Wormhole Metric...... How is this screwed up.

[Vmedvil]

1 minute ago, Mordred said:

If you apply the above to each particle species to each corresponding equation of state derived using the above and using the Bose-Einstein/Fermi_Dirac statistics and can maintain a homogenous and isotropic state under rotation as the volume increases then yes. However keep in mind the article I posted on the upper boundary limits I posted earlier which applies the above.

Hold on stealing now.

[Mordred]

Forgot to add particles are always created in pairs matter/antimatter. Expansion separates those pairs allowing the decoupling from equilibrium.

[Vmedvil]

12 minutes ago, Mordred said:

Forgot to add particles are always created in pairs matter/antimatter. Expansion separates those pairs allowing the decoupling from equilibrium.

I made this equation to be easily changed but explain it detail what all that does it so i understand how it is to be used.

∇E_b(x,y,z,ω,M,R,I,ρ) = ∇(1/((1-(((2M_bG / R_s) - (I_sω_s²/2M_b) + (((8πG/3)((g/(2π)³)∫E(pf_pd³p) - (kC²/R²) + (Λ/3))^1/2Δx(1/3.08567782*10¹⁹)))²/C²))^1/2))M_bC²

Taking in account for now.

Edited November 22, 2017 by Vmedvil

[Mordred]

Ok this gets a bit complex. Think of particles as field excitations. Under QFT the operators correspond to the field itself as being the operator. Now particle production always occur in pairs to maintain the conservation laws applicable to the Eightfold Wayen. Conservation of charge, lepton number, parity, flavor,color,parity etc. Ordinarily these pairs would annihilate however they get separated via expansion depending on their momentum and rate of expansion in essence. Now unfortunately we encounter an assymetry in this in that for some unknown reason the number density of matter vs antimatter don't stay balanced. Which is good as the universe wouldn't exist without this assymmetry. This is one of the unsolved problems called leptogenesis and baryogenesis. Afiak the best viable solution involves the Higg's field but this work is still under scutiny.  Its actually where my current studies is focusing on The Higg's field involvement in the FRW metric though I have run into a few problems. Mainly lack of applicable observational data lol though that is coming in gradually via CERN etc. The main problem is the seesaw mechanism itself

Edited November 22, 2017 by Mordred

[Vmedvil]

3 minutes ago, Mordred said:

Ok this gets a bit complex. Think of particles as field excitations. Under QFT the operators correspond to the field itself as being the operator. Now particle production always occur in pairs to maintain the conservation laws applicable to the Eightfold Wayen. Conservation of charge, lepton number, parity, flavor,color,parity etc. Ordinarily these pairs would annihilate however they get separated via expansion depending on their momentum and rate of expansion in essence. Now unfortunately we encounter an assymetry in this in that for some unknown reason the number density of matter vs antimatter don't stay balanced. Which is good as the universe wouldn't exist without this assymmetry. This is one of the unsolved problems called leptogenesis and baryogenesis. Afiak the best viable solution involves the Higg's field but this work is still under scutiny.  Its actually where my current studies is focusing on The Higg's field involvement in the FRW metric though I have run into a few problems. Mainly lack of applicable observational data lol though that is coming in gradually via CERN etc. The main problem is the seesaw mechanism itself

Second question when it says ρ =(g/(2π)³)∫E(p f(p )d³p

is f(p ) with respect to or an actual variable, same with d³p

Edited November 22, 2017 by Vmedvil

[Mordred]

function of the momentum ie momentum as a function

Edited November 22, 2017 by Mordred

[Vmedvil]

34 minutes ago, Mordred said:

function of the momentum ie momentum as a function

So, as respect to, then this is wrote correctly.

∇E_b(x,y,z,ω,M,R,I,ρ) = ∇(1/((1-(((2M_bG / R_s) - (I_sω_s²/2M_b) + (((8πG/3)((g/(2π)³)∫E(pf_pd³p) - (kC²/R²) + (Λ/3))^1/2Δx(1/3.08567782*10¹⁹)))²/C²))^1/2))M_bC²

Basically, are those nested variables or with respects to, respects get subbed.

Wait I see what you did now, okay Hold on.

∇E_b(x,y,z,ω,M,R,I,ρ) = ∇(1/((1-(((2M_bG / R_s) - (I_sω_s²/2M_b) + (((8πG/3)((g/(2π)³)∫(p² + m_p²)^1/2(1/e^E-μ/T±1)d³p) - (kC²/R²) + (Λ/3))^1/2Δx(1/3.08567782*10¹⁹)))²/C²))^1/2))M_bC²

Edited November 22, 2017 by Vmedvil

[SuperPolymath]

25 minutes ago, Mordred said:

Ok this gets a bit complex. Think of particles as field excitations. Under QFT the operators correspond to the field itself as being the operator. Now particle production always occur in pairs to maintain the conservation laws applicable to the Eightfold Wayen. Conservation of charge, lepton number, parity, flavor,color,parity etc. Ordinarily these pairs would annihilate however they get separated via expansion depending on their momentum and rate of expansion in essence. Now unfortunately we encounter an assymetry in this in that for some unknown reason the number density of matter vs antimatter don't stay balanced. Which is good as the universe wouldn't exist without this assymmetry. This is one of the unsolved problems called leptogenesis and baryogenesis. Afiak the best viable solution involves the Higg's field but this work is still under scutiny.  Its actually where my current studies is focusing on The Higg's field involvement in the FRW metric though I have run into a few problems. Mainly lack of applicable observational data lol though that is coming in gradually via CERN etc. The main problem is the seesaw mechanism itself

Yeah, I had heard about that. We shouldn't exist because am & m should have cancelled during the big bang. That's probably the only problem my pet theory thread didn't address intentionally. I was more focused on unification, de & the cosmological constant & the essence of mass (dm & higgs field included) & paradoxes & spookiness in QM. Suffice it to say, with what I addressed I would have had to have inadvertently addressed the m & am issue in some way.

Edited November 22, 2017 by SuperPolymath

[Mordred]

2 minutes ago, SuperPolymath said:

Yeah, I had heard about that. We shouldn't exist because am & m should have cancelled during the big bang. That's probably the only problem my pet theory thread didn't address intentionally. I was more focused on unification, de & the essence of mass (dm & higgs field included) & paradoxes & spookiness in QM. Suffice it to say, with what I addressed I would have had to have inadvertently addressed the m & am issue in some way.

Yes correct you would have at some point needed it.

20 minutes ago, Vmedvil said:

So, as respect to, then this is wrote correctly.

∇E_b(x,y,z,ω,M,R,I,ρ) = ∇(1/((1-(((2M_bG / R_s) - (I_sω_s²/2M_b) + (((8πG/3)((g/(2π)³)∫E(pf_pd³p) - (kC²/R²) + (Λ/3))^1/2Δx(1/3.08567782*10¹⁹)))²/C²))^1/2))M_bC²

Basically, are those nested variables or with respects to, respects get subbed.

Wait I see what you did now, okay Hold on.

∇E_b(x,y,z,ω,M,R,I,ρ) = ∇(1/((1-(((2M_bG / R_s) - (I_sω_s²/2M_b) + (((8πG/3)((g/(2π)³)∫(p² + m²)^1/2f_pd³p) - (kC²/R²) + (Λ/3))^1/2Δx(1/3.08567782*10¹⁹)))²/C²))^1/2))M_bC²

man I hate reading equations in this format let me go thru this tomorrow its late atm and I'm starting to not think clearly

[Vmedvil]

∇E_b(x,y,z,t,ω,M,I,ρ) = ∇(1/((1-(((2M_bG / R_s) - (I_sω_s²/2M_b) + (((8πG/3)((g/(2π)³)∫(p² + m_p²)^1/2(1/e^(E-μ/T)±1)d³p) - (kC²/R²) + (Λ/3))^1/2Δx(1/3.08567782*10¹⁹)))²/C²))^1/2))M_bC²

Okay, I finally got what those meant when i was rereading the post.

 

Edited November 22, 2017 by Vmedvil

[Mordred]

this will be better if I work up some FRW solutions to see the above but will have to do this tomorrow. It will help understand how the EoS applies to the fluid equations via the FRW metric.

[SuperPolymath]

35 minutes ago, Mordred said:

Yes correct you would have at some point needed it.

I remember thinking that what annihilation would leave in its wake were rapidly evaporating microversal scale cosmic unit black holes in a pre-CMB, CDM state, just like a big rip. Whatever is pulled back by the expansion generated by BH shrinkage would have to be causally synchronized by gravity, just like all particle pairs

You can have a duodecillion black holes, each with a different spin, if they merge, there's only going to be one spin.

Some of the ideas in that thread were out there, but I think they could have been, possibly, applicably prescient. Way ahead of the norm.

Highly imaginative & speculative, stoically poetic even, but somehow infused with a certain grounded logic. It was about addressing the greatest amount of questions with the fewest amount of answers - & those answers seem to work for everything that's challenging them.

Edited November 22, 2017 by SuperPolymath

[Vmedvil]

1 hour ago, Vmedvil said:

∇E_b(x,y,z,t,ω,M,I,ρ) = ∇(1/((1-(((2M_bG / R_s) - (I_sω_s²/2M_b) + (((8πG/3)((g/(2π)³)∫(p² + m_p²)^1/2(1/e^(E-μ/T)±1)d³p) - (kC²/R²) + (Λ/3))^1/2Δx(1/3.08567782*10¹⁹)))²/C²))^1/2))M_bC²

Okay, I finally got what those meant when i was rereading the post.

 

Actually this solved cleaner than I thought, now ω_s²  = k² + m_k²

∇E_b(x,y,z,t,ω,M,I,ρ,m) = ∇(1/((1-(((2M_bG / R_s) - (I_s(k_s² + m_k²)/2M_b) + (((8πG/3)((g/(2π)³)∫(p² + m_p²)^1/2(1/e^{((E - μ)/T)}±1)d³p) - (k_sC²/R_s²) + (Λ/3))^1/2(Δx/3.08567758128*10¹⁹)))²/C²))^1/2))M_bC²

 

45 minutes ago, Vmedvil said:

Actually this solved cleaner than I thought, now ω_s²  = k² + m_k²

∇E_b(x,y,z,t,ω,M,I,ρ,m) = ∇(1/((1-(((2M_bG / R_s) - (I_s(k_s² + m_k²)/2M_b) + (((8πG/3)((g/(2π)³)∫(p² + m_p²)^1/2(1/e^{((E - μ)/T)}±1)d³p) - (k_sC²/R_s²) + (Λ/3))^1/2(Δx/3.08567758128*10¹⁹)))²/C²))^1/2))M_bC²

 

Where I_s = (1/12)ML²

∇E_b(x,y,z,t,ω,M,I,ρ,m) = ∇(1/((1-(((2M_bG / R_s) - (M_bL_s²(k_s² + m_k²)/24M_b) + (((8πG/3)((g/(2π)³)∫(p² + m_p²)^1/2(1/e^{((E - μ)/T)}±1)d³p) - (k_sC²/R_s²) + (Λ/3))^1/2(Δx/3.08567758128*10¹⁹)))²/C²))^1/2))M_bC²

Or I_s = (1/2)MR²

∇E_b(x,y,z,t,ω,M,I,ρ,m) = ∇(1/((1-(((2M_bG / R_s) - (M_bR_s²(k_s² + m_k²)/4M_b) + (((8πG/3)((g/(2π)³)∫(p² + m_p²)^1/2(1/e^{((E - μ)/T)}±1)d³p) - (k_sC²/R_s²) + (Λ/3))^1/2(Δx/3.08567758128*10¹⁹)))²/C²))^1/2))M_bC²

Back to unsolved for anything.

∇E_b(x,y,z,t,ω,M,I,ρ) = ∇(1/((1-(((2M_bG / R_s) - (I_sω_s²/2M_b) + (((8πG/3)((g/(2π)³)∫(p² + m_p²)^1/2(1/e^(E-μ/T)±1)d³p) - (kC²/R²) + (Λ/3))^1/2(Δx/3.08567758128*10¹⁹)))²/C²))^1/2))M_bC²

Edited November 22, 2017 by Vmedvil

[Vmedvil]

7 hours ago, Vmedvil said:

Actually this solved cleaner than I thought, now ω_s²  = k² + m_k²

∇E_b(x,y,z,t,ω,M,I,ρ,m) = ∇(1/((1-(((2M_bG / R_s) - (I_s(k_s² + m_k²)/2M_b) + (((8πG/3)((g/(2π)³)∫(p² + m_p²)^1/2(1/e^{((E - μ)/T)}±1)d³p) - (k_sC²/R_s²) + (Λ/3))^1/2(Δx/3.08567758128*10¹⁹)))²/C²))^1/2))M_bC²

 

Where I_s = (1/12)ML²

∇E_b(x,y,z,t,ω,M,I,ρ,m) = ∇(1/((1-(((2M_bG / R_s) - (M_bL_s²(k_s² + m_k²)/24M_b) + (((8πG/3)((g/(2π)³)∫(p² + m_p²)^1/2(1/e^{((E - μ)/T)}±1)d³p) - (k_sC²/R_s²) + (Λ/3))^1/2(Δx/3.08567758128*10¹⁹)))²/C²))^1/2))M_bC²

Or I_s = (1/2)MR²

∇E_b(x,y,z,t,ω,M,I,ρ,m) = ∇(1/((1-(((2M_bG / R_s) - (M_bR_s²(k_s² + m_k²)/4M_b) + (((8πG/3)((g/(2π)³)∫(p² + m_p²)^1/2(1/e^{((E - μ)/T)}±1)d³p) - (k_sC²/R_s²) + (Λ/3))^1/2(Δx/3.08567758128*10¹⁹)))²/C²))^1/2))M_bC²

Back to unsolved for anything.

∇E_b(x,y,z,t,ω,M,I,ρ) = ∇(1/((1-(((2M_bG / R_s) - (I_sω_s²/2M_b) + (((8πG/3)((g/(2π)³)∫(p² + m_p²)^1/2(1/e^(E-μ/T)±1)d³p) - (kC²/R²) + (Λ/3))^1/2(Δx/3.08567758128*10¹⁹)))²/C²))^1/2))M_bC²

In any case, this would work in the L form.

You knew I would try it, chronon which equals  6.27×10^-24 Seconds where t_p = 5.39×10^-44
 seconds

 

Which goes to something odd with an electron. 

∇E_b(x,y,z,t,ω,M,I,ρ,m) = ∇(1/((1-(((2M_bG / R_s) - (M_b(ℓ(ℓ+1))ħ²(1.112121525278619076*10^-68)(((6.27×10^-24)Δ(e_c²(2.5669699216746244*10^-38)/6πε₀M_bC³)/(5.39×10^-44)Δt_p)(k_s² + m_k²)^1/2/24M_b) + (((8πG/3)((g/(2π)³)∫(p² + m_p²)^1/2(1/e^{((E - μ)/T)}±1)d³p) - (k_sC²/R_s²) + (Λ/3))^1/2(Δx/3.08567758128*10¹⁹)))²/C²))^1/2))M_bC²

e_c = -1

ℓ = 2

ħ = 1

R_s = radius of electron in meters.

M_b= Rest Mass of electron in Kilograms.

 

Edited November 22, 2017 by Vmedvil

[SuperPolymath]

16 hours ago, Vmedvil said:

We have not gotten to that part yet we are proofing this, where your model enters when ω² = k² + m² , somehow this needs to take account for expansion the equation which that is a solution to.

I think y'all have yet to define all 3 sources of the dynamic dark energy in my thread. You have late entropy stage mother black holes increasing the space-time via evaporation surrounding early entropy stage CMB bodies causing the isotropic qg plasma to break apart into the first atoms there. What happens with this new cosmic portion is anisotropic black hole sizes. As the universe section ages macro bh's become larger as they consume mass from matter & micro black holes (the higgs field that gives matter-energy mass & DM) shrink overall until a new late entropy section forms overlapping the previous one where those monster black holes of the previous one have been reduced to micro-bh's. 

Now those 2 sources alone would end in  an omega entropy state if not for source 3, the horizon of the white hole with contour=infinity is constantly absorbing parallel white holes beyond its horizon, continously adding additional energy-matter & space-time. This is the positive approx 2.5 dimensions (fractal geometry which allows the scale relativity Lorentz transformations in this model) that we experience, beyond that is an approx negative 2.5 dimension, these two space-times (de sitter & anti de sitter space) are literally the same but with opposite directions of space-time & negative matter-energy. Anti de sitter space is literally these perpendicular dimensions that give energy-matter mass as space-time gets turned inside out flowing through their event horizons it's curtain is yanked, these black holes of an infinity variety of sizes that occupy literally every point in space is behind the fundamental interactions (gravity, electromagnetic, strong & weak nuclear).

This 5 dimensional hypersphere is like a cosmic yin-yang symbol, or an infinitely long snake eating it's own tail.

Edited November 22, 2017 by SuperPolymath

[Mordred]

OK lets do some math to show some details first lets describe how the Bose Einstein works in a heuristic manner ie a more familiar examiniation

[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. You can fit that into the previous post where I detailed those statistics. This shoulld better help you understand that portion.

Now lets supply some details on GR in particular the Newton limit

Central potential and Newton limit

In the presence of matter or when matter is not too distant physical distances between two points change. For example an approximately static distribution of matter in region D. Can be replaced by the equivalent mass

[latex]M=\int_Dd^3x\rho(\overrightarrow{x})[/latex] concentrated at a point [latex]\overrightarrow{x}_0=M^{-1}\int_Dd^3x\overrightarrow{x}\rho(\overrightarrow{x})[/latex]

Which we can choose to be at the origin

[latex]\overrightarrow{x}=\overrightarrow{0}[/latex]

Sources outside region D the following Newton potential at [latex]\overrightarrow{x}[/latex]

[latex]\phi_N(\overrightarrow{x})=-G_N\frac{M}{r}[/latex]

Where [latex] G_n=6.673*10^{-11}m^3/KG s^2[/latex] and [latex]r\equiv||\overrightarrow{x}||[/latex]

According to Einsteins theory the physical distance of objects in the gravitational field of this mass distribution is described by the line element.

[latex]ds^2=c^2(1+\frac{2\phi_N}{c^2})-\frac{dr^2}{1+2\phi_N/c^2}-r^2d\Omega^2[/latex]

Where [latex]d\Omega^2=d\theta^2+sin^2(\theta)d\varphi^2[/latex] denotes the volume element of a 2d sphere

[latex]\theta\in(0,\pi)[/latex] and [latex]\varphi\in(0,\pi)[/latex] are the two angles fully covering the sphere.

The general relativistic form is.

[latex]ds^2=g_{\mu\nu}(x)dx^\mu x^\nu[/latex]

By comparing the last two equations we can find the static mass distribution in spherical coordinates.

[latex](r,\theta\varphi)[/latex]

[latex]G_{\mu\nu}=\begin{pmatrix}1+2\phi_N/c^2&0&0&0\\0&-(1+2\phi_N/c^2)^{-1}&0&0\\0&0&-r^2&0\\0&0&0&-r^2sin^2(\theta)\end{pmatrix}[/latex]

Now that we have defined our static multi particle field.

Our next step is to define the geodesic to include the principle of equivalence. Followed by General Covariance.

Ok so now the Principle of Equivalence.

You can google that term for more detail but in the same format as above [latex]m_i=m_g...m_i\frac{d^2\overrightarrow{x}}{dt^2}=m_g\overrightarrow{g}[/latex] [latex]\overrightarrow{g}-\bigtriangledown\phi_N[/latex]

Denotes the gravitational field above.

Now General Covariance. Which use the ds^2 line elements above and the Einstein tensor it follows that the line element above is invariant under general coordinate transformation(diffeomorphism)

[latex]x\mu\rightarrow\tilde{x}^\mu(x)[/latex] Provided ds^2 is invariant [latex]ds^2=d\tilde{s}^2[/latex] an infinitesimal coordinate transformation [latex]d\tilde{x}^\mu=\frac{\partial\tilde{x}^\mu}{\partial x^\alpha}dx^\alpha[/latex] With the line element invariance [latex]\tilde{g}_{\mu\nu}(\tilde{x})=\frac{\partial\tilde{x}^\mu \partial\tilde{x}^\nu}{\partial x^\alpha\partial x^\beta} g_{\alpha\beta}x[/latex] The inverse of the metric tensor transforms as[latex]\tilde{g}^{\mu\nu}(\tilde{x})=\frac{\partial\tilde{x}^\mu \partial\tilde{x}^\nu}{\partial x^\alpha\partial x^\beta} g^{\alpha\beta}x[/latex] In GR one introduces the notion of covariant vectors [latex]A_\mu[/latex] and contravariant [latex]A^\mu[/latex] which is related as [latex]A_\mu=G_{\mu\nu} A^\nu[/latex] conversely the inverse is [latex]A^\mu=G^{\mu\nu} A_\nu[/latex] the metric tensor can be defined as [latex]g^{\mu\rho}g_{\rho\nu}=\delta^\mu_\mu[/latex] where [latex]\delta^\mu_nu[/latex]=diag(1,1,1,1) which denotes the Kronecker delta.

Finally we can start to look at geodesics.

Let us consider a free falling observer. O who erects a special coordinate system such that particles move along trajectories [latex]\xi^\mu=\xi^\mu (t)=(\xi^0,x^i)[/latex] Specified by a non accelerated motion. Described as [latex]\frac{d^2\xi^\mu}{ds^2}[/latex] Where the line element ds=cdt such that [latex]ds^2=c^2dt^2=\eta_{\mu\nu}d\xi^\mu d\xi^\nu[/latex] Now assume that the motion of O changes in such a way that it can be described by a coordinate transformation. [latex]d\xi^\mu=\frac{\partial\xi^\mu}{\partial x^\alpha}dx^\alpha, x^\mu=(ct,x^0)[/latex] This and the previous non accelerated equation imply that the observer O, will percieve an accelerated motion of particles governed by the Geodesic equation. [latex]\frac{d^2x^\mu}{ds^2}+\Gamma^\mu_{\alpha\beta}(x)\frac{dx^\alpha}{ds}\frac{dx^\beta}{ds}=0[/latex] Where the new line element is given by [latex]ds^2=g_{\mu\nu}(x)dx^\mu dx^\nu[/latex] and [latex] g_{\mu\nu}=\frac{\partial\xi^\alpha}{\partial\xi x^\mu}\frac{\partial\xi^\beta}{\partial x^\nu}\eta_{\alpha\beta}[/latex] and [latex]\Gamma^\mu_{\alpha\beta}=\frac{\partial x^\mu}{\partial\eta^\nu}\frac{\partial^2\xi^\nu}{\partial x^\alpha\partial x^\beta}[/latex] Denote the metric tensor and the affine Levi-Civita connection respectively.

now as the topic of Higg's came up lets supply some details on this.

Higg's field details that will make understanding the Higg's itself simpler. Keep in mind I am using Lewis Ryder "Introductory to General Relativity" for this. You may find more recent articles with slightly different metrics. (PS this will take me some time to type in and latex)First we need to notice that there is actually 4 field quanta in electro-weak theory. [latex]\gamma, W^-, W^+, and, Z^o.[/latex] notice the second and third is an antiparticle pair. Now the problem is we need a mechanism to give the neutrinos mass without giving photons mass. This is where the Higg's mechanism steps in. To start with Peter Higg's looked at superconductivity. The defining characteristic of conductivity is that at a temperature below a critical temperature [latex]T_c[/latex] some metals lose all electrical resistance. Resistance literally becomes zero, not merely very small. [latex](E=Rj) =j=\sigma E[/latex] where [latex]\sigma[/latex] is the conductivity. A metal in conductivity state then exhibits a persistant current even in no field:[latex]j=\not=0[/latex] when E=0. The key to understanding superconductivity is to describe the current as supercurrent [latex]j_s[/latex]. But unlike the equation above to realize this is proportional not to E but to the vector potential A. [latex]j_s=-k^2A[/latex] with a negative proportionality. This is the London equation. The relevant property we however are seeking is the Meissner effect, which is a phenomena that the magnetic flux is expelled from superconductors. Higg's then showed that suitably transformed into a relativistic theory, this is the equivalent to showing the photon has mass. (just not rest mass lol) The reasoning goes as follows. First the London equation explains the Meissner effect, for taking the curl of Amperes equation[latex]\nabla*BB=j[/latex] gives [latex]\nabla(\nabla^2B=\nabla*j[/latex] noting that [latex]\nabla*B=0[/latex] (no magnetic monopoles) gives [latex]\nabla^2B=k^2B[/latex] which is equal to [latex]\nabla^2A=k^2A[/latex]

In one dimension the solution to this is [latex]B(x)=B(0)exp(-kx)[/latex] which describes the Meissner effect-the magnetic field is exponentially damped inside the superconductor, only penetrating to a depth of order 1/k. This however is still non relativistic. To make it relativistic [latex]\nabla^2[/latex] is replaced by the Klein_Gordon operator [latex]\Box[/latex] and A by the four vector [latex]A^\mu=(\phi,A)[/latex]

giving [latex](\frac{1}{c^2}\frac{\partial^2}{\partial t^2}+\frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}+\frac{\partial^2}{\partial x^2})A^\mu=k^2A^\mu[/latex] the vector potential is a field but we are currently interested in the photon, the quantum of the field. so we make the transition to quantum theory by the usual description.

[latex]\frac{\partial}{\partial t}\mapsto-\frac{i}{\hbar}E, \frac{\partial}{\partial}{\partial x}\mapsto\frac{i}{\hbar p_x}....[/latex]etc giving the quantum of the field [latex]A^\mu[/latex], [latex]E^2-p^2c^2=k^2c^2\hbar^2[/latex] where E is the total, including rest energy of the field quantum an p isits momentum comparison to [latex]E^2-p^2c^2=m^2c^4[/latex] implies that the mass of the quantum in a superconductor is [latex]m_\gamma=\frac{k\hbar}{c}[/latex] the photon behaves as a massive particle in a superconductor. This is the import of the Meissner effect. Now we need to make a further connection to the Bardeen-Cooper_Schreiffer (BCS theory) of superconductivity which is a microscopic theory that accounts for superconductivity by positing a scalar field [latex]\phi[/latex] (spin zero for scalar fields). Which describes a Cooper pair of electrons, the pairing is in momentu space rather than coordinate space. You can correlate the many particle wave function of Cooper pairing with the above. I'm trying to save time here lol and this is already getting lengthy. The main difference between a superconductor and the Higg's field is that the Higg's field is all pervasive unlike (unlike BCS which is inside a superconductor) The Higg's field through treatment gives rise to the mass of the above neutrinos in the same manner but not to photons. In point of detail the Higg's field can be treated as 4 separate fields one for each of the above. latex]\gamma, W^-, W^+, and, Z^o.[/latex] Now the Higg's potential when [latex]t<t_c[/latex] has a maximum at [latex]\phi=0[/latex] and two minima at [latex]\phi=\pm A[/latex] when[latex] t>t_c][/latex] there is only a minimal at [latex]\phi=0[/latex] THIS is the Mexican hat potential. [latex]V \phi=\frac{m^2}{2}\phi^2+\frac{\lambda}{4}\phi^4[/latex] where [latex]\phi^4[/latex] is the quartic self interaction.. The extremal values of [latex]V\phi[/latex], given by [latex]\partial V/\partial \phi=0[/latex] becomes[latex]\phi=0,\pm\sqrt{\frac{-m^2}{\lambda}}=0,\pm a[/latex]when there is no field [latex]\phi=0[/latex], the energy is not a mimimal but at a maximal, further more the lowest energy is a state in which the field does not vanish and is also two fold degenerate. I hope that helps better understand the Higg's field and how it came about ie was derived in the first place. Section 10.10 Lewis Ryder "Introduction to General Relativity"..

Scalar field Dynamics here we need to couple the scalar field to gravitation.

[latex]\frac{1}{2}\dot{\phi}^2+\frac{1}{2}(\triangledown\phi^2)+V(\phi)[/latex] and the dynamics can be described by two equations. ::Friedmann equations [latex]H^2+\frac{k}{a^2}=\frac{8\pi}{3M^2_P}(\frac{1}{2}(\dot{\phi})^2+V(\phi)[/latex] and the Klein Gordon equation obeys the scalar fields [latex]\ddot{\phi}+3H\dot{\phi}+\acute{V}(\phi)=0[/latex] if the [latex]\phi_a[/latex] is large we have [latex](\triangledown \phi_a^2)<<V(\phi_2)[/latex] the speed of expansion [latex]H=\frac{\dot{a}}{a}[/latex] is dominated by the potential [latex]V(\phi_a)[/latex] in equation[latex]H^2+\frac{k}{a^2}=\frac{8\pi}{3M^2_P}(\frac{1}{2}(\dot{\phi})^2+V(\phi)[/latex] the advantage of Higg's inflation is that inflation is readily modelled using just the standard model of particles. We do not need k-Fields, inflatons, curvatons, Quintessence or any other quasi particle or field. Secondly we can model inflation as a symmetry phase transistion which is extremely important as we tie inflation with the electro-weak symmetry breaking itself.

Higg's inflation.

Higg's field. Is a complex scalar field [latex]SU(2)_w[/latex] doublet. [latex]\phi=(\begin{matrix}\phi_1 & \phi_2 \\ \phi_3& \phi_4 \end{matrix})[/latex] the vector bosons (guage bosons) interact with the four real components [latex]\phi_i[/latex] of the [latex]SU(2)_{w^-}[/latex] symmetric field [latex]\phi[/latex] false vacuum corresponds to [latex]\phi=0 or \phi_1=\phi_2=\phi_3=\phi_4=0[/latex] the true vacuum corresponds to [latex]\phi_1=\phi_2,,,\phi_3^2=\phi_4^2=constant>0[/latex]

 

 

assign V on the Y axis, [latex]\phi_3[/latex] on the x axis, [latex]\phi_4[/latex] on a 45 degree between the x and Z axis. when you have conditions [latex]\phi_4=0,\phi_3>0[/latex] then the rotational symmetry is spontaneously broken. The Higg's boson becomes massive as well as the vector bosons W+,W-Z and photons the two neutral fields [latex]B^0 and W^0[/latex] form the linear combinations [latex]\gamma=B^0 cos\theta_w+W^0sin\theta_w[/latex] [latex]Z^0=-B^0sin\theta_w+W^0cos\theta_w[/latex] where Z becomes massive. whee as our ordinary photon [latex]\gamma[/latex] remains massless as the photon does not interact with the electro-weak Higg's field. It is electro-weak neutral. The electroweak symmetry is given by [latex]SU(2)_w\otimes U(1)_{b-L}[/latex] as time decreases the vacuum expectation value [latex]\theta_0[/latex] decreases. (expansion in reverse) the true minimal of the potential is [latex] \phi=0[/latex] this occurs above the critical temperature [latex]T_c=\frac{2\mu}{\sqrt{\lambda}}[/latex] at this point the field interactions take on in essence superconductivity properties.

Now isn't that far more precise than images???

Every formula in physics has a mathematical proof, every definition has a mathematical precision.

This is only a very miniscule portion of developing an effective GUT>>>

We haven't even touched on [math]SO(10)\otimes SO(5)\otimes SO(3)\otimes SO(2)\otimes U(1)[/math]

 

7 hours ago, SuperPolymath said:

I think y'all have yet to define all 3 sources of the dynamic dark energy in my thread. You have late entropy stage mother black holes increasing the space-time via evaporation surrounding early entropy stage CMB bodies causing the isotropic qg plasma to break apart into the first atoms there. What happens with this new cosmic portion is anisotropic black hole sizes. As the universe section ages macro bh's become larger as they consume mass from matter & micro black holes (the higgs field that gives matter-energy mass & DM) shrink overall until a new late entropy section forms overlapping the previous one where those monster black holes of the previous one have been reduced to micro-bh's. 

Now those 2 sources alone would end in  an omega entropy state if not for source 3, the horizon of the white hole with contour=infinity is constantly absorbing parallel white holes beyond its horizon, continously adding additional energy-matter & space-time. This is the positive approx 2.5 dimensions (fractal geometry which allows the scale relativity Lorentz transformations in this model) that we experience, beyond that is an approx negative 2.5 dimension, these two space-times (de sitter & anti de sitter space) are literally the same but with opposite directions of space-time & negative matter-energy. Anti de sitter space is literally these perpendicular dimensions that give energy-matter mass as space-time gets turned inside out flowing through their event horizons it's curtain is yanked, these black holes of an infinity variety of sizes that occupy literally every point in space is behind the fundamental interactions (gravity, electromagnetic, strong & weak nuclear).

This 5 dimensional hypersphere is like a cosmic yin-yang symbol, or an infinitely long snake eating it's own tail.

Do you actually believe your images compares to the mathematical precision involved in symmetry breaking via the SO(10)??? How does one make a single prediction with nothing more than images? How can you possibly determine all possible paths involved in a two particle interaction let alone a multi particle system?

Edited November 23, 2017 by Mordred

[Dubbelosix]

Mordred, you are the only one here who makes coherent sense. Vmedril, a word of warning, I am not even a mod, but even I can see through the bullshit. You have done this to me on another site, you inundated a previous thread of mine with complete nonsense. This is complete trash you are posting and it is actually annoying me... which takes quite a bit.

It annoys me because you become part of the new age anti-scientific regime. The world is crumbing to pseudo scientists and here you are posting rubbish that doesn't even make sense when you study it closely. Just like your manipulations of my equations on another site without regard about complexities involving dimensional consistency. 

Edited November 23, 2017 by Dubbelosix

[Mordred]

One thing I truly appreciate about your threads Dubbelsix is you spent literally dozens of posts simply to accurately describe the length of a vector. One of the most vital aspects of group theory. You then applied that under a precise coordinate basis. A vast majority of your posts literally applied to a complete tensor closure. Unfortunately not many understood the Dirac notation. You then specified at every post including your own site that you are toy modelling. Not once have I ever seen you state this is the way it is. Yet you always maintained proper mathematical rigor in every examination you performed.

The bonus is you much like me can pick up any professional peer review topic and understand it correctly via understanding the mathematics and not the written descriptives or images. That is the true advantage learning vector calculus and differential geometry provides...

Like I said every equation has a precise mathematical proof that must be properly understood before trying to manipulate it. After 25 years of intensive study of physics. One becomes amazed on just how interconnected various theories are

Edited November 23, 2017 by Mordred

[SuperPolymath]

Vmedvil is listening to Mordred, & actually made this thread admitting he was taking your model too far 006...& admitting that it was off. Mordred, I at least appreciate helping with Vmedvil's equations. Mordred I'm only trying to see IF my ideas can be interpreted through math.

[Mordred]

Any representation including images can be described via math. The question becomes how to properly do so. Start with breaking your images to a coordinate basis. Then attempt to break said image into vectors.

Finally look for symmetry and assymetry relations to organize said vectors. 

I wish I could recall a particular theory that literally breaks any picture one can take and describe it under math. Its not strictly physics but the mathematics can be related to physics.

 The problem I found reading your post on the other thread was the lack of proper descriptives via proper terminology. You tend to try to apply a scattering of random theories, some of which have little to do with one another. 

Its actually a struggle to figure out where to start to help you advance your ideas to proper physics descriptives. Unfortunately as Vmedvil started this post as the OP the priority I applied is more to his posts than yours. This is to prevent thread hijacking.

I suggest starting a seperate thread under Speculation so I can properly focus on your particular ideas.

One other rule to follow, never reply to a thread with personal models. Always answer via mainstream physics.

Edited November 23, 2017 by Mordred

[SuperPolymath]

I'd need a PhD in astrophysics if I meant me interpreting it.

Anyone want to risk the time for a potential Nobel? Lol.

21 minutes ago, Mordred said:

 

 The problem I found reading your post on the other thread was the lack of proper descriptives via proper terminology. You tend to try to apply a scattering of random theories, some of which have little to do with one another. 

Every theory is attempting to describe the same thing, that's why.

As far as terminology, anything I could do to get the point across my mind was a chaotic place trying to collate the massive data I was collecting

Edited November 23, 2017 by SuperPolymath

[Vmedvil]

2 hours ago, Dubbelosix said:

Mordred, you are the only one here who makes coherent sense. Vmedril, a word of warning, I am not even a mod, but even I can see through the bullshit. You have done this to me on another site, you inundated a previous thread of mine with complete nonsense. This is complete trash you are posting and it is actually annoying me... which takes quite a bit.

It annoys me because you become part of the new age anti-scientific regime. The world is crumbing to pseudo scientists and here you are posting rubbish that doesn't even make sense when you study it closely. Just like your manipulations of my equations on another site without regard about complexities involving dimensional consistency. 

Well, now I know who down-voted me and no I was trying to resolve them to a Planck length Dubblesoix that was all did I know exactly how to do it, No, but yes I did totally hijack that thread under thinking that my model could include Hilbert space at the volume spot of your equation and where yours could be on Planck level as well, I did with a series of redirects fix that would have said nothing if I had known it were going to piss you off.So, people would know that it was too simple to be Real universe I had thought it was close enough to be "Real Universe". When it said dV, I tried to solve for dV on the scale the hillbert space happens which is a Planck length which then tried to convert into meters as it said "ΔE" using elementary constants, If that  1/L_p = Meters, that's why it said that, if you still don't understand you are not as good at this as you thought even with your master's degree in physics, Secondly your symbol were in ∇ where ∇E should have solved for when you said "Oh its Energy" 

 

Edited November 23, 2017 by Vmedvil

[Mordred]

43 minutes ago, SuperPolymath said:

I'd need a PhD in astrophysics if I meant me interpreting it.

Anyone want to risk the time for a potential Nobel? Lol.

Every theory is attempting to describe the same thing, that's why.

As far as terminology, anything I could do to get the point across my mind was a chaotic place trying to collate the massive data I was collecting

Thats where the mathematical precision comes into play. Once you define a state under math it becomes trivial to apply it to different theories.

One can readily apply every equation I posted in this thread to QFT, Loop quantum gravity and even string theory etc or simply describe the above under a classical approximation.

 No it wouldn't require a Ph.D but one can easily think it would. There is nothing preventing someone learning physics and even self teaching with the correct diligence.

(here is a little secret, the most complex models derive from the simplest).

Would it surprise you that every equation I posted can be broken down to its basic kinematic components taught in grade school? Ie scalar and vector quantities 

Edited November 23, 2017 by Mordred

[Vmedvil]

On 9/19/2017 at 3:18 PM, Dubbelosix said:

Abstract

 

I explore the anticommutating spacetime relation in context of gravity by seeing commutation happen in two connections of the gravitational field, one concerned with space, the other time. We learn nothing revolutionary this time around, but we do explore it in a finite dimensional, Hilbert space-context. I do offer though, in a new context, an equation proposed by Anandan, which can describe the difference of geometries directly related to the L2 space we explore as a Cauchy Schwarz spacetime. My ultimate hope is that it will catch on that the latter gives a natural mechanism for fluctuations in spacetime, as we relate fluctuations to the energy time relationship ΔEΔt .  

 

 

 

 

 

The commutation relationship known as the spacetime uncertainty is established to satisfy a direct interpretation into the antisymmetric tensor, 

Rμ,ν=[∇x,∇0]=∇x∇0−∇0∇x≥1ℓ2

 

That is, a space x and 0 (time) notation. I worked out the Christoffel symbols and I calculate in the normal way as two connections: 

 

[∇i,∇j]=(∂i+Γi)(∂j+Γj)−(∂j+Γj)(∂i+Γi)

 

=(∂i∂j+Γi∂j+∂iΓj+ΓiΓj)−(∂j∂i+∂jΓi+Γj∂i+ΓjΓi)

 

=−[∂j,Γi]+[∂i,Γj]+[Γi,Γj]

 

From here, we reinterpreted this in terms of the Cauchy Schwarz inequality to give spacetime an ''instrinsic relationship'' to the uncertainty principle - which may serve as an origin to fluctuations in spacetime - at least this was my motivation - I later discover through more investigation this makes it part of L2 space and thus, a finite dimensional Hilbert space.  The expectation of the uncertainty is the mean deviation of curvature in the system is:

 

|<∇2i><∇2j>|−−−−−−−−−−−−−−−√≥12i(<ψ|∇i∇j|ψ>+<ψ|∇j∇i|ψ>)=12<ψ|[∇i,∇j]|ψ>=12<ψ|Rij|ψ>

 

=12<ψ|−[∂j,Γi]+[∂i,Γj]+[Γi,Γj]|ψ>

 

I also speculate in terms of the spacetime uncertainty, anticommutation will exist in the Bianchi identities. The Bianchi identity is true up two three Cyclic Christoffel symbols:

 

Rσρ[ij]gσρ=∂iΓj−∂jΓi+ΓiΓj−ΓjΓi

 

Rσi[jρ]gσi=∂jΓρ−∂ρΓj+ΓjΓρ−ΓρΓj

 

Rσj[ρi]gσj=∂ρΓi−∂iΓρ+ΓρΓi−ΓiΓρ

 

You can write these three relationships out in the Bianchi identity, we can write the commutation again, on the indices

 

Rσρ[ij]+Rσi[jρ]+Rσj[ρi]=0

 

Again, the last two indices reveal antisymmetric properties. I worked out a static model for superpositionng will not satisfy the fundamental spacetime relationship! Using J. Anandan's equation which I investigated:

 

E=kGΔΓ2  

 

I noted the equation confused me early on, but it seems it is constructed in the following way

 

<ΔΓ2>=∑<ψ|(Γρij−<ψ|Γρij|ψ>)2|ψ>  

 

I think I realized what was implied by Anandans first equation by noticing his missing constant of proportionality is c4 . Then an integral of the volume yields the energy

 

E=c4G∫ΔΓ2 dV  

 

We have argued, that the squared component of the connection can be interpreted in terms of the curvature tensor in Anandan's equation. This is related to the energy of the difference of geometries and that is given now as

 

ΔE=c48πG∫<ΔRij> dV=c48πG∫<ψ|(Rij−<ψ|Rij|ψ>)|ψ> dV

 

This is actually related to the difference found in Penrose's model of an induced gravitational collapse in a superpositioned system - albiet, ours is quantum geometry related directly to the Riemann tensor. You may have noticed, the energy equation that describes the difference in superpositioned geometry ~

 

ΔE=c48πG∫<ΔRij> dV=c48πG∫<ψ|(Rij−<ψ|Rij|ψ>)|ψ> dV

Shares the difference between two expectation values of the system:

 

|<∇2i><∇2j>|−−−−−−−−−−−−−−−√≥12i(<ψ|∇i∇j|ψ>+<ψ|∇j∇i|ψ>)=12<ψ|[∇i,∇j]|ψ>=12<ψ|Rij|ψ>

 

That coefficient of 12 may indeed attach to that energy, just like a kinetic energy term. So really, when you saw this object: <ψ|Rij|ψ> as we have shown, we had already calculated this identity very early on in the work. So the energy equation is compatible in a Cauchy-Schwarz interpretation of spacetime. How do you vary the expectation value in the equation?

<ΔE>=c48πG∫<ΔRij> dV=c48πG∫(<ψ|Rij|−<ψ|Rij|ψ>)|ψ> dV

The total variation will split each two terms,

<ψ|Rij|−<ψ|Rij|ψ>)|ψ>

into

<δaRij>=<ψ|Rij|δaψ>+<δaψ|Rij|ψ>

<δbRij>=<ψ|Rij|δbψ>+<δbψ|Rij|ψ>

where the subscript of δab denotes a ''two particle system.'' So it will become a four-component equation with variations in each term of the wave function. In the main work, we also discussed shortly, my model being related to Penrose's model for the collapse of gravity in a superpositioned state. Penrose has suggested a graviational self energy related to a collapse time model

T≈ℏE

And in the Penrose model, the energy is given as

E=14πG∫(∇ϕ′−∇ϕ)d3x

We can derive a more general case that can be used to measure the density variations of spacetime. Deriving the gravitational binding between any coherent gravitational superpositioning state can be given the following way:

The gravitational field inside a radius r=r(0) is given as

dMdR=4πρR2

and the total mass is

Mtotal=∫4πρR2dR

and so can be understood  in terms of energy (where gtt is the time-time component of the metric),

M=4π∫ρR2gttdR=4π∫ρR2(1−Rr)dR

The difference of those two mass formula is known as the gravitational binding energy:

ΔM=4π∫ρR2(1−1(1−Rr))dR

Distribute c^2 and divide off the volume we get:

ρ¯=ρc2−ρc2(1−Rr)

Were we have used a notation ρ¯ for the energy density. Fundamentally, the equations are the same, just written differently. Notice that ∇2ϕ=4πGρ from Poisson's formula, in which we notice the same terms entering

ΔM=4π∫ρR2(1−1(1−Rr))dR

E=14πG∫(∇ϕ′−∇ϕ)d3x

So while Penrose suggests calculating the binding energy directly from the gravitational potential ϕ there are ways as shown here, to think about it in terms of the gravitational energy density and the gravitational binding between the two. 

http://sci-hub.bz/10.1007/BF02105068

 

 

 

 

Note*

 

It is also possible to write a version of Anandan's equation like the following

 

E=c4G∫(∇Γ)2 dV=c4G∫1R2dϕdR(R2dϕdR) dV

 

This part 

 

1R2dϕdR(R2dϕdR)

 

Is just another way to write a squared product dϕdR⋅dϕdR . And of course, this is just ∇2ϕ2 . We've stated this identity before in an equation - note also, ϕ is dimensionless. 

 

Do you see dubbesoix where you said  R_ij = [∇_i,∇_j] , What is the volume of Δ[∇_i,∇_j] dV , if not a planck unit, if your volume is not in meters then why did you say this equals ΔE being joules when takes times (C⁴/8πG)........................... Why can your masterfully perfect Equation not take a simple meters calculation for volume in L_p

Edited November 23, 2017 by Vmedvil

[SuperPolymath]

7 minutes ago, Mordred said:

13 minutes ago, Mordred said:

Thats where the mathematical precision comes into play. Once you define a state under math it becomes trivial to apply it to different theories.

One can readily apply every equation I posted in this thread to QFT, Loop quantum gravity and even string theory etc or simply describe the above under a classical approximation.

 No it wouldn't require a Ph.D but one can easily think it would. There is nothing preventing someone learning physics and even self teaching with the correct diligence.

(here is a little secret, the most complex models derive from the simplest)

 Diligence & whatever I have come from two opposite parts of the brain. Structured learning would be like pouring concrete down a holy well. Vmedvil's pretty diligent though. He's way better than me academically. He's been adopting my concepts, I think he's been testing to see if they're flawed too. Now this is how we network,