Science > Physics > Quantum Gravity 102.4: Riccati Equation with a Square Term for Charge in Dark Energy using Ohm's Law
| Topic: |
Science > Physics |
| User: |
"OsherD" |
| Date: |
15 Mar 2007 04:55:41 PM |
| Object: |
Quantum Gravity 102.4: Riccati Equation with a Square Term for Charge in Dark Energy using Ohm's Law |
From Osher Doctorow
I will consider that Ohm's Law is applicable, either in very early
Universe or under Dark Energy conditions.
From the Larmor Formula (e.g., Wikipedia's "Larmor Formula"), total
power P radiated by a nonrelativistic accelerating electron is:
1) P = a^2 Q^2/((3/2)c^3) in cgs Units, a = acceleration, Q = charge
of electron
From recent Sections of this thread we have for Dark Energy E:
2) E = (h/k)P
and therefore:
3) E = (2/3)(h/k)a^2 Q^2/c^3
However, from Ohm's Law:
4) E = IR = (dQ/dt) R
equating E in (3) and (4), we obtain:
5) R dQ/dt = (2/3)(h/k)(a^2/c^3) Q^2
which for constant R and a is a Riccati Differential equation in Q,
that is to say of form:
6) dQ/dt = A(t) + B(t)Q + C(t)Q^2
with A(t) = B(t) = 0 and C(t) = (2/3)(h/k)(a^2/c^3)
Let's incorporate all constants in (5) into a single constant k1 and
write (5) as:
7) dQ/dt = k1 Q^2
Then we have to integrate:
8) dQ/Q^2 = k1dt
which yields:
9) -1/Q = k1t + k2, k2 constant of integration
Let k2 be defined as:
10) k2 = -k1T_f, T_f a late ("terminal") time
Then (9) becomes:
11) -1/Q = k1t =k1T_f
and therefore:
12) 1/Q = k1(T_f - t)
As t --> T_f from the left (that is to say, t is less than T_f but
gets closer and closer to it), then since k1 is positive, the right
hand side of (12) must --> 0+ (from the right), and hence Q -->
infinity.
So electron charge-mass shielding would make sense in this scenario.
A possible scenario where Ohm's Law does not apply globally is to
regard it as applying in a very small neighborhood of any point,
somewhat analogously to GR's "SR locality at each point".
Osher Doctorow
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| User: "Nomen Lapetos" |
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| Title: Re: Quantum Gravity 102.4: Riccati Equation with a Square Term for Charge in Dark Energy using Ohm's Law |
15 Mar 2007 08:36:27 PM |
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"OsherD" <mdoctorow@comcast.net> wrote in message
news:1173995741.553101.314570@y66g2000hsf.googlegroups.com...
From Osher Doctorow
I will consider that Ohm's Law is applicable, either in very early
Universe or under Dark Energy conditions.
quack, QUACK! How are you going to see in the Dark Energy if Ohms Law works
? Got a Flashlight?
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| User: "OsherD" |
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| Title: Re: Quantum Gravity 102.4: Riccati Equation with a Square Term for Charge in Dark Energy using Ohm's Law |
15 Mar 2007 11:59:11 PM |
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On Mar 15, 5:36 pm, "Nomen Lapetos" <nos...@nospam.com> wrote:
quack, QUACK! How are you going to see in the Dark Energy if Ohms Law works
? Got a Flashlight?
Osher Doctorow: I was going to see by the "light" from your Violence
Orientation: > )
Say, "Nomen" alias Nospam dot com, who's giving you the clues, Uncle
Al or Aunt La-La?
Osher
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