Modeling the Anaverse

[swampfox]

Here goes . . .

 

How can we possibly find out what came before the Big Bang and what caused it? Most people would say we can't but I'm beginning to think we may one day: Our world is massively non-linear. We see examples of this all around us and model it in the form of non-linear differential equations. In fact the equations of mathematical physics are mostly non-linear. A common property of non-linearity is "catastrophe"; the dynamics flows smoothly unless a "critical point" is reached at which point the state of the system changes abruptly and qualitatively. The perfect example of this is the cubic differential equation which models the "cusp catastrophe".

 

To me, non-linear dynamics I see all around us are echos of a larger dynamic: the Universe itself giving us hints of its origin. The Big Bang may have been a critical point reached by a larger dynamic system. If so, how could we ever know what that larger dynamic system was?

 

Maybe using the principle of "analytic continuation" we could gain some insight . This idea is commonly used in Complex Analysis to "extend" a function to a larger domain. The Zeta function is a good example: A sum originally defined for real numbers, can be "continued" to a complex function defined on the complex numbers.

 

Can we "Analytically continue" the Universe, we see now, its dynamics I mean, to a larger dynamic system which has a critical point allowing for a qualitative change giving rise to dynamics we see emerging in the Standard Model of Cosmology?

 

I'm not implying this could be done all at once but perhaps a sufficiently complex "simulation" could begin to show signs of this. For example a system that would give rise to the heat, wave, and Laplace dynamics would be a start. In time, improvement to the simulator would move it closer to our universe. It would be no guarantee of course that it faithfuly represented what came before the Big Bang but I this this is a possible approach to the matter.

[Fatstep]

Well, simply put, there will never be any proof of what happened before the creation of our universe, however it was made, so all theories are as valid as their adversaries.

[swampfox]

Well, simply put, there will never be any proof of what happened before the creation of our universe, however it was made, so all theories are as valid as their adversaries.

 

Why do you think that part is forever inaccessible to us? It's so easy to look back in our history and come up with examples of ideas that were thought impossible but later shown to be otherwise. I'm not offering a proof but only a possible avenue for investigation that I believe is based on sound reason.

[jungjedi]

isnt there some buddhist cone that goes "what was the look on your face before you were born" and if you mean your question to be a paradigm shift as to thinking outside the box.my first impulse would be to say the universe was lonely and had the intention of makeing new friends.

[sanctus]

For this model wouldn't you have to describe the universe as in cosmology, ie as a (maybe pertubated) perfect fluid? So wouldn't you get a kind of analogue of the Navier-Stokes equation to be able to the describe the evolution of that fluid?

[HappytheStripper]

Okay.. I know I've said this a few times before.. probably here.. possibly in other places.. however.. Im going to say it again..

 

Man jumped through the eye of a needle.. How did he do it..??

 

It may be the same way the Universe formed.. Simple as it may seem.. and as complex as a thought may be.. that may be exactly how it happened.. with one thought.. the eye to the universe was no longer blind.. and in jumped a life of another.. luck or opportunity.. ?? Who knows.. ;)

 

Luck I think is where preparedness meets opportunity through a simple series of time and space events coming together to synchronistically form what we know now..

 

So what was the intention.. ?? It could have been to make new friends.. haha I do like that idea.. and thats all we are supposing.. ideas.. no-one person really knows.. I do however know I am very lucky to be here at this time debating this idea with you ..

 

Although historically.. we are capable of looking back in time and space.. and science can prove many things now-a-days.. we have yet to prove the formation of the universe in its entirety..

It may be likened and related to many things including conception and childbirth.. one of many suppositions available for your belief..

 

Should you happen to stumble across the answer in the near future.. and prove its worth.. would you let me know please.. thanks..

 

By the way.. the rooster came first.. :lol: Ashley

[swampfox]

I don't know sanctus. Never worked with Navier-Stokes but I'm pretty good with PDEs. Also, I'm not very familiar with the Standard Model and wouldn't know how to proceed with applying this continuation to it. I think I'm right about the concept though. I welcome everyone's comments and will try to reply . . . well the one about Buddhism and . . . not sure about the other one . . . anyway I've read them and appreciate your thoughts.

[sanctus]

The standard model doesn't seem to me something you can analytically expand.

You just have to know that pretty good with PDEs is not enough, as no one has found a general solution yet to the Navier-Stokes equation (there are solution with supposition like the fluid is incompressible, etc.)

[swampfox]

Hello sanctus. I think if this approach were to be successful (I'm optimistic), it would be an emergent one: start small and then build up. The goal would not be to continue the standard model initially but rather to study the principle in general: Can ANY physical process in nature, even a very simple one, be modeled by a larger dynamical system which has a critical point giving rise to the process? I suspect this could be done but my knowledge of non-linear systems is restricted to ordinary ones and even these show hints of an underlying universal dynamics: catastrophe. To me, the model of the Anaverse IS the cubic differential equation albeit in very simple terms:

 

[math]\frac{dy}{dt}=a+by-y^3[/math]

 

The dynamics modeled by this equation flows smoothly over most of a "folded sheet", the "equilibrium surface". At the edge of this surface however, it doesn't but rather "falls" off onto the bottom fold rather abruptly. This is the critical point, a catastrophe. I imagine the Anaverse as that sheet with the pre-existence the top fold. Something pushed the dynamics to the catastrophe point, the Big Bang occurred, quickly sending the dynamics towards the bottom fold. That trajectory, from top fold towards the bottom fold, we we now perceive as the universe.

 

I wonder how much richer more complicated ones must be, how much richer massively coupled ones could be. Something would emerge I'm sure of it as the level of complexity of such equations reaches its own critical point.

[sanctus]

Why this equation and not one like [math]\frac{dy}{dt}=a+by-cy^3[/math]

or

[math]\frac{dy}{dt}=a+by-y^3+y^5[/math]?

[swampfox]

It's the simplest and I'm big on starts. Rene' Thom defines seven elementary catastrophes. The example I gave above is the cusp catastrophe. The next one is the swallowtail catastrophe but it's surface is 4 dimensional so we can't draw it completely (when I get up to 10 posts in the group -- the minimum required -- I'll come back and post a picture of the equilibrium surface showing the cusp catastrophe. The swallowtail would be:

 

 

[math]\frac{dy}{dt}=w+vy+uy^2+zy^4[/math]

 

but I'm not sure. Your equation even with x^5 is still a cusp catastrophe. You can see that by plotting:

 

[math]y(x)=bx-x^3+x^5[/math]

 

and noting it still has three real roots.

[sanctus]

That's why I wrote to the power of 5, it has a similar form than the power of 3...hence my question.

[jungjedi]

Hello sanctus. I think if this approach were to be successful (I'm optimistic), it would be an emergent one: start small and then build up. The goal would not be to continue the standard model initially but rather to study the principle in general: Can ANY physical process in nature, even a very simple one, be modeled by a larger dynamical system which has a critical point giving rise to the process? I suspect this could be done but my knowledge of non-linear systems is restricted to ordinary ones and even these show hints of an underlying universal dynamics: catastrophe. To me, the model of the Anaverse IS the cubic differential equation albeit in very simple terms:

 

[math]\frac{dy}{dt}=a+by-y^3[/math]

 

The dynamics modeled by this equation flows smoothly over most of a "folded sheet", the "equilibrium surface". At the edge of this surface however, it doesn't but rather "falls" off onto the bottom fold rather abruptly. This is the critical point, a catastrophe. I imagine the Anaverse as that sheet with the pre-existence the top fold. Something pushed the dynamics to the catastrophe point, the Big Bang occurred, quickly sending the dynamics onto the bottom fold which we now perceive as the universe.

 

I wonder how much richer more complicated ones must be, how much richer massively coupled ones could be. Something would emerge I'm sure of it as the level of complexity of such equations reaches its own critical point.

 

would these critical points you speak of be considered lagrange points?

Lagrangian point - Wikipedia, the free encyclopedia

[swampfox]

That's why I wrote to the power of 5, it has a similar form than the power of 3...hence my question.

 

I don't understand. What do you mean it "has a similar form than the power of three"? Do you mean simpler and if so how?

[swampfox]

would these critical points you speak of be considered lagrange points?

 

I checked. I don't thing lagrange points would be considered critical points but perhaps. Usually though, critical points are points in systems where the dynamics changes usually abruptly and often qualitatively. For example, the freezing point of water is a critical point, snapping a twig is another, loading concrete to the breaking point still another, avalanches, warring nations, punctuated equilibrium, cambrian explosion, nuclear fission, nova, black holes . . . big bang?

[jungjedi]

i find your theory very similiar to the concept of spontaneous symmetry breaking.where you talk about folded sheets and equilibrium surfaces at which points the potential of the universe falls off abrubtly.much like a 'MEXICAN HAT" model.

Spontaneous symmetry breaking - Wikipedia, the free encyclopedia

[swampfox]

i find your theory very similiar to the concept of spontaneous symmetry breaking.where you talk about folded sheets and equilibrium surfaces at which points the potential of the universe falls off abrubtly.much like a 'MEXICAN HAT" model.

 

That looks interesting and new for me. Thanks for the link. Good deal then. I'm up to 10 with this one and so I'll post another with the picture of the cusp. Just figured out how to do that a few days ago and think it's neat.