipate, terminate and give way to larger structures as has always been the case.

-Mike

 

[yuiop]

If the big bang happened everywhere at the same time, then the problem I have with an initially infinite universe, is how was such an event synchronised? An initially infinite universe would require infinitely fast signals to coordinate a simultaneous start time everywhere and that would require a hitherto unknown FTL signalling mechanism. The requirement for the big bang to start everywhere simultaneously is a requirement that comes from the constraint that the universe is homogenous on large scales.

In short, it would seem that an initially infinite universe requires faster than light communication or rejection of large scale homogenous principle.

 

[Cuetek]

In short, it would seem that an initially infinite universe requires faster than light communication or rejection of large scale homogenous principle.

Yeah, Kev, the idealized notion of either an infinitely vast, infinitely dense continuum or a finite yet enormous singularity as the cosmic "starting point" has always been the boogy man behind modern cosmic reasoning.

To imagine that such neat arrangements of the entire context of reality are anywhere close to being true descriptors is not only difficult to comprehend under current theoretical knowledge, it is historically "the man behind the curtain" of all future expansion of astrophysical understanding.

In that all material phenomenon ever examined have proven to be finite, multiply manifest, and constituent to a larger contexts (both material and temporal) so too will the Big Bang be found to be a very large, but finite phenomenon in an indefinitely diverse surrounding context. In that the black hole is the only astronomical object other than the Big Bang to which we attribute singularity, that the black hole is the destination for all matter, plus the notion that a black hole can get as large as necessary to contain whatever amounts to a Big Bang's worth of matter, it is far more likely that the Big Bang is some normal stage of a black hole's life cycle than the complete and sufficient descriptor of all reality we like to imagine it to be.

Imagining ourselves instead to be on the surface of an electron in an expanding plasma field of an early stage Supernova gives us a fairly plausible allegorical context for our current foolishness. The universe always has another hierarchical context waiting in the wings. Even after 2000 years of this same sequence of discoveries, we still try to define what we see at any given time as a complete model when time and again we are shown the truth of the matter. The universe is bigger and more involved that we can see from here. Period. That is the field of evidence at hand. That's what the historical data unequivocally indicates. We think we are smart, but we are only theoretical giants. We are psychological dwarfs.

-Mike

 

[Havanyani]

You may coin this as my Principle: "Infinite space is not capable of objective existence". Where in an infinite space can you place anything? An infinite space has no frame of reference for anything it may contain. But spacetime can grow towards infinity in that the Universe may continue to expand indefinitely. Still, that will never make it infinite. A sphere or a ring may be unbounded, but that is not infinite. We know its area or its circumference, respectively.

I have read a lot about the volume of the universe and how it is finite and unbounded et cetera. How does one resolve the problem of space-time interconvertibility? Is the volume of the universe measured in cubic light years (distance) or in Giga years (time). The beginning of the universe is about 14 billion light years away (a measure of distance), yet it occurred 14 billion years ago (time). The boundary limit of the universe is made up of the Beginning, the Big Bang, which is all around us, 14 billion light years away. We cannot go farther than the beginning in our attempts to measure its diameter. Looking yonder is really looking inwards. We are trapped in this thing.

 

[twofish-quant]

The only real difference it should make in science is in what we expect to find. If we expect to find homogeneity we won't look very hard for any faint asymmetries in the CMB and recession data. And we should look just as hard for inhomogeneity as we do for homogeneity (the bulk of publications on the subject are looking for homogeneity).

The tests are similar, and the fact that people haven't found inhomogeneity isn't for lack of trying. Also I'm not expecting anything, but as a theorist, I'd be *MUCH* more interested in signs of inhomogeneity.

If there is a specific measurement for inhomogenity that you think should be used but hasn't, then that's worth a paper.

But just because we can make an idealized model of a homogeneous universe that works mathematically, is not sufficient to rely on it beyond the range of data at hand.

Actually it is. You make an idealized model of the universe and then you look at the data to see how it breaks. It's really obvious for example that the universe *isn't* homogeneous at small scales, and thing get put in as corrections to the model. If you want to introduce deviations at large scales, it's not hard to put those in also.

The current state of play is that it's likely that the length scale at which things are homogenous is much larger than anything that we can easily observe. Also there is an interesting theoretical reason for this. If the big bang started out very inhomogenous, cosmic inflation is going to smooth things out so that any inhomogenity is going to be at length scales that we can't observe (which was a *big* problem with BB models in the 1970's).

If it was the situation that the assumption of homogenity *was* causing some sort of observational blind spot, then this would cause a problem, but I don't see any reason to think that is the case.

Also assumptions are assumptions. Just because I assume something doesn't mean I believe it.

 

[twofish-quant]

Every physical behavior or structure ever observed proved to be both finite in extent (finite rule) and multiply manifest (plurality principle).

That may be because if there are lots of copies of something, you are more likely to find one. The trouble with "principles" is that while they may be good ad-hoc rules for making guesses for what direction to head toward while you are stumbling in the dark, it doesn't lead to particularly good physics.

From quarks to molecules to flatworms to physicists to supernovae to galaxy clusters, whatever physical phenomenon you care to identify, you can find both it's spatial limits as well as other examples of it scattered about the universe.

But that's because you are looking only for things with multiple examples. To give an example of a phenonmenon with no spatial limits or other examples of it scattered about the universe, let me present the bankruptcy of Lehman and the near collapse of AIG. This is not a spatially limited phenonmenon. Lehman never went bankrupt in the history of the universe and never well again. To give another example, the industrial revolution or the computer revolution are non-spatial things that never happened before.

One reason that astrophysics and cosmology is useful in finance is that in finance you have to deal with a lot of "one-off" phenonmenon that aren't exactly like anything that has ever happened before or anything that will ever happen again.

 

[twofish-quant]

Using the red shift recession data, it claims "no hope for unbounded fractal distributions," which basically supports a total projection of the visible homogeneity. However, he bases his presumption on the two point correlation function which is dependent on the fair sample hypothesis which is itself a derivative of the cosmological principle.

It really isn't. It's saying that the universe cannot have a certain type of homogeneity. Again, there is a difference between I can show that X is false, and I cannot rule out that X is true or not. It turns out with the current data you *can* rule out certain fractal distributions of the universe.

This approach constitutes the same potentially true but ultimately false presumptions we have always made when characterizing the universe beyond the data at hand. We always make the presumption that the data we have is sufficient to explain "everything."

No we don't. We have data. We try to figure out as much from the data as we can. Using the data we have we can usually rule out certain scenarios. Also, there are some theoretical reasons to question the cosmological principle, and there are some people that really have some attachment to the anthropic principle.

If we were living on an electron of a hydrogen atom in the middle of the ocean, we would be perfectly justified in presuming the universe was made entirely of water molecules, and all our calculations would work perfectly, but we would still be wrong.

Or we could be right, or it may not matter. A lot of equations in physics are of the form "assume a spherical cow". You make an assumption that may be wrong, or you make an assumption that you *KNOW* is wrong, so that you can do a calculation and figure out something about the situation you are looking at.

For most cosmological calculations it turns out that it doesn't *matter* what the super-large scale structure of the universe is, so you can assume that everything is the same, since that let's you do a computation and it greatly simplifies the math.

All I'm saying is that a Bayesian examination across the widest possible spectrum of the existing data (the hierarchical structure of of the known material universe from quarks to galaxy clusters and across the history of scientific investigation) says that the universe is hierarchical and not homogeneous across all scales and that whenever we try to terminate that hierarchy is precisely where our theories have historically proven weakest.

And I'm arguing that this notion is completely flawed because you are taking data from a known region and extrapolating it to an unknown region. Sometimes you have to look in the mirror and just say *I DON'T KNOW* and my experience is that you are better off is you just say *I DON'T KNOW* than to assume that you do know something you don't.

The other issues here is that the hierarchy does terminate. Electrons are point objects, and the Heisenberg uncertainty principle basically says that there is no structure below the quark scale.

And the CP is that point of weakest presumption in modern cosmology.

Maybe, but the cosmological principle is a rule of thumb, and it's something that shouldn't be taken too seriously. If you ask a random sample of cosmologists and ask them about the super-large scale structure of the universe, you'll get a diverse set of answers which basically boil down to "I don't know."

Also the fact that the universe is more or less homogenous at certain scales is an observational result, not a theoretical assumption. It's actually something that caused all sorts of problems in the 1970's which were fixed by inflation. The idea behind inflation is that because of inflation, we have homogenity at very large scales because any inhomogenous before inflation were washed out when the universe expanded extremely rapidly.

For people to get upset to the point of indignation over the suggestion that the Big Bang may ultimately be a finite phenomenon is more an artifact of psychology than of science.

It's not. It's more frustration when people come up with strawman arguments.

Also, no one is going to get annoyed if you *suggest* that the BB is a finite phenonmenon. A lot of annoyance comes in if you *insist* that the BB is a finite phenonmenon, because to justify that you have to use arguments that are basically outside the realm of science. If you come up and argue that the big bang *may be* a small part of a larger whole, that's not controversial at all. It's when you come up and say that the BB *is* that way, that you cause problems since you are trying to justify this by arguments that are philosophical rather than scientific.

People do get very touchy about distinguishing what the data says and what it doesn't because there is an effort to prevent "religious wars." If you look at the data, you can come to some consensus about what it says and what it doesn't. If you start going beyond the data and start making guesses based on quasi-religious principles, there isn't any way of resolving disputes. Personally, being a Buddhist, I have some totally nutty ideas on the ultra-large scale structure of the universe (i.e. that after one dies one ends up reincarnated in some other part of the cosmos), but unless I have data, that stuff stays out when I put on my physicist hat.

That it is possible for the cosmological principle to be true is not the same thing as being inevitable.

And I don't think that anyone in the field thinks otherwise. One thing about cosmological is that the cosmological principle has undergone some severe hits in the last decade to the point that there are people that seriously suggest that we ought to abandon it as a rule of thumb.

 

[twofish-quant]

To imagine that such neat arrangements of the entire context of reality are anywhere close to being true descriptors is not only difficult to comprehend under current theoretical knowledge, it is historically "the man behind the curtain" of all future expansion of astrophysical understanding.

But if you have to do a calculation based on available data, you remove any complexity. It's the old joke "assume a spherical cow". Of I have to do a calculation and I don't know the shape of a cow, I assume that it's a sphere, because with that assumption I get results which I can compare with observations. If I stop everything and don't guess at a shape, I don't end up with any theoretical results that I can compare with observations.

In order to get to the truth of the situation, you have to make calculations based on assumptions that could be false or sometimes that you *know* are false. If you want me to make a quick calculation of the gravitational pull of a cow, my first calculation will assume the cow is spherical even though I know that the cow isn't.

Similarly, the FRW metric starts with the (manifestly incorrect) assumption that the universe is perfectly homogenous (which it isn't).

In that all material phenomenon ever examined have proven to be finite, multiply manifest, and constituent to a larger contexts (both material and temporal) so too will the Big Bang be found to be a very large, but finite phenomenon in an indefinitely diverse surrounding context.

That's a *huge* philosophical assumption, and one that I personally find untrue. One thing that you quickly figure out when you study supernova and galaxies and stars, is that each one is unique. There is no supernova that was exactly like 1987A and there never will be again. There is no object in the universe which is exactly like the moon.

Now to gain some sort of understanding of what is going on, you do try to classify and analogize, but you do find out that astronomical objects are unique once you see them clearly.

The other thing is that "we've never see this before, therefore it can't happen" is something that doesn't work for me. I work on Wall Street and the idea that the future will be anything like the past is something that will get yourself bankrupted if you take it seriously enough. One-off phenonomenon *routinely* happen.

It so happens that the methods of analysis used in physics work best when you have multiple similar objects (which is why you end up with a mess when you apply them to social sciences), but if you spend all your time looking at blue objects, you can't conclude that everything in the world is blue.

Imagining ourselves instead to be on the surface of an electron in an expanding plasma field of an early stage Supernova gives us a fairly plausible allegorical context for our current foolishness.

Science doesn't work through allegories.

The universe is bigger and more involved that we can see from here. Period. That is the field of evidence at hand. That's what the historical data unequivocally indicates. We think we are smart, but we are only theoretical giants. We are psychological dwarfs.

I see things very differently because I've been in finance and as the old saying goes "past experience is no guarantee of future results." Just because you've *never* seen something happen before, doesn't mean that it can't happen. So how do you deal with things that have *never* happened. Well... Thinking about that is why I like my job (and why banks hire astrophysicists).

I really think you are punching a strawman since you are criticizing people for beliefs that most of them don't hold. All I'm saying is that when presented with a lack of evidence, the logical thing to do is to say "I don't know." I can guess, but I really don't know. It's really important to distinguish from what you *know* to what you are merely guessing about, since thinking that you know something that you don't tends to blind you to incoming data.

I don't see why that's particularly controversial.

 

[Cuetek]

Once again, the cosmological principle is based on taking the symmetry seen at a single scale and projecting it however necessary to devise an ostensibly complete and sufficient model of the cosmos that by definition requires terminating the material hierarchy of the universe.

The error here is twofold. The primary error is presuming that humans are in the position to make complete models of the universe (never have come demonstrably close). The secondary error is in the interpretation of the data of one single scale overriding the very consistent hierarchical nature of the data from all of the rest of the scales we've been able to examine across 40 orders of scalar magnitude.

You can hem an haw about all manner of exceptions you like based on some anthropomorphic emphasis on one scale in the hierarchy over the others, but you will be making the same mistake of taking specific data to refute the wider body of evidence (probably the most common scientific error of all time).

The sum of the data is unambiguously in favor of a hierarchical universe extending in both directions of scale beyond our detection. You cannot rationally refute the finite rule or the plurality principle. All observable material structures have proven over time to be finite in extent and constituent to larger structures. All observable phenomena have proven over time to be multiply manifest. Presuming the data accumulated across all scales as more significant than the data from any single scale is clearly the more rational approach.

We are no more the center of the scalar universe than we are at the center of the spatial universe. It's a pretty simple rationale whose time has come. Let's quit trying to imagine we can describe the whole universe from our perspective stuck at one scale and one location. It's time to accept the high probability that all human knowledge is more realistically viewed as a set of local relationships in an indefinitely vast, ongoing hierarchical continuum.

-Cuetek

 

[twofish-quant]

Once again, the cosmological principle is based on taking the symmetry seen at a single scale and projecting it however necessary to devise an ostensibly complete and sufficient model of the cosmos that by definition requires terminating the material hierarchy of the universe.

I'm not interested in making complete and sufficient models of the cosmos. My interest is to create models which summarize the essence of a physical process, which means removing anything that isn't essential to the model. If I want to calculate helium abundances in the BB, I start with the assumption, and possibly wildly incorrect assumption that the universe is homogeneous, since if I don't I'm not going to get any predictions out. It turns out that if I make that assumption I get out good helium numbers so that the actual reality of the situation is close enough to my assumptions that I can use them to get helium numbers.

In turns out that in some situations (quantum field theory) my assumptions lead to internal self-contradictions, which I have to deal with. It turns out that in assuming that the universe is infinite, there aren't any theoretical contradictions. At that point I look for differences in observations, and there aren't any. Which means that when I run my models, I can assume that the universe is infinite, and that will give me good enough numbers for the things that I happen to be interested in.

The sum of the data is unambiguously in favor of a hierarchical universe extending in both directions of scale beyond our detection.

No it's not. Heisenberg uncertainty theorem puts a lower limit on structure. As far as upper limits, there is no evidence of any hierarchy outside of the observable universe. That's not to say that there isn't. It's just to say that people have looked for it, and we haven't found anything.

You cannot rationally refute the finite rule or the plurality principle.

If I can't rationally refute it, then we are having a theological argument rather than a scientific one. This is the big problem that I have with your insistence that the universe *has* to work in a certain way. You are making some philosophical assumptions about how the universe works. That's fine. If it gives you a research program, its wonderful, but what I'm telling you is that science doesn't work this way because it *can't* work this way.

It turns out that different people have different philosophical assumptions so if you try to piece together how the universe works that way, you end up with "religious wars." People insisting that their philosophical assumptions are correct and privileged. You have some assumptions about how the world works that I just don't hold, and we try to have this discussion without observational evidence, we are just going to get nowhere.

Cosmologists and physicists do share a minimal set of philosophical assumptions that allows people to communicate, but it has to be a very minimal set. You are stating a set of assumption, and if I say, I just don't accept those, then we are at an impass. Your only response would be that I'm somehow irrational, but I don't *seem* irrational.

[All observable material structures have proven over time to be finite in extent and constituent to larger structures. All observable phenomena have proven over time to be multiply manifest. Presuming the data accumulated across all scales as more significant than the data from any single scale is clearly the more rational approach.

And I say no it isn't. But we are having a theological discussion here, and not a scientific one. This is the type of discussions theologians have all the time. It's the type of discussion that physicists avoid if at all possible, and there is no reason I can see to bring up this discussion since we are talking about things that are observationally unfalsifible. Now if we did have observations that could resolve this, then it again would be a pointless discussion since we just look at the observations.

We are no more the center of the scalar universe than we are at the center of the spatial universe.

People that support the anthropic principle would disagree with that statement.

It's time to accept the high probability that all human knowledge is more realistically viewed as a set of local relationships in an indefinitely vast, ongoing hierarchical continuum.

At extremely large scales this is a theological discussion. At small scales it isn't because Heisenberg wipes out any hierarchical structure that occurs below the level of quarks and electrons. Unless there is something very seriously wrong with the way we understand QM, there is no structure smaller than quarks and electrons.

 

[DevilsAvocado]

The sum of the data is unambiguously in favor of a hierarchical universe extending in both directions of scale beyond our detection.

I’m only a layman and absolutely not a mathematician, but your 'scientific proof' (numerical justification) seems very strange... even to me.

http://www.thegodofreason.com/rules-of-discovery.pdf

p(E|Fm) = The probability of finding evidence E (the existence of smaller objects collectively assembled within the current object) assuming that phenomenon Fm (all objects being finite and multiply constituent of a larger object) is true. This value is necessarily (tautologically) 1 or true.

Says who!? This is not numerical justification. This is recursive justification – My theory is correct and therefore it’s true. (or you could say its tautological guessing)

(Objection #2; Does Bayes' theorem really allow 1 for true and 0 for false? Division by zero is always hard work...?)

So we take one of the smallest object we can currently detect (the neutron) that we know contains yet smaller objects (quarks) ...

Recursive justification again. Why not start with a quark like the electron (that is clearly detected by my old TV). In this case p(E|Fm) is surely not 1 or true.

But I’m going to be nice, and let you have p(E|Fm) = 1 with the following complaint:

p(E|~Fm) = The probability of evidence E (the existence of smaller objects collectively assembled in the current object) being true presuming that our hypothesis Fm (all objects are finite constituents of larger objects) is not true. We will assign p(E|~Fm) = 0.5 generously allowing that the hierarchical evidence we see in all matter observed so far has an equal chance of being some how unrelated contrary to our hypothesis.

Ehhh... excuse me, but this Boolean algebra is probably turning Bayes in his grave. If p(E|Fm) = 1/true then p(E|~Fm) must be = 0/false! This value cannot be picked by 'generosity'!?

True = 1
False = 0
Not True = False
Not False = True​

Let’s run Bayes' theorem with the correct values:

$$p(Fm|E) = \frac{1 * 0.5}{(1 * 0.5) + (0 * 0.5)}\,$$

$$p(Fm|E) = 1$$​

The calculated Bayesian probability of neutrons being finite constitutes of yet larger objects is overwhelmingly true... and the proceeding sequence to bigger objects will be a joke...

Sorry Cuetek, but this playing with words, statistics and probability doesn’t work. To me, it looks like a crackpot theory.

 

[twofish-quant]

Anytime you mention the word "God" then we are having a theological or philosophical discussion. It's fine to discuss theology or philosophy, but my point is that we are not discussing physics.

The problem with Bayesian arguments is that you have to specify your prior probabilities, and if people with radically different prior probabilities you aren't going to get anywhere.

 

[DevilsAvocado]

... The problem with Bayesian arguments is that you have to specify your prior probabilities ...

Agree. It’s not healthy science when you provide the illusion of objectivity – "for neutrality’s sake we start with a 50/50 split between Fm and ~Fm" – when the whole thing is a mathematical setup to promote Cuetek’s most subjective and not verified ideas, omitting crucial facts about the elementary particles (quarks) as the fundamental constituent of matter.

I do think it’s a stimulating 'philosophical idea', but cannot understand why Cuetek has to wrap it in bogus math. It spoils all the fun...

And I do see severe problems in the "hierarchical universe extending in both directions". The quantum-world is not that easy to handle... and it hasn’t anything to do with the tininess of things...

 

[twofish-quant]

The two problems here are there is that priors are subjective and also you are using a different P(E|p) at each step. It's an interesting argument which physicists can and often do talk about over drinks at conferences or it might be something you could put into a paragraph at the front of a journal article, but it's nothing that would survive any sort of peer review to be publishable in a physics journal since the argument is not a physics argument. It's extremely weak, and part of the problem is that I don't think OP realizes how weak the argument really is.

 

[twofish-quant]

Agree. It’s not healthy science when you provide the illusion of objectivity

Personally, I think that objectivity is overrated. There's a huge amount of subjectivity in physics, and for the most part you deal with it by having people with different subjective views look at the same data. That's why data is so important since data creates a common pool of reality that people can look at. WIthout data, you quickly get into "religious wars" that cannot be resolved.

omitting crucial facts about that the elementary particles (quarks) as the fundamental constituent of matter.

Or omitting the fact that many physicists just don't agree about his characterization of the facts. Now it is possible to deal with this by marking someone as irrational. If someone absolutely insists that the universe is 6000 years old, then they just can't do good cosmology. Period. So you *can* argue that someone's philosophical assumptions place them outside the bounds of science.

Except that's not going to work for me. Whatever philosophical beliefs I have, they certainly are compatible with doing physics and cosmology.

And I do see severe problems in the "hierarchical universe extending in both directions". The quantum-world is not that easy to handle... and it hasn’t anything to do with the tininess of things...

The only problem that I have is that it doesn't fit the data at small scales. As a tool for thinking up new ideas and for solving problems, symmetry principles are wonderful. Sometimes you invoke a symmetry principle and you "get lucky" and you catch the fish. A lot of times, you don't. For example, if you invoke the principle that the universe must look the same through space and time, you end up with the steady-state theory, which is beautiful, elegant, and wrong. If you invoke symmetry to grade-Lie algebras, you end up with supersymmetry, which is also beautiful and elegant and predicts a bizillion particles that people haven't found. Then there is Bode's law.

So I really have no problem with people using symmetry principles as "artistic inspiration." I *do* have big, big problems (and so to most people in physics) with using them as "ground truth."

 

[DevilsAvocado]

... I don't think OP realizes how weak the argument really is.

Agree again. On a quick look at the 'mathematical proof', it looks pretty 'serious' (especially to a layman like me).

But if you scrutinize what OP is really saying, the bottomline is:

I have looked at neutrons, atoms, planets, stars, galaxies, cluster and Big Bang. My theory works on these objects, and I know that the Bayesian Theorem (that just calculates probabilities) can help me to promote the idea that these relations also continues at the 'next level' – even if it has absolutely nothing to do with the physical reality.

If the topic was Bayesian spam filtering – the idea would be absolutely great, and would most probably work.

In the real physical world, this means nothing.

 

[DevilsAvocado]

Personally, I think that objectivity is overrated.
...
So I really have no problem with people using symmetry principles as "artistic inspiration." I *do* have big, big problems (and so to most people in physics) with using them as "ground truth."

In 1905 the formula E=mc² was probably looked upon as Einstein's most subjective perspective on the world of matter and energy. Or to quote 'the father of nuclear physics', Ernest Rutherford in 1930:

"Anyone who expects a source of power from the transformation of the atom is talking moonshine."

In 1945 the 'moonshine' got pretty harsh...

Wild and stimulating (philosophical) ideas is fun & cool – if it’s presented as that, and not as the "ground truth".

I love Max Tegmark and his Multiverse.

 

[Cuetek]

I'm not interested in making complete and sufficient models of the cosmos. My interest is to create models which summarize the essence of a physical process, which means removing anything that isn't essential to the model.

By not formally assuming the higher probability that the Big Bang is a finite phenomenon in a much larger, materially hierarchical context, you assume the Big Bang is unaffected by larger forces of scale. Your peers talk in terms of the universe being flat or convex when such curvature is almost certainly regional. Your peers talk in terms of the universe's fate from expansion, when such fate is more probably a function of structures you have yet to characterize. This is the more probable disposition. Just like the Copernican model was found to be under the larger influence of the Galactic "island universe" model the Big Bang will be subject to the hierarchical disposition at a greater scale.

I can assume that the universe is infinite, and that will give me good enough numbers for the things that I happen to be interested in.

Infinite is fine, but only in terms of an infinite context within which a hierarchical material disposition is assumed, at least with respect to what to expect in the near term for the next evolution of scale, until the data shows definitively *otherwise.* Which it has not over the entire history of our investigations even though we terminated the hierarchy every time we ever made a new cosmology. It's time to break that bad habit.

No it's not. Heisenberg uncertainty theorem puts a lower limit on structure.

It does no such thing. The only lower limit is one assumed at the plank length and that leaves enormous room for further infinitesimal hierarchy. To think that we have a good idea of what all is happening in the material world at the scale of the quark is overzealous at best.

As far as upper limits, there is no evidence of any hierarchy outside of the observable universe. That's not to say that there isn't. It's just to say that people have looked for it, and we haven't found anything.

No evidence? The entire balance of all the universe we have examined is hierarchical, not homogeneous. All the evidence indicates a very high probability that it continues hierarchically, not homogeneously. Only the narrow focus on a local homogeneity indicates otherwise and the universe is full of local areas of homogeneity that blows the doors off of the galactic level symmetry.

The symmetry you see in the galactic distribution in the visible universe is not anywhere close to say the symmetry at the atomic level of a single drop of water made of trillions of molecules, now put that drop in an ocean. Now THAT's some serious homogeneity.

Oh, sure, you may presume a limited range of homogeneity based on one scale of galactic observations, but not infinite. Even an ocean of trillions upon trillions of molecules of symmetry eventually ends just like every other material structure or phenomenon EVER OBSERVED.

If I can't rationally refute it, then we are having a theological argument rather than a scientific one.

When I say you can't rationally refute the finite rule or plurality principle, it is because they are true for every material phenomenon ever observed, not because they are theological. You can't rationally refute the probability of a coin toss coming up heads at roughly 50% because it's true, not because it's religious.

This is the big problem that I have with your insistence that the universe *has* to work in a certain way. You are making some philosophical assumptions about how the universe works. That's fine. If it gives you a research program, its wonderful, but what I'm telling you is that science doesn't work this way because it *can't* work this way.

I'm not saying it "has" to. I'm saying it is far and away more probable. It's not philosophical either. You are the one being philosophical by insisting that the homogeneous symmetry at one scale is more important than the hierarchical symmetry across all observable scales, even across those which show far more staggeringly enormous ranges of homogeneity than the one you call your "evidence."

It turns out that different people have different philosophical assumptions so if you try to piece together how the universe works that way, you end up with "religious wars." People insisting that their philosophical assumptions are correct and privileged. You have some assumptions about how the world works that I just don't hold, and we try to have this discussion without observational evidence, we are just going to get nowhere.

You are the one being philosophical by your insistence that one scale of evidence is more significant than all scales of evidence. But, I actually sympathize with your position. It is really difficult to realize the assumptions that are being made if everyone has been making them for a long time. Agreement is a very compelling social force. Religions get almost all their enormous social power from just such long held unwarrented agreement.

Cosmologists and physicists do share a minimal set of philosophical assumptions that allows people to communicate, but it has to be a very minimal set. You are stating a set of assumption, and if I say, I just don't accept those, then we are at an impass. Your only response would be that I'm somehow irrational, but I don't *seem* irrational.

I'm content with you feeling that we have come to an impasse.

Now if we did have observations that could resolve this, then it again would be a pointless discussion since we just look at the observations.

The observations are as follows. Every material phenomenon that humans have ever observed have proven to be finite in extent and multiply manifest. All of them. The only phenomenon that has not been proven to be finite or multiply manifest is the expanding profile of the galaxy cluster's which imply the Big Bang. But only because we have yet to devise the instrument that will finally show where it ends. We can't see all of it, so it cannot count as evidence of an exception to the finite rule and plurality principle.

Ask yourself, how do we usually find out that something we thought was the biggest object in the universe, turned out not to be? We find a way to see far enough that we see evidence of another example of what we thought the largest object, and collectively *those* objects form the next thing we call the largest object. See a trend here?

The evidence for presuming a hierarchical universe is substantial, in both historical and scientific terms.

-Cuetek

 

[DevilsAvocado]

... To think that we have a good idea of what all is happening in the material world at the scale of the quark is overzealous at best ...

Would you dare to say that to the 9 billion dollar budget guys at LHC Cern??

 

[Chronos]

You need to run bayesian statistics using multiple assumptions to derive boundaries.

 

[twofish-quant]

By not formally assuming the higher probability that the Big Bang is a finite phenomenon in a much larger, materially hierarchical context, you assume the Big Bang is unaffected by larger forces of scale.

Absolutely. Then you do calculations, test that assumption against observations, and for the observations we can do, those assumptions seem to work. There are some "smoking gun" things that would lead people to reconsider that assumption, but right now we haven't found them.

It's like assuming a flat earth. For a lot of things, assuming that the Earth is flat works pretty well. For some things it works very badly. If you start out by assuming a flat earth, and then things don't make sense, then you change your assumptions. Also some assumptions that people make are clearly false, but useful. The standard models of the big bang assume that the universe is totally homogenous, which is clearly false. I'm staring at a computer screen which is different from the air around it, and the standard models of the cosmology just classify both as "baryonic matter" which are evenly distributed.

Your peers talk in terms of the universe being flat or convex when such curvature is almost certainly regional.

Since we have no data, saying whether something is regional or global is something that we can't say. However one of the cool facts about differential geometry is that it doesn't matter. Any smooth geometry can be approximated by a flat surface. If a flat surface assumption breaks down, then you can approximate things with a simple curvature. Now it's possible that if you look at large enough scales, that will break down, but at that point you are pushing observations past their limits.

Your peers talk in terms of the universe's fate from expansion, when such fate is more probably a function of structures you have yet to characterize. This is the more probable disposition. Just like the Copernican model was found to be under the larger influence of the Galactic "island universe" model the Big Bang will be subject to the hierarchical disposition at a greater scale.

You are making theological statements that are not supported by data. As I mentioned there is nothing particularly wrong with that as long as you realize that you are going past the available data. Ultimately, the problem is that you look at things, and you think "everything supports infinite hierarchy" whereas the astrophysical objects that I study tend not to have "infinite hierarchies." One example is the Kormogarov cascade. It turns out that turbulence is self-similar across a huge range of scales, but the hierarchy cuts out at extremely large scales and extremely small ones. The other thing to point out is that space is mostly nothing. If you look at the sky, you see mostly nothing.

Infinite is fine, but only in terms of an infinite context within which a hierarchical material disposition is assumed, at least with respect to what to expect in the near term for the next evolution of scale, until the data shows definitively *otherwise.*

The problem is that if you try to create this sort of cosmology you end up with something that just doesn't fit the data. Any cosmology that assumes larger structures at this point just ends up being either irrelevant or inconsistent with the data. If you assume a self-similar fractal distribution of galaxies, you end up with galaxy distributions that just don't match what we see.

Which it has not over the entire history of our investigations even though we terminated the hierarchy every time we ever made a new cosmology. It's time to break that bad habit.

Saying "I don't know" is not a bad habit. I think it's a good habit. If you can't see distant galaxies, you can't assume that anything is or is not there.

The only lower limit is one assumed at the plank length and that leaves enormous room for further infinitesimal hierarchy.

No it doesn't. The problem is that if you have something that is localized in space, then it's momentum becomes non-localized, and that means that any hierarchy gets washed out. Unless there is something basically wrong with our understanding of Heisenberg, then there are no new structures between the scales that we can see and Planck's length. Once you get to Planck's length, then quantum mechanics and GR become inconsistent, so there is new physics at smaller scales.

Also quantum mechanics imposes a lot of information limits. One electron is exactly the same as any other electron which means that there is no internal structure that you can use to mark an electron. The trouble with assuming structure is that you run into the Gibbs paradox. Basically the behavior of gases depends on the statistics of quantum mechanical structure. If there was structure, then gases would behave differently, because you could distribute energy across more states.

To think that we have a good idea of what all is happening in the material world at the scale of the quark is overzealous at best.

Actually, we *do* have a pretty good idea of what happens at the scale of quarks.

No evidence? The entire balance of all the universe we have examined is hierarchical, not homogeneous.

And I look at the universe, and it looks pretty homogenous to me. Unless you can come up some reason why I'm irrational, you have to take that into account.

All the evidence indicates a very high probability that it continues hierarchically, not homogeneously.

I think you aren't familiar with the cosmological evidence. The models that cosmologists use *assume* that the universe is homogenous with things like stars and subway trains being "irrelevant corrections." People make this assumption, because it happens to give answers that fit observations. Now you can assume otherwise, but there is no reason to do so.

Oh, sure, you may presume a limited range of homogeneity based on one scale of galactic observations, but not infinite. Even an ocean of trillions upon trillions of molecules of symmetry eventually ends just like every other material structure or phenomenon EVER OBSERVED.

You are making philosophical arguments and not scientific ones. Also most physicists are aware of some blind spots. If you have something happen that is a one off event with no symmetry, then its something that will likely get ignored by physicists because there's no way of analyzing it.

One reason I look at things differently is that I study supernova. Every supernova that has ever happened is different from any other supernova that has every happened. You classify and analyze, but if you have something that is really, really different, it's going to get ignored.

When I say you can't rationally refute the finite rule or plurality principle, it is because they are true for every material phenomenon ever observed, not because they are theological.

And I say it's not true. Supernova 1987A was different from every other supernova that happened. The electric and gravitational field that an electron produces is not limited by space. Also the term "material phenomenon" is a interesting dodge, since it's not clear to me what is material and what isn't. Is light material? What about energy? What about money?

Look, you are on a bulletin board with people that have a lot of experience looking at astrophysical phenomenon, and no one other than you seems to think that the finite rule or the plurality principle is something that is an intrinsic characteristic of the universe. Unless, you want to argue that we are all irrational, then this means that those ideas are at least debatable.

You can't rationally refute the probability of a coin toss coming up heads at roughly 50% because it's true, not because it's religious.

I flip the coin. I've seen coins that *don't* come up heads 50% of the time.

I'm not saying it "has" to. I'm saying it is far and away more probable.

And I'm saying that it's a bad idea to assign probabilities to things that you know nothing about, whether it's the big bang or the odds of a failure of a major investment bank. Part of the reason this matters is that it impacts my day job. I'm very, very skeptical of assigning a single number to a one off event, since this really killed people when Lehman Brothers happened.

So if you can't assign a probability to a one time event, then how do you manage it? Not sure, but I get paid to think about stuff like that. The problem is when you say "this is more probable" what do you mean? The answer that I've come up with is that with one time events, "probability" is a measure of psychological certainty, which may have nothing to do with the physical situation or likelihood of the event. That definition of probability very, very nicely models things like credit default swaps (i.e. the probability is how likely the market thinks that Lehman will default which is a psychological measure that may have nothing to do with the likelihood that Lehman will actually default).

But if you use that definition of probability, then it tells you nothing about the real world (which is great since if there is a difference between psychological probability and physical probability, you can make tons of money).

It's not philosophical either. You are the one being philosophical by insisting that the homogeneous symmetry at one scale is more important than the hierarchical symmetry across all observable scales, even across those which show far more staggeringly enormous ranges of homogeneity than the one you call your "evidence."

One problem here is that you really can't avoid being philosophical, because ultimately you have to come up with some basic rules for evaluating evidence. What is truth? How do you evaluate data?

Something that should be very obvious by now is that the rules you are using to establish truth are very, very different from the ones that most physicists are using, which is the point that I'm trying to make to you.

But, I actually sympathize with your position. It is really difficult to realize the assumptions that are being made if everyone has been making them for a long time. Agreement is a very compelling social force. Religions get almost all their enormous social power from just such long held unwarrented agreement.

You have to make some assumptions about the world, but the thing that physicists (and for that matter Catholic theologians) try to do is to be explicit about those assumptions. What I'm trying to tell you is that the assumptions you are making and the arguments that you are trying to establish, simply will not hold water among most cosmologists.

It's useful to talk to people with radically different assumptions about how the world works, because then you figure out how you are seeing the world and why. Something that should be obvious to you is that if you are trying to create a moral or ethical code around science, you are likely to get nowhere. Science is all about doubt, and getting up in front of people and saying "I just don't know."

The observations are as follows. Every material phenomenon that humans have ever observed have proven to be finite in extent and multiply manifest. All of them.

You keep saying that and I say that's not true.

The only phenomenon that has not been proven to be finite or multiply manifest is the expanding profile of the galaxy cluster's which imply the Big Bang.

Supernova 1987A, the collapse of Lehman Brothers, the electric field of the electron. Electric fields are not finite. Supernova 1987A and the collapse of Lehman Brothers are not multiply manifest. There are things that are finite and multiple manifest, but as far as "all phenomenon" that's not true, and that's not even close. Most of the things I study *aren't* multiply manifest or finite, and I think that's true for physicists in general, which is why no one seems to be agreeing with you.

Ask yourself, how do we usually find out that something we thought was the biggest object in the universe, turned out not to be? We find a way to see far enough that we see evidence of another example of what we thought the largest object, and collectively *those* objects form the next thing we call the largest object. See a trend here?

House prices between 2001 and 2005 were going up radically. See a trend here?

 

[twofish-quant]

If you want to explain my philosophy of truth. Truth=survival. If you jump off a 100 story building, you aren't going to leave too many descendants. If you jump off a five story building, you break some bones and learn never to do that again. Over time (i.e. hundreds of millions of years), organisms become programmed to look for truth.

This matters with modeling, because in the last year the world just took an economic jump off a five story building, and so people have concluded that it's not a good idea to do that again. A lot of the problems involved taking models that were perfectly good for one domain and applying it where there was no data to support them. People took models of collaterialized default obligations that work beautifully with junk bonds and applied them to mortgage securities, which was a really really bad idea. (The basic problem is that when say an electronics factory goes bust, then the odds are that the concrete factory next to it still works. If one subprime mortgage goes bad, then chances are that all of the subprime mortgages in the world are also going bad at the same time.)

A lot of what I do involves thinking about probability and correlations, and there are some arguments that you use that get you punched in the gut by reality and some arguments that don't, and the probability arguments that the OP are using are a bit too much like the probability arguments that people used to justify a lot of the CDO non-sense. Certainty will get you killed in the markets. If you can model interest rates with 70% certainty, you are going to be a billionaire. The thing is that most people can't and the one's that seem to usually just got lucky.

It's actually curious but the mathematics of finance resemble a lot the mathematics of general relativity. There is a lot of modelling surfaces and curvative.

 

[Cuetek]

Agree again. On a quick look at the 'mathematical proof', it looks pretty 'serious' (especially to a layman like me).

As a layman maybe you should stay away from the math. Bayes theorem is a probability theorem. Probability theorems by definition cannot be proof of anything. Hope this helps.

But if you scrutinize what OP is really saying, the bottomline is:

I have looked at neutrons, atoms, planets, stars, galaxies, cluster and Big Bang. My theory works on these objects, and I know that the Bayesian Theorem (that just calculates probabilities) can help me to promote the idea that these relations also continues at the 'next level' – even if it has absolutely nothing to do with the physical reality.

Good lord, listen to yourself. You are saying that the rest of the examined universe has "absolutely nothing to do" with predicting the nature of the part of it that lies just beyond our view. Good luck with that philosophy.

-Cuetek

 

[Cuetek]

Absolutely. Then you do calculations, test that assumption against observations, and for the observations we can do, those assumptions seem to work.

I have. It's a high probability based on both the widely extant structure of the universe and the history of our discovery of it.

Since we have no data, saying whether something is regional or global is something that we can't say.

We have plenty of data. I use that data (the visible universe) to predict that we should look not for homogeneity but for differentiation (a dipole in the CMB for example).

You are making theological statements that are not supported by data.

Wrong. We are both projecting the visible data beyond our view. You with the cosmological principle and me with the hierachical principal. Mine is more extensive than yours is all.

As I mentioned there is nothing particularly wrong with that as long as you realize that you are going past the available data.

The cosmological principle goes past it as well. Apples and apples.

Ultimately, the problem is that you look at things, and you think "everything supports infinite hierarchy" whereas the astrophysical objects that I study tend not to have "infinite hierarchies."

Wrong. I only say that we should presume hierarchical diversity instead of homogeneity in the neear term. The new data will tell the tale (probably just like it has in the past showing us more and more of the hierarchy).

The problem is that if you try to create this sort of cosmology you end up with something that just doesn't fit the data. Any cosmology that assumes larger structures at this point just ends up being either irrelevant or inconsistent with the data. If you assume a self-similar fractal distribution of galaxies, you end up with galaxy distributions that just don't match what we see.

The homogeneity has only been measuered (WMAP) to a fine enough degree to assume a homogeneity for about 5000 times the diameter of the particle horizon (14 bil Lt Yr.) Anything beyond that, the distribution could begin to change up or down and we'd have no way of knowing.

Saying "I don't know" is not a bad habit. I think it's a good habit. If you can't see distant galaxies, you can't assume that anything is or is not there.

But the cosmological principle doesn't say that does it?

No it doesn't. The problem is that if you have something that is localized in space, then it's momentum becomes non-localized, and that means that any hierarchy gets washed out. Unless there is something basically wrong with our understanding of Heisenberg, then there are no new structures between the scales that we can see and Planck's length. Once you get to Planck's length, then quantum mechanics and GR become inconsistent, so there is new physics at smaller scales.

Also quantum mechanics imposes a lot of information limits. One electron is exactly the same as any other electron which means that there is no internal structure that you can use to mark an electron. The trouble with assuming structure is that you run into the Gibbs paradox. Basically the behavior of gases depends on the statistics of quantum mechanical structure. If there was structure, then gases would behave differently, because you could distribute energy across more states.

Translating what is giong on at infinitesimal levels seems to be very enigmatic. Nonetheless, quarks make nutrons make atoms make molecules, etc etc. hierarchy.

Actually, we *do* have a pretty good idea of what happens at the scale of quarks.

Sure we do.

(schnype) Ran out of time. Got to go to work.

House prices between 2001 and 2005 were going up radically. See a trend here?

Yes the trend went up. But the larger trend shows that house prices went up and down a lot. That's why I use all the scales of the universe rather than just one. See the trend here?

-Cuetek

 

[DevilsAvocado]

You need to run bayesian statistics using multiple assumptions to derive boundaries.

Agree. And most of all – you need not to exclude things that doesn’t fit the 'predefined' theory, like quarks.

 

[twofish-quant]

I have. It's a high probability based on both the widely extant structure of the universe and the history of our discovery of it.

However the fact that your arguments and probabilities seem to be unconvincing to people that work in cosmology and astrophysics should at least give you some cause for concern. In particular, unless you want to conclude that most astrophysicists are irrational, you do have to admit that rational people can at least debate and disagree with the principles that you suggest.

They may be self-evidently true to you, but they aren't to me, and they don't seem to be self-evidently true to most of the people in the field that have commented on this thread.

Part of the reason I don't want to go past the data, is that we are already making a ton of crazy assumptions and suppositions in our cosmological models of the universe. There's no point that I can see in adding anything that the data doesn't absolutely force you to make.

Wrong. We are both projecting the visible data beyond our view. You with the cosmological principle and me with the hierachical principal. Mine is more extensive than yours is all.

No I'm not. I'm saying that we can't make many statements about the ultra large scale structure of the universe. The assumption of a homogenous universe is something like a spherical cow or a flat earth. It's a guess that seems to give the right numbers, but it may be totally wrong for the problems I'm interested in, and it's obviously wrong for some of the one's that I'm not. The standard big bang model assumes that the Earth and sun do not exist, and that the whole universe is filled with a homogenous gas.

It's a workable model. Whether it's the ultimate truth or not is anyone's guess, but I'm a physicist. I'm in the numerical modeling business and not the ultimate truth business.

The big difference is that I'm at least willing to consider that the cosmological principle might will be wrong, and it's good for nothing more than "artistic inspiration." The other difference is that I can calculate helium and deuterium abundances, and you can't.

Wrong. I only say that we should presume hierarchical diversity instead of homogeneity in the near term.

Why? It just makes it more difficult to calculate deuterium abundances and galaxy clustering coefficients or think about galaxy formation.

The homogeneity has only been measuered (WMAP) to a fine enough degree to assume a homogeneity for about 5000 times the diameter of the particle horizon (14 bil Lt Yr.) Anything beyond that, the distribution could begin to change up or down and we'd have no way of knowing.

The point of a theorist is to come with observational tests. If you are convinced that the universe is hierarchical, then this is great for "artistic inspiration". Come up with some observational signature for that sort of model. There's a whole industry of people trying to do just that. It's a hard problem.

Suppose the density of the universe suddenly went up or down 6000 times the diameter of the particle horizon. What happens? Is it something we can detect? It is something that we can lobby Congress for to build some instrument that we can detect? What sort of statistics are we looking for?

But the cosmological principle doesn't say that does it?

What I'm trying to get across is what a "principle" means in physics. It's artistic inspiration. Invoking a principle is a start of a conversation and not a resolution to one. The reason for this is that people have invoked principles that turned out to be wrong. Two examples of this are the perfect cosmological principle in the steady-state universe or the static universe principle. You are not going to win an argument in physics by invoking any sort of principle, because so many of them have ended up being just wrong.

 

[DevilsAvocado]

As a layman maybe you should stay away from the math. Bayes theorem is a probability theorem. Probability theorems by definition cannot be proof of anything. Hope this helps.

Thanks for the advice and the very friendly attitude! Though I have not yet decided if I will accept your mentorship. It depends on if you can prove your own mathematical status, by explaining your choice of Boolean values in your own "numerical justification" of this very weird 'theory':

p(E|Fm) = 1 (true)
p(E|~Fm) = 0.5 ('half-true' !?)​

This is completely nutty and I haven’t decided if you do this on purpose to fit the 'theory' – or you just don’t know what you are doing, and don’t understand the rules of Bayes' Theorem.

The Boolean negation of true is not 'half-true', it’s false (0) and as a 'mathematical grand genius' you should know that.

If you avoid answering this mathematical question, https://www.physicsforums.com/showpost.php?p=2507923&postcount=50", I can only come to the conclusion that you are even more a layman than me, and then naturally the 'mentorship' is rejected. Sorry.

 

[DevilsAvocado]

As a layman maybe you should stay away from the math. Bayes theorem is a probability theorem. Probability theorems by definition cannot be proof of anything. Hope this helps.

Good lord, listen to yourself. You are saying that the rest of the examined universe has "absolutely nothing to do" with predicting the nature of the part of it that lies just beyond our view. Good luck with that philosophy.

-Cuetek

Maybe it’s a good idea you start listen to yourself. This is getting pretty close to the physics of Fawlty Towers.

Since when is science, physics and cosmology the art of statistically "predicting the nature"!? Running Bayes' Theorem to find a law of nature!? What would the world look like if Einstein worked for years on the solution for something like p(E|mc2)...!? OMG

The key to this is "the part of it that lies just beyond our view". When do you expect to get any data from that just beyond our view? Any measurements? Anything, besides homemade bayesian assumptions...?

This is a play with words and half-rotten math.

Let’s skip the math, and bring it down to (my) hillbilly-level, so we all can join the discussion. Now what you are saying is basically this:

1) A foreigner without maps visits Las Vegas for the first time.
2) He gets bored, and decides to visit Great Basin National Park, and rents a car.
3) After driving 40 km on the very straight U.S. Route 93 highway in Nevada, he gets extremely tired.

4) He’s a player and knows how to calculate probabilities. He runs Bayes' Theorem in his head and finds that the odds for the highway to continue like this are very good, 99.6%.
5) He activates the cruise control and falls asleep, feeling safe.
6) 10 km later he crashes at Pahranagat Valley.

Now, when we react on this behavior and don’t want to join the 'bayesian car', you act like a clown and don’t want to hear what we are saying...

"Probability theorems by definition *cannot* be proof of anything."

I absolutely agree.

 

[Cuetek]

However the fact that your arguments and probabilities seem to be unconvincing to people that work in cosmology and astrophysics should at least give you some cause for concern. In particular, unless you want to conclude that most astrophysicists are irrational, you do have to admit that rational people can at least debate and disagree with the principles that you suggest.

Well, as arrogant as it seems, I am saying that most astrophysicists are irrational on this one point. I'm saying that this irrationality is due to adherance to an old concept that is imminently understandable, but one that is by it nature is impossible to prove or disprove. I am saying that the more probable presumption is that the hierarchy of the universe will prevail. I am not saying that the cosmological principle is worthless. I am saying that it is only locally relavant.

They may be self-evidently true to you, but they aren't to me, and they don't seem to be self-evidently true to most of the people in the field that have commented on this thread.

Part of the reason I don't want to go past the data, is that we are already making a ton of crazy assumptions and suppositions in our cosmological models of the universe. There's no point that I can see in adding anything that the data doesn't absolutely force you to make.

I totally agree with the "we've already gone too far. But I think such trends are due to lack of data and prior insufficient assumptions that have led to us relying to completely on highly developed math models and not data. Many of those models are based on assumptions like the cosmological principle. It's not that scientists say that they believe the cosmological principle is true, but their research is predominantly based on how the cosmos would behave if it were true. Going back to the data, there is more data that says somewhere out there we will find that the cosmological principle will not longer be useful. If were are going to go too far, we should look at the widest possible interpretation of the data.

Bayes theorem is widely used in cosmology. The cosmological principle is, in fact, Bayesian. You look at the homogenety and imagine it goes much farther. But all Bayesian projections are limit at both ends of the scale. So too, in all probqability, will the hierarchical assumption be found wanting at some scale. But at our current point in history, it is more useful to guide our search for the nature of the universe beyond our instrumentation. More and more we will need to make wider assumptions as the data gets harder and harder to come by.

No I'm not. I'm saying that we can't make many statements about the ultra large scale structure of the universe. The assumption of a homogenous universe is something like a spherical cow or a flat earth. It's a guess that seems to give the right numbers, but it may be totally wrong for the problems I'm interested in, and it's obviously wrong for some of the one's that I'm not. The standard big bang model assumes that the Earth and sun do not exist, and that the whole universe is filled with a homogenous gas.

It's a workable model. Whether it's the ultimate truth or not is anyone's guess, but I'm a physicist. I'm in the numerical modeling business and not the ultimate truth business.

You are going to make an assumption one way or the other. Your models are fine, but should be formally limited to some 5000 times the particle horizon. The universe is strange. Think about the boson of gravity. While some bosons are bigger than others. No one in their right would think that a boson could be really big. But if the hierarchical principle is true, the forces that govern the structures at meta scales would have to be bigger and bigger as well.

The weak nuclear is very short range. The strong nuclear acts across a larger range. The electrical force, while theoretically infinite, acts mostly across molecular distances and some larger scales like lightning and even some theoretical cosmic scales. Gravity is clearly the farthest ranging, but near indetectable at molecular scales. So it would be prudent to imaging newer forces emerging at meta scales "above" the vis universe scale.

The boson for those meta scale forces might be huge by quantum standards. What if the graviton was the black hole? What if all matter derived gravity from by induction from being in the grip of a black hole field. If the big bang were a massive black hole most of the matter might still be on one side of us and we may be in an enroumous meta scale gravitational field. Perhaps it is ultimately that field alone which contributes the gravity ehibited by matter in it's grip.

I'm not saying this is how it is, just how a hierarchy might behave at larger scales. If the hierarchy prevails there will be larger forces of scale to organize the structures with additional meta scale explanations. Anything that moves us into such mindsets would be valuable if the hierarcy is true. And I feel the data we do have suggests the hierarchy is far more likely to prevail than is the homogeneity. Call it philosophical if you like, but it's a data-based philosophy and the theorist is going to have to make one or the other assumption. Assuming the CP is limited to 5000+ x the particle horizon makes both assumptions possible. (Actually, make it 50,000+ times the particle horizon, because it's absolutely homogenous out to 5000, so it will most probably remain roughly homogeneous much farther out.)

The big difference is that I'm at least willing to consider that the cosmological principle might will be wrong, and it's good for nothing more than "artistic inspiration." The other difference is that I can calculate helium and deuterium abundances, and you can't.

The CP is perfectly fine for local modeling, like curvature of the regions, just not for modeling the curvature of the "universe".

Why? It just makes it more difficult to calculate deuterium abundances and galaxy clustering coefficients or think about galaxy formation.

The CP is fine for local (5000+ times the particle horizon) calculation. The hierarchical principle should be used with hypothesizing beyond that limit.

The point of a theorist is to come with observational tests. If you are convinced that the universe is hierarchical, then this is great for "artistic inspiration". Come up with some observational signature for that sort of model. There's a whole industry of people trying to do just that. It's a hard problem.

The data will tell the tale sooner later no matter what. I'm just saying what the tale will more probably be in the long run. Such presumption will accelerate the process over waiting for the data to accurately limit the prior presumption.

Suppose the density of the universe suddenly went up or down 6000 times the diameter of the particle horizon. What happens? Is it something we can detect? It is something that we can lobby Congress for to build some instrument that we can detect? What sort of statistics are we looking for?

I've found numerous papers supporting the CP as fact (homogeneity inevitable) and only one paper defining it's limits (homogeneity currently reliable only out to 5000 x particle horizon). As I've suggested looking for a faint dipole in the CMB radiation is the first thing I'd do, or look for one side of the sky to have slightly larger voids etc. But it's what the expectation of inhomogeneity does to the thoerist's mindset that would have the most impact on research.

What I'm trying to get across is what a "principle" means in physics. It's artistic inspiration. Invoking a principle is a start of a conversation and not a resolution to one. The reason for this is that people have invoked principles that turned out to be wrong. Two examples of this are the perfect cosmological principle in the steady-state universe or the static universe principle. You are not going to win an argument in physics by invoking any sort of principle, because so many of them have ended up being just wrong.

I am gratified by the way you describe it above. You didn't sound so equivocal when we first started discussing this. My own grasp as to how to talk about it has improved as well. Peace. -Mike Harmon

 

[Cuetek]

p(E|Fm) = 1 (true)
p(E|~Fm) = 0.5 ('half-true' !?)​

This is completely nutty and I haven’t decided if you do this on purpose to fit the 'theory' – or you just don’t know what you are doing, and don’t understand the rules of Bayes' Theorem.

The Boolean negation of true is not 'half-true', it’s false (0) and as a 'mathematical grand genius' you should know that.

In Bayes theorem the variables you mention above are necessarily probabilities, not Boolean variables. The allowable values of these varables range inclusively between 0 and 1. If you like you can fudge them all around however you like to make the results come out however you see fit. That's the subjective nature of Bayes probability theorem. The assignment of the variables is the whole deal. I will be glad to debate why I chose the values I did, but you need to bone up on probability theorms first.

 

[twofish-quant]

I am saying that the more probable presumption is that the hierarchy of the universe will prevail. I am not saying that the cosmological principle is worthless. I am saying that it is only locally relavant.

What I'm saying is you are basically misinterpreting how astrophysicists think.

1) The cosmological principle is not some sort of dogma, but a guess and a rough rule that allows people to make calculations
2) Without data, it's impossible to make firm statements about whether it is globally true or not. It *is* possible with the current data to say that assuming the cosmological principle allows us to make predictions about the universe that seem to accord with observations.

But I think such trends are due to lack of data and prior insufficient assumptions that have led to us relying to completely on highly developed math models and not data. Many of those models are based on assumptions like the cosmological principle.

Right, because you can then take the model and make predictions about the universe. The point that I'm making is that just because an astrophysicist makes an assumption in a model, doesn't mean that they think that assumption is true. If you want to *disprove* the cosmological principle, then what you need to do is to create a model that *assumes* that the principle is true, show that that model inherently creates results that don't match observations.

The highly developed math is because it is a really, really painful and difficult thing to go from theory to observational test. Suppose you were to assert that the density of the universe falls off very strongly an 2x the observational horizon. Going from that assumption to COBE power spectrum measurements is extremely painful.

It's not that scientists say that they believe the cosmological principle is true, but their research is predominantly based on how the cosmos would behave if it were true.

Which is exactly the approach you need to take if you doubt that it is true. Let's assume that the cosmological principle is false. You predict X. You see X. That tells you absolutely nothing. So let's assume that the cosmological principle is true. You predict X. You see not-X. At this point the cosmological principle is proven wrong.

If you were seeing increases in the power spectrum at higher and higher scales, then we'd have a big problem. If there were systematic differences in the CMB in different parts of the sky, we'd have a big problem. You *assume* something is true, so that you have some idea what to look for in order to prove that it is false.

Your models are fine, but should be formally limited to some 5000 times the particle horizon.

Why? I make statements about what the world looks like 10^6 times the particle horizon and that see if it makes any difference.

The CP is fine for local (5000+ times the particle horizon) calculation. The hierarchical principle should be used with hypothesizing beyond that limit.

Why? What you really need to do is to make a million different hypothesis and then throw them against the wall to see what sticks.

As I've suggested looking for a faint dipole in the CMB radiation is the first thing I'd do, or look for one side of the sky to have slightly larger voids etc.

Which is what people have done.

But it's what the expectation of inhomogeneity does to the thoerist's mindset that would have the most impact on research.

What I'm saying is that I think you are misinterpreting what theorists are doing. Most papers in cosmology have nothing to do with the ultra-large scale structure of the universe, so there people assume the cosmological principle because the math is simpler, and if what you are doing isn't impacted by the ultra-large scale structure of the universe, you want to assume spherical cows and flat Earth's. Most papers in astrophysics outside of very narrow fields use Newtonian gravity because GR is just a pain to calculate.

If you are *expecting inhomogenity* then you assume homogenity. At that point you write papers invoking the cosmological principle, figure out the implications, and the look for deviations from observations. The problem with create models of inhomogenity is that once you've done that, you've restricted yourself to a particular model, which causes problems if both the CP and the inhomogenous model is wrong.

If you want to kill the CP, you need to absolutely avoid presenting an alternative model, and you need to focus on writing papers that assume the CP is true.

Also you be careful not to extrapolate someone's beliefs from the papers that they write. I don't know whether the CP is correct or not, but I'd certainly be depressed if it where.