Could the Universe be infinite?

[willard]

ok so I've been curious about this theory for a while but just haven't started digging into it until tonight :

if energy creates gravity no matter how small, couldn't the universe be infinite and coincide with Newtons second law of thermodynamics;
if when the heat death of the universe happens the potential energy starts pooling together and eventually creates a black hole from the density of all that energy in one place, and the heat from the black hole changes the potential energy into kinetic and that turns into quirks and then protons neutrons electrons atoms and what not.

I apologize if this isn't understandable I've not studied physics or anything this has just been bugging me and so I thought I would ask here

 

[PeroK]

If you are asking whether the universe could be infinite in spatial extent, then the answer is yes. Currently the best cosmological model suggests the universe may be infinite. To put it another way: there is no evidence that it is finite.

I'm not able to make sense of the rest of your post.

 

[sysprog]

. . .Newtons second law of thermodynamics . . .

Historically, the Second Law of Motion is credited to Isaac Netwon, and the Second Law of Thermodynamics is credited to Nicolas Carnot.

 

[mcastillo356]

Hi, willard
Very interesting. There is informative literature, but your post makes me think you deserve more: go ahead, study!
Greetings!
PS: I make the same questions to myself.

 

[jbriggs444]

if when the heat death of the universe happens the potential energy starts pooling together and eventually creates a black hole from the density of all that energy in one place

You seem to be contemplating a universe in which an eventual collapse occurs. At one time that scenario was considered possible. However, measurements have shown that our own universe is well beyond the conditions in which an eventual collapse will occur.

The heat death of the universe will take place when the universe is cold and dark and sparse and all of the black holes have evaporated. [At least if our understanding of black hole evaporation is well founded].

The topology around the eventual singularity in a hypothetical collapsing universe is not a Schwarzschild "black hole", but we can let that slide.

The universe is not Newtonian. It follows the rules of general relativity instead.

 

[willard]

Historically, the Second Law of Motion is credited to Isaac Netwon, and the Second Law of Thermodynamics is credited to Nicolas Carnot.

oh i knew that thank you

 

[Buzz Bloom]

To put it another way: there is no evidence that it is finite.

Hi @PeroK:

I wonder if your "no evidence" might possibly be an exaggeration. Page 40 of

https://www.cosmos.esa.int/documents/387566/387653/Planck_2018_results_L06.pdf​

gives the equation 47b saying:

The joint results suggests our Universe is spatially flat to a 1 σ accuracy of 0.2 %.​

If the mean of Ω_k is zero, a 1 σ accuracy (assuming approximately a Gaussian distribution) gives quite a bit of plausible evidence that it is only about 68% likely that the universe is flat, and 16% it is positive, and 16% it is negative. However, the mean is not zero. It is 0.0007, with σ = 0.0019. This indicates that if the universe is not flat, it is much more likely to be finite than infinite.

Regards,
Buzz

 

[sysprog]

@Buzz Bloom, that's conjecture; not evidence.

 

[Buzz Bloom]

that's conjecture; not evidence.

Hi @sysprog:

I would much appreciate it if you can explain to me the nature of the non-conjecture evidence that the universe is flat, and how this evidence is superior (except for it having a greater probability of correctness) to the "evidence" I presented to support the finite universe possibility.

Regards,
Buzz

 

[sysprog]

Hi @sysprog:

I would much appreciate it if you can explain to me the nature of the non-conjecture evidence that the universe is flat, and how this evidence is superior (except for it having a greater probability of correctness) to the "evidence" I presented to support the finite universe possibility.

Regards,
Buzz

I didn't assert a possibility of existence of any such evidence, so I don't think that's it's incumbent on me to postulate what could constitute such evidence.

I merely agreed with @PeroK's assertion that there isn't any.

I repeat that the stuff about probabilities that you characterized as evidence is conjecture and not evidence.

There's no way to test the postulated probabilities, so they're at best conjectures.; there's no evidence to support them, so they aren't themselves evidence. You would have to employ a non-standard defition of 'evidence' to say otherwise, and in doing that, you would depart from common language.

If you're just playing around here, @Buzz Bloom, please be reminded that some of the readers might take the nonsense seriously, especially when they can tell their friends that a PF Science Advisor said it; you are well aware that no human utterance can be evidence for or against a non-testable hypothesis.

 

[Buzz Bloom]

I didn't assert a possibility of existence of any such evidence, so I don't think that's it's incumbent on me to postulate what could constitute such evidence.

I merely agreed with @PeroK's assertion that there isn't any.

I repeat that the stuff about probabilities that you characterized as evidence is conjecture and not evidence.

There's no way to test the postulated probabilities, so they're at best conjectures.; there's no evidence to support them, so they aren't themselves evidence. You would have to employ a non-standard defition of 'evidence' to say otherwise, and in doing that, you would depart from common language.

If you're just playing around here, @Buzz Bloom, please be reminded that some of the readers might take the nonsense seriously, especially when they can tell their friends that a PF Science Advisor said it; you are well aware that no human utterance can be evidence for or against a non-testable hypothesis.

Hi @sysprog:

I am not "just playing around". I am uncertain about the criteria which constitutes cosmology "evidence". I well understand that there is no certainty in physics, but evidence does exist generally (but not always) to provide some support for commonly accepted conjectures.

The @ParoK quote which I responded to in my post #7 seem to say that there is a difference between a flat universe and a finite universe with respect to flat having evidence and the finite not. I now interpret the quote above is saying that you choose not to discuss the nature of the evidence which is what the ParoK quote seemed to imply exists.

Your statement that "There's no way to test the postulated probabilities, so they're at best conjectures," seems to say that probabilities are never evidence. I find that articles like the one I quoted is about probabilities and nothing else. I gather that you might be saying that articles such as

https://www.cosmos.esa.int/documents/387566/387653/Planck_2018_results_L06.pdf​

do not include any evidence regarding the probabilities of the conjectures they discuss.

Regards,
Buzz

 

[PeroK]

Hi @sysprog:

I am not "just playing around". I am uncertain about the criteria which constitutes cosmology "evidence". I well understand that there is no certainty in physics, but evidence does exist generally (but not always) to provide some support for commonly accepted conjectures.

The @ParoK quote which I responded to in my post #7 seem to say that there is a difference between a flat universe and a finite universe with respect to flat having evidence and the finite not. I now interpret the quote above is saying that you choose not to discuss the nature of the evidence which is what the ParoK quote seemed to imply exists.

Your statement that "There's no way to test the postulated probabilities, so they're at best conjectures," seems to say that probabilities are never evidence. I find that articles like the one I quoted is about probabilities and nothing else. I gather that you might be saying that articles such as

https://www.cosmos.esa.int/documents/387566/387653/Planck_2018_results_L06.pdf​

do not include any evidence regarding the probabilities of the conjectures they discuss.

Regards,
Buzz

I'm afraid I can't follow this. What evidence is there that the universe is finite? And what is thereby the estimated size of the universe?

 

[sysprog]

I think that probabilities are or should be based on evidence, but they are not themselves evidence, and without evidence to support them, they are at best conjectures. If I observe a roughly 50-50 split on a hundred tosses of a coin, I can say that I have evidence, i.e. my observations, and correlaries, e.g.the regular-disc nature of the coin, to support my saying that on any toss, either side of the coin has approximately a 50% probability of turning up. But I don't have any such observation that I can point to regarding past experiences of finite and non-finite universes.

 

[Buzz Bloom]

I'm afraid I can't follow this. What evidence is there that the universe is finite? And what is thereby the estimated size of the universe?

Hi @PeroK:

I think my view of the "evidence" does not match yours. What I see as evidence is the collection of cosmological observation data that leads to values (with ranges for probabilistic uncertainty) for the standard five parameters with respect to the Friedman equations,

https://en.wikipedia.org/wiki/Friedmann_equations#Detailed_derivation​

Ω_r, Ω_m, Ω_k, Ω_Λ, and H₀.​

The five values constitute the best fit corresponding to the cosmological data being modeled. In particular the value of the parameter Ω_k determines the best estimate for the universe curvature. Since the flat universe corresponds to the exact value Ω_k = 0. The "evidence" for flatness depends on the fact that the model value for Ω_k is close to (but not exactly) zero. This fact leads to a conjecture regarding the existence of the inflation period. As best as I can understand it, this closeness to zero constitutes "evidence" that the universe is flat. I do not know of any specific evidence that the likelihood of flatness has any specific probability of being a correct model. On the other hand, the value of the mean and standard deviation for Ω_k gives a basis for a specific probability that the universe is finite rather than infinite. Regarding the size of the finite universe, an approximation of a probability distribution for the radius of the hypersphere 3D finite universe can be derived, as well as a probability distribution of the curvature of the hyperbolic infinite universe.

Regards,
Buzz

 

[Hornbein]

To make a long story short, the measurements are consistent with a flat universe. Thats as far as I would go as to assigning a probability. The possibility of repeated trials is limited.

 

[Buzz Bloom]

the measurements are consistent with a flat universe.

Hi @Hornbein:

Is your statement (quoted above) based on the value of Ω_k being close to zero by a certain amount? If the basis is as I bolded the above segment, then is it not also the case that a positive value of Ω_k is consistent with a finite universe? If your basis is not what is bolded, can you clarify what the specific definition of the measurement is that is consistent with flatness?

Regards,
Buzz

 

[George Jones]

the standard five parameters with respect to the Friedman equations,

https://en.wikipedia.org/wiki/Friedmann_equations#Detailed_derivation​

Ω_r, Ω_m, Ω_k, Ω_Λ, and H₀.​

The five values constitute the best fit corresponding to the cosmological data being modeled.

There are only four independent parameters here, i.e., it always the case that
$$1 = \Omega_k + \Omega_r + \Omega_m + \Omega_\Lambda.$$

 

[Buzz Bloom]

But I don't have any such observation that I can point to regarding past experiences of finite and non-finite universes.

Hi @sysprog:

I am interpreting the quote above as saying that a probability is only evidence if it is derived from past multiple trials, and that a probability derived from other methods is never evidence. If this is a correct interpretation, can you please post a reference to an article or a text that explains the reason for the usage of this limited definition?

A quote from https://en.wikipedia.org/wiki/Bayesian_probability:

Bayesian probability is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation[1] representing a state of knowledge[2] or as quantification of a personal belief.[3]​

I confess my usage of Bayesian probabilities is very limited, but I understand that a sequence of trials is not a Bayesian method. Would you claim that a Bayesian probability would not be evidence?

Regards,
Buzz

 

[Hornbein]

To use Baysian inference one has an a priori estimate of the probability. I don't see there can be such a thing in this case.

 

[Buzz Bloom]

There are only four independent parameters here

Hi @George Jones:

I still count five parameters, even though the sum of four of them is always equal to 1. One might say that there are only four independent parameters since each of the four Omegas can be designated as being dependent on the other three.

Regards,
Buzz

 

[Buzz Bloom]

To use Baysian inference one has an a priori estimate of the probability. I don't see there can be such a thing in this case.

Hi @Hornbein:

I did a search in the Planck_2018 paper. I did not find any occurrence of "Bayesian" in the body, but there were five references to "Bayesian" in the list of references.

Cardona, W., Kunz, M., & Pettorino, V., Determining H0 with Bayesian hyper-
parameters. 2017, JCAP, 3, 056, arXiv:1611.06088

Dirian, Y., Changing the Bayesian prior: Absolute neutrino mass constraints in
nonlocal gravity. 2017, PRD, 96, 083513, arXiv:1704.04075

Feeney, S. M., Mortlock, D. J., & Dalmasso, N., Clarifying the Hubble con-
stant tension with a Bayesian hierarchical model of the local distance ladder.
2018a, MNRAS, 476, 3861, arXiv:1707.00007

Iliadis, C., Anderson, K., Coc, A., Timmes, F., & Starrfield, S., Bayesian
Estimation of Thermonuclear Reaction Rates. 2016, ApJ, 831, 107,
arXiv:1608.05853

Mason, C. A., Treu, T., Dijkstra, M., et al., The Universe Is Reionizing at z ∼ 7:
Bayesian Inference of the IGM Neutral Fraction Using Lyα Emission from
Galaxies. 2018, ApJ, 856, 2, arXiv:1709.05356

I consider this as "evidence" that Bayesian probabilities play some role in the work done for producing the Planck_2018 paper. The following 2019 thread also discusses this concept clarifying some errors in my understanding.

https://www.physicsforums.com/threads/questions-about-error-range-from-bayesian-statistics.973377/​

​

Regards,
Buzz

 

[Buzz Bloom]

Hi @PeroK, @sysprog, @Hornbein:

I have been thinking about the issue of "evidence" as it relates to cosmology, and I found an interesting (to me) article on the topic. However, since the article discusses the issue as philosophical, I am concerned about giving the reference since I understand philosophy to be a no-no in the Physics Forums. I am not suggesting that this article should be discussed here, but only that it may be of interest to you as well as myself.

https://plato.stanford.edu/entries/cosmology/​

Regards,
Buzz

 

[sysprog]

@Buzz Bloom, I'm by no means an authority here, but I can say that yes, you're right about philosophy being off-limits on PF - the staff consensus is that even in 'lounge area' discussions, it tends to produce content that isn't in keeping with PF's mission ##-## of course, there are many places on the net where you can commingle discussion of physics and philosophy, but PF isn't one of them ##-## thanks for understanding.

 

[Hornbein]

Hi @PeroK, @sysprog, @Hornbein:

I have been thinking about the issue of "evidence" as it relates to cosmology, and I found an interesting (to me) article on the topic. However, since the article discusses the issue as philosophical, I am concerned about giving the reference since I understand philosophy to be a no-no in the Physics Forums. I am not suggesting that this article should be discussed here, but only that it may be of interest to you as well as myself.

https://plato.stanford.edu/entries/cosmology/​

Regards,
Buzz

Seems quite orthodox to me. Many big mysteries remain in this field.

As to the "flatness" or lack thereof of the Big U:

• Flatness: An FLRW model close to the “flat” model, with nearly critical density at some specified early time is driven rapidly away from critical density under FLRW dynamics if Λ=0Λ=0 and ρ+3p>0ρ+3p>0. Given later observations, the initial state has to be very close to the flat model (or, equivalently, very close to critical density, Ω=1Ω=1) at very early times.[37]

This is why it is "standard" to believe that the Universe is flat. It seems unreasonable to be that close to 1 at the beginning without actually being 1 for some as-yet unknown reason. But this is just a heuristic until some genius comes up with that reason.

 

[Buzz Bloom]

Hi @Hornbein:

I am puzzled by the statement that seems to imply that a finite universe has a curvature Ω_k which gets larger as the universe expands. Ω_k is inversely proportional to the radius R of the finite universe. Since the radius gets bigger over time, Ω_k gets closer to zero, that is closer to flatness. I think that the statement that the critical density (assumed to be greater than 1) approaches 1 (and then is larger as the size is smaller) is also incorrect. This was the case for Ω_Λ = 0, but not so for the currently best fit where Ω_Λ ~= 0.7.

Regards,
Buzz

 

[StevieTNZ]

@Buzz Bloom, I'm by no means an authority here, but I can say that yes, you're right about philosophy being off-limits on PF - the staff consensus is that even in 'lounge area' discussions, it tends to produce content that isn't in keeping with PF's mission ##-## of course, there are many places on the net where you can commingle discussion of physics and philosophy, but PF isn't one of them ##-## thanks for understanding.

As far as I'm aware, philosophical discussions are permitted at the discretion of the mentors.

Philosophical discussions are permitted only at the discretion of the mentors and may be deleted or closed without warning or appeal

If the ruling is no philosophy at all, then the rules need updating.

 

[sysprog]

As far as I'm aware, philosophical discussions are permitted at the discretion of the mentors.
If the ruling is no philosophy at all, then the rules need updating.

That's what it says in the Terms; however, recently this exchange took place:

Maybe I'm biased, as it was one of my undergrad fields of study, but what's the reason PF doesn't allow talk of philosophy - even in General Discussion/non-science sections?

Seems like all sorts of fields of study are allowed, from economics to art history, in the non-science-y areas.

We’ve never found a way to effectively moderate these discussions. They tend to end up in the Internet equivalent of Gresham’s Law, with uninformed and argumentative posters overwhelming the thoughtful and knowledgeable.

Shortly thereafter @Evo thanked the participants and closed the thread with post #14.

 

[StevieTNZ]

That's what it says in the Terms; however, recently this exchange took place:Shortly thereafter @Evo thanked the participants and closed the thread with post #14.

Then the rules need updating. Rt Hon @Greg Bernhardt

 

[StevieTNZ]

My ruling is, if the rules have not been updated yet, then philosophical discussions are allowed at the discretion of mentors.

This will be entered into Speakers' Rulings.

 

[WWGD]

I think that probabilities are or should be based on evidence, but they are not themselves evidence, and without evidence to support them, they are at best conjectures. If I observe a roughly 50-50 split on a hundred tosses of a coin, I can say that I have evidence, i.e. my observations, and correlaries, e.g.the regular-disc nature of the coin, to support my saying that on any toss, either side of the coin has approximately a 50% probability of turning up. But I don't have any such observation that I can point to regarding past experiences of finite and non-finite universes.

Well, one may use data to conduct a chi-square test to test for observed vs expected to test the fit of a probability model.

 

[collinsmark]

I suspect there's not enough available information to assign probabilities to any of the imagined "possibilities" regarding whether the universe is infinite or not. ["Possibilities" such as a) vast, yet closed, finite universe with slightly positive curvature, b) flat and infinite, c) flat and finite (e.g., torus shaped), d) open and infinite with a slightly negative curvature.]

Here's a tale of caution regarding probabilities which involve infinity. It's a purely mathematical story and doesn't even touch on the physical unknowns that are pertinent to this thread. If it's even on topic at all, it doesn't become on-topic until 13:30 or so of the second video.





Forgive me if this isn't on topic. This isn't exactly my area of expertise.

 

[Hornbein]

Hi @Hornbein:

I am puzzled by the statement that seems to imply that a finite universe has a curvature Ω_k which gets larger as the universe expands. Ω_k is inversely proportional to the radius R of the finite universe. Since the radius gets bigger over time, Ω_k gets closer to zero, that is closer to flatness. I think that the statement that the critical density (assumed to be greater than 1) approaches 1 (and then is larger as the size is smaller) is also incorrect. This was the case for Ω_Λ = 0, but not so for the currently best fit where Ω_Λ ~= 0.7.

Regards,
Buzz

I don't understand it. I just quote experts. There are discussions on this topic elsewhere at PF, I would suppose under Cosmology.

 

[Buzz Bloom]

Hi @collinsmark:

Wikipedia has a very clear explanation of the paradox.

https://en.wikipedia.org/wiki/Bertrand_paradox_(probability)​

It is an excellent example that the probability distribution of a variable depends on the method used to define an instance of the variable. A different method results in a different distribution.

I do not think this paradox is applicable to the topic of calculating the distribution of a cosmological variable, but I could be mistaken. I would be only moderately surprised if it should be found out that the recent strange difference in results between two methods of calculating H₀ is an example of this paradox.

Regards,
Buzz

 

[Evo]

Sorry, we really do not allow philosophy at PF, with the exception in Quantum Physics, at the mentors discretion in that forum, it's a fine line.

So thanks again to everyone for keeping the thread from going off the rails, but alas, time to close it before people outside of PF find the thread and begin quoting unicorns and fairies.