Posted: Jun 22, 2016 6:59 pm
Thank you very much for your knowledgeable answer, Calilasseia 
Got it. So in this respect, would you approve of an analogy to abiogenesis and evolution? (the BB analogous to the latter in that respect).
Thank you for your more rigorous explanation of what a singularity is.
I was only familiar with the more layman version of it, that it represents a point of infinite density that is infinitely small.
Are these infinities what you referred to when you wrote about functions "ceasing to be defined"?
By "well behaved", do you mean that they can be accurately described mathematically?
So is this the heart of the trouble scientists have been having for decades, that they can't happily "marry" the required General Relativity and quantum mechanics to describe singularities?
Is this braneworld cosmology related to Witten's M-Theory in any way?
Are these branes described in the mathematics? Do they come directly out of them?
If this is so, how does a brane look in its native language mathematics?
I wouldn't understand it, but I would LOVE to see how a brane is represented mathematically anyway. If it's not too much trouble, perhaps you could post an example when you have time? I'm really curious about it.
Wow. That does sound promising!
I had read this Krauss article about it when they confirmed they found the gravitational waves.
http://www.nytimes.com/2016/02/14/opini ... egion&_r=0
I am truly astounded about what scientists can do and measure these days! The accuracy of the equipment!
So then I suppose the "signature", the spectrum of gravitational waves from colliding branes would necessarily be much more obvious and easy to detect than the ones they saw with the colliding black holes, yes?
So, when the time comes and we find them, what would be the next step to test this theory further? What else would be convincing of braneworld cosmology?
Just for speculation, what else could gravitational waves be an indicative of? What else, besides mega-collisions, could create them?
Thank you again for your time and your knowledge, Calilasseia
Calilasseia wrote:First of all, the Big Bang theory was only intended to explain the behaviour of the universe once it was instantiated. What happened before this was never the remit of Big Bang theory.
Got it. So in this respect, would you approve of an analogy to abiogenesis and evolution? (the BB analogous to the latter in that respect).
Calilasseia wrote:
The idea of space-time coming into existence upon said instantiation, was in part a consequence of physicists not being in a position to develop ideas about what happened before, because the standard cosmological model at the time involved a singularity. Singularities constitute a sort of mathematical no-go area - they are, in effect, locations within a function domain for which the function in question ceases to be well-behaved, or worse still, ceases even to be defined. If you can't even define a function at a given point in the function domain, you can't really say much about how that function behaves at that point. The Big Bang singularity represented, in effect, a point where the functions representing the behaviour of physical systems cease to be defined. It was therefore thought that no progress beyond that point could be made.
Thank you for your more rigorous explanation of what a singularity is.
I was only familiar with the more layman version of it, that it represents a point of infinite density that is infinitely small.
Are these infinities what you referred to when you wrote about functions "ceasing to be defined"?
By "well behaved", do you mean that they can be accurately described mathematically?
So is this the heart of the trouble scientists have been having for decades, that they can't happily "marry" the required General Relativity and quantum mechanics to describe singularities?
Calilasseia wrote:
This view changed as a result of several developments. The one I'm best acquainted with is braneworld cosmology, which proposes that the universe was instantiated as a result of two branes colliding. This model requires that spacetime has always existed, and that as a result, the "t=0" of the Big Bang theory merely delineates the moment at which the instantiating collision occurred from the standpoint of the instantiated universe entity. Since that entity didn't exist beforehand, a "t<0" from the standpoint of that entity makes no sense, but does make sense from the standpoint of other entities that did exist beforehand.
Is this braneworld cosmology related to Witten's M-Theory in any way?
Are these branes described in the mathematics? Do they come directly out of them?
If this is so, how does a brane look in its native language mathematics?
I wouldn't understand it, but I would LOVE to see how a brane is represented mathematically anyway. If it's not too much trouble, perhaps you could post an example when you have time? I'm really curious about it.
Calilasseia wrote:
What makes braneworld collision particularly worth pursuing further, is that [1] it doesn't involve singularities (or, more rigorously, doesn't involve non-regularisable singularities - a quick look at complex analysis, and how singularities are treated therein, will explain how singularities can be regularised, provided they are of the correct type), and [2] provides a potential empirical test of the theory, Braneworld collisions, if they are genuinely responsible for instantiating universe-type entities, leave within those universe-type entities evidence of their having taken place, in the form of a particular spectrum of primordial gravitational waves. If that spectrum is observed (hence the expense being spent on LIGO etc), then this is an indication that braneworld cosmology is something more than mere speculation.
Wow. That does sound promising!
I had read this Krauss article about it when they confirmed they found the gravitational waves.
http://www.nytimes.com/2016/02/14/opini ... egion&_r=0
I am truly astounded about what scientists can do and measure these days! The accuracy of the equipment!
So then I suppose the "signature", the spectrum of gravitational waves from colliding branes would necessarily be much more obvious and easy to detect than the ones they saw with the colliding black holes, yes?
So, when the time comes and we find them, what would be the next step to test this theory further? What else would be convincing of braneworld cosmology?
Just for speculation, what else could gravitational waves be an indicative of? What else, besides mega-collisions, could create them?
Thank you again for your time and your knowledge, Calilasseia