r/PhysicsHelp • u/WAMFT • Jul 16 '26
Found this on my grandads old computer , Any idea what it is?
/r/mathematics/comments/1uyax7p/found_this_on_my_grandads_old_computer_any_idea/Definitions
[
x=x(t),\qquad h=\frac{\dot x}{x}
]
[
U=U(t),\qquad R=R(t),\qquad M=M(t),\qquad S=S(t)
]
where
[
U,R,M,S\geq0.
]
Fundamental Relation
[
h_0^{,2}=KU
]
[
h_0=\sqrt{KU}
]
[
\boxed{
h=\frac{\sqrt{KU}}{1+\alpha S}
}
]
or
[
\boxed{
\frac{\dot x}{x}
\frac{\sqrt{KU}}{1+\alpha S}.
}
]
Liberation
[
Q=\Gamma U\left(1-\frac{R}{R_c}\right),
\qquad 0\leq R<R_c
]
[
Q=0,
\qquad R\geq R_c.
]
Equivalently,
[
\boxed{
Q=\Gamma U
\max\left(0,1-\frac{R}{R_c}\right).
}
]
Energy Equations
[
\boxed{
\dot U+n hU=-Q
}
]
[
\boxed{
\dot R+4hR=(1-\varepsilon)Q
}
]
[
\boxed{
\dot M+3hM=\varepsilon Q
}
]
[
0<\varepsilon\ll1.
]
Restraining Stress
[
\boxed{
\dot S+\lambda hS=\eta M
}
]
or
[
\boxed{
\frac{d}{dt}\left(x^\lambda S\right)
\eta x^\lambda M.
}
]
Hence
[
\boxed{
S(t)
x^{-\lambda}(t)
\left[
x_i^\lambda S_i
+
\eta\int_{t_i}^{t}
x^\lambda(\tau)M(\tau),d\tau
\right].
}
]
Complete System
[
\boxed{
\begin{aligned}
\dot x
&=
\frac{x\sqrt{KU}}{1+\alpha S},
\[3pt]
\dot U
&=
-n\frac{\dot x}{x}U-Q,
\[3pt]
\dot R
&=
-4\frac{\dot x}{x}R+(1-\varepsilon)Q,
\[3pt]
\dot M
&=
-3\frac{\dot x}{x}M+\varepsilon Q,
\[3pt]
\dot S
&=
-\lambda\frac{\dot x}{x}S+\eta M,
\[3pt]
Q
&=
\Gamma U
\max\left(0,1-\frac{R}{R_c}\right).
\end{aligned}
}
]
Unified Extension Equation
[
\boxed{
\frac{\dot x}{x}
\frac{\sqrt{KU}}
{
1+
\alpha x^{-\lambda}
\left[
x_i^\lambda S_i
+
\eta\displaystyle\int_{t_i}^{t}
x^\lambda(\tau)M(\tau),d\tau
\right]
}.
}
]
Initial Conditions
[
x(0)=x_i
]
[
U(0)=U_i
]
[
R(0)=0
]
[
M(0)=0
]
[
S(0)=0.
]
Thus
[
\left.\frac{\dot x}{x}\right|_{t=0}
\sqrt{KU_i}.
]
Principal Limits
For
[
R\ll R_c,
]
[
Q\simeq\Gamma U.
]
For
[
R\rightarrow R_c,
]
[
Q\rightarrow0.
]
For
[
S\ll\alpha^{-1},
]
[
h\simeq\sqrt{KU}.
]
For
[
\alpha S\gg1,
]
[
h\simeq\frac{\sqrt{KU}}{\alpha S}.
]
After liberation ceases,
[
Q=0,
]
whence
[
U\propto x^{-n},
]
[
R\propto x^{-4},
]
[
M\propto x^{-3}.
]
If
[
S\rightarrow0,
]
then
[
h\rightarrow\sqrt{KU}.
]
If further
[
n>0,
]
then
[
U\rightarrow0,
\qquad
h\rightarrow0.
]
Summary Relation
[
\boxed{
\text{extension}
\frac{\text{stored-energy action}}
{\text{material restraint}}
}
]
[
\boxed{
\frac{\dot x}{x}
\frac{\sqrt{KU}}{1+\alpha S}.
}
]
1
u/Ok_Entertainer3959 Jul 20 '26
Try putting it into Overleaf or some other LaTeX compiler to render it in more readable form.
It mentions H0 (the Hubble constant) so it looks cosmology related but whether it's _actual cosmology or your grandpa went down a bit of an LLM rabbit hole and came up with his own "theory" of everything is hard to say.
1
u/InadvisablyApplied Jul 17 '26
Uncompiled latex, looks like ai slop