Conservation of Energy…
Revisited
E = mc2 ??
A thinking
duck ??
Conservation of Energy…
Revisited
I’m a goose!
A thinking
duck ??
E=
2
mc
E=
2
mc
E=
2
mc
OK, egghead.
So what’s this
all about then?
This equation
simply shows how
matter and energy
are related.
Let me put this in
a way that a duck
can understand…
Goose!
Let’s say you have 100 Euros
and you want to convert it to US Dollars…
What DO you do?
Well, you could go to the bank.
Friendly Neighborhood European Bank
Well, you could go to the bank.
Friendly Neighborhood European Bank
They will calculate, using the current
EXCHANGE RATE,
how many American Dollars you can get for 100 Euros.
(for our purposes, let us ignore the inevitable service charge)
100 EUROS
=
?? US DOLLARS
According to the exchange rate for Euros into Dollars, you get 1.5 Dollars for every 1 Euro.
So €100 gets you $150.
100 EUROS
=
?? US DOLLARS
According to the exchange rate for Euros into Dollars, you get 1.5 Dollars for every 1 Euro.
So €100 gets you $150.
€ 100
100 EUROS
=
?? US DOLLARS
According to the exchange rate for Euros into Dollars, you get 1.5 Dollars for every 1 Euro.
So €100 gets you $150.
€ 100
EXCHANGE RATE
100 EUROS
=
?? US DOLLARS
According to the exchange rate for Euros into Dollars, you get 1.5 Dollars for every 1 Euro.
So €100 gets you $150.
€ 100
EXCHANGE RATE
$ 150
So, in the transformation of Euros into Dollars,
the amount of dollars ($) is obtained by multiplying
the amount of Euros (€) by the exchange rate (x).
We can express this in a formula:
$=€x
where x = 1.5 dollars per euro
Now, let’s say you have
Matter
with a mass of 100 kilograms (kg)
that you want to convert to
Energy,
which we shall measure in joules (J)…
What DO you do?
Well, first we have to go to a different bank.
Well, first we have to go to a different bank.
Universal Bank of the Universe
(Local Group Affiliate)
Well, first we have to go to a different bank.
Universal Bank of the Universe
(Local Group Affiliate)
Nature will calculate, using her
EXCHANGE RATE,
how many joules of Energy (E) you can get for a mass (m) of 100 kg.
(again, we shall assume that there is no service charge)
E
m
100 kilograms
=
?? joules
According to the exchange rate for mass into energy, you get
90,000,000,000,000,000 J of energy (E) for every 1 kg of mass (m).
So 100 kg gets you 9,000,000,000,000,000,000 J !
E
m
100 kilograms
=
?? joules
According to the exchange rate for mass into energy, you get
90,000,000,000,000,000 J of energy (E) for every 1 kg of mass (m).
So 100 kg gets you 9,000,000,000,000,000,000 J !
m
100 kg
E
m
100 kilograms
=
?? joules
According to the exchange rate for mass into energy, you get
90,000,000,000,000,000 J of energy (E) for every 1 kg of mass (m).
So 100 kg gets you 9,000,000,000,000,000,000 J !
m
100 kg
EXCHANGE RATE
E
m
100 kilograms
=
?? joules
According to the exchange rate for mass into energy, you get
90,000,000,000,000,000 J of energy (E) for every 1 kg of mass (m).
So 100 kg gets you 9,000,000,000,000,000,000 J !
E
m
100 kg
EXCHANGE RATE
9,000,000,000,000,000,000 J
So, in the transformation of mass into energy,
the amount of energy (E) is obtained by multiplying
the amount of mass (m) by the exchange rate.
But unlike the first bank, Nature’s exchange rate is fixed,
and it has a value of 90,000,000,000,000,000 joules per kilogram.
This is no arbitrary value. It is the square of the speed of light.
So, in the transformation of mass into energy,
the amount of energy (E) is obtained by multiplying
the amount of mass (m) by the exchange rate.
But unlike the first bank, Nature’s exchange rate is fixed,
and it has a value of 90,000,000,000,000,000 joules per kilogram.
This is no arbitrary value. It is the square of the speed of light.
The speed of light is a universal constant and is given the symbol ‘c’.
The value for c is 300,000,000 m/s ,
so c × c = c2 =90,000,000,000,000,000 m2/s2
(You should convince yourself that m2/s2 and J/kg are equivalent units. See “Units” in the Background Materials.)
So, in the transformation of mass into energy,
the amount of energy (E) is obtained by multiplying
the amount of mass (m) by the exchange rate.
But unlike the first bank, Nature’s exchange rate is fixed,
and it has a value of 90,000,000,000,000,000 joules per kilogram.
This is no arbitrary value. It is the square of the speed of light.
The speed of light is a universal constant and is given the symbol ‘c’.
The value for c is 300,000,000 m/s ,
so c × c = c2 =90,000,000,000,000,000 m2/s2
(You should convince yourself that m2/s2 and J/kg are equivalent units. See “Units” in the Background Materials.)
We can express all of this in a formula:
E = mc2
So you see, my
feathered
friend…
…at the bank I
can transform
one CURRENCY
into another.
Both are money,
but they are in
different forms.
Matter and energy are
also simply different
forms of the same thing…
— I prefer to call
it
MASS-ENERGY.
The one can be
transformed
into the other.
In the
transformation of
mass to energy…
…the EXCHANGE RATE
is the square of the
speed of light:
c2
…the EXCHANGE RATE
is the square of the
speed of light:
c2
Does this
guy ever
shut up?
And since c has a
VERY large value and
we are squaring it…
Does this
guy ever
shut up?
…we get an enormous
amount of energy…
…we get an enormous
amount of energy…
OK,
thank you
…for a tiny amount of
matter.
OK,
thank you
Now, the
transformation
energy to mass,
Now, the
transformation
energy to mass,
You know, I just
remembered,
I have an
appointment…
…you know,
that can
happen, too!
You know, I just
remembered,
I have an
appointment…
Energy can
transform
into mass!
Energy can
transform
into mass!
sigh
Let’s say you now have 100 US Dollars
and you want to convert it into Euros…
100 DOLLARS
=
?? EUROS
Let’s say you now have 100 US Dollars
and you want to convert it into Euros…
100 DOLLARS
=
?? EUROS
Remembering that $ = €x, then rearranging gives
€= $
−
x
You will get
100 ÷ 1.5 = € 66.67
You will get
100 ÷ 1.5 = € 66.67
$ 100
You will get
100 ÷ 1.5 = € 66.67
$ 100
=
€ 66.67
Likewise, to convert energy to mass we rearrange
E = mc2 and use
E
m=−
c2
So, for example…
Likewise, to convert energy to mass we rearrange
E = mc2 and use
E
m=−
c2
So, for example…
E
100 J
Likewise, to convert energy to mass we rearrange
E = mc2 and use
E
m=−
c2
So, for example…
E
100 J
=
0.0000000000000011 kg
And…?
That’s it.
Would you
like to see my
monkey?
HOW EINSTEIN ACTUALLY PHRASED IT…
"It followed from the special theory of relativity that mass
and energy are both but different manifestations of the
same thing – a somewhat unfamiliar conception for the
average mind. Furthermore, the equation E = mc2, in which
energy is put equal to mass, multiplied by the square of the
velocity of light, showed that very small amounts of mass
may be converted into a very large amount of energy and
vice versa. The mass and energy were in fact equivalent,
according to the formula mentioned above."
Universal Bank of the Universe
(Local Group Affiliate)
And finally, a word about those bank service charges:
Universal Bank of the Universe
(Local Group Affiliate)
And finally, a word about those bank service charges:
If we want to take advantage of the very large amount of energy that can be obtained
from a very small amount of mass, then we could get it from a nuclear reaction.
But there will be a service charge on that exchange — and it is huge:
For example, only a tiny fraction of the mass of fissionable uranium is converted into energy.
The rest goes into making lighter elements. That is the fee.
Universal Bank of the Universe
(Local Group Affiliate)
And finally, a word about those bank service charges:
If we want to take advantage of the very large amount of energy that can be obtained
from a very small amount of mass, then we could get it from a nuclear reaction.
But there will be a service charge on that exchange — and it is huge:
For example, only a tiny fraction of the mass of fissionable uranium is converted into energy.
The rest goes into making lighter elements. That is the fee.
However, when matter and antimatter annihilate,
the conversion from mass to energy is absolute.
There is no service charge with this particular transformation of mass to energy.