Universal 'Now' at Time-Zero

[Mordred]

No problem, now in Cosmology we deal more with the global influences rather than localized. The equations above provide an adequate demonstration of how large scale structure formation affect the global density of matter.

Rather than use the numerous localized hydrodynamic equations, we can average the matter/radiation etc influence into a value called critical density. The critical density without the cosmological constant, is a calculated value that represents the turning point between a contracting or expanding universe. The actual density average compared to the critical density, gives us the universe curvature constant. k

I wrote an article covering this in my universe geometry article on the site in my signature.
http://cosmology101.wikidot.com/universe-geometry

page 2
http://cosmology101.wikidot.com/geometry-flrw-metric/

I didn't go into detail on the FLRW fluid equation nor the deceleration equation as I focused on the distance metrics. However the Weise article has those key formulas

 

To focus on your original question, since we know so little about the initial Planck epoch is there any point in even attempting to define predecessors?

 

The article previously linked by Strange seems to suggest that there are very few quantities to consider. Just a speck of Bose-Einstein condensate (edit) 'stuff' at the Planck temperature crammed into the infinitesimally tiny Planck volume.

 

There's probably quite a few paradoxes at large here, but one that sparks my interest is what's happening to system entropy. If any physical laws do persist back to such phases, I'm guessing the 2nd Law has as good a chance as any. The old definition

 

dS=dQ/T

 

.

 

 

the equation you want in this instance is the thermodynamic equation of an adiabatic fluid. Meaning no net inflow or outflow.

 

I wrote this earlier to demonstrate how the radiation and matter equations of state are derived from the first law of thermodynamics.

 

[latex]DU=pdV[/latex].

First take the first law of thermodynamics.
[latex]dU=dW=dQ[/latex]
U is internal energy W =work.
As we dont need heat transfer Q we write this as [latex]DW=Fdr=pdV[/latex]
Which leads to [latex]dU=-pdV.[/latex]. Which is the first law of thermodynamics for an ideal gas.
[latex]U=\rho V[/latex]
[latex]\dot{U}=\dot{\rho}V+{\rho}\dot{V}=-p\dot{V}[/latex]
[latex]V\propto r^3[/latex]
[latex]\frac{\dot{V}}{V}=3\frac{\dot{r}}{r}[/latex]
Which leads to
[latex]\dot{\rho}=-3(\rho+p)\frac{\dot{r}}{r}[/latex]
We will use the last formula for both radiation and matter.
Assuming density of matter
[latex]\rho=\frac{M}{\frac{4}{3}\pi r^3}[/latex]
[latex]\rho=\frac{dp}{dr}\dot{r}=-3\rho \frac{\dot{r}}{r}[/latex]
Using the above equation the pressure due to matter gives an Eos of Pressure=0. Which makes sense as matter doesn't exert a lot of kinetic energy/momentum.
For radiation we will need some further formulas. Visualize a wavelength as a vibration on a string.
[latex]L=\frac{N\lambda}{2}[/latex]
As we're dealing with relativistic particles
[latex]c=f\lambda=f\frac{2L}{N}[/latex]
substitute [latex]f=\frac{n}{2L}c[/latex] into Plancks formula
[latex]U=\hbar w=hf[/latex]
[latex]U=\frac{Nhc}{2}\frac{1}{L}\propto V^{-\frac{1}{3}}[/latex]
Using
[latex]dU=-pdV[/latex]
using
[latex]p=-\frac{dU}{dV}=\frac{1}{3}\frac{U}{V}[/latex]
As well as
[latex]\rho=\frac{U}{V}[/latex]
leads to
[latex]p=1/3\rho[/latex] for ultra relativistic radiation.
Those are examples of how the first law of thermodynamics fit within the equations of state. There is more intensive formulas involved. In particular the Bose-Einstein statistics and Fermi-Dirac statistics

Edited August 23, 2016 by Mordred

[sethoflagos]

 

the equation you want in this instance is the thermodynamic equation of an adiabatic fluid. Meaning no net inflow or outflow.

 

I wrote this earlier to demonstrate how the radiation and matter equations of state are derived from the first law of thermodynamics.

 

[latex]DU=pdV[/latex].

First take the first law of thermodynamics.

[latex]dU=dW=dQ[/latex]

U is internal energy W =work.

As we dont need heat transfer Q we write this as [latex]DW=Fdr=pdV[/latex]

Which leads to [latex]dU=-pdV.[/latex]. Which is the first law of thermodynamics for an ideal gas.

[latex]U=\rho V[/latex]

[latex]\dot{U}=\dot{\rho}V+{\rho}\dot{V}=-p\dot{V}[/latex]

[latex]V\propto r^3[/latex]

[latex]\frac{\dot{V}}{V}=3\frac{\dot{r}}{r}[/latex]

Which leads to

[latex]\dot{\rho}=-3(\rho+p)\frac{\dot{r}}{r}[/latex]

We will use the last formula for both radiation and matter.

 

 

 

 

It certainly adds an extra dimension to trumpet practice to know that much the same basic equations that describe the isentropic interchange of internal energy and kinetic energy inside a trumpet can also be used to describe the evolution of the universe (albeit with a slightly different cosmological constant - the trumpet universe needs to expand and collapse indefinitely).

 

Isn't physics wonderful!!

[Mordred]

Yes people get distracted by pop media coverage of dark matter and dark energy when it comes to expansion.

Those people tend to gloss past the related math, so seldom see the thermodynamic relations. Another pop media distraction is the entropy arrow of time. In statistic mechanics this is simply time reversal symmetry.

 

Everyday statistic mechanics is an essential aspect to understand expansion of the universe. Baryonic matter, dark matter and radiation are all described.

 

Dark energy aka the Cosmological constant is still giving scientists trouble. Not because its present but that it is so fine tuned and constant as the volume expands.

 

Unlike any other particle field in statistic mechanics.

 

However if the Higgs metastability proves accurate, the cosmological constant and inflation could very well be explained via the Higgs field in SO (10) MSM.

 

MSM is minimal symmetric model (minimal standard model).

 

Just remember the universe follows an adiabatic expansion ( no inflow or outlow) there is no need for an outside of the universe. The container walls are determined by other particles and the rate of particle movement in a medium. (those sound waves for example of the CMB.)

 

Now here is a key detail....

 

In a homogeneous and isotropic distribution. There is no net directional flow, nor is there any density gradient.

 

So although temperature or pressure can perform the work for expansion, expansion is not described accurately as a higher density flowing to a lower density. Though lower density is a result, there is no flow. The expansion is a relationship between the universe self gravity vs the inherent kinetic energy of the particle contributors. Much like the same relation in the matter dominant and Jeans instability relations I described previously.

 

PS sounds to me that you have a decent understanding of the ideal gas laws and thermodynamics. This is excellent for understanding Cosmology. It places you ahead of many members that ignore those thermodynamics. When you get down to it, statistical mechanics is just as important as relativity and particle physics in cosmology.

Edited August 23, 2016 by Mordred

[sethoflagos]

Now here is a key detail....

 

In a homogeneous and isotropic distribution. There is no net directional flow, nor is there any density gradient.

 

So although temperature or pressure can perform the work for expansion, expansion is not described accurately as a higher density flowing to a lower density. Though lower density is a result, there is no flow. The expansion is a relationship between the universe self gravity vs the inherent kinetic energy of the particle contributors. Much like the same relation in the matter dominant and Jeans instability relations I described previously.

 

 

 

Much like bread dough or cake mix rising?

 

 

PS sounds to me that you have a decent understanding of the ideal gas laws and thermodynamics. This is excellent for understanding Cosmology. It places you ahead of many members that ignore those thermodynamics. When you get down to it, statistical mechanics is just as important as relativity and particle physics in cosmology.

 

 

Small advantage of spending much of my 40 year career designing steam and gas turbine based power generation plant, and natural gas compression and processing facilities. Be a sorry state of affairs if I hadn't picked up some understanding of it

 

Now that I don't work full time, it's good to be able to look at some of the more interesting stuff that never made it into any of my past project engineering scopes of work.

Edited August 23, 2016 by sethoflagos

[Mordred]

Much like bread dough or cake mix rising?

 

.

Very much so in terms of geometric seperation distances and angles between measurement points. Just remember there is no outside in the raisin bread analogy.

 

It also shows the pressure relations to seperation relations.

 

take each raisin as a measurement point. Each raisin has the same surrounding pressure (the bread dough). By Newtons laws there is no net directional force. The seperation is due to density reduction of the dough. Yet no raisin can gain inertia by Newtons laws as they have a surrounding fluid that is uniform in density.

Edited August 23, 2016 by Mordred

[sethoflagos]

Very much so in terms of geometric seperation distances and angles between measurement points. Just remember there is no outside in the raisin bread analogy.

 

If I was very small and buried deep inside the mix, I guess the concept of an external crust would be simply speculative.

[Mordred]

A crust would indicate a bound universe or finite universe. We don't know if the universe is finite or infinite. The metrics we show for expansion is our Observable portion of the entire universe. Thankfully those metrics still work regardless if the universe is finite or infinite. The finite point of the BB being smaller than an atom is only our observable portion in the past. By the way +1 on your comprehension thus far.

Edited August 23, 2016 by Mordred

[sethoflagos]

By the way +1 on your comprehension thus far.

 

Thanks for pitching your answers at a level that's accessible to the layman. I'll start to struggle when Riemann manifolds and Hamiltonians start being mentioned. Kreysig's Engineering Mathematics didn't cover that kind of stuff.

 

One impression I've got from these discussions is that as we track back to the earliest history, vectors and tensor quantities tend to disappear in phase transitions leaving simpler (to me!) scalar quantities like temperature, density, and (as I understand it - I don't) the Higgs.

 

Is there some sense that 'direction' ceases to be meaningful, or is this just another figment of my imagination?

 

 

PS. I'm quite prone to saying 'That's the wrong question' myself, so I won't sulk if that's the best answer!

Edited August 23, 2016 by sethoflagos

[Mordred]

I'm assuming your asking when a vector vs a scalar quantity best describes the system state. This is a seemingly easy question but one has to be careful on answering. The care being what the scalar or vector quantity being measured represents. Certain quantities such as temperature and spin zero particle fields suit being scalar fields as there is no inherent direction to those fields. A spin zero particle field being the Higg's field. The electromagnetic field however has charge, this charge has two inherent directions adding degrees of freedom to the system state. This type of interaction is best described by vector fields. Now particle color, and flavor adds additional degrees of freedom. You can think of color and flavor as a form of charge, but in the case of color you have 3 charges. Which describes your strong force. Gravity suits spin 2 statistics, which is rather tricky to describe. You would have to google quadrupole wave to see what I mean.

 

However that's the spin aspects of the Bose-Einstein and Fermi-Dirac statistics...which I assume the question relates to.

 

So essentially as the temperature rises, more and more particles reach thermal equilibrium. This reduces the number of degrees of freedom. As the guage bosons for each force reach thermal equilibrium, we lose the interactions of those forces. When the electomagnetic, weak force and strong force all unify we no longer have any charge dynamics. This system can now be modelled as a scalar field regardless of scale. In terms of thermodynamics this state occurs at the Vacuum expectation value or VeV.

 

The equation of state for a scalar field is the last formula on this page.

 

https://en.wikipedia.org/wiki/Equation_of_state_%28cosmology%29

 

under scalar modelling...

 

For the four forces treating gravity as a force.

 

electromagnetic spin 1

weak spin 1

strong spin 1.

gravity spin 2.

 

As you study the Weise paper chapter 3 and 4 pay attention to the degrees of freedom due to the boson to fermionic interactions in terms of spin.

Ie spin 1/2 electron with photon spin 1 as the guage boson...

 

Higgs field isn't a force but its field is spin 0.

Edited August 23, 2016 by Mordred

[sethoflagos]

 

 

However that's the spin aspects of the Bose-Einstein and Fermi-Dirac statistics...which I assume the question relates to.

 

 

Hmm, it was the wrong question wasn't it.

 

Just really trying to get a feel for what factors dominate the dynamics of 'fluids' that are unfamiliar to me.

 

I'm having difficulty coming to terms with the concept of 'radiation density' in the Friedmann Equation you posted earlier. My mind was forever corrupted by inaccurate explanations of the Crookes Radiometer at school. I can sort of get my head around waves gaining mass by confinement within a particle, and grasp the concept of mass-energy equivalence at an algebraic level at least. But I'm still unable to visualise 'free' photons having a mass density. If it's by some form of confinement, then what's confining them?

 

EDIT: Your post has grown since I last looked at it! Some wonderful stuff there. Yes, degrees of freedom is very relevant to where my head was going - the development of complexity, or some analogue of the progression from simple streamline flow to fully turbulent (locally chaotic/globally homogeneous).

Edited August 23, 2016 by sethoflagos

[Mordred]

Your missing a key detail on mass, which as you already know is "resistance to inertia change". however although the photon has no "rest mass" now called invariant mass. The photon has inertia mass equivalence. What used to be called relativistic mass.

 

the formula [latex]e=mc^2[/latex] isn't complete, when you add the momentum term the total energy of the particle becomes.

 

[latex]e^2=p^2c^2+m^2c^4[/latex]

 

so lets use an everyday real world test...

 

a particle accelerator fires two protons, as the protons gain inertia they gain total energy. This allows us to create particles will far higher mass than the rest mass of the two protons. Ever wonder how two protons could make a Higg's Boson?

 

This applies to relativistic radiation. We apply the total energy of all particles, also the sequence that particles drop out of thermal equilibrium also depends on total energy of the particle. So the photon has one of the highest "total mass" values. Due to its extreme kinetic energy...

 

https://en.wikipedia.org/wiki/Mass#Inertial_vs._gravitational_mass

Edited August 23, 2016 by Mordred

[sethoflagos]

Your missing a key detail on mass.......

 

the formula [latex]e=mc^2[/latex] isn't complete.......

 

[latex]e^2=p^2c^2+m^2c^4[/latex]

 

 

THAT makes a difference! (I'll go and sleep on that one. Good night, and thank you again!)

[Mordred]

 

EDIT: Your post has grown since I last looked at it! Some wonderful stuff there. Yes, degrees of freedom is very relevant to where my head was going - the development of complexity, or some analogue of the progression from simple streamline flow to fully turbulent (locally chaotic/globally homogeneous).

 

excellent +1particularly (locally chaotic/globally homogeneous and isotropic aka uniform)

Edited August 24, 2016 by Mordred

[michel123456]

 

THAT makes a difference! (I'll go and sleep on that one. Good night, and thank you again!)

What do you really know?

[sethoflagos]

What do you really know?

 

About what, Michel?

[michel123456]

About what, Michel?

about [latex]e^2=p^2c^2+m^2c^4[/latex]

It is a very basic formula.

All your previous posts gave me a mixed feeling of someone who knows much less than what he pretends to know.

[sethoflagos]

And where exactly in this thread did I claim any meaningful prior knowledge of cosmology? Though in the last 48 hours Mordred has been kind enough to open quite a few doors that were previously closed to me,

 

I don't really know why I'm bothering to respond to this. If you've nothing better than petulant ad hominems to offer, then you've nothing to offer. I suggest you learn to live with your mixed feelings.

[michel123456]

And where exactly in this thread did I claim any meaningful prior knowledge of cosmology? Though in the last 48 hours Mordred has been kind enough to open quite a few doors that were previously closed to me,

 

I don't really know why I'm bothering to respond to this. If you've nothing better than petulant ad hominems to offer, then you've nothing to offer. I suggest you learn to live with your mixed feelings.

I can do that.

[Bird11dog]

Gosh. I wonder why none of the experts in GR and cosmology have never considered that...

 

 

Good question, I would like to know.

[tar]

Mordred,

 

How does one properly conceive, all at once, of a cosmos whose size defies the possibility of it all happening at the same time?

 

Regards, TAR

[Bird11dog]

You can't or at least I can't.

[StringJunky]

Mordred,

 

How does one properly conceive, all at once, of a cosmos whose size defies the possibility of it all happening at the same time?

 

Regards, TAR

My original question related to when the universe was very dense, homogenous and the vacuum of space was yet to emerge

[tar]

StringJunky,

 

I apologize. I posted without reading the thread. But still, even dense and homogeneous, space, even without the vacuum in between matter, was still real. That is, something could be next to the thing next to it and two things away from the thing on the other side of the thing next to it. Immediate motion from one movement, affecting the entire collection of material, would not be possible any more than it is today, with vacuum of space between.

 

Regards, TAR

even the balls hanging in a row, where the end ball flies out when the other end is swung against the line, does not happen in a instant. The impulse takes some time to propagate according to the flex and recoil of the material the balls a made from. Fast as sound perhaps, but not instantaneous.

 

But that does ask the question of whether a 196 thousand mile long solenoid plunger, when engaged would have both ends move at the same time...meaning a signal could be transmitted instantaneously a light second away.

conceptualizing a cosmos has some drawbacks

 

during a concept, "here" is in the space between your ears

during a cosmos, here is as big as the place

Edited April 4, 2017 by tar

[Strange]

But that does ask the question of whether a 196 thousand mile long solenoid plunger, when engaged would have both ends move at the same time...meaning a signal could be transmitted instantaneously a light second away.

 

 

The signal would be transmitted at the speed of sound in the material.

[tar]

so "now" needs a reference point, in space

universal now would be as if time and space started at the same point. Same here, same now. Then as it progressed and bifurcated each piece could progress by the same amount of time, meaning the thing over here is happening at the same time as the thing over there, even though the impulses created by the one event would take time to get to the other here, and those impulses would arrive later.

 

Requiring two nows. The universal one, and the here and now one, experienced by any point in the cosmos. No point experiences the universal now, once there is more than one point. Vacuum of space, or homogeneous...same difference.

Strange,

 

I understand, but if the electromagnet that engages the solenoid shaft is on space station B and the one end of the shaft is on space station A and the other on space station C, the impulse moves through the shaft like a sound wave through steel and both ends, being 98 thousand miles from B would move at the same time. In StringJunky's dense and homogenous, prior vacuum cosmos, the impulse would move at the speed of sound, quite a bit slower than light, once the vacuum is available. Unless other sub atomic forces are as fast as light, in which case the solenoid shaft might not be limited to compressing a rarifying at the speed of sound, and communication between matter might be at light speed...or faster.

 

Regards, TAR

when you poke something with a stick, does it take the same time for sound to travel the distance of the stick as it does for the poke to travel the distance?