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


Vmedvil

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3 minutes ago, SuperPolymath said:

 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,

And no Superpolymath they were never your concepts, I adopted concepts from string theory, not yours which yours are made from, that why I always say "stealing" the Hubble constant and etc. 

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Unfortunately I read far too many misconceptions of string theory being applied on the other forum that I cannot see any accuracy of string theory being applied. Though you at least had a decent understanding of the involved symmetry groups. ie the [math]E_8[/math] group as one example.

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6 minutes ago, Vmedvil said:

And no Superpolymath they were never your concepts, I adopted concepts from string theory, not yours which yours are made from, that why I always say "stealing" the Hubble constant and etc. 

String theory involves 11 dimensional hyperspace, not 5. There's no fractal geometry or special relativity beyond the speed of light in string theory either 

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3 minutes ago, SuperPolymath said:

String theory involves 11 dimensional hyperspace, not 5. There's no fractal geometry or special relativity beyond the speed of light in string theory either 

define a dimension under math... yes there is an answer

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3 minutes ago, Mordred said:

Unfortunately I read far too many misconceptions of string theory being applied on the other forum that I cannot see any accuracy of string theory being applied.

I think we should stop discussing my idea here. I'll make a separate thread for your thoughts on my pet idea later

 

But I'm not planning on learning advanced calculus. 

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I'm actually not asking you to. There is no way to teach that on a forum if you don't follow the math.

I am asking you to start at the basics and giving you the tools to develop to the advanced. The choice is yours to accept the assist or not.

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3 hours ago, Mordred said:

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

DU=pdV .

First take the first law of thermodynamics.

dU=dW=dQ U is internal energy W =work. As we dont need heat transfer Q we write this as DW=Fdr=pdV Which leads to dU=pdV. . Which is the first law of thermodynamics for an ideal gas. U=ρV U˙=ρ˙V+ρV˙=pV˙ Vr3 V˙V=3r˙r Which leads to ρ˙=3(ρ+p)r˙r We will use the last formula for both radiation and matter. Assuming density of matter ρ=M43πr3 ρ=dpdrr˙=3ρr˙r 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. L=Nλ2 As we're dealing with relativistic particles c=fλ=f2LN substitute f=n2Lc into Plancks formula U=w=hf U=Nhc21LV13 Using dU=pdV using p=dUdV=13UV As well as ρ=UV leads to p=1/3ρ 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

M=Dd3xρ(x) concentrated at a point x0=M1Dd3xxρ(x)

Which we can choose to be at the origin

x=0

Sources outside region D the following Newton potential at x

ϕN(x)=GNMr

Where Gn=6.6731011m3/KGs2 and r||x||

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

ds2=c2(1+2ϕNc2)dr21+2ϕN/c2r2dΩ2

Where dΩ2=dθ2+sin2(θ)dφ2 denotes the volume element of a 2d sphere

θ(0,π) and φ(0,π) are the two angles fully covering the sphere.

The general relativistic form is.

ds2=gμν(x)dxμxν

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

(r,θφ)

Gμν=1+2ϕN/c20000(1+2ϕN/c2)10000r20000r2sin2(θ)

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 mi=mg...mid2xdt2=mgg gϕN

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)

xμx~μ(x) Provided ds^2 is invariant ds2=ds~2 an infinitesimal coordinate transformation dx~μ=x~μxαdxα With the line element invariance g~μν(x~)=x~μx~νxαxβgαβx The inverse of the metric tensor transforms asg~μν(x~)=x~μx~νxαxβgαβx In GR one introduces the notion of covariant vectors Aμ and contravariant Aμ which is related as Aμ=GμνAν conversely the inverse is Aμ=GμνAν the metric tensor can be defined as gμρgρν=δμμ where δμnu =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 ξμ=ξμ(t)=(ξ0,xi) Specified by a non accelerated motion. Described as d2ξμds2 Where the line element ds=cdt such that ds2=c2dt2=ημνdξμdξν Now assume that the motion of O changes in such a way that it can be described by a coordinate transformation. dξμ=ξμxαdxα,xμ=(ct,x0) This and the previous non accelerated equation imply that the observer O, will percieve an accelerated motion of particles governed by the Geodesic equation. d2xμds2+Γμαβ(x)dxαdsdxβds=0 Where the new line element is given by ds2=gμν(x)dxμdxν and gμν=ξαξxμξβxνηαβ and Γμαβ=xμην2ξνxαxβ 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. γ,W,W+,and,Zo. 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 Tc some metals lose all electrical resistance. Resistance literally becomes zero, not merely very small. (E=Rj)=j=σE where σ is the conductivity. A metal in conductivity state then exhibits a persistant current even in no field:j=0 when E=0. The key to understanding superconductivity is to describe the current as supercurrent js . But unlike the equation above to realize this is proportional not to E but to the vector potential A. js=k2A 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 equationBB=j gives (2B=j noting that B=0 (no magnetic monopoles) gives 2B=k2B which is equal to 2A=k2A

In one dimension the solution to this is B(x)=B(0)exp(kx) 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 2 is replaced by the Klein_Gordon operator and A by the four vector Aμ=(ϕ,A)

giving (1c22t2+2x2+2y2+2x2)Aμ=k2Aμ 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.

tiE,xipx.... etc giving the quantum of the field Aμ , E2p2c2=k2c22 where E is the total, including rest energy of the field quantum an p isits momentum comparison to E2p2c2=m2c4 implies that the mass of the quantum in a superconductor is mγ=kc 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 ϕ (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 t<tc has a maximum at ϕ=0 and two minima at ϕ=±A whent>tc] there is only a minimal at ϕ=0 THIS is the Mexican hat potential. Vϕ=m22ϕ2+λ4ϕ4 where ϕ4 is the quartic self interaction.. The extremal values of Vϕ , given by V/ϕ=0 becomesϕ=0,±m2λ=0,±a when there is no field ϕ=0 , 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.

12ϕ˙2+12(ϕ2)+V(ϕ) and the dynamics can be described by two equations. ::Friedmann equations H2+ka2=8π3M2P(12(ϕ˙)2+V(ϕ) and the Klein Gordon equation obeys the scalar fields ϕ¨+3Hϕ˙+V´(ϕ)=0 if the ϕa is large we have (ϕ2a)<<V(ϕ2) the speed of expansion H=a˙a is dominated by the potential V(ϕa) in equationH2+ka2=8π3M2P(12(ϕ˙)2+V(ϕ) 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 SU(2)w doublet. ϕ=(ϕ1ϕ3ϕ2ϕ4) the vector bosons (guage bosons) interact with the four real components ϕi of the SU(2)w symmetric field ϕ false vacuum corresponds to ϕ=0orϕ1=ϕ2=ϕ3=ϕ4=0 the true vacuum corresponds to ϕ1=ϕ2,,,ϕ23=ϕ24=constant>0

 

220px-Mecanismo_de_Higgs_PH.png

 

assign V on the Y axis, ϕ3 on the x axis, ϕ4 on a 45 degree between the x and Z axis. when you have conditions ϕ4=0,ϕ3>0 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 B0andW0 form the linear combinations γ=B0cosθw+W0sinθw Z0=B0sinθw+W0cosθw where Z becomes massive. whee as our ordinary photon γ 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 SU(2)wU(1)bL as time decreases the vacuum expectation value θ0 decreases. (expansion in reverse) the true minimal of the potential is ϕ=0 this occurs above the critical temperature Tc=2μλ 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 SO(10)SO(5)SO(3)SO(2)U(1)

 

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?

In any case, before Dubblesoix invaded, which was fair an eye for an eye, saying that I was going to cause the end of the world not via zombie apocalypse what where you saying Mordred.

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22 minutes ago, Vmedvil said:

And no Superpolymath they were never your concepts, I adopted concepts from string theory, not yours which yours are made from, that why I always say "stealing" the Hubble constant and etc. 

But, a few pages ago you said "remove hyperspace". I know at some level there was collaboration. Perhaps not as much as with 006 or Mordred...but

I'd hoped/hope my idea would get used at some point

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Dimension under math is an independant variable.

A variable that can change without affecting any other variable.

Common example spatial dimensions. A given length x can change without affecting y.

This applies even under string theory... it is not a seperate universe etc thats science fiction and pop media 

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1 minute ago, Mordred said:

Dimension under math is an independant variable.

A variable that can change without affecting any other variable.

Common example spatial dimensions. A given length x can change without affecting y.

This applies even under string theory... it is not a seperate universe etc thats science fiction and pop media 

Was that applying to my post or Polymath's

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1 minute ago, Vmedvil said:

In any case, before Dubblesoix invaded, which was fair an eye for an eye, saying that I was going to cause the end of the world not via zombie apocalypse what where you saying Mordred.

 In essence your trying to model the universe via the Schwartzchild metric but there is a distinct difference.

The Schwartzchild is a static metric (the coordinates do not change)

however under the FRW the coordinates do change (commoving coordinates ) I posted the above to demonstrate the necessity of understanding the proofs behind the equations your trying to adapt. For example you tried to combine the Equations of state proofs via the Bose-Einstein statistics directly to the FRW metric but the statistics is part of the proof behind the FRW equations of state. ie matter w=0 Lambda w=1.

 The statistics is where those values come from in relation to the commoving volume itself. So combining the the two is incorrect as one is used to derive the other.

The Higgs section was to demonstrate an example of how mass is attributed via field interactions 

mass = "resistance to inertia change"

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12 minutes ago, Mordred said:

 In essence your trying to model the universe via the Schwartzchild metric but there is a distinct difference.

The Schwartzchild is a static metric (the coordinates do not change)

however under the FRW the coordinates do change (commoving coordinates ) I posted the above to demonstrate the necessity of understanding the proofs behind the equations your trying to adapt. For example you tried to combine the Equations of state proofs via the Bose-Einstein statistics directly to the FRW metric but the statistics is part of the proof behind the FRW equations of state. ie matter w=0 Lambda w=1.

 The statistics is where those values come from in relation to the commoving volume itself. So combining the the two is incorrect as one is used to derive the other.

Yes, Gravity only as the Schwarzchild metric other parts use other parts, otherwise there would be no negative against it, which goes back to 

∇Eb(x,y,z) = ∇(1/((1-(((2MbG / Rs) - (Isωs2/2Mb) + V)2/C2))1/2))MbC2

Where V = C and C - C = 0 which is the same as saying 0 + V2

Where in space is wrote in SR as it solves for Δx'

∇'(x',y',z') = ∇(1-(((2MbG / Rs) - (Isωs2/2Mb))2/C2))1/2

Edited by Vmedvil
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16 minutes ago, Mordred said:

Dimension under math is an independant variable.

A variable that can change without affecting any other variable.

Common example spatial dimensions. A given length x can change without affecting y.

This applies even under string theory... it is not a seperate universe etc thats science fiction and pop media 

So only variables that are independent are mathematical dimensions? What about dependent variables? Which are the only variables you'd deal with in real life.

Real dimensions are geometric structures in any case. Independent variables are just called by the same name to prevent people from knowing this

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7 minutes ago, SuperPolymath said:

So only variables that are independent are mathematical dimensions? What about dependent variables? Which are the only variables you'd deal with in real life.

Real dimensions are geometric structures in any case. Independent variables are just called by the same name to prevent people from knowing this

Polymath read about Reimann Geometry. 

Introduction to Riemann Geometry.

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12 minutes ago, SuperPolymath said:

So only variables that are independent are mathematical dimensions? What about dependent variables? Which are the only variables you'd deal with in real life.

Real dimensions are geometric structures in any case. Independent variables are just called by the same name to prevent people from knowing this

One can have a complex variable they are not independant.

Lets look at the simplest example. Spacetime...

you have three independant variables x,y,z. Spatial dimensions.(space) two points with a seperation is a vector (magnitude and direction) Cauchy Schwartz inequality with the Kronecker delta describes this as the triangle inequality ie a^2+b^2=c^2 Pythagorous theorem (Euclidean geometry) 

Spacetime is any metric where time is treated as a dimension of length via ct.

Time is an independant variable as it can change without affecting the others example Galiliean relativity (for Newton approximation under GR)

Now for the Kaluzu Klien which leads to String theory charge is an independant variable. As charge is symmetric ie + or - the only difference in the two charge vectors is direction we only require one additional variable that can change without affecting the other variables.

For the De-Sitter/Anti-Desitter it is a charged field ie vector field that can change without affecting other fields that they do not interact with.

String theory must track particle interactions but not every particle interacts with every other particle.

Key example neutrnos don't interact with the electromagnetic but in order to have a GUT you must track all interactions as well as isolate the non interactions.

This corresponds to a particles degrees of freedom and its cross section. Hence why one must use higher dimensions

3 spatial, 1 time, 1 charge, 3 flavor, 3 color etc.

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38 minutes ago, Mordred said:

One can have a complex variable they are not independant.

Lets look at the simplest example. Spacetime...

you have three independant variables x,y,z. Spatial dimensions.(space) two points with a seperation is a vector (magnitude and direction) Cauchy Schwartz inequality with the Kronecker delta describes this as the triangle inequality ie a^2+b^2=c^2 Pythagorous theorem (Euclidean geometry) 

Spacetime is any metric where time is treated as a dimension of length via ct.

Time is an independant variable as it can change without affecting the others example Galiliean relativity (for Newton approximation under GR)

Now for the Kaluzu Klien which leads to String theory charge is an independant variable. As charge is symmetric ie + or - the only difference in the two charge vectors is direction we only require one additional variable that can change without affecting the other variables.

For the De-Sitter/Anti-Desitter it is a charged field ie vector field that can change without affecting other fields that they do not interact with.

String theory must track particle interactions but not every particle interacts with every other particle.

Key example neutrnos don't interact with the electromagnetic but in order to have a GUT you must track all interactions as well as isolate the non interactions.

This corresponds to a particles degrees of freedom and its cross section. Hence why one must use higher dimensions

3 spatial, 1 time, 1 charge, 3 flavor, 3 color etc.

You just jumped from basic to advanced.

Now I see how 5 dimensions translates to ~+/-2.5 spatial, ~+/-.5 temporal, ~+/-.5 charge, ~+/-2.5 flavor, ~+/-2.5 color for a total of 17 dimensions. 8.5 in de sitter space, connected via heterotic string w/ scale relativitic Lorentz transformations of c, l, & t within the asymptote of the infinite contour of its center, to -8.5 dimensional anti de sitter space, 

Still different from string theory,not quite super string theory either. It's it's own thing, & that's because of the fractal geometry & the fact that scale relativity beyond the Planck length & C has replaced the roles of quantum & super gravity. Well, space-time does get transferred to both sides of the heterotic string, so I guess that's your super gravity.

Edited by SuperPolymath
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40 minutes ago, SuperPolymath said:

You just jumped from basic to advanced.

Now I see how 5 dimensions translates to ~+/-2.5 spatial, ~+/-.5 temporal, ~+/-.5 charge, ~+/-2.5 flavor, ~+/-2.5 color for a total of 17 dimensions. 8.5 in de sitter space, connected via heterotic string w/ scale relativitic Lorentz transformations of c, l, & t within the asymptote of the infinite contour of its center, to -8.5 dimensional anti de sitter space, 

Still different from string theory,not quite super string theory either. It's it's own thing, & that's because of the fractal geometry & the fact that scale relativity beyond the Planck length & C has replaced the roles of quantum & super gravity. Well, space-time does get transferred to both sides of the heterotic string, so I guess that's your super gravity.

Do you really wanna know what the problem with all that is, YOU CANNOT DEFINE IT Below that in math. It has to be Defined if you generate it from nothing it would take like 500 years or more just like mankind and that was with 100,000 + people that really knew what they were doing. So good luck you have 500,000,000 years of work ahead of you.

1 hour ago, Vmedvil said:

Yes, Gravity only as the Schwarzchild metric other parts use other parts, otherwise there would be no negative against it, which goes back to 

∇Eb(x,y,z) = ∇(1/((1-(((2MbG / Rs) - (Isωs2/2Mb) + V)2/C2))1/2))MbC2

Where V = C and C - C = 0 which is the same as saying 0 + V2

Where in space is wrote in SR as it solves for Δx'

∇'(x',y',z') = ∇(1-(((2MbG / Rs) - (Isωs2/2Mb))2/C2))1/2

And where you cannot call this wrong why, this is the reason why. 

Evidence of rotation = C

Edited by Vmedvil
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2 hours ago, Mordred said:

Building models of advanced physics without understanding basic physics would be like building a house without a foundation.

But that's exactly what I did. & it works to a degree, it's just not precise.

 

If you have 3 dimensions, my theory had 5. If you have 11, my theory has 17.

 

So make the rest of it precise

20 minutes ago, Vmedvil said:

Do you really wanna know what the problem with all that is, YOU CANNOT DEFINE IT Below that in math. It has to be Defined if you generate it from nothing it would take like 500 years or more just like mankind and that was with 100,000 + people that really knew what they were doing. So good luck you have 500,000,000 years of work ahead of you.

Again, you have to set limits purely for the sake of calculation, even if they aren't actually there. The approximate solution should yield within 4 orders of magnitude of c for qe even at 1.6x10^-1000 meters. So try it at whatever can be calculated. Max wolfram out

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Or better yet, use a perfect 22 dimensional built on the heterotic string bridging positive space-time & matter-energy with negative space-time & matter-energy, map out the 11 dimensions of 1/2 of the heterotic string for all particle interactions in a change from 1 symmetry breaking CMB to 18x 1 current observable universe, & then fractize the 11 dimensions into 8.5 dimensions by reducing all Planck values. Basically what was a length of 1.6x10^-35 meters gets a new length of 1.6x(10^-1(35^(1.6x10^35))) meters, a velocity of C gets a new velocity of C^C, & same with Planck time...then you get a more accurate model. This can be done infinite times, each time you do it your model gets more accurate in predicting the behavior of quantum particles. Remember

 

Edited by SuperPolymath
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5 hours ago, Vmedvil said:

Do you see dubbesoix where you said  Rij = [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 Lp

Speaking with you was arduous, because even when I corrected you, you continued to make the same mistakes - in other words, you where blatantly ignoring what was being said to you, such as the dimensional consistency of equations. I appreciate you have an fascination for physics, but along the way, who are you trying hustle?

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17 minutes ago, Dubbelosix said:

Speaking with you was arduous, because even when I corrected you, you continued to make the same mistakes - in other words, you where blatantly ignoring what was being said to you, such as the dimensional consistency of equations. I appreciate you have an fascination for physics, but along the way, who are you trying hustle?

Dimension consistency can be altered at any time to another property, it does not matter it can be recombined to be consistent if needed. Hustle no, I need to know something, it is of extreme importance to me personally, time is of the essence in this matter.

Edited by Vmedvil
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