An alternate explanation of E=mc^2
frank...@yahoo.com
that this means that energy is matter and matter is energy which means
that they are basically the same thing. But does this really make any
sense? If you take a ball of energy, can you really make it into hard
matter?
At first glance, this doesn't make any sense because energy could be
thought of as the motion of a particle and how can more movement lead
to more particle?
I have an alternate explanation for why the formula E=mc^2 is true.
This isn't a statement of mass/energy equivalence any more than the
classical formuala for kinetic energy KE = 1/2 mv^2. We would never
confuse this formula as equating energy with mass. It is just a simple
statement that mass M moving at speed V, posseses energy KE. Simple as
that.
The form of the E=mc^2 and KE = 1/2mv^2 formulas are practically
identical. If v = c then they only differ by the constant of 1/2. Is
this just a coincidence? The constant is important, because we do
experimentally see that E = mc^2 exactly, and not E = 1/2mc^2.
To understand what the true relationship is between energy and mass,
consider a meteor hitting Earth at nearly the speed of light. In this
case the kinetic energy of the meteor is 1/2mc^2. This is a totally
non-elastic collision and according to Newton's third law, the Earth
provides a force which is equal and opposite of the meteor. Since the
Earth hardly moves in this collision, the Earth must provide an energy
close to 1/2mc^2 in the opposite direction of the meteor in order to
not change position. Now if we take the energy of the meteor plus the
energy provided by the Earth in resisting this energy, we get E =
1/2mc^2 + 1/2mc^2 = mc^2. Using nothing more than classical mechanics,
we get E=mc^2 for the special case of an inelastic collision happening
at the speed of light. No long tensor calculus calculations and strange
math formulas, just straight elementary grade arithmetic.
To put this in perspective, if the meteor were a 5 pound sphere, it
would relase the same amount of energy as if an atomic bomb containing
5 pounds of plutonium were exploded. Truely, a monumental amount of
energy. But in the case of the meteor, no matter needed to be converted
to energy. All the mass of the meteor can be found on the Earth. No
conversion of mass to energy has occurred, only a conversion of kinetic
energy into thermal energy.
Now the $10,000 question is, what does this have to do with atomic
energy E=mc^2? We have 2 derivations of the same equation, but a
radically different interpretation of what it means. Is this just
coincidence, or is there a deeper meaning? I think there is a deeper
meaning, but I will leave that for a later post.
fhuemc
Sam Wormley
> What does the famous formual E=mc^2 really mean? It is commonly thought
> that this means that energy is matter and matter is energy which means
> that they are basically the same thing. But does this really make any
> sense?
See: http://www.fourmilab.ch/etexts/einstein/E_mc2/e_mc2.pdf
Androcles
<frank...@yahoo.com> wrote in message
news:1127455275.7...@z14g2000cwz.googlegroups.com...
| What does the famous formual E=mc^2 really mean?
It means you get a lot of sunshine from a big ball in the sky without
the big ball wearing away too fast.
Androcles.
Dirk Van de moortel
> that this means that energy is matter and matter is energy which means
> that they are basically the same thing. But does this really make any
> sense? If you take a ball of energy, can you really make it into hard
> matter?
>
> At first glance, this doesn't make any sense because energy could be
> thought of as the motion of a particle and how can more movement lead
> to more particle?
>
> I have an alternate explanation for why the formula E=mc^2 is true.
> This isn't a statement of mass/energy equivalence any more than the
> classical formuala for kinetic energy KE = 1/2 mv^2. We would never
> confuse this formula as equating energy with mass. It is just a simple
> statement that mass M moving at speed V, posseses energy KE. Simple as
> that.
>
> The form of the E=mc^2 and KE = 1/2mv^2 formulas are practically
> identical. If v = c then they only differ by the constant of 1/2. Is
> this just a coincidence? The constant is important, because we do
> experimentally see that E = mc^2 exactly, and not E = 1/2mc^2.
>
> To understand what the true relationship is between energy and mass,
> consider a meteor hitting Earth at nearly the speed of light. In this
> case the kinetic energy of the meteor is 1/2mc^2.
No, it would not be 1/2 m c^2.
You probably mean that it would be *nearly* 1/2 m c^2.
And even that would be wrong.
At high speeds Kinetic energy is not defined as 1/2 m v^2.
In special relativity energy is defined as
E = m / sqrt(1-v^2/c^2) c^2
and kinetic energy as
KE = E - m c^2
= m / sqrt(1-v^2/c^2) c^2 - m c^2
For small values of v (as compared to c) this can be approximated to
KE(small v) = m ( 1 + 1/2 v^2/c^2 ) c^2 - m c^2
= 1/2 m v^2
The quantity m c^2 is called the rest energy of the mass.
Hope this helps.
Dirk Vdm
TomGee
frank...@yahoo.com wrote:
> What does the famous formual E=mc^2 really mean? It is commonly thought
> that this means that energy is matter and matter is energy which means
> that they are basically the same thing. But does this really make any
> sense?
>
>
been taught it implies. But it implies no such thing. It does not say
that matter and energy are basically the same thing.
People often see things where they do not exist because they fail to
comprehend what they're looking at. The formula simply states that to
determine the amount of energy in a given mass, multiply the mass by
c^2. That is all it says and nothing more. There is no implication of
equivalency. It is just a mathematical construct which is a formula
designed to provide us with a measure of energy in a given mass. Even
in that, however, it fails.
It fails because it ignores the energy attributable to its motion and
so the result is invalid and thus false. It can be true only wrt
another object moving at the same velocity, where their velocities
cancel out and the difference in their masses can be compared.
I for one await that later post. However, what you describe is not
Einstein's version of the formula but the original version which
includes the energy of motion in a moving mass, or, E=mc^2+(energy of
motion). You say you "take the energy" of the mass, and means you're
including the energy it has due to its motion, or, momentum. AE's
version cannot work in your scenario because it leaves off the
energy-of-motion factor which is a major part of the total energy of
the meteor.
PD
frank...@yahoo.com wrote:
> What does the famous formual E=mc^2 really mean? It is commonly thought
> that this means that energy is matter and matter is energy which means
> that they are basically the same thing. But does this really make any
> sense? If you take a ball of energy, can you really make it into hard
> matter?
If it is commonly thought that this means energy is matter and matter
is energy, then that is a common misperception.
But yes, if I have a ball of energy, I can really turn it into a bunch
of flying objects that contain hard matter. A common example is
high-energy proton-antiproton collisions, where the sum of the matter
of the particles that come flying out of the collision is larger than
the mass of the proton plus the mass of the antiproton.
>
> At first glance, this doesn't make any sense because energy could be
> thought of as the motion of a particle and how can more movement lead
> to more particle?
Well, no, energy could not be thought of as motion of a particle. There
is energy in a coiled spring without any motion.
>
> I have an alternate explanation for why the formula E=mc^2 is true.
> This isn't a statement of mass/energy equivalence any more than the
> classical formuala for kinetic energy KE = 1/2 mv^2. We would never
> confuse this formula as equating energy with mass. It is just a simple
> statement that mass M moving at speed V, posseses energy KE. Simple as
> that.
>
> The form of the E=mc^2 and KE = 1/2mv^2 formulas are practically
> identical. If v = c then they only differ by the constant of 1/2.
One problem with this is that KE = (1/2)mv^2 is not a good formula for
kinetic energy for v anywhere close to c. In fact, it is about 1 part
in 50 wrong for a v about 1 tenth of c.
> Is
> this just a coincidence? The constant is important, because we do
> experimentally see that E = mc^2 exactly, and not E = 1/2mc^2.
>
> To understand what the true relationship is between energy and mass,
> consider a meteor hitting Earth at nearly the speed of light. In this
> case the kinetic energy of the meteor is 1/2mc^2.
No, it is not. That formula is a low-speed approximation *only*.
> This is a totally
> non-elastic collision and according to Newton's third law, the Earth
> provides a force which is equal and opposite of the meteor.
Newton's third law has nothing to do with whether it is an elastic or
inelastic collision. Newton's third law applies to both kinds of
collisions and everything on the continuous scale in between.
> Since the
> Earth hardly moves in this collision, the Earth must provide an energy
> close to 1/2mc^2 in the opposite direction of the meteor in order to
> not change position.
No, this is completely gumbled up. In an inelastic collision, the
heavier object does not *add* energy to the lighter object to get it to
slow down. I have no idea where you got that notion. In general, most
of the kinetic energy in an inelastic collision is *removed* and turned
into heat or other non-recoverable forms.
> Now if we take the energy of the meteor plus the
> energy provided by the Earth in resisting this energy, we get E =
> 1/2mc^2 + 1/2mc^2 = mc^2. Using nothing more than classical mechanics,
> we get E=mc^2 for the special case of an inelastic collision happening
> at the speed of light. No long tensor calculus calculations and strange
> math formulas, just straight elementary grade arithmetic.
And it's wrong, due to misunderstanding of classical mechanics,
including Newton's third law, energy in inelastic collisions, and
kinetic energy at speeds near the speed of light.
>
> To put this in perspective, if the meteor were a 5 pound sphere, it
> would relase the same amount of energy as if an atomic bomb containing
> 5 pounds of plutonium were exploded.
Only a tiny fraction of the 5 lbs of plutonium is converted into energy
in an atomic bomb. Were you aware of that?
> Truely, a monumental amount of
> energy. But in the case of the meteor, no matter needed to be converted
> to energy. All the mass of the meteor can be found on the Earth. No
> conversion of mass to energy has occurred, only a conversion of kinetic
> energy into thermal energy.
>
> Now the $10,000 question is, what does this have to do with atomic
> energy E=mc^2? We have 2 derivations of the same equation, but a
> radically different interpretation of what it means. Is this just
> coincidence, or is there a deeper meaning? I think there is a deeper
> meaning, but I will leave that for a later post.
>
I wouldn't call your analysis a derivation. It is more like numerology.
To understand what E=mc^2 really means, I would ask you first to think
about what you mean by the quantity m and the quantity E. What *is*
mass, and what *is* energy?
PD
Sam Wormley
>
> People often see things where they do not exist because they fail to
> comprehend what they're looking at. The formula simply states that to
> determine the amount of energy in a given mass, multiply the mass by
> c^2. That is all it says and nothing more.
Gravity is a universal interaction in Newtonian theory between all
mass, and, since E = mc^2, in relativistic gravity between all forms
of energy.
TomGee
Sam Wormley
Energy's equivalent mass have gravity.
Sam Wormley
> Um, were you trying to say something, Worms?
>
Energy's equivalent mass has gravity.
TomGee
kdt...@yahoo.com
> about what you mean by the quantity m and the quantity E. What *is*
> mass, and what *is* energy?
>
E=mc2 is the formalism of the law of conservation of matter and energy.
Using the specific units obtained by Einstien, it allows the correct
calculation of the energy released by the fusion of two hydrogen atoms
into a helium atom according to the mass defect of the helium atom. It
is an essential formula for physics and correct.
A quantity of energy can only be defined as it's ability to move mass
(gram, centimeter/ second). Kinetic energy once aquired, is not lost
as an object loses momentum, but must be converted into another form of
energy such as heat, which is radiation and molecular vibration.
Light is pure energy. The energy of a laser beam is easy to calculate
because all the photons are of the same frequency, If one knows the
flux density of the photons and using Planck's constant or hv.
It is well documented experimentally that light imparts momentum, the
mass of each photon being m=E/c^2, it's momentum mc. This momentum is
not the energy of the photon however which is mc^2.
Sam Wormley
frank...@yahoo.com
amount of energy released when 2 objects collide at nearly the speed of
light in a totally inelastic collision where the resulting momentum is
zero, so all kinetic energy is converted to thermal energy.
The question I posed was whether there was any connection to this
scenario and the the release of atomic energy E=mc^2. The only way I
think they could possibly be connected was if it were discovered that
the release of atomic energy or generation of matter by energy is
somehow the result of a collision resulting in the production of
kinetic energy or matter.
One of the simplest cases of energy being converted into mass is pair
production whereby a photon of sufficient energy is able to produce
both an electron and positron out of nothing. The energy of the photon
required to do this matches E = mc^2 where m is the rest mass of the
particles produced.
There are two particles produced (electron, positron), so the energy
required by each particle is 1/2mc^2 which also happens to be the
kinetic energy formula. The particles produced head out at near light
speed and if the normal kinetic energy formula holds, then the total
kinetic energy of the two particles adds back up to mc^2, so the photon
energy is converted entirely into kinetic energy and total energy is
conserved in the reaction.
So here we can see a direct relationship between E=mc^2 and E=1/2mv^2.
The intuitive explanation is that E=mc^2 in matter production because
whenever matter is produced, it always makes a matter and anti-matter
pair which carry away half of the incoming energy. This explains the
1/2 difference between the two formulas.
However, this doesn't explain the mystery of where the electron and
positron came from. It could be explained if the electron and positron
were just sitting there and then got hit by photon which caused the 2
particles to go zooming out at nearly the speed of light.
Science currently presumes that empty space is "empty" which leads us
to the conclusion that the electron/positron came out of "nothing".
While you could accept that as a postulate, it doesn't make a whole lot
of sense for something to appear out of nowhere.
The only way for it to make sense is if empty space were actually
filled with something. People have suggested that space is filled with
electrons and this would partially solve how an electron gets kicked
out of so called "empty space". But I don't think this explains the
positron.
My own model of space suggests that space is actually filled with
neutron-like objects. I say "neutron-like" since I'm not sure whether
these are the same things as neutrons, but the particle would be
similar in that it would be fundamentally be composed of a bound proton
and electron. This particle forms the "aether" - a concept routinely
rejected by modern science, but in this case, it helps to explain where
particles come from during pair production without resorting to a
magical "they somehow appear from out of nowhere" postulate. The goal
of science should be to explain all phenomenon without resorting to
unexplainable postulates.
For those who will say that the Michaelson-Morely experiment disproved
the aether, if you actually read the original paper, they didn't say
they didn't find an aether drift. They, in fact, detected a tiny .01
fringe shift. The paper goes on to admit the limitations of the
experiment and suggests better experiments to determine the question of
aether drift. Later experiments by Dayton Miller further confirmed that
an aether drift in the order of about 10km/s were detectable. This
results have been routinely rejected and ignored. Not even Michaelson
ever believed in the "non-aether" picture of the world. Look it up!
See:
This is a summary of the 1887 paper:
http://www.softcom.net/users/greebo/MMexp.htm
This is the actual 1887 paper (1.6 MB)
http://www.aip.org/history/gap/PDF/michelson.pdf
This is an analysis of the Dayton Miller experiments
http://www.orgonelab.org/miller.htm
Another characteristic of the aether is that it posesses a magnetic
moment due to its composition being slightly polar which causes the
aether particles to line up like tiny magnets. A very rough analogy
would be like how Na and Cl ions line up in a salt crystal, but instead
replaced by protons and electrons.
In this model, photons are pure wave phenomenon which use the aether as
the wave medium. The effect is to cause slight forward and back
movements of the aether particles. You might imagine that if you shook
one of the aether particles with a sufficiently high energy wave, that
you might get it to break down into component electron and proton.
Since the electron is so much less massive than the proton, we would
naturally expect to see electrons ejected well before protons.
Waves normally propagate at the speed of light through the aether, but
in the case of an electron ejection, the forward movement of the wave
at the electron's location is transferred entirely to the electron
causing it to acclerate away at nearly the speed of light.
When the electron is ejected from the aether matrix, what it leaves
behind is a hole in the alternating proton/electron aether matrix. This
is the positron. It is not postively charged due to it having some
inherent charge. It is positively charged because the surrounding
positive protons are not neutralized by the missing electron. This
positron is also acclerated away at nearly the speed of light.
So now we have a complete picture of pair production which doesn't rely
on any mysterious postulates or anything that we would find out of the
ordinary in classical mechanics. It does rely on the existence of an
aether, but this is nothing mysterious and has a simple physical
representation as an array of neutrons.
The meaning of E=mc^2 now becomes clear. This equations does not imply
that energy is converted into matter, rather this is the energy
required to eject matter out of the aether which is normally invisible.
This explains how energy can produce matter. I suppose the next
question is whether a similar explanation holds for matter producing
energy. I don't have the answer to that yet, perhaps in a later post.
The information in this post is part of my "Theory of Everything". To
see how this fits into the grand scheme of things, see:
Dirk Van de moortel
<frank...@yahoo.com> wrote in message news:1127540306.5...@g49g2000cwa.googlegroups.com...
> In my previous post
... you were shown dead wrong.
With an attitude like that you will probably remain wrong for the
rest of your silly life.
Dirk Vdm
Ole D. Rughede
Have a look again at the Einstein paper. If v = sqrt(2)c, v^2 = 2c^2.
All mass is transmuted into radiant energy ˝m*v^2 = ˝m*2c^2 = mc^2 = E,
indicating that c as also in gtr is a variable vith a universal maximum
value sqrt(2)*c. E = mc^2 is true but says nothing about the conditions
for E -> m or m -> E.
This is also what follows from modern aether theory where Newtonian G
and c are variables depending on the local energy density of the aether,
considered in the lambda term in gtr.
The aether is pure radiant energy flowing superpositioned in all
directions at any point in space. Without the aether physical space,
time or matter would not exist, why physical space is the aether space
where the aether is the medium of all physical fields and forces.
The aether space is a continuum of wavy energy without holes, breaks or
dusty Dirac particles to pop up and down. The specifik aether energy U
is exclusively positive like all mass, whether of positive or negative
electric charge as in antiparticles.
E = mc^2 is true at any velocity of light, as i seen from dimension
analysis, because any energy has an equivalent mass. In gravitation the
force represents energy over the same distance between masses. The
energy has an equvalent virtual mass that gravitates like regular
ponderable mass. It follows that gravitational energy is aether energy,
why the force on the masses is delivered by an enduring energy excange
between mass and aether.
Ole D. Rughede
PD
frank...@yahoo.com wrote:
> In my previous post, I had concluded that E=mc^2 happens to be the
> amount of energy released when 2 objects collide at nearly the speed of
> light in a totally inelastic collision where the resulting momentum is
> zero, so all kinetic energy is converted to thermal energy.
>
> The question I posed was whether there was any connection to this
> scenario and the the release of atomic energy E=mc^2. The only way I
> think they could possibly be connected was if it were discovered that
> the release of atomic energy or generation of matter by energy is
> somehow the result of a collision resulting in the production of
> kinetic energy or matter.
>
> One of the simplest cases of energy being converted into mass is pair
> production whereby a photon of sufficient energy is able to produce
> both an electron and positron out of nothing. The energy of the photon
> required to do this matches E = mc^2 where m is the rest mass of the
> particles produced.
>
> There are two particles produced (electron, positron), so the energy
> required by each particle is 1/2mc^2
Uh, no. The energy required is at least 2mc^2, where m is the mass of
the positron or electron. You're flippancy about getting at factors of
(1/2) by saying things like "there are two particles produced" shows
that you are trying to reproduce formulas without understanding them.
Your generalization fails immediately for cases where there are three
or four particles produced in the final state, for example, yet you
don't see the problem with that. You only see "hey I found the factor
1/2" without wondering whether it applies broadly. This is the mark of
someone who is looking for data to fit their model, rather than someone
who is looking for a model that fits data.
> which also happens to be the
> kinetic energy formula.
Which doesn't apply at relativistic speeds. Which has been pointed out
to you before.
> The particles produced head out at near light
> speed and if the normal kinetic energy formula holds, then the total
> kinetic energy of the two particles adds back up to mc^2, so the photon
> energy is converted entirely into kinetic energy and total energy is
> conserved in the reaction.
>
> So here we can see a direct relationship between E=mc^2 and E=1/2mv^2.
> The intuitive explanation is that E=mc^2 in matter production because
> whenever matter is produced, it always makes a matter and anti-matter
> pair which carry away half of the incoming energy. This explains the
> 1/2 difference between the two formulas.
>
> However, this doesn't explain the mystery of where the electron and
> positron came from.
Sure it does. You just said so. The energy of the photon is equivalent
to the mass of the electron-positron pair. There is not "nothing" in
the initial state -- there is the photon, which carries momentum and
energy and (usually with two photons, not one) invariant mass.
> It could be explained if the electron and positron
> were just sitting there and then got hit by photon which caused the 2
> particles to go zooming out at nearly the speed of light.
>
> Science currently presumes that empty space is "empty" which leads us
> to the conclusion that the electron/positron came out of "nothing".
> While you could accept that as a postulate, it doesn't make a whole lot
> of sense for something to appear out of nowhere.
>
> The only way for it to make sense is if empty space were actually
> filled with something. People have suggested that space is filled with
> electrons
They have? This can be immediately ruled out as it would imply a net
charge to free space.
> and this would partially solve how an electron gets kicked
> out of so called "empty space". But I don't think this explains the
> positron.
>
> My own model of space suggests that space is actually filled with
> neutron-like objects. I say "neutron-like" since I'm not sure whether
> these are the same things as neutrons, but the particle would be
> similar in that it would be fundamentally be composed of a bound proton
> and electron.
I've already explained to you the numerous ways we have indications
this is not the case.
> This particle forms the "aether" - a concept routinely
> rejected by modern science, but in this case, it helps to explain where
> particles come from during pair production without resorting to a
> magical "they somehow appear from out of nowhere" postulate.
But this is NOT postulated and I don't know where you got the idea they
do.
> The goal
> of science should be to explain all phenomenon without resorting to
> unexplainable postulates.
>
> For those who will say that the Michaelson-Morely experiment disproved
> the aether, if you actually read the original paper, they didn't say
> they didn't find an aether drift. They, in fact, detected a tiny .01
> fringe shift. The paper goes on to admit the limitations of the
> experiment and suggests better experiments to determine the question of
> aether drift. Later experiments by Dayton Miller further confirmed that
> an aether drift in the order of about 10km/s were detectable. This
> results have been routinely rejected and ignored. Not even Michaelson
> ever believed in the "non-aether" picture of the world. Look it up!
> See:
>
> This is a summary of the 1887 paper:
> http://www.softcom.net/users/greebo/MMexp.htm
>
> This is the actual 1887 paper (1.6 MB)
> http://www.aip.org/history/gap/PDF/michelson.pdf
>
> This is an analysis of the Dayton Miller experiments
> http://www.orgonelab.org/miller.htm
>
> Another characteristic of the aether is that it posesses a magnetic
> moment due to its composition being slightly polar which causes the
> aether particles to line up like tiny magnets. A very rough analogy
> would be like how Na and Cl ions line up in a salt crystal, but instead
> replaced by protons and electrons.
Right, and this is not experimentally supported.
>
> In this model, photons are pure wave phenomenon which use the aether as
> the wave medium. The effect is to cause slight forward and back
> movements of the aether particles. You might imagine that if you shook
> one of the aether particles with a sufficiently high energy wave, that
> you might get it to break down into component electron and proton.
> Since the electron is so much less massive than the proton, we would
> naturally expect to see electrons ejected well before protons.
>
> Waves normally propagate at the speed of light through the aether, but
> in the case of an electron ejection, the forward movement of the wave
> at the electron's location is transferred entirely to the electron
> causing it to acclerate away at nearly the speed of light.
>
> When the electron is ejected from the aether matrix, what it leaves
> behind is a hole in the alternating proton/electron aether matrix. This
> is the positron. It is not postively charged due to it having some
> inherent charge. It is positively charged because the surrounding
> positive protons are not neutralized by the missing electron. This
> positron is also acclerated away at nearly the speed of light.
Why is the hole accelerated? And can you predict which direction
(relative to the electron) it would be moving?
>
> So now we have a complete picture of pair production which doesn't rely
> on any mysterious postulates or anything that we would find out of the
> ordinary in classical mechanics. It does rely on the existence of an
> aether, but this is nothing mysterious and has a simple physical
> representation as an array of neutrons.
Except neutrons have mass and a scattering cross-section. Cosmic rays
could not travel long distances in a field of neutrons. A
neutron-composed space is EXPERIMENTALLY RULED OUT.
Androcles
| amount of energy released when 2 objects collide at nearly the speed
of
| light in a totally inelastic collision where the resulting momentum is
| zero, so all kinetic energy is converted to thermal energy.
Sheesh, you do go on a lot. Never mind.
What happens when you play the movie backwards?
All the thermal energy vanishes and two particles fly apart, right?
What the energy of each particle? 1/2 mv^2, perhaps?
Androcles
frank...@yahoo.com
it at:
http://www.geocities.com/franklinhu/emc.html
I have added a section justifying why the normal kinetic energy formula
might hold in the pair production case instead of the relativity
kinetic energy formula.
This is part of my growing theory of everything which can be viewed at:
http://www.geocities.com/franklinhu/theory.html
John C. Polasek
It's nice to see someone question the status quo. Your "musings" are
interesting, so you might be interested to see my extremely detailed
analysis (on the website below, paper #1) of what the "ether" must
be, that is, the only possible structure that can give us the observed
value for permittivity of 8.8 uuFd/m. Since you don't include any
equaitons in your paper, you might be put off by the math.
And you may agree with my analysis that the electron requires 1/2 mc2
to pop out of its cell and 1/2 mc2 to gain the velocity of light.
Take a look.
John Polasek
http://www.dualspace.net