stephaneww
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 Birthday 10/02/1968
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The end of the quantum vacuum catastrophe ?
stephaneww replied to stephaneww's topic in Speculations
oops sorry, this is only another writing of the equation of the vacuum catastrophe = 1/tp^2 * 1/Λ * 8pi. does this mean tant 1/tp^2 can't be considered as an energy in quantum mechanics as we do for Λ in the relativity? I don't know. only the begining is perhaps interesting, but I'm not sure of that 
The end of the quantum vacuum catastrophe ?
stephaneww replied to stephaneww's topic in Speculations
hello in my opinion, there is really something auround squares or square roots and 8 pi about the vacuum catastrophe : [latex]\frac{\hbar^2*\Lambda}{L_p^3* E_p} /8\pi=[/latex] the exact value of volumic energy density of cosmological constant exprimed in Joules/m^3 [latex]\hbar[/latex] reduced Planck constant (Joules*s) [latex]\Lambda[/latex] cosmological constant (s^2) [latex]L_p[/latex] Planck length (meters) and [latex]E_p[/latex] Planck energy (Joules) thank you in advance if you can explain it to me or correct me please. 
The end of the quantum vacuum catastrophe ?
stephaneww replied to stephaneww's topic in Speculations
there is no question finaly : it's an another form of equations I posted before, sorry 
The end of the quantum vacuum catastrophe ?
stephaneww replied to stephaneww's topic in Speculations
oops I thougt I had find something interresting but not finaly, sorry finaly I let this : when we make energy density per volume of the cosmological constant (in Joule / m ^ 3) / Planck force (in Newton) * 8 * pi, I find exactly the numerical value of the cosmological constant in m ^ 2. can you explain to me why, confirm or correct me please? 
The end of the quantum vacuum catastrophe ?
stephaneww replied to stephaneww's topic in Speculations
and so Mordred please : is the factor 3 link to a question of pression (states equations with [latex]w[/latex])? 
The end of the quantum vacuum catastrophe ?
stephaneww replied to stephaneww's topic in Speculations
=[latex]\frac{3*c^2*H_0^2}{8\pi G}=\rho_c[/latex] to use the formula... (with LFRW equations)... it will be clearer 
The end of the quantum vacuum catastrophe ?
stephaneww replied to stephaneww's topic in Speculations
Hello. Certainly I didn't succed to prove ma first proposition with the equations of state, but using my method for the vacuum catastrophe applied to the Hubble constant, a parallel of the same type can be made from a point of view of quantum mechanics relativistic deterministic [latex]H_0=67,9 Km/s/Mpc = 2,2005*10^{18} s^{1}[/latex], [latex]T(Gly)=13,787*10^9[/latex] [latex]\frac{\hbar*H_0}{l_p^3}=5,4965*10^{52}\text{ Joules/m^3} \text{, }(H_0 \text{ in }s^{1})[/latex] to follow the method of the vacuum catastrophe used in this tread we raise this volumetric energy density at square : [latex](\frac{\hbar*H_0}{l_p^3})^2=3,0211*10^{105}\text{ Joules^2/m^6}[/latex] [latex]\frac{E_p}{l_p^3}=4,6332*10^{113}\text{ Joules/m^3}[/latex] [latex](\frac{\hbar*H_0}{l_p^3})^2/\frac{E_p}{l_p^3}/8/\pi*3=7,7834*10^{10}\text{ Joules/m^3}=[/latex] [latex]\text{exactly critical density of energy per volume at Hubble radius (edit : not necessarily at Hubble radius) in }\Lambda \text{CDM model}[/latex] the difference with the vacuum catastrophe is a factor 3 Is it enough to validate the method? ________________________ notes: Hubble radius based on [latex]T(Gly)=13,787*10^9[/latex] convert in seconds =[latex]4,3509*10^{17}s[/latex] is [latex]R=T(s)*c=4,3509*10^{17}s*299792458m/s=1,3044*10^{26}m[/latex] [latex]c= \text{light speed in vacuum}[/latex] for calculation of critical densité, I use [latex]H_0=67,9 Km/s/Mpc = 2,2005*10^{18} s^{1}[/latex] 
The end of the quantum vacuum catastrophe ?
stephaneww replied to stephaneww's topic in Speculations
That's perfectly true ... ... And so, I think that it's not me who can finish that work Of course, other contributions, in addition to what has been written to confirm or invalidate the first message of the thread, are welcome ... 
The end of the quantum vacuum catastrophe ?
stephaneww replied to stephaneww's topic in Speculations
well, I'm not sure, but I don't see how inclued my approach for equation of state w=1. Furthermore, I find [latex]\frac{\ddot{a}}{a}[/latex] at about a numeric value of 1 while, [latex]\frac{4\pi G}{3c^2}*(\epsilon+3P)[/latex] is about a numeric value of [latex]10^{35}[/latex] so I tend to think that equality is not verified, and therefore my proposal on the vacuum catastrophe is wrong ... edit : I wanted to say energy and not critical density 
The end of the quantum vacuum catastrophe ?
stephaneww replied to stephaneww's topic in Speculations
I'm still very slow, yet I'm pretty sure it's very simple ... 1. [latex]\ddot{a}[/latex] is almost ok. If I just put a ratio on the colone [latex]R(Gly)[/latex]. Otherwise, I spent 2 days on the problem without progress .... 2. To agree on the numeric values of the data, I propose to use the values you took for the Cosmological Calculator, at the bottom of page 2 of this thread (With "Number of Steps = 20") . For example I find, [latex]S=3,208, H=7,244*10^{18}s^{1}[/latex] and [latex]\epsilon=8,435*10^{10}[/latex]Joules/m^3 for [latex]T(Gly)=2,9777[/latex], and finally [latex]\epsilon_\Lambda=5,394*10^{10}[/latex]Joules/m^3, which is [latex]\Lambda=1,007*10^{35}*10^{35}s^{2}[/latex] 3. On this link: http://www.astronomy.ohiostate.edu/~dhw/A5682/notes4.pdf, I tried to use this formula to no avail: [latex]P=w \epsilon[/latex] with [latex]w=1[/latex]. (page 5 of notes4.pdf) where [latex]( \epsilon+3P)=2P[/latex]. Is [latex]\epsilon[/latex] the critical density ??? 4. I do not find the equality Eq. (9) from http://www.scholarpedia.org/article/Cosmological_constant and I can not find the result: For [latex]\frac{\ddot{a}}{a}[/latex], I find values in [latex]10^{35}[/latex] for the second part of the tie 5. I especially think that my brain is getting too old to learn alone... 
The end of the quantum vacuum catastrophe ?
stephaneww replied to stephaneww's topic in Speculations
well, always slowly I went to school again. I had look here : https://en.wikipedia.org/wiki/Derivative , but I don't find what is [latex]\Delta y[/latex] and what is [latex]\Delta x[/latex] for this thread edit: if I have the answer for [latex]\dot{a}(t)[/latex], I think I'll find [latex]\ddot{a}(t)[/latex] 
The end of the quantum vacuum catastrophe ?
stephaneww replied to stephaneww's topic in Speculations
edit latex and most importantly, I do not see how to derive [latex]a[/latex] to get [latex]\dot{a}(t)[/latex] and [latex]\ddot{a}(t)[/latex] 
The end of the quantum vacuum catastrophe ?
stephaneww replied to stephaneww's topic in Speculations
Sorry for the timeout, I was busy IRL. You and Marcus. Jorrie did a great job to help people . I'm sure you already know where I go, but you want to make me work Well, I move slowly : [latex] a[/latex] is a scaling factor, i.e. a multiplier of an elastic ruler between two combile points (i.e. fixed without expansion) for example, between two combile points [latex] A[/latex] and [latex] B[/latex], at [latex]t_0[/latex] the distance is [latex]D_0[/latex], then at [latex] t_1[/latex] the distance between [latex] A[/latex] and [latex] B[/latex] will be [latex] a(t_1)*D[/latex] [latex]S=1/a[/latex] and [latex]z=S1[/latex] , now it's clear to me. But, I don't understand this quote... surface of the sphere of CMB ??? temperature of the CMB ??? with whitch unit ??? where come "88 Gyrs into the future" ??? and most importantly, I do not see how to derive [latex]a[/latex] to get [latex]\dot{a(t)}[/latex] and [latex]\ddot{a(t)}[/latex] 
The end of the quantum vacuum catastrophe ?
stephaneww replied to stephaneww's topic in Speculations
Eh eh. not bad pages 1,2,3,4 .... starting with page 1 I may be able to get there for [latex] a [/latex] and [latex] z [/latex] 
The end of the quantum vacuum catastrophe ?
stephaneww replied to stephaneww's topic in Speculations
Where can we find one or more examples of numerical computations with [latex] a [/latex] , [latex] \dot{a} [/latex] , and [latex] \ddot{a} [/latex] please ? I think it will help me a lot to understand [latex] a [/latex] . I unterstand the text (end of page 5 and page 6) but I haven't the maths keys to demonstrate w=1 for now