Write4U:
But AFAIK, there is an outer limit to the universe itself, else the universe could not be expanding, no?
There's no need for an outside.
A common analogy for this is the loaf-of-raisin-bread picture. The universe is like an unbaked loaf of raisin bread. The raisins represent galaxies and the bread represents space. We put the bread in the oven to bake it and the bread expands. All of the raisins in the loaf move away from one another as the loaf expands.
The analogy breaks down because the loaf of bread has edges. So now imagine an
infinite loaf, still full of raisins, baking in an infinite oven. The raisins
still all move away from one another as the bread expands, but now there is no "outside" that the loaf is expanding into. Everything is loaf.
The universe is like that.
Events occur inside the universe and may create their own NOWs separately from the Universal NOW.
In the "block time" picture from relativity, events are
points in spacetime. They do not "create" anything. We can talk about other events that are simultaneous with any given event, but if we're going to do that we must first specify a particular frame of reference, because there is no "preferred" or "universal" time.
Trusting the science that proposes the big bang and the absolute lack of knowledge of what was before the big bang, I visualized that before the BB there was only anfinite, timeless, dimensionless, permittive condition of nothingness.
According to Krauss that scenario should not be rejected out of hand.
Personally, I don't think the phrase "before the big bang" has been defined well enough to give it any clear meaning for me. In the general relativistic descriptions, time starts at the moment of the big bang. There is no "before" in those descriptions.
Perhaps it is possible to define some kind of time-like thing separate from our observable universe. In Hawking's
A brief history of time, I read some stuff about "imaginary time", but I don't really understand what he was on about with that. Probably I don't know enough general relativistic cosmology.
Krauss's definition of "nothingness" (e.g. in his book
A universe from nothing) is a bit slippery, I think. As far as I can tell, he suggested some kind of quantum field that fluctuated to cause the big bang. I personally wouldn't describe any quantum field as "nothing".
You keep mentioning "permittive" nothingness. You even emphasise the word "permittive". What does that mean? Does it mean anything more than you're imagining a prior condition that permits a big bang to occur, similar to Krauss's quantum field?
If that is stipulated, then the BB was the beginning of everything we know. But as inflation occurred in a purely permittive condition, the rate of energetic expansion was @ FTL until the energetic plasma cooled and the first particles began to self-form from the Chaos.
I don't know what you mean by a "purely permittive condition". What are the degrees of "permittivity"? What would a partially permittive condition look like?
It is at this point measurable time of duration emerged and added a temporal aspect to the expanding wholeness and attached a universal temporal dimension to the continued spatial existence of the universal wholeness.
GR cosmological theories have time already running during the proposed inflationary period. Your own hypothesis sounds different to that.
I know this sounds simplistic, but I am an absolute denier of "irreducible complexity"and "something from nothing" seems the least complex scenario that can be imagined.
The least complex scenario I can imagine for the universe would be the so-called steady-state theory, in which the universe stays approximately the same at all times. Observational data refuted that hypothesis, however.
Therein lies the crux. At what point does the expanding universe acquire mathematical properties and dynamic guiding principles that permit some interactions and forbid other interactions and here I agree with the concept that physical interactions of inherent generic elemental values cannot do other than what a logical generic mathematical language allows or forbids the output of certain specific results from specific value inputs. Universal constant functions that allowed the self-formation and emergence of the first physical patterns from the early inflationary chaos.
I don't know what you mean by "mathematical properties". If you just mean the universe has properties that we can describe using mathematics, then I'd say the universe probably had those from the moment of the big bang. I'm not saying that our current mathematical theories provide a full description of the entire evolution of the universe, because of course they don't.
You write as if you think that "universal constant functions" can cause physical effects. They cannot. Mathematics is an abstraction - an idea in your head. Mathematics doesn't create "stuff" or cause physical effects (Tegmark notwithstanding).
My position is very simple. The Universe is a singular dynamic object that is subject to the emergence of time along with its duration of existence.
Okay. I can live with that. I agree that the universe is a thing, and that it has time and that it has existed for quite a while now.
But that is exactly what you have been discussing all along "synchronizing clocks in accordance with the appropriate differential equations" over time.
I don't think so. Where did I mention any differential equations?
As bookkeeper and bid-supervisor I used "differential equations" for several economic predictions that required time-dependent derivative answers.
"A derivative is the rate of change of something with respect to something else. You can, for instance, model changes in revenue with respect to changes in capital expenditure—that would be a derivative. Also common are models which explain changes in price with respect to time."
Yes, a derivative is a rate of change of something with respect to something else. A simple physical example would be speed, which is the rate of change of distance with respect to time. Technically, there is an important difference between instantaneous speed and average speed. Mathematically, average speed is just total distance travelled divided by total time taken, but instantaneous speed is the derivative $dx/dt$, which involves the idea of a mathematical limit as the time interval becomes infinitesimally small.
A differential equation is any equation that includes a derivative. Technically, the equation $v(t)=dx/dt$ is a differential equation. This one has many possible solutions. For example, if velocity is a constant, $v_0$ say, then we have $dx/dt=v_0$, which means $x(t) = v_0 t + k$, where $t$ is the time variable and $k$ is some other constant (which in this case turns out to be the position at time $t=0$). Much more complicated differential equations exist, some of which involve higher-order derivatives. Here's one example:
$\frac{d^2 x}{dt^2} +\omega^2 x = 0$.
This one describes simple harmonic motion, which is a type of regular oscillatory motion. The derivative in the first term, in this case, is a second order derivative of distance with respect to time (which is actually the
acceleration). One "solution" to this particular equation is:
$x(t) = A \sin (\omega t)$
which, again, gives us a description of how the position, $x$ of some object changes as the time variable $t$ changes.
You have heard me cite the exponential function. This is a logical (first order ) differential equation because the exponential function equals its own derivative.
Mathematically, the relevant differential equation would be something like
$\frac{dn}{dt} = 0.693 n$
where, for example, the variable $n$ could be the number of rabbits in a population at a given time $t$. In this case, the differential equation says "the rate of increase in the number of rabbits per unit time is 0.693 times however many rabbits are currently alive".
One possible solution to this differential equation is:
$n(t) = 2^t$, which would mean that at time $t=1$ there are 2 rabbits, at time $t=2$ there are 4 rabbits, at time $t=3$ there are 8 rabbits, at time $t=5$ there are 32 rabbits, at time $t=10$ there are 1024 rabbits, at time $t=20$ there are 1,048,576 rabbits and so on, which is an example of exponential growth. (They breed like rabbits!)
