Quantum equations suggest the big bang never happened

  • Thread starter Thread starter iDimension
  • Start date Start date
  • Tags Tags
    Big bang Quantum
Click For Summary
Two physicists are challenging the Big Bang theory, suggesting it may never have occurred, which has sparked debate in the scientific community. Their approach utilizes quantum equations to propose an alternative model that eliminates the singularity associated with the Big Bang. While some participants in the discussion express skepticism about the validity of this claim, others argue that the work merits further examination despite its speculative nature. The conversation also touches on the limitations of current cosmological models and the complexities of understanding the universe's origins. Overall, the debate highlights the ongoing exploration of cosmological theories and the need for rigorous scientific scrutiny.
  • #31
magneticnorth said:
Hoyle's model was rejected with the discovery of the red shifted light spectrum of objects observed , indicating a velocity away from us . Hoyle basically argued that the redshift was being misinterpreted . Hence Hoyle was arguing that the Universe was perpetual . This is similar in part to what Das is indicating .
Yes but eternal inflation also says that the universe is eternal, and what's more, it is in a steady state overall-- much more like Hoyle's idea. So the Big Bang, plus eternal inflation, is actually very close to steady-state cosmology (not static cosmology, note). Putting in quantum corrections that eliminate eternal inflation thus takes the whole picture very far away from steady-state cosmology, I don't think Hoyle would have liked it, though he would have liked the absence of an origin.

I didn't say I subscribed to it , just noted an irony ,since what they are saying resembles more closely in one respect, to what Hoyle was arguing .
I realize you are not arguing in favor of the model, nor I against it, I'm merely pointing out that nothing has really changed because we have no new observations, and no more reason to believe in or reject inflation. Also, the Das model is farther from Hoyle's cosmology.
I just found it curious that Hoyle , in view of those discoveries , still held to the Steady State model .
I think Hoyle ended up with a view that was a lot like eternal inflation. His view was always consistent with cosmological redshifts, but not with changing populations in the universe, like quasars. But when it was clear quasars did exist, Hoyle just modified his views to allow some secular evolution, but still an ongoing creation process that preserves a steady state overall. That's pretty much exactly what eternal inflation is, but there would be no need to invoke eternal inflation with the Das approach.
 
Space news on Phys.org
  • #32
Ken G said:
Yes but eternal inflation also says that the universe is eternal, and what's more, it is in a steady state overall-- much more like Hoyle's idea. So the Big Bang, plus eternal inflation, is actually very close to steady-state cosmology (not static cosmology, note). Putting in quantum corrections that eliminate eternal inflation thus takes the whole picture very far away from steady-state cosmology, I don't think Hoyle would have liked it, though he would have liked the absence of an origin.

I realize you are not arguing in favor of the model, nor I against it, I'm merely pointing out that nothing has really changed because we have no new observations, and no more reason to believe in or reject inflation. Also, the Das model is farther from Hoyle's cosmology.
I think Hoyle ended up with a view that was a lot like eternal inflation. His view was always consistent with cosmological redshifts, but not with changing populations in the universe, like quasars. But when it was clear quasars did exist, Hoyle just modified his views to allow some secular evolution, but still an ongoing creation process that preserves a steady state overall. That's pretty much exactly what eternal inflation is, but there would be no need to invoke eternal inflation with the Das approach.
Thank you for that explanation Ken G . I would agree , especially with the discovery of quasars , which in Hoyle's Steady State would be contradictory . I think it important to learn what they are , because it is curious that galaxies at 13 billion light years look the same , one would think, looking back that far in time and expect to observe an evolution/ formation of galaxies .
 
  • #33
magneticnorth said:
The measurement of particles is by their electrical charge is it not ?

That's one way of measuring particles that have charge, yes. But it has nothing to do with what was being measured in the Casimir effect experiment. The plates were uncharged. The virtual particles in question (in the usual QFT model of the experiment) are virtual photons, not virtual electrons. Photons have no charge.

magneticnorth said:
Those detected in the Cassimir experiment were questioned by other scientists and the experiment deemd inconclusive , since all wavelengths were not measured , so that there was no assurance that those wavelengths had not already been existing .

Do you have a reference for any of this? It doesn't match what I know of the experiment at all.
 
  • #34
magneticnorth said:
Some theoretical quantum mathematicians implied that it is from such a vacuum , that is one, devoid of matter space and time , that by quantum fluctuations the Universe popped into existence and inflation began . They used the results of the cassimir experiment as a possibility for this .

Do you have a reference for the last statement? I'm not aware of anyone citing the Casimir effect in any theoretical discussion about the quantum fluctuation hypothesis for the origin of the universe.
 
  • #35
magneticnorth said:
Nothing comes from nothing , something can not come from nothing - as it relates to Inflation arising from a DeSitter quantum vacuum .

Are you saying you don't think this model of inflation is valid? If not, why not? Do you have a reference for such an argument?

magneticnorth said:
The Cassimir effect was used by some to hypothesize the inflation as possibly coming from such .

Again, do you have a reference?
 
  • #36
Ken G said:
the Big Bang, plus eternal inflation, is actually very close to steady-state cosmology (not static cosmology, note).

I don't think so, except in the trivial sense that the universe is eternal in both cosmologies. The steady-state cosmology involves a very different detailed description of the dynamics of the universe, compared to Big Bang + eternal inflation.
 
  • #37
PeterDonis said:
Do you have a reference for the last statement? I'm not aware of anyone citing the Casimir effect in any theoretical discussion about the quantum fluctuation hypothesis for the origin of the universe.
Yes , it is an article from Scientific American http://www.scientificamerican.com/article/what-is-the-casimir-effec/ If I have misinterpreted this , please specify .
 
  • #38
magneticnorth said:

I don't see anything here about the universe originating in a quantum fluctuation; it's just a discussion of the Casimir effect and the issue with the vacuum energy calculation. Also, there's nothing here about particles being detected; the experiments just measure the attractive force between the "mirrors".

(I also don't like the use of the word "mirrors" in the article; the Casimir effect is not limited to mirrors. I've been dissatisfied with Scientific American for some time now because of things like this; I'm not sure if it's the scientists taking liberties because it's not a peer-reviewed journal, or the editors just not catching misstatements, but either way it's disturbing.)
 
  • #39
PeterDonis said:
I don't think so, except in the trivial sense that the universe is eternal in both cosmologies. The steady-state cosmology involves a very different detailed description of the dynamics of the universe, compared to Big Bang + eternal inflation.
Different in detail, yes, but the overall spirit of the later versions of the steady-state cosmology is that it could exhibit oscillations that could mimic transitions from deceleration to acceleration, and associated oscillations in matter creation could create the illusion of finite-age universes being created. So you could have periods when matter is injected, followed by periods when the matter injection is turned off, and it all plays out against a secular exponential expansion. So that could sound a lot like eternal inflation, though the details certainly do differ a lot-- the steady state model does not trace back even to a recombination epoch. So I probably should not say "very close to" in terms of the details, only in terms of the overall philosophy of an eternal universe that shows locally transient behaviors that distinguish that place and time from the overall evolution of the universe as a whole, and look like origins of "bubble" universes as Hoyle called them.

The relevance to the Das paper is only that the concept of bubble universes is much more like eternal inflation than like what Das is saying, because Das only needs one of these "bubbles" and still gets that it exists eternally. Of course, if one simply regards a Das universe as a single "bubble" out of many, then again one can return to a picture much like Hoyle's, except for things like the rejection of an epoch of recombination or other such completely different states of the universe. The main distinction in kind between these models, however, is something that is not at all well constrained in any of these theories-- what is the meaning of time when it is not something corresponding to the period when we actually do have observations of the universe.
 
Last edited:
  • #40
PeterDonis said:
I don't see anything here about the universe originating in a quantum fluctuation; it's just a discussion of the Casimir effect and the issue with the vacuum energy calculation. Also, there's nothing here about particles being detected; the experiments just measure the attractive force between the "mirrors".

(I also don't like the use of the word "mirrors" in the article; the Casimir effect is not limited to mirrors. I've been dissatisfied with Scientific American for some time now because of things like this; I'm not sure if it's the scientists taking liberties because it's not a peer-reviewed journal, or the editors just not catching misstatements, but either way it's disturbing.)
Thank you for that clarification .
 
  • #41
But keep in mind that inflation (which takes over after the Big Bang) is completely based on Quantum Mechanics.
 
  • #42
The characterization of inflation as occurring "after" the Big Bang is a big part of the problem with the whole idea that "the Big Bang never happened." The Big Bang is not the title of an event that originated the universe. Indeed, no such event is ever included in any Big Bang models other than highly speculative ones like brane collisions and such, and no respectable scientist could ever claim that we have incontrovertible evidence that the universe originated in some kind of creation event, nor that it existed forever, nor even that the concept of time we apply in the here and now had any meaning prior to a given stage of our history. Imagining that the "Big Bang" refers to an instant of creation, perhaps in a singular point in space, is an incorrect characterization that dominates popular media. In astrophysics, the Big Bang is a model of the history of the universe that obeys two rules: it is governed by general relativity under an assumption of spatial homogeneity, and its free parameters are fit to match observations throughout the accessible timeline of our universe. As such, the Big Bang model plays out after inflation, not before, although some may include inflation as part of it-- while others who view inflation as more speculative may choose to omit that aspect of the overall Big Bang model. Most educators and textbooks include it in some way, but with significant caveats.

The salient features of the scientifically demonstrated aspects of "the Big Bang" are that the universe has evolved substantially over a period of 13.8 billion years, during which time it went from a vastly high energy density to the situation we find today, passing through stages of nucleosynthesis, recombination, galaxy formation, and stellar nucleosynthesis. When using the language about our cosmological models properly, it is clear that nothing in the Das paper suggests "the Big Bang never happened."
 
Last edited:
  • #43
Ken G said:
As such, the Big Bang model plays out after inflation, not before, although some may include inflation as part of it--

Can you please clarify this statement in light of this simplification diagram that generally places the "big bang" prior to "inflation"?

1280px-History_of_the_Universe.svg.png


You say that "In astrophysics, the Big Bang is a model of the history of the universe that obeys two rules: it is governed by general relativity under an assumption of spatial homogeneity, and its free parameters are fit to match observations throughout the accessible timeline of our universe." but how does this statement justify placing the big bang after inflation?
 
Last edited:
  • #44
The picture you are showing, that includes t=0, is just pop science. What "the Big Bang" means in real science can be found in quotes like this: (http://en.wikipedia.org/wiki/Big_Bang)
"The Big Bang theory is the prevailing cosmological model for the earliest known periods of the universe.[1][2][3] It states that the Universe was in a very high density state and then expanded.[4] If the known laws of physics are extrapolated beyond where they are valid there is a singularity."
Note the actual theory is about expansion, and one only gets a singularity if one extrapolates the idea "beyond where it is valid," as pop sci inevitably does. So unfortunately, we see that the term "Big Bang" is used in two completely different ways-- the pop sci meaning of some kind of "creation event", and the way professional scientists use the term in real astronomy applications. In the latter, and in scientifically responsible astronomy education, the term is used to describe an evolutionary model that tells a story of expansion of the universe, whose phases have been well checked against observations, the way science does. But this model also has a strange element, which some regard as its greatest flaw and others as its most exquisite feature-- as time goes backward, the theory leads to a question mark where the laws of physics as we know them break down. This happens prior to reaching a "singularity", so we already know that no model that includes such a singularity could ever be part of a self-consistent description of the universe that is based on well-tested laws of physics.
 
  • #45
He's saying that the placement of the "Big Bang" in the diagram is not covered by the Big Bang model itself, which is mum on the existence of any actual event that originated the universe. The early hot, dense phase that cosmologists identify with the nascent universe occurred after inflation as part of a process called "reheating". It is therefore common for people to refer to the "hot big bang" as occurring after inflation, but by this they don't mean literally the big bang singularity -- just the early hot phase of the universe relevant to observations.
 
  • #46
Perfect, thank you gentlemen for this clarification.
 
  • #47
bapowell said:
He's saying that the placement of the "Big Bang" in the diagram is not covered by the Big Bang model itself, which is mum on the existence of any actual event that originated the universe. The early hot, dense phase that cosmologists identify with the nascent universe occurred after inflation as part of a process called "reheating". It is therefore common for people to refer to the "hot big bang" as occurring after inflation, but by this they don't mean literally the big bang singularity -- just the early hot phase of the universe relevant to observations.
The Big Bang is therefore just a conceptual visualization , for an event that would start the inflation of space time .Time however must be figured in with all postulations regarding inflation .
 
  • #48
magneticnorth said:
The Big Bang is therefore just a conceptual visualization , for an event that would start the inflation of space time .Time however must be figured in with all postulations regarding inflation .
No, I'm saying that the "hot big bang" is identified with the *end* of inflation, known as reheating.
 
  • #49
magneticnorth said:
The Big Bang is therefore just a conceptual visualization , for an event that would start the inflation of space time .Time however must be figured in with all postulations regarding inflation .
That would be the pop-sci meaning of "Big Bang," but scientists already view that meaning as problematical, and prefer to use the term as the label for the well-tested theory of expansion, which bapowell is calling the "hot big bang" model. It's truly unfortunate that this term traces back to a kind of joke by Hoyle, this has allowed the term to be used in highly imprecise ways because it is such a pictorial phrase in the first place. Basically, the model says something very bizarre and unknown must have happened as we extrapolate back toward t=0, but no part of the scientific evidence in favor of the expansion of the universe, often called "the pillars of the Big Bang" (taking the hot big bang model meaning), have anything to do with a creation event. Instead, we have a 13.8 billion year timeline that makes sense. It is significant that the timeline that makes sense against observations is a finite timeline, but "what happened at the t=0 mark" in that timeline is simply not on the timeline, nor is how much longer that timeline could be extended if we ever actually have an observation that motivates us to do so. As of yet, we have no such motivation-- and no such motivation is provided by a speculative theory. The purpose of speculative theories is to motivate new observations, and help interpret them, not to create headlines that only play off on a widespread misunderstanding about the meanings of awkwardly pictorial scientific terms.
 
  • #50
Ken G said:
That would be the pop-sci meaning of "Big Bang," but scientists already view that meaning as problematical, and prefer to use the term as the label for the well-tested theory of expansion, which bapowell is calling the "hot big bang" model. It's truly unfortunate that this term traces back to a kind of joke by Hoyle, this has allowed the term to be used in highly imprecise ways because it is such a pictorial phrase in the first place. Basically, the model says something very bizarre and unknown must have happened as we extrapolate back toward t=0, but no part of the scientific evidence in favor of the expansion of the universe, often called "the pillars of the Big Bang" (taking the hot big bang model meaning), have anything to do with a creation event. Instead, we have a 13.8 billion year timeline that makes sense. It is significant that the timeline that makes sense against observations is a finite timeline, but "what happened at the t=0 mark" in that timeline is simply not on the timeline, nor is how much longer that timeline could be extended if we ever actually have an observation that motivates us to do so. As of yet, we have no such motivation-- and no such motivation is provided by a speculative theory. The purpose of speculative theories is to motivate new observations, and help interpret them, not to create headlines that only play off on a widespread misunderstanding about the meanings of awkwardly pictorial scientific terms.
I agree , nothing is known beyond the point at which we can extrapolate and trace back to . The term itself assumes an explosion in purely visual terms . When an idea like that is presented to the general public , you can not expect anyone to understand or visualize "something very bizarre and unknown " , as the Big Bang has been presented as an explosion , originating from a Singularity . Rightly or wrongly that is the perception , and that is what is depicted in elementary Science books . Only when one looks deeper into the subject , they will quickly realize that no one knows what preceded or caused the inflation , or atleast , that which can be reasonably postulated to date .
 
  • #51
magneticnorth said:
I agree , nothing is known beyond the point at which we can extrapolate and trace back to . The term itself assumes an explosion in purely visual terms . When an idea like that is presented to the general public , you can not expect anyone to understand or visualize "something very bizarre and unknown " , as the Big Bang has been presented as an explosion , originating from a Singularity . Rightly or wrongly that is the perception , and that is what is depicted in elementary Science books . Only when one looks deeper into the subject , they will quickly realize that no one knows what preceded or caused the inflation , or atleast , that which can be reasonably postulated to date .
Well, we have a date for when the expansion of the observable universe began, around 13.8 bya. As for the misconceptions about the big bang, yes, sadly explosions and singularities are still woefully common in the public treatment. But, hey, that's what PF is for!
 
  • Like
Likes Greg Bernhardt
  • #52
The fact of the matter remains that even though the Big Bang is widely accepted And supported y mainstream science, we shouldn't question those who go against it and keep an open mind. Remember the Renaissance, Galileo underwent extreme scrutiny from the public eye. No genius is truly happy in their lifetime, but their legacy, is remembered by history. The fact of the matter remains that there are actually several other opinions in the scientific community on how the universe started or if it ever did at all
 
  • #53
Science2Dmax said:
The fact of the matter remains that even though the Big Bang is widely accepted And supported y mainstream science, we shouldn't question those who go against it and keep an open mind. Remember the Renaissance, Galileo underwent extreme scrutiny from the public eye. No genius is truly happy in their lifetime, but their legacy, is remembered by history. The fact of the matter remains that there are actually several other opinions in the scientific community on how the universe started or if it ever did at all
Yes, if someone presents a verifiable alternate theory we should pay attention. So far there haven't been any. The "look what happened in history" argument is usually bogus. "Questioning those who go against it" should not be equated with "listen to kooks".
 
  • #54
Yes, we must always be receptive to criticism because scientific knowledge is necessarily incomplete and imperfect. But that does not equate to accepting any and all proposals equally, and the "lone genius" story is effectively irrelevant. Many a crank cite Galileo and Einstein and other pioneers whose ideas agitated the mainstream in their time; however, paradigm shifts of that magnitude are very rare. If they make empirical claims, let's test them; if not, let's remain at best agnostic.

In any enterprise with many individuals working to evolve the field, there are inevitably differences in opinion. But, as science progresses and we converge on an ever tighter corroboration of hypotheses, these differences in opinion will diminish. We know this, because science works.
 
  • #55
The takeaway messages from all this is that science is constantly self-correcting when it has new information it needs to fit into its understanding (but these new developments do not actually represent much in the way of new information), and that "the Big Bang" is not a model of some origin event, it is an evolution story that is tested at every step that is part of the model.

The reason a headline like "The Big Bang Never Happened" makes little sense is that it is completely nonresponsive to both of those points, instead it reflects an almost complete misunderstanding of both science, and what the the Big Bang scientific model actually is. So no one with any regard for science needs to enter into an argument about whether or not "the Big Bang really happened", what they need is to explain what science actually is, and what the well-tested Big Bang model actually is. That should include explaining to pop sci articles, and even textbooks if necessary, that no part of the well-tested Big Bang model says that the universe began in a singularity, it says that the laws of physics as we know them, and the observations we have to constrain the history of the universe, are presently completely moot about what happened 13.8 billion years ago that got that evolutionary ball rolling. Also, what the model says about what happened after that gets progressively more uncertain the closer the model gets to the start of its own timeline. A little hard to get into a headline, I realize.
 
Last edited:
  • #56
Ken G said:
The takeaway messages from all this is that science is constantly self-correcting when it has new information it needs to fit into its understanding (but these new developments do not actually represent much in the way of new information), and that "the Big Bang" is not a model of some origin event, it is an evolution story that is tested at every step that is part of the model.

The reason a headline like "The Big Bang Never Happened" makes little sense is that it is completely nonresponsive to both of those points, instead it reflects an almost complete misunderstanding of both science, and what the the Big Bang scientific model actually is. So no one with any regard for science needs to enter into an argument about whether or not "the Big Bang really happened", what they need is to explain what science actually is, and what the well-tested Big Bang model actually is. That should include explaining to pop sci articles, and even textbooks if necessary, that no part of the well-tested Big Bang model says that the universe began in a singularity, it says that the laws of physics as we know them, and the observations we have to constrain the history of the universe, are presently completely moot about what happened 13.8 billion years ago that got that evolutionary ball rolling. Also, what the model says about what happened after that gets progressively more uncertain the closer the model gets to the start of its own timeline. A little hard to get into a headline, I realize.
Indeed , in fact it has never been the headline .Almost every exposition of the Universe uses the term Big Bang , shows an explosion , even in the both Cosmos tv productions . The non-scientific public will always correlate the term Big Bang with an explosion . That is not the fault of the Physicists , because they never got full playing time , it was always the Astronomers that put forward the narrative . I would be willing to say that 90 % [ or more ] of the general public , have no idea of the issues discussed as they pertain to the expansion of the Universe and it's cause . That is , the known physics can only pertain to such a period looking backwards in time, to 3 Planck time segments after whatever initiated the inflation . Anything before that is simply not known .
 
  • #57
Yes, I think a very un-nuanced understanding of the "Big Bang" has been handed to the public, but it is because it was not thought that a sophisticated understanding of what science does would be necessary. The educators and pop-sci authors thought it would be all right to say that the universe started in a point, just to kind of amaze people and change their perspective from a universe that just stays the same. They didn't realize that if they said the universe started in a point, and someone came up with a different picture that was equally unconstrained by observations, it would lead creationists and climate change deniers to say, in effect, if they could be wrong about that then how do we know the universe isn't actually 10,000 years old.
 
  • #58
That might be true if you were preaching to a kindergarten class, but, I think the interested lay public would find that offensive.
 
  • Like
Likes Chiclayo guy
  • #59
I do not know what you mean, my words would be quite hard for kindergartners, and the Glen Beck's of the world, to understand. The goal is to get them to see the nonsense in saying "well, if the Big Bang never happened, then we can't really believe anything the scientists are saying about the history of the universe, right?" That's just what those mentioned in the OP were saying, and it is because they have a kindergarten understanding of science.
 
  • #60
I thought the concept of "singularity" came from Hawking, then was subsequently dismissed by him, rather than arising directly from pop-science.

My philosophical concern with a bang or inflation (however gentle) that has a proposed beginning, is that of Newtons 3rd law, "for every action there is an equal and opposite reaction". If we are to conserve this law everywhere, and if an action did not exist in perpetuity, where's the other half when the first "action" began? Or is the law already conveniently contained for introduction within the actions and forces we have today (I wonder)? Or perhaps, to save face, Newton's laws break down, as does Einstein's, in such a "too early" application.

In an eerie coincidence in early February (before this threads referred press release), I was trying to come up with a proper reference to help support an iffy statement I had made here regarding the early universe. A couple of days later it dawned on me that the elusive reference I sought should have been Newtons 3rd Law, but it was too late to possibly save my thread. A few days later yet, this present topic press release came out including such a reference to Newtons 3rd Law (I don't know much about the integrity of this source.)

Regarding Newtons 3rd Law, it seems to me that the total sum of actions, and total sum of reactions should preferably be identical for all time in perpetuity, throughout the universe. It seems the way to see this would therefore be to pit all established inertial actions against all resultant inertial actions, and we might even include gravity if the Equivalence principle (to inertial acceleration) is to hold (a+b=b+a). All these continuous actions, and counteractions, must in turn, be transmitted by electrostatic repulsion. Then the total forces involved in actions by both inertial mass and gravitational mass logically, and indefinately, would exactly equal the total force of repulsions at any given time, or in grand total altogether. In a way, gravity and electrostatics seem to naturally be conditionally united (albeit opposed but united), as we cannot technically acknowledge existence of one without the other.

The preceeding is not to argue the vastly different potential strengths of electrostatic forces vs gravity, but merely that they are at least observed to be matched in opposing equilibrium where ever mass makes near contact with other mass. As Feynman said, my hand does not pass through the table because electrostatic forces prevent it from doing so, in spite of all atoms being mostly open space. The same is true of my feet on the floor as I stand in gravity... or stand in Einsteins accelerating elevator in Equivalence to gravity. Of course an object (or heavenly body) in free-fall experiences no forces of either kind and does not count.

To conserve Newton's 3rd Law throughout all history, I think it might be possible to more fully apply Newtons 3rd Law, in that we generally observe inertial action to have an equal counterpart in electrostatic repulsion, quite representative of two presently known fundamental forces (if gravity is truly Equivalent). I'm thinking this perspective is now simply more self-evident rather than speculative, or I would not suggest it as food for thought, nor question it here. And it seems to me, to only work if there were no distinct beginning as the thread topic suggests.

And for the record, the forces would be measured in dynes... not joules... argh... as I mis-stated in my earlier thread. It is probably less harmful when I call my children by the wrong name. Perhaps I was vaguely thinking of how all work must be transferred and mixed them.

This is admittedly a different way to look at things. I hope it is not entirely invalid nor useless.

Wes
...
 

Similar threads

  • · Replies 20 ·
Replies
20
Views
1K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 56 ·
2
Replies
56
Views
8K
Replies
43
Views
5K
  • · Replies 12 ·
Replies
12
Views
3K
  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 80 ·
3
Replies
80
Views
11K
  • · Replies 14 ·
Replies
14
Views
3K
Replies
8
Views
9K