Re: what does E=mc^2 means anyway?
- From: dwhig265@xxxxxxxxxxxx
- Date: Sat, 17 Nov 2007 10:25:36 -0800 (PST)
On Nov 16, 9:06 pm, "Pmb" <some...@xxxxxxxxxxxxx> wrote:
"Jean Paul" <jcorriv...@xxxxxxx> wrote in messageHi Pete, Odenwald explained to me that E is expressed in ergs or
news:152fe318-bbbe-4b22-b10d-b1958df05b6e@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Hello.
Go easy on me because I do not know much about physics.
I've been thinking about that famous equation E=mc^2. What I know of
it is that it represents the amount of energy that mass contains.
This is often pictured by an atomic bomb explosion: matter transforms
into energy.
This is a common misunderstanding. Inertial mass (aka "relativistic mass) m
does not "convert" to energy since both mass and energy are conserved
quantities. What happens is that the form of the mass changes. For example;
consider electron-positron annihilation where the particles annihilate each
other resulting in the production of two photons. These photons have both
mass and energy. It is the form of the mass and energy that has changed. The
mass has changed from inertial mass (i.e. kinetic energy + rest energy) to
mass in the form of radiation (the mass of a photon is m = E/c^2 = hf/c^2).
The equation E = mc^2 was first concieved by others before Einstein. However
it was Einstein who proved it in a more fundamental way and in relativistic
terms. There is an article on the history of E = mc^2 that I have. I can
upload it to my website for you if you'd like to read it. If I do so then it
will remain there for one week.
First off Einstein did *not* prove that a body at rest contains energy. That
is an assumption that Einstein starts with. A simple example of a body
containing energy would be that of a charged capacitor. Einstein then let
the body radiate EM energy in equal amounts and in opposite directions. He
then considered the process from another inertial frame moving relative to
the first. Analyzing the process in this frame and comparing it to the
original frame Einstein showed that it a body of releases energy of the
amount E then the rest mass of that body will decrease by the amount dm =
E/c^2.
From herein I'd need to know how much physics and math you know already. If
you have some math background such as intermediate algebra then you should
be able to understand this derivationhttp://www.geocities.com/physics_world/sr/mass_energy_equiv.htm
To get a better understanding of nuclear energy released in, say, and atomic
wardhead then seehttp://www.geocities.com/physics_world/sr/nuclear_fission.htm
To read a proof that if 3-momentum is conserved then inertial mass is
conserved then seehttp://www.geocities.com/physics_world/sr/conservation_of_mass.htm
But is it really that simple?
Yes, if you understand what is meant by E = mc^2.
Consider any object, say a pen. Its mass
contains energy in at least two different ways:
1. The *mass* itself. That is the variable 'm' above.
I guess you could say it like that so yes.
2. The motion of particles inside that matter. This includes electrons
circling around the nucleus of an atom. That is kinetic energy. That
energy is not represented in the equation above. Correct?
If one goes by the definition that mass is the m in p = mv then kinetic
energy contributes to mass. Mass defined in this way is refered to as
"inertial mass." m is ten a function of speed so that m = m(v). If one
defines "mass" as the M in M = m(0) then still the answer is yes. This is
because one can evaluate the mass in the rest frame of the atom by measuring
the entire energy of the atom, including the kinetic energy of the
electrons. Let that value be E. Then the proper mass (aka rest mass) has the
value M = E/c^2.
Am I making sense? Am I asking the right questions?
Yes and yes. :)
Please could someone clarify this energy thing? What is the total
amount of energy of a body *at rest* (not to be confused with the
particles inside it that buzz around).
If E_0 is the rest energy of the body as measured in the rest frame then the
total amount of mass will be m = E_0/c^2 (regardless of how one defines
"mass" since they will have the same value in this case)
Also that equation E=mc^2 expresses that mass can be transformed into
energy.
No. I have another article on this point also. If you'd like to read it then
please let me know.
joules (a certain amount of them are required to do an amount of work)
and is derived my multiplying one gram of any kind of matter by the
speed of light in centimeters squared which is an awfully big
number.
DWH again. I prefer to say that E is the "stuff" that matter is madeBut it also expresses that energy can be transformed into mass
(matter).
No. That is not true.
out of but only Mother Nature knows what and where it is and how to
transform it. The last time she did it was more than 13.7 billion
years ago, if that is the correct age of the galaxies in our local
group.Regards.
But what are the conditions in nature that make creation of
mass possible?
There are none.
Best wishes
Pete
.
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