Pre-Big Bang Phase And The Implications For Physics

[Dubbelosix]

[math]\frac{3072}{60} = 51.2[/math]

which is a nice clean decimal number as some may go. We can convert to a mixed number, for instance

[math]Qoutient \cdot (\frac{Remainder}{Devisor})[/math]

Which is a way to ''simplify'' it to

[math]51 \cdot (\frac{12}{60})[/math]

I say simplify but its actually quite a long series of derivations and manipulations - the best way to view it is that the ratio

[math]\frac{3072}{60}\ is\ 51\ with\ a\ remainder\ of\ 12[/math]

With a divisor of course of [math]60[/math].

So we go back and realize the quotients:

[math]\frac{3072}{60} \frac{\zeta(4)}{\zeta(3)}[/math]

Can be rewritten also as

[math]51 \cdot (\frac{12}{60}) \frac{\zeta(4)}{\zeta(3)}[/math]

It's nice we can retreive a whole number, now what we have to look at is the remaining numbers

[math](\frac{12}{60}) \frac{\zeta(4)}{\zeta(3)}[/math]

and see what happens when we crunch them in various ways.

Edited May 1, 2019 by Dubbelosix

[Dubbelosix]

now...

 

[math]\frac{12}{60} = 0.2[/math]

 

and [math]0.2[/math] as most know, is just [math]\frac{1}{5}[/math]. Just as in similar fashion, [math]\frac{1}{2}[/math] is [math]0.5[/math]. We know [math]\zeta(4)[/math] has in the numerator a factor of [math]\pi^4[/math] so first we play with this - from it we get

 

[math]\frac{12}{60}\pi^4 = \frac{\pi^4}{5}[/math]

 

straight forward so far I guess... but of course with Zeta 4 we also have another factor of 90 in the denominator. So let's see how this comes into play....

 

[math] \frac{\pi^4}{5 \cdot 90} = \frac{\pi^4}{450} =0.21646 [/math]

 

So nothing too curious so far, but believe ,me when I say, I'll be covering as many angles as I physically am capable of doing. We do, for instance, have Zeta 3 to take into account. We already know the value for this as

 

[math]\zeta(3) = 1.2020569032[/math]

 

So let's try something different: We'll go back to the ratio

 

[math]\frac{12}{60} = 0.2[/math]

 

The Zeta 3 exists in the denominator

 

[math]\frac{12}{60 \zeta(3)} = 0.166381475[/math]

 

since

 

[math]12 \cdot \pi^4 = 1168.90909[/math]

 

then[math]\frac{12 \cdot \pi^4}{60 \zeta(3)} = 0.166381475[/math]

 

With

 

[math]60 \cdot \zeta(3) = 72.1234142[/math]

 

we then have[math]\frac{1168.90909}{72.1234142} = 16.20706816178428[/math]

 

More number crunching, found some interesting simplifications, but still nothing too obvious, if at all, at the end of this tunnel. Will continue other various forms later today.

Edited May 1, 2019 by Dubbelosix

[Dubbelosix]

So after some number crunching, I find this approach most interesting, but it doesn't necessarily mean it has to be right, I just find it interesting for the p-distribution denoted as [math]\alpha[/math],

 

 

[math]3072 = 2^{10} × 3[/math]

 

[math]\frac{\phi}{c^2} \cdot \int\ (\frac{\ddot{T}}{T} + \frac{kc^2}{a^2})\frac{1}{\rho_{\alpha}}\ d\log_V = \frac{ 2^{10} × 3}{60} \frac{\zeta(4)}{\zeta(3)}(\frac{v^2}{2c^2} + \Psi + (\frac{T_0}{T})\frac{P}{\rho}) = \mathbf{C}[/math]

 

Again, [math]\frac{3}{60}[/math]

 

[math]\alpha[/math] is commonly set to [math]0.05, 0.01, 0.005, or 0.001[/math] so we can re-express the equation simply as

 

[math]\frac{\phi}{c^2} \cdot \int\ (\frac{\ddot{T}}{T} + \frac{kc^2}{a^2})\frac{1}{\rho_{\alpha}}\ d\log_V =  2^{10} \cdot \alpha \cdot \frac{\zeta(4)}{\zeta(3)}(\frac{v^2}{2c^2} + \Psi + (\frac{T_0}{T})\frac{P}{\rho}) = \mathbf{C}[/math]

 

What this will lead to I am unsure right now, I am not a pure mathematician... in fact, I don't even class myself as any kind of mathematician, at the very best, just a theoretician. I will get into the cosmological constant more.

Edited May 4, 2019 by Dubbelosix

[Dubbelosix]

 

[math]\frac{\phi}{c^2} \cdot \int\ (\frac{\ddot{T}}{T} + \frac{kc^2}{a^2})\frac{1}{\rho_{\alpha}}\ d\log_V =  \frac{3072}{60} \cdot \frac{\zeta(4)}{\zeta(3)}(\frac{v^2}{2c^2} + \Psi + (\frac{T_0}{T})\frac{P}{\rho}) = \mathbf{C}[/math]

 

 

 

 

Ok, so we spoke about [math]C[/math] being a constant, today we know it is related to energy and the main main reason why this Freidmann expansion melding into Bernoulli's principle was not a ''an assumption'' as was challenged by someone who followed the work, because he seemed to be unaware that we work with fluid dynamics when working with an expanding  universe, which relies on different pressures through various complicated parameters. In other words, the two have stronger relationships to each other than most would like to agree on, or have been unaware of.

 

To present the laws spoken in previous posts, a general application from the last equation would be to distribute an energy, such that the constant on the right hand side, is a constant of energy. We will leave out the right hand side until I can try and simplify it further, the real equation we should concentrate will be of the form:

 

[math]  \frac{3072}{60} \cdot \frac{\zeta(4)}{\zeta(3)}(\frac{v^2}{2c^2} + \Psi + (\frac{T_0}{T})\frac{P}{\rho})E = \mathbf{C}_{vac}[/math]

 

where now [math]C[/math] is no longer ''just a constant'' but is define under the units of energy defined through the vacuum contribution.

 

This model, finally is becoming a unified equation for the universe.... but there is one final thing to do... and that will be the last highlight of the thread, an implication no less, of a driving force which we may consider as an interpretation of the cosmological constant. To do so, we require the work of Fritz Rohrlich who demonstrated that the force on a moving system (as in opposition to one at rest) is important when considering the mass-energy equivalence.

 

The model he proposed considered in a frame that moves with velocity to the left, the driving force moving to the left is redshifted, while the driving force moving to the right is blueshifted. The blue light carries more momentum than the red light, so that the momentum of the light in the moving frame is not balanced - in other words, a cosmological constant is interpreted here-on-in as a non-balanced force since the energy is carrying some net momentum to the right.

 

The object has not changed its velocity before or after the emission, however, in this frame it has lost some right-momentum to the energy driving it in a particular direction. The only way it could have lost momentum is by losing mass - this may be also a statement of non-conservation and is not only quintessentially tied to Poincaré's radiation paradox, it also solves it.

 

So the right-moving energy carries extra momentum [math]\Delta p[/math] we then have

 

[math]\Delta p =\frac{v}{2c^2}E[/math]

 

The left-moving energy will carry a little less momentum, by the same quantity [math]\Delta p[/math] such that the total right-momentum in the energy is twice the value of [math]\Delta p[/math]. This is the right-momentum energy lost from the system (universe)

 

[math]2\Delta p=\frac{v}{c^2}E[/math]

 

The momentum of the universe moving in the directional frame after the emission is reduced by the amount of 

 

[math]p′ = mv−2\Delta p = (m − \frac{E}{c^2})v[/math]

 

So the change in the universes mass is equal to the total energy lost divided by the speed of light squared - the big implication here is that any emission of energy can be carried in a two-step process in which energy used by the universe is converted to mass, while the emission of an energy is accompanied by a loss of the mass in the universe. The pressure differences will lead to a mechanical explanation without an ad hoc assumptions on what the nature of the cosmological constant comes from, or how it came into being. To do so, we require the work of Fritz Rohrlich who demonstrated that the force on a moving system (as in opposition to one at rest) is important when considering the mass-energy equivalence.

 

The model he proposed considered in a frame that moves with velocity to the left, the driving force moving to the left is redshifted, while the driving force moving to the right is blueshifted. The blue light carries more momentum than the red light, so that the momentum of the light in the moving frame is not balanced - in other words, a cosmological constant is interpreted here-on-in as a non-balanced force since the energy is carrying some net momentum to the right.

 

The object has not changed its velocity before or after the emission, however, in this frame it has lost some right-momentum to the energy driving it in a particular direction. The only way it could have lost momentum is by losing mass - this may be also a statement of non-conservation and is not only quintessentially tied to Poincaré's radiation paradox, it also solves it.

 

So the right-moving energy carries extra momentum [math]\Delta p[/math] we then have

 

[math]\Delta p =\frac{v}{2c^2}E[/math]

 

The left-moving energy will carry a little less momentum, by the same quantity [math]\Delta p[/math] such that the total right-momentum in the energy is twice the value of [math]\Delta p[/math]. This is the right-momentum energy lost from the system (universe)

 

[math]2\Delta p=\frac{v}{c^2}E[/math]

 

The momentum of the universe moving in the directional frame after the emission is reduced by the amount of 

 

[math]p′ = mv−2\Delta p = (m − \frac{E}{c^2})v[/math]

 

So the change in the universes mass is equal to the total energy lost divided by the speed of light squared - the big implication here is that any emission of energy can be carried in a two-step process in which energy used by the universe is converted to mass, while the emission of an energy is accompanied by a loss of the mass in the universe. We notice then from the equation/principle provided by Bernoulli is, before we distribute through the parenthesis the energy of the universe as:

 

[math]  \frac{3072}{60} \cdot \frac{\zeta(4)}{\zeta(3)}(\frac{v^2}{2c^2}E + \frac{\Psi}{\psi}E + (\frac{T_0}{T})\frac{P}{\rho}E) = \mathbf{C}_{vac}[/math]

 

Let's distribute the energy for clarity:

 

And it is this factor, I wish us to concentrate on [math]\frac{v^2}{2c^2}E[/math] for we will recall the importance of this term through the modified Einstein mass-equivalence as being now a momentum operator:

 

So the right-moving energy carries extra momentum [math]\Delta p[/math] we then have

 

[math]\Delta p =\frac{v}{2c^2}E[/math]

 

again, to keep on the same page, the left-moving energy will carry a little less momentum, by the same quantity [math]\Delta p[/math] such that the total right-momentum in the energy is twice the value of [math]\Delta p[/math]. This is the right-momentum energy lost from the system (universe)

 

[math]2\Delta p=\frac{v}{c^2}E[/math]

 

The momentum of the universe moving in the directional frame after the emission is reduced by the amount of 

 

[math]p′ = mv−2\Delta p = (m − \frac{E}{c^2})v[/math]

 

But these extra equations will come later into the model. In direct replacement of the given term of interest we now have an energy equation

 

[math]\frac{6114}{60} \cdot \frac{\zeta(4)}{\zeta(3)}(\Delta p + \frac{\Psi}{\psi}\frac{v}{c^2}E + (\frac{T_0}{T})\frac{P}{\rho}\frac{v}{c^2}E) = \mathbf{C}_{vac}\ (\frac{1}{v})[/math]

 

The first modified term in the parenthesis on the left hand side, now takes into respect its full glory - it is telling which way the universe should expand based from the physics we unified throughout these posts. I'll leave it at that for now... we'll see if it takes any interest or perhaps some people will like to add their own knowledge to these thoughts.

Edited May 5, 2019 by Dubbelosix

[Dubbelosix]

I meant to say, we have a new coefficient, not of 3072 but now with 6114 obtained from the factor of 2 with follows from the modified Einstein  mass energy equivalence equation

 

 

[math]  \frac{6114}{60} \cdot \frac{\zeta(4)}{\zeta(3)}(\Delta p + \frac{\Psi}{\psi}\frac{E}{v} + (\frac{T_0}{T})\frac{P}{\rho}\frac{E}{v}) = \frac{1}{v}\mathbf{C}_{vac}[/math]

 

Or simply retrieve

 

 

[math]  \frac{6114}{60} \cdot \frac{\zeta(4)}{\zeta(3)}(\Delta p v + \frac{\Psi}{\psi}E + (\frac{T_0}{T})\frac{P}{\rho}E) = \mathbf{C}_{vac}[/math]

 

With [math]2 \Delta pv = \frac{v^2}{c^2}E[/math].

Edited May 5, 2019 by Dubbelosix

[Dubbelosix]

Number Crunching

 

And since we have been number crunching in the last posts, the new coefficient should be given the same respect… so much work, will probably take a good few weeks of investigation, assuming anything interesting can be found.

 

 

[math]\frac{6114}{60} = 67\ \frac{84}{90}[/math]

 

We get this by converting the improper fractions, like before, into mixed numbers for

 

[math]\frac{3072}{60} = 51\ \frac{12}{60}[/math]

 

In another approach, we did consider

 

[math]\frac{3072}{60 \cdot 90}[/math]

 

In which the denominator of [math]90[/math] (which came from [math]\zeta(4) = \frac{\pi^4}{90}[/math] can be considered with its conversation into mixed numbers yield

 

[math]\frac{3072}{60} = 34\ \frac{12}{90}[/math]

Edited May 5, 2019 by Dubbelosix

[Dubbelosix]

And of course, will be continued later.

[Dubbelosix]

And of course, will be continued later.

 

You can follow as usual the compact work found here:

 

https://prebigbangstate.quora.com/Talking-About-A-Mechanical-Cosmological-Constant?fbclid=IwAR1k-phhLyYqNCln1ig8oafAojpMuS-H6R_nyct3b4RqihK21DJeWxpsOGo

 

edit: after more number crunching, I will write up the full derivation so it can be followed through more concisely. If you keep up with it, you are probably doing better than most at the forum and better yet, if you ever see something that takes your eye, speak up, as it will be noted in my blog with a reference.

Edited May 5, 2019 by Dubbelosix

[Dubbelosix]

Fair enough question - I haven't changed my mind as such, because both these idea's are important for different reasons. For instance, a rotating universe could explain dark energy as a pushing force outwards (centrifugal) but the rotation imprint on the background no longer exists, so my question wasn't entirely resolved then, because what would continue the expansion? Of course, rotation was important in my eyes to justify the full Poincare group of space symmetries.

 

On the other hand, we have this model in this thread, one which proposes a purely classical model and explains the dark energy as a difference in fluid pressure. If I was to be asked which model I favor, I would say this one, because it is more exact with what we could possibly measure, more exact perhaps, in the sense there is no ad hoc argument, everything has a mechanical, classical and almost complete explanation. There are details I need to work through though. The Friedmann equation, is a fluid equation - that can be easily shown from similarities I found between the expanding model and that found in equations describing sonoluminscence.

 

Now for the other questions... yes, dark energy in this model will become a type of pressure difference. Photons do indeed travel at the speed of light, except for in gravitational fields - that type of investigation would lead to a gravitational aether. The speed of light, would be accordingly, slower in the past due to strong gravitational fields, but that premise depends on the permittivity and permeability of space as well. Deriving a speed of light would be relatively simple, so long as you properly attribute the varying properties of spacetime (including the important parameters) [math]c^2 = \frac{1}{\mu_0 \epsilon_0}[/math] ~ https://en.wikipedia.org/wiki/Permittivity

 

The idea of a varying speed of light has been considered in the past - Barrow for instance, took a different approach and said the speed of light was many magnitudes larger than what we observe today. But how to make sense of that with an extremely dense gravitational past, is uncertain to me. As for the last question, I try and stay away from extra universes, or inflation idea's. There are good reasons to suggest the latter, but what nature of inflation we speak of is a very important question and perhaps we should only remain with the science which can be tested through observation.

 

The unification of a Friedmann universe with Bernoulli's principle, seemed like a natural thing to do in my eyes, what I never contemplated to find was a very natural explanation for why the universe prefers to expand than to contract. Whether this is important, may just be in the eyes of the beholder (me). To others, the idea may seem like a waste of time.

Edited May 7, 2019 by Dubbelosix

[Dubbelosix]

I mentioned the HUP as a possible cause for any inflationary pressure, there are other possibilities of radiation pressure, including the HUP/zero point energy, CBR, and even radiation from super novaes, suns and black holes event horizons. It is known that radiation pressure can cause a pressure.

 

I mentioned Penroses Aeons not multiverses, which gives recurring big bangs separated by vast distances of time. Yes no evidence has been found for such a thing, but Penrose and his students are looking.

 

A gradual increase in acceleration of the universe might lead to an Inflationary stage as gravitational effects tend towards zero. What I was musing over is could the expansion of space in regions where there are no galaxies be growing faster than near galaxies, inflation does not need to be uniform, except in an idealized simplified model. Some dark matter effects seen in apparently empty areas of space could be due to something like this, perhaps resulting in particle creation via separation of virtual particle pairs. This could result in clouds of gas like nebulae that could form stars but from a cold origin.

 

The CBR is evidence for particle creation in the theoretical hot big bang, It could also be evidence for particle creation and annihilation at much lower temperatures, in an expanding/inflationary region of space. CBR seems fairly uniform, and apart from a mathematical model :) that shows in the beginning there was light, and a hot big bang. It could be due to something else testable in the lab.

 

Considering particle creation at low temperature > We know in a vacuum photons and even particles can on occasion spontaneously occur. Could this be due to a localized inflationary event, at the quantum level separating virtual particle pairs, rather than on a universal scale happening in fractions of a second.

 

Slow particle creation over Aeons resulting in nebulae might be more plausible than an instantaneous big bang. When virtual particles are separated momentarily and come back together, they have inertia, which could result in them giving of a photon on annihilation, which might cause more radiation pressure and more expansion causing the universe to expand. An argument against this is the universe would get hot, but would this be the case if it was expanding at approximately the correct speed, or photons are being absorbed by blackholes etc.

 

 

 

Sure, the idea of Aeons coalesces well with the predictions we can try and make, but remember I also said that the model of a recurring big bang suffers a comprehensive flaw concerning density. In Penroses model, he suggests the universe gets large enough that it ''forgets'' its own size (because there are no longer clocks in the universe, just pure radiation) and it starts all over again - for his model to succeed it would require that it also forgets what density it also is - we know with good accuracy the past phase of the universe was extremely dense, while this later phase is in all respects, much more diluted, a radiation phase over vast distances (due to the Aeons it takes for these supermassive black holes to finally give up the last of their mass due to Hawking radiation).

 

Radiation pressure certainly would be one of the first causes I would venture to look for - also notice in Penroses model, we do not require a universe to ''come from'' a quark gluon plasma, all you need is radiation and the right conditions for that radiation phase to transpose into matter. Indeed, there are good reasons to think that in the beginning, there was light, as the Bible states - we think it is a possibility because of the special decay process as a universal law to all matter systems when they interact with antimatter. You could, and this is purely theoretical, imagine a total equality of a creation of matter and antimatter in the most earliest phases and what we call the distant radiation phase was in fact a result of this collision, but then we would have to seek a CPT violation to explain why the radiation transposed more into matter than antimatter.

 

Remember our conversations on the issue of gravitational binding - as I said, and I still stand by this, the cosmological constant really is a constant and it is the gradual expansion which increases due to a weakening of the gravitational binding, but this requires a whole new refreshing look at a new type of cosmology where we might have to ignore inflation altogether. Let me explain, for instance, it was a while back, you don't need inflation to explain a synthesis of matter, it was originally proposed to try and explain the homogeneity of the distribution of light and matter in the universe. Barrow and possibly Narlikar had shown that a slow expanding universe, which slowly synthesized particles as it grew, would answer the homogeneity problem without inflation.

 

That would mean inflation no longer would be required to explain nucleosynthesis, instead, we would require a purely gravitational explanation, quantized no less and it was distributed evenly as it grew in size. The apparent acceleration would not be due to a changing cosmological constant but instead it would only appear to change. The real factor that has been largely ignored is the weakening of gravity as it grows. So if the constant of dark energy is indeed, constant, then the intensity of that constant would only appear to change, but is really due to a weakening of the binding energy as it grew.

 

I don't hold much confidence in early models, because for these early models, which include inflation and other various parameters, to be just right, to me seems very unlikely. How many times has classical physics been reconstructed to make sense of the curvature of spacetime? To think we had it right on the first go, would be very egocentric - but you can't blame physicists for being gung-ho concerning these matters, when they have spent most of their life on them. But as Hawking once said, the best science comes from falsification, not the models which get it right first time, and even then, who is to say the theory is right. All we need is a model, which makes testable predictions that can help shed light on different aspects of the universe that we have so insidiously attempted to explain with archaic models which for some reason, took the stage and hasn't budged for new models to take hold. Even Hawking entertained that the universe could very well spinning, its only that it can only be currently spinning at a very slow speed (dark flow). That doesn't rule out of course that the spinning nature cannot exponentially decrease and in fact was shown again by Hoyle and Narlikar that a rotary property of a universe does indeed exponentially decay as linear expansion takes over, so dark flow in conclusion, could be the last evidence of this ''primordial spin'' ... something I myself has called a residue but possibly an important feature we need to look more into.

Edited May 7, 2019 by Dubbelosix

[Dubbelosix]

In short, the cosmology we have learned, is likely not how it all is, if it is at all. Cosmology needs to make remarkable steps to investigate all avenues, then logic can proceed from that to determine which model is most likely.

[Dubbelosix]

Also, I should have mentioned, a rotary property in past, must require a Lorentz violation in which there is in fact a preferred frame - this would lead to a CPT violation for how radiation transposed into matter rather than antimatter. Such approaches will also lead to absolute accelerations (according the Carrol).

[rhertz]

The Phase Transition Equation (as I call it) is not however a unification equation, it's a phase transition formula for how a universe can change from a condensed form, possibly an all-matter or all-energy form pre existing the big bang as we know it...

 

https://prebigbangstate.quora.com/Key-Equation-To-Argue-For-a-Pre-Big-Bang-Phase

 

The Unification Equation, involves not unification per se, but will pave a way towards the unification process: The instructions from the modified Friedmann equation I developed applied non-classical laws to the Friedmann equation

 

The energy of each oscillator needs to be attributed to the Planck law as (using dimensionless form of entropy this time):

 

[math]\frac{\dot{R}}{R} (\dot{H} + H^2 + \frac{kc^2}{a}) = \frac{8 \pi G}{3}\ \sum_k\ ( [n_k + n S_k + n S_{ik}]\ \frac{\hbar \omega}{\frac{\hbar \omega}{k_BT} - 1})\frac{\dot{T}}{T}[/math]

 

 

With all due respect, as I'm not following the theory developed in this thread, I think that there is a mistake at the formula of each planckian oscillator.

 

It's something that I  noticed trying to follow the theory from the beggining.

 

Note: I can't write hbar here, so I'm replacing it with "h" and also replacing "w:omega" with "f".

 

The formula that appears is:   hf/( hf/(k_BT) - 1) , and it seems to represent the energy of a single planckian resonator.

 

The formula lacks the exponential term at the denominator, and should be:

 

hf/( e ^hf/(k_BT) - 1)

 

I hope you approve this correction.

 

Also, given the time derivative of T and the presence of the constant G, the term on the right side has units:

 

m^-3.N. m².kg⁻².erg.sec.sec^-1 = Newton².kg^-2  = Joule².m².kg^-2     (each color corresponds to each contributing term: n, G, hf and dT/dt)

 

On the left side term, the units seem to be:

 

s^-1. km².s^-2.km⁻¹   =  km.s^-3

 

Is this correct?

 

If not, I apologize for my errors interpreting the initial formula.

[Dubbelosix]

There is no mistake - I have already applied zero point energy oscillators to the equation, it turned out it was unnecessary - if at anything, it may turn out to be semi-classical solution. But this is leagues beyond what I have calculated, I have found a purely classical solution to the cosmological constant.

 

As I said to previous posters, if you are unsure about something, I will gladly explain, I will even reiterate these zero point corrections to an expanding universe. The zero point energy is electromagnetic in nature, which is why the previous poster (flummoxed) pointed out the obvious - radiation pressure can happen in any electromagnetic situation.

[Dubbelosix]

Your units are wrong, probably based on a misconception on how I invited to remove the constant G. We use in this example, a cgs unit base for Newtons constant. Otherwise, everything is dimensionally sound, been over it several times just to make sure, which is why I am confident. I have shown it to at least one scientist who didn't seem to object. 

[Dubbelosix]

I certainly approve the correction, but you need to follow links provided which shows this correction for the Friedmann expansion phase. 

[rhertz]

I certainly approve the correction, but you need to follow links provided which shows this correction for the Friedmann expansion phase. 

 

Thanks. it means a lot for me, coming from you.

 

Greetings,

 

Richard