nothing grows nothing

[AntonioLao]

The exponential growth of any physical system which would certainly include the whole universe itself can be represented by a few idealized mathematical models. If M is the initial amount of matter, R is the growth rate, T is the elapsed time, and (1+R) is called the growth factor then the total amount accumulated at the end of a time period T is given by A=M(1+R)^(T). However, since the binomial expansion in powers of T for integer values of T is more complicated than its equivalent expansion in the natural base of logarithm for integer powers of T, the general form of the exponential function can be properly expressed as A=Mexp(BT)+K where B=ln(1+R) or exp(B)=(1+R). Consequently, the infinite series expansion of exp(BT) is given by (BT)º/0!+(BT)¹/1!+(BT)²/2!+(BT)³/3!+… or equivalently Σ(BT)^(n)/n! for n=0,1,2,3,…,∞ such that the constants of the exponential function are M, K, and B=ln(1+R) or exp(B)=(1+R). Nonetheless, these constants cannot all equal to zero otherwise nothing grows nothing.

On the other hand, nonzero values of these constants imply that the respective infinitesimal changes ∆M, ∆K, and ∆B are also nonzero. However, the product of any two ∆M∆K or ∆M∆B or ∆K∆B could also imply a form that is a general covariance with the quantum condition of the uncertainty principle: ∆M∆K>0 or ∆M∆B>0 or ∆K∆B>0. All these imply that the fundamental form of the exponential function is given by f(x)=a^(x) where the base a must always be positive and never equal to unity: a≠1. Consequently, at x=0 the exponential function is always equal to unity: f(0)=1, that is to say any quantity raise to the power zero is always unity. The behavior of the exponential function can be determined by the values of the base for increasing values of x. If the base is less than unity then the function represents an exponential decay. If the base is greater than unity then and only then does the function represents an exponential growth. The former was used for understanding the processes of half lives of radioactivity while the latter was used for understanding the exponential growth of global human populations. If the latter is used to account for the accelerated expansion of the universe then it suggests that the value of the base is very near the value of unity but never exactly equal to unity, that is to say a little bit grow into an infinite number of bits. These bits are the quanta of space-time charges as squares of infinitesimal zero-point energies of the quantum vacuum fluctuations.

[Profpat]

There is a concept called sustainable growth. Do you think the universe can keep on expanding forever?

[AntonioLao]

sustainable growth

Thanks. Is that the same as a growth based on a 'check and balance' or between 'prey and predator'? I think the universe will expand forever unless the base of the exponential function becoming less than 1 for a universal exponential decay. But at the level of elementary particles the half lives of both electrons and protons are infinite, meaning that together with photons, electrons and protons will live forever.

[Profpat]

Forever. WOW. I have no problem with forever but I would like to see the closed cyclic universe model, win over the open model

The main problem I have Antonio is why 14 billion years ago. Why not a 1,000 godzillion years ago? If this is really a one shot thing, that happens once in an eternity, we are but babies.

[AntonioLao]

The problem is believing a singularity of creation. But the alternative belief of a triple point of existence of matter, energy and square of energy (quanta of space-time charges) allows us to add another state as the space-time continuum which binds the three states of matter and energy or matter and square of energy or energy and square of energy. In the relative beginning which is not really an absolute beginning, supposing that squares of energy dominate the universe then these transform into energy or into matter with different probabilities or energy into matter with again different probabilities. The transformation of squares of energy into matter has practically zero probability but its rate of creation is almost infinity, together of zero probability and infinite rate could physically look like a big bang singularity.

[Profpat]

The problem is believing a singularity of creation. But the alternative belief of a triple point of existence of matter, energy and square of energy (quanta of space-time charges) allows us to add another state as the space-time continuum which binds the three states of matter and energy or matter and square of energy or energy and square of energy. In the relative beginning which is not really an absolute beginning, supposing that squares of energy dominate the universe then these transform into energy or into matter with different probabilities or energy into matter with again different probabilities. The transformation of squares of energy into matter has practically zero probability but its rate of creation is almost infinity, together of zero probability and infinite rate could physically look like a big bang singularity.

That's an interesting concept 0 probabilty and infinite rate.

[AntonioLao]

0 probabilty and infinite rate

Together it simulates a big bang explosion or simply an expanding quantum wavefunction.