# A new model that predicts no Big Bang **URL:** \ **Category:** Factual Questions\ **Created:** [February 10, 2015, 6:36pm UTC](https://boards.straightdope.com/t/a-new-model-that-predicts-no-big-bang/712314 "2015-02-10T18:36:04Z")\ **Posts on this page:** 20\ **Page:** 2
**Author:** ![leahcim](https://avatars.discourse-cdn.com/v4/letter/l/b4bc9f/32.png) [@leahcim](https://boards.straightdope.com/u/leahcim)\ **Post date:** [February 11, 2015, 6:07pm UTC](https://boards.straightdope.com/t/a-new-model-that-predicts-no-big-bang/712314/21 "2015-02-11T18:07:22Z")
> [@DrCube](#): > > Black holes occur in nature. I’d also bank on that if you asked 100 physicists if there was _really_ a singularity at the centre of a black hole, most would say that there is probably some physics we don’t understand “smears out” the singularity so the density is not completely infinite. Normally when you have a model where the equations give an infinity in some circumstance, you think, “my model doesn’t apply in that circumstance” rather than “my model totally works and that circumstance actually results in infinite quantities”. ---
**Author:** ![Really\_Not\_All\_That\_Bright](https://avatars.discourse-cdn.com/v4/letter/r/e8c25b/32.png) [@Really\_Not\_All\_That\_Bright](https://boards.straightdope.com/u/Really_Not_All_That_Bright)\ **Post date:** [February 11, 2015, 6:51pm UTC](https://boards.straightdope.com/t/a-new-model-that-predicts-no-big-bang/712314/22 "2015-02-11T18:51:36Z")
Dumb question: if the universe is expanding, how can it have been around forever? Wouldn’t everything be infinitely far from anything else? ---
**Author:** ![TroutMan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/troutman/32/6721_2.png) [@TroutMan](https://boards.straightdope.com/u/TroutMan)\ **Post date:** [February 11, 2015, 6:55pm UTC](https://boards.straightdope.com/t/a-new-model-that-predicts-no-big-bang/712314/23 "2015-02-11T18:55:30Z")
> [@Really\_Not\_All\_That\_Bright](#): > > Dumb question: if the universe is expanding, how can it have been around forever? Wouldn’t everything be infinitely far from anything else? Easy answer, it hasn’t necessarily been expanding forever. But I don’t know if that’s the _right_ answer. ---
**Author:** ![levdrakon](https://avatars.discourse-cdn.com/v4/letter/l/49beb7/32.png) [@levdrakon](https://boards.straightdope.com/u/levdrakon)\ **Post date:** [February 11, 2015, 6:57pm UTC](https://boards.straightdope.com/t/a-new-model-that-predicts-no-big-bang/712314/24 "2015-02-11T18:57:33Z")
When did time start? Did it always exist or did it start with expansion? Can the universe have always existed without time? ---
**Author:** ![Asympotically\_fat](https://avatars.discourse-cdn.com/v4/letter/a/e47c2d/32.png) [@Asympotically\_fat](https://boards.straightdope.com/u/Asympotically_fat)\ **Post date:** [February 11, 2015, 8:10pm UTC](https://boards.straightdope.com/t/a-new-model-that-predicts-no-big-bang/712314/25 "2015-02-11T20:10:43Z")
> [@Really\_Not\_All\_That\_Bright](#): > > Dumb question: if the universe is expanding, how can it have been around forever? Wouldn’t everything be infinitely far from anything else? The scale factor a(t) is a positive valued function of cosmological time and it keeps track of how distances change with cosmological time. By definition at the present time a(t) = 1 and when a(t) = 2 it means that all galaxies\* are twice as faraway as they are now, when a(t) = 0.5 it means that all galaxies are half the distance they are now, etc , etc. a’(t) is the first derivative of a(t) wrt to t and if a’(t) \> 0 then the Universe is expanding, if a’(t) \< 0 then it means the Universe is contracting. A big bang/big crunch singularity\*\* occurs when a(t) = 0, so the only requirement for a big bang/big crunch singularity to be avoided is that a(t) never goes to zero for some finite value of t. You can even have ever expanding Universes with infinite pasts, we just need to find a function to represent a(t) that is strictly increasing and for which a(t)\>0 for all t. For example a(t) = e^t fulfills those requirements and is in fact an empty Universe with a positive cosmological constant (with units chosen such that its value is equal to 1). \*This is a bit of an approximation as for example if galaxies are close enough gravity will have a bigger influence over how their distance changes with time. \*\*NB as notions of distance and time depend on spacetime coordinates this could actually be a coordinate singularity rather than a more fundamental spacetime singularity. However a good choice of coordinates makes this point moot. ---
**Author:** ![Finagle](https://avatars.discourse-cdn.com/v4/letter/f/b19c9b/32.png) [@Finagle](https://boards.straightdope.com/u/Finagle)\ **Post date:** [February 11, 2015, 8:46pm UTC](https://boards.straightdope.com/t/a-new-model-that-predicts-no-big-bang/712314/26 "2015-02-11T20:46:03Z")
> [@Cardboard](#): > > Not to be nit-picky, but wouldn’t it be “suggests no Big Bang,” rather than “predicts no Big Bang,” since you cannot predict something that already happened (or didn’t happen)? I’d give them a pass on “predict”. Scientists predicted that they would find the Higgs Bosun based on theory, and it already existed. So in this usage, “predicts” can mean “if you run these experiments, we predict you’ll find”. ---
**Author:** ![leahcim](https://avatars.discourse-cdn.com/v4/letter/l/b4bc9f/32.png) [@leahcim](https://boards.straightdope.com/u/leahcim)\ **Post date:** [February 11, 2015, 9:41pm UTC](https://boards.straightdope.com/t/a-new-model-that-predicts-no-big-bang/712314/27 "2015-02-11T21:41:11Z")
> [@Finagle](#): > > Scientists predicted that they would find the Higgs Bosun based on theory, and it already existed. Now if they could only find the rest of the Higgs Able Seamen. Matt Strassler wrote an [article](http://profmattstrassler.com/2014/03/21/did-the-universe-begin-with-a-singularity/) on the singularity at the start of the universe a while back. Basic conclusion: Probably not one. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [February 11, 2015, 10:38pm UTC](https://boards.straightdope.com/t/a-new-model-that-predicts-no-big-bang/712314/28 "2015-02-11T22:38:27Z")
No, the Higgs Bosun is that really tough guy from _Girl Genius_. ---
**Author:** ![Really\_Not\_All\_That\_Bright](https://avatars.discourse-cdn.com/v4/letter/r/e8c25b/32.png) [@Really\_Not\_All\_That\_Bright](https://boards.straightdope.com/u/Really_Not_All_That_Bright)\ **Post date:** [February 11, 2015, 11:34pm UTC](https://boards.straightdope.com/t/a-new-model-that-predicts-no-big-bang/712314/29 "2015-02-11T23:34:06Z")
> [@Asympotically\_fat](#): > > The scale factor a(t) is a positive valued function of cosmological time … > > … a good choice of coordinates makes this point moot. You’re fucking with me, right? ---
**Author:** ![TroutMan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/troutman/32/6721_2.png) [@TroutMan](https://boards.straightdope.com/u/TroutMan)\ **Post date:** [February 12, 2015, 12:16am UTC](https://boards.straightdope.com/t/a-new-model-that-predicts-no-big-bang/712314/30 "2015-02-12T00:16:18Z")
> [@Really\_Not\_All\_That\_Bright](#): > > You’re fucking with me, right? This was my first reaction as well. But then I got my brain going and I’m understanding parts of this. > [@Asympotically\_fat](#): > > The scale factor a(t) is a positive valued function of cosmological time and it keeps track of how distances change with cosmological time. By definition at the present time a(t) = 1 and when a(t) = 2 it means that all galaxies\* are twice as faraway as they are now, when a(t) = 0.5 it means that all galaxies are half the distance they are now, etc , etc. > > a’(t) is the first derivative of a(t) wrt to t and if a’(t) \> 0 then the Universe is expanding, if a’(t) \< 0 then it means the Universe is contracting. OK, I’m with you. The derivative is the rate of change of the distance over time, which is acceleration. Positive acceleration = expanding. > [@](#): > > A big bang/big crunch singularity\*\* occurs when a(t) = 0, so the only requirement for a big bang/big crunch singularity to be avoided is that a(t) never goes to zero for some finite value of t. Still with you. > [@](#): > > You can even have ever expanding Universes with infinite pasts, we just need to find a function to represent a(t) that is strictly increasing and for which a(t)\>0 for all t. For example a(t) = e^t fulfills those requirements and is in fact an empty Universe with a positive cosmological constant (with units chosen such that its value is equal to 1). I get the first part of this, but why does e^t represent an empty universe? > [@](#): > > \*\*NB as notions of distance and time depend on spacetime coordinates this could actually be a coordinate singularity rather than a more fundamental spacetime singularity. However a good choice of coordinates makes this point moot. You lost me here, but I fear this might be beyond what can be explained to non-physicists in a thread like this. ---
**Author:** ![Apollon](https://avatars.discourse-cdn.com/v4/letter/a/e47774/32.png) [@Apollon](https://boards.straightdope.com/u/Apollon)\ **Post date:** [February 12, 2015, 12:16am UTC](https://boards.straightdope.com/t/a-new-model-that-predicts-no-big-bang/712314/31 "2015-02-12T00:16:46Z")
[QUOTE=Really Not All That Bright] Dumb question: if the universe is expanding, how can it have been around forever? Wouldn’t everything be infinitely far from anything else? [/QUOTE] An infinitely old universe doesn’t necessarily contradict expansion. It could be that expansion has also always existed. It was slower in the past, but never zero. When looking back in time, the speed of expansion approaches zero, but never reaches (originates from) it. It’s like the thing that happens when you continually halve a number that’s not a multiple of 2: you keep on halving, and the result gets smaller, approaching zero, but never reaching it. [QUOTE=rsa] why in a universe of infinite age would something special happen about 14 Bya? [/QUOTE] That was just the point during its eternal expansion, that the universe had reached a sufficient size for matter to form. All the things that we know about in the universe, are larger than Planck length. They could only come into being, when the universe was large enough to accommodate them. ---
**Author:** ![sich\_hinaufwinden](https://avatars.discourse-cdn.com/v4/letter/s/c5a1d2/32.png) [@sich\_hinaufwinden](https://boards.straightdope.com/u/sich_hinaufwinden)\ **Post date:** [February 12, 2015, 4:44pm UTC](https://boards.straightdope.com/t/a-new-model-that-predicts-no-big-bang/712314/32 "2015-02-12T16:44:48Z")
> [@TroutMan](#): > > …The derivative is the rate of change of the distance over time, which is acceleration. Positive acceleration = expanding. I’m not sure either of those of those comments is correct. Isn’t rate of change of distance over time velocity? (Rate of change of velocity over time is acceleration.) Also, I don’t know that positive acceleration = expanding. For example, something that is shrinking at an ever slower rate would have a negative “velocity” but a positive “acceleration”. ---
**Author:** ![Asympotically\_fat](https://avatars.discourse-cdn.com/v4/letter/a/e47c2d/32.png) [@Asympotically\_fat](https://boards.straightdope.com/u/Asympotically_fat)\ **Post date:** [February 12, 2015, 8:44pm UTC](https://boards.straightdope.com/t/a-new-model-that-predicts-no-big-bang/712314/33 "2015-02-12T20:44:51Z")
> [@TroutMan](#): > > OK, I’m with you. The derivative is the rate of change of the distance over time, which is acceleration. Positive acceleration = expanding. If x(t) describes position as a function of time, then x’(t) (the first time derivative) is velocity and x’'(t) (the second time derivative) is acceleration. a(t) isn’t position as a function of time, it is scale as a function of time; however there is certainly an analogy. If a’(t)\>0 then we say the Universe is expanding, and if a’'(t)\>0 too we say that the expansion is accelerating. > [@](#): > > I get the first part of this, but why does e^t represent an empty universe? To find out why you have to look at the dynamics of the Universe as described by the [Friedmann equations](http://en.wikipedia.org/wiki/Friedmann_equations#Equations): i.e. how the contents of the Universe affect expansion. If you look at the 2nd equation you may be able to see that a(t) = e^t implies that, for the matter and radiation contained in the Universe, density + 3\*(pressure) must be constant in time. However the density and pressure of matter and radiation in an expanding Universe both decrease with time unless they are equal to zero (an expanding Universe gets less dense as it expands and pressure is reduced due to cosmological red shift), therefore they must be equal to zero and hence the Universe must be empty. > [@](#): > > You lost me here, but I fear this might be beyond what can be explained to non-physicists in a thread like this. A singularity is some sort of pathological behaviour, the problem in describing this purely in terms of coordinates is that the pathological behaviour may actually reside in the coordinate system and not in the spacetime and choosing another coordinate system can get rid of the behaviour. ---
**Author:** ![TroutMan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/troutman/32/6721_2.png) [@TroutMan](https://boards.straightdope.com/u/TroutMan)\ **Post date:** [February 12, 2015, 10:50pm UTC](https://boards.straightdope.com/t/a-new-model-that-predicts-no-big-bang/712314/34 "2015-02-12T22:50:03Z")
Thanks, **Asympotically fat**. That makes sense. ---
**Author:** ![eschereal](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eschereal/32/18939_2.png) [@eschereal](https://boards.straightdope.com/u/eschereal)\ **Post date:** [February 12, 2015, 11:35pm UTC](https://boards.straightdope.com/t/a-new-model-that-predicts-no-big-bang/712314/35 "2015-02-12T23:35:39Z")
> [@leahcim](#): > > > [@DrCube](#): > > > > Black holes occur in nature. > > I’d also bank on that if you asked 100 physicists if there was _really_ a singularity at the centre of a black hole, most would say that there is probably some physics we don’t understand “smears out” the singularity so the density is not completely infinite. > > Normally when you have a model where the equations give an infinity in some circumstance, you think, “my model doesn’t apply in that circumstance” rather than “my model totally works and that circumstance actually results in infinite quantities”. I would think that we have never observed a fully formed black hole. When the collapse reaches a certain point, the extreme time dilation means that nanosecond events within the collapsing object could take trillions of years to transpire relative to our frame of reference. Thus, black holes are dynamic entities in the process of constant formation, but it is such a dilated event that they look static to us. The fairly recent paper that claimed that black holes cannot form because they would destroy themselves with virtual-particle evaporation (Hawking radiation) could be correct and yet still tolerate what we have observed if the time dilation from the gravitational gradient makes the process, for all intents and purposes, appear to take forever. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [February 12, 2015, 11:40pm UTC](https://boards.straightdope.com/t/a-new-model-that-predicts-no-big-bang/712314/36 "2015-02-12T23:40:11Z")
Simple example of a coordinate singularity: For (almost) any point on Earth, you can specify its latitude and longitude, and if you change either coordinate, you’re looking at a different point. But what’s the longitude of the North Pole, and where are you if you change your longitude starting from the North Pole? The coordinate system behaves weirdly there. But that’s just a point on the sphere, not inherently any different from any other point on the sphere. Standing at the North Pole, you can step forward, or backwards, or left or right, and it works just like anywhere else on the surface. Latitude and longitude have a coordinate singularity at the North Pole, but not a real singularity. ---
**Author:** ![eschereal](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eschereal/32/18939_2.png) [@eschereal](https://boards.straightdope.com/u/eschereal)\ **Post date:** [February 13, 2015, 12:08am UTC](https://boards.straightdope.com/t/a-new-model-that-predicts-no-big-bang/712314/37 "2015-02-13T00:08:25Z")
The North Pole is still kind of arbitrary, you could define any co-ordinate scheme for the earth centered on any point or pair of points. The body of the earth has four major axes of motion, the north and south poles are fixed in relation to only one of them. ---
**Author:** ![TroutMan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/troutman/32/6721_2.png) [@TroutMan](https://boards.straightdope.com/u/TroutMan)\ **Post date:** [February 13, 2015, 12:10am UTC](https://boards.straightdope.com/t/a-new-model-that-predicts-no-big-bang/712314/38 "2015-02-13T00:10:15Z")
Great example, **Chronos**. Now it _really_ makes sense. ---
**Author:** ![Asympotically\_fat](https://avatars.discourse-cdn.com/v4/letter/a/e47c2d/32.png) [@Asympotically\_fat](https://boards.straightdope.com/u/Asympotically_fat)\ **Post date:** [February 13, 2015, 1:34am UTC](https://boards.straightdope.com/t/a-new-model-that-predicts-no-big-bang/712314/39 "2015-02-13T01:34:19Z")
> [@Chronos](#): > > Simple example of a coordinate singularity: For (almost) any point on Earth, you can specify its latitude and longitude, and if you change either coordinate, you’re looking at a different point. But what’s the longitude of the North Pole, and where are you if you change your longitude starting from the North Pole? The coordinate system behaves weirdly there. But that’s just a point on the sphere, not inherently any different from any other point on the sphere. Standing at the North Pole, you can step forward, or backwards, or left or right, and it works just like anywhere else on the surface. Latitude and longitude have a coordinate singularity at the North Pole, but not a real singularity. This is a bit of a sidetrack (I only brought it up because it was in my mind at the time), but the specific example I was talking about was is when you set p, ρ and Λ as equal to zero in the Friedmann equations (i.e. an empty Universe with no cosmological constant), **but** k = -1 (i.e. negative spatial curvature). a(t) = 0 for some finite t in the past which suggests a big bang singularity, but it is just a coordinate singularity/removable singularity: the spacetime curvature doesn’t diverge and worldlines can be extended through the singularity. In fact what you have is just a wedge of flat Minkowski spacetime. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [February 13, 2015, 2:28am UTC](https://boards.straightdope.com/t/a-new-model-that-predicts-no-big-bang/712314/40 "2015-02-13T02:28:54Z")
> [@](#): > > Quoth **eschereal** : > > The North Pole is still kind of arbitrary, you could define any co-ordinate scheme for the earth centered on any point or pair of points. The body of the earth has four major axes of motion, the north and south poles are fixed in relation to only one of them. Right, the arbitrariness of the North Pole is kind of the point. Under the coordinates we usually use, there’s a singularity there. But we could, if we chose, set up a different set of coordinates that behaved just fine there, but which had a singularity somewhere else. And in fact, I don’t think that there’s any set of coordinates for the surface of a sphere that doesn’t have at least one coordinate singularity somewhere, even though none of the points is inherently pathological. [Previous page](https://boards.straightdope.com/t/a-new-model-that-predicts-no-big-bang/712314.md?page=1) [Next page](https://boards.straightdope.com/t/a-new-model-that-predicts-no-big-bang/712314.md?page=3)