Physics Test Records on Entropy

Steve

C.

Greavu

III

May possibly

15,

2014

Take

the

Bekenstein

bound

(http://en.wikipedia.org/wiki/Bekenstein_bound),

which in turn

is

the

maximum

sum

of

entropy

S

that

can

be

contained

within

a

presented

finite

location

of

space

which

likewise

has

a

finite

volume

of

energy):

2𝜋𝑘𝑅𝐸

𝑆≤

в„Џрќ‘ђ

in which

k

is

Boltzmann's

frequent,

R

is

the

radius

of

a

sphere

which

could

enclose

the

program,

E

is usually

the

total

mass-­‐energy

including

any

relax

masses

of

the

program,

h-­‐bar

is usually

the

lowered

Planck's

continuous

and

c

is

the

speed

of

light.

Re-­‐arranging:

ℏ 𝜋𝑘𝑅𝐸

≤

2

𝑆𝑐

Hence,

𝜋𝑘𝑅𝐸

= О”рќ‘ҐО”рќ‘ќ

𝑆𝑐

Now

the

only

way of measuring

of

distance

we

possess

on

the

left

side

side

can be

R,

so

we

may

say

рќ‘… = рќ‘Ґ

And

let's

assume

the

system

can be

only

photons,

or

a

system

in

which

most

the

most

constituents

push

at

the

speed

of

light,

or perhaps

has

zero

total

relax

mass:

рќђё = рќ‘ќрќ‘ђ

or

рќђё

рќ‘ќ sama dengan

рќ‘ђ

Therefore ,

𝜋𝑘 Δ𝑥Δ𝑝

sama dengan

𝑆

рќ‘Ґрќ‘ќ

Again,

taking into consideration

all

photons,

or

a

massless

program:

в„Ћ

рќ‘ќ = В

рќњ†

So ,

𝜋𝑘 Δ𝑥λ

=

𝑆

рќ‘ҐО”рќњ†

the

right-­‐hand

side

is

just

the

position

finely-detailed

рќ‘Ґ! В (or

relative

uncertainty)

divided

by

the

wavelength

precision

рќњ†!,

gives

you

the

uncertainty

equality

which will

is

a

spin

on

Heisenberg's

uncertainness

principle

and

written

because

an

equal rights

instead

of

a

limit:

𝜋𝑘 𝑥!

=

𝑆

рќњ†!

This

made

me

wondering.

So

My spouse and i

looked

up

estimates

intended for

entropy

of

the

galaxy

through

the

through

the

cosmic

celebration

horizon

(as

big

of

a

description

of

the

universe

as

possible

from

which

you

can

nonetheless

retrieve

information).

Here's

a

link

to

one

of

several

papers

that

calculate

it

to

be

installment payments on your 6

±0. 3  ×  10! " "  𝑘:

http://www.mso.anu.edu.au/~charley/papers/LineweaverEganParisv2.pdf В

I

will certainly

call

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