Mass-Energy Equivalence [Math]

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From: Tony M on 6 Apr 2010 23:33

On Apr 6, 3:22 pm, PD <thedraperfam...(a)gmail.com> wrote:
> On Apr 6, 7:58 am, Tony M <marc...(a)gmail.com> wrote:
>
>
>
> > On Apr 5, 2:40 pm, PD <thedraperfam...(a)gmail.com> wrote:
>
> > > On Apr 5, 1:35 pm, "Sue..." <suzysewns...(a)yahoo.com.au> wrote:
>
> > > > On Apr 5, 2:18 pm, PD <thedraperfam...(a)gmail.com> wrote:
>
> > > > > On Apr 4, 12:53 am, Koobee Wublee <koobee.wub...(a)gmail.com> wrote:
>
> > > > > > On Apr 3, 10:23 pm, Tom Roberts wrote:
>
> > > > > > > Tony M wrote:
> > > > > > > > As per the mass-energy equivalence, can I assume the following is
> > > > > > > > valid?
>
> > > > > > > In relativity, which I assume is the context for your question, mass and energy
> > > > > > > are not "equivalent" in the manner you seem to think. They are in certain
> > > > > > > circumstances inter-convertible, but are most definitely not the same.
>
> > > > > > This is unbelievable. Self-styled physicists came up with (E = m
> > > > > > c^2). Now, they are walking away from it and speak with a forked
> > > > > > tongue. These clowns are very liberally interpreting the scripture
> > > > > > according to their religion. That's what you get for liberal-art
> > > > > > schools, I guess. <shrug>
>
> > > > > E=mc^2 in no way implies that mass and energy are equivalent, any more
> > > > > than F=ma implies that force and acceleration are equivalent.
>
> > > > > The equation relates the quantitative values of two distinct physical
> > > > > variables. That's what equations do.
>
> > > > > If you cannot read an equation, then perhaps you should read some
> > > > > sentences that precede and follow the equation where it is presented.
>
> > > > <<...an electron and a positron, each with a mass
> > > > of 0.511 MeV/c2, can annihilate to yield 1.022 MeV of energy.>>http://en.wikipedia.org/wiki/Electronvolt
>
> > > > Sue...
>
> > > Yes, indeed. There is the numerical equality I was talking about. Note
> > > that a processes where the collision of two objects with mass produces
> > > a predictable amount of energy does not imply that mass and energy are
> > > equivalent. Perhaps you have the same difficulty that KW is having.- Hide quoted text -
>
> > > - Show quoted text -
>
> > I think you're right PD, mass and energy are not the same thing. Maybe
> > "equivalence" is not the best word, "duality" is probably better. The
> > way I see it, mass and energy are two sides of the same coin, one
> > cannot convert mass to energy and vice-versa. For a certain amount of
> > energy in a system there will always be a corresponding amount of
> > mass, as per E=mc2.
>
> > Sue's example of electron-positron "annihilation" can be a bit
> > misleading, making one believe that mass gets converted to energy,
> > when that's not the case. The isolated system consisting of the
> > electron and positron has the same total energy and corresponding mass
> > before and after the "annihilation", except now instead of electron
> > and positron we have gamma photons (and maybe some other particles).
>
> One must be a little bit careful about the meaning of mass here.
> The invariant mass of the system (m^2 = E^2 - p^2) is indeed ...
> well ... invariant, but you'll notice this quantity is not the
> summative mass, namely the sum of the rest masses of the particles
> involved. Where mass-energy conversion takes place, it is summative
> mass that is usually being referred to.

Yes PD, one must be careful about the meaning of mass, especially when
talking about "rest" or "invariant" mass. This will surely confuse a
lot of people. One must keep in mind that there is ONLY ONE MASS. The
problem is that the VALUE of that one mass is observer dependent. In
order to provide a common ground for all the observers scientists have
defined these standard frames of reference. If everyone measures the
mass in the same standard frame of reference then they will all get
the same value. For the "rest" mass (which applies to one particle)
the frame of reference is at rest with that particle. The "invariant"
mass applies to systems of particles and is defined in the frame of
reference in which the system is at rest, even though individual
particles in the system are not. But we know there is no preferred
frame of reference in relativity, and it's postulated that all the
laws of physics are the same in any of them, so these standardized
frames are no more special than the infinite number of other frames of
reference one can choose. (I'm talking about inertial frames in SR
here.) The equation E = m c^2 IS the general form for the TOTAL ENERGY
in any arbitrary frame of reference, where m is the relativistic mass
in that frame of reference.

From: mpc755 on 7 Apr 2010 00:04

On Apr 6, 9:31Â pm, BURT <macromi...(a)yahoo.com> wrote:
> On Apr 6, 3:23Â pm, mpc755 <mpc...(a)gmail.com> wrote:
>
>
>
> > On Apr 6, 6:08Â pm, BURT <macromi...(a)yahoo.com> wrote:
>
> > > On Apr 6, 2:34Â pm, mpc755 <mpc...(a)gmail.com> wrote:
>
> > > >http://cfa-www.harvard.edu/Walsworth/pdf/PT_Romalis0704.pdf
>
> > > > "A possible candidate for dark energy that avoids some of the fine-
> > > > tuning problems associated with the cosmological is quintessence, a
> > > > very low-energy field with a wavelength comparable to the size of the
> > > > known universe. In addition to its effect on the expansion of the
> > > > universe, quintessence might also manifest itself through its possible
> > > > interactions with matter and radiation."
>
> > > >http://dictionary.reference.com/browse/quintessence
>
> > > > "quinÂ·tesÂ·sence
> > > > â â/kwÉªnËtÉsÉns/ Show Spelled[kwin-tes-uhns] Show IPA
> > > > ânoun
> > > > 1. the pure and concentrated essence of a substance.
> > > > 2. the most perfect embodiment of something.
> > > > 3. (in ancient and medieval philosophy) the fifth essence or element,
> > > > ether, supposed to be the constituent matter of the heavenly bodies"
>
> > > > A low-energy field with a wavelength comparable to the size of the
> > > > known universe is aether as a one something.
>
> > > > Aether and matter are different states of the same material.
>
> > > > Matter is compressed aether and aether is uncompressed matter.
>
> > > > Aether is the pure essence of matter.
>
> > > > "quintessence might also manifest itself through its possible
> > > > interactions with matter"
>
> > > > Aether interacts with matter by being displaced by matter.
>
> > > > The pressure exerted by aether displaced by matter manifests itself as
> > > > gravity.
>
> > > > The physical effects the expansion of matter transitioning to aether
> > > > has on the neighboring matter and aether manifests itself as energy..
>
> > > > 'DOES THE INERTIA OF A BODY DEPEND UPON ITS ENERGY-CONTENT? By A.
> > > > EINSTEIN'http://www.fourmilab.ch/etexts/einstein/E_mc2/e_mc2.pdf
>
> > > > "If a body gives off the energy L in the form of radiation, its mass
> > > > diminishes by L/c2."
>
> > > > The mass of the body does diminish, but the matter which no longer
> > > > exists as part of the body has not vanished. It still exists, as
> > > > aether. As the matter transitions to aether it expands in three
> > > > dimensions. The effect this transition has on the surrounding aether
> > > > and matter is energy.
>
> > > Why would the universal speed limit squared define the fundamental
> > > energy in mass?
>
> > > Mitch Raemsch
>
> > It could be the relationship of matter to aether. The equation may be
> > written as:
>
> > A=Mc^2, where A is Aether and M is matter.- Hide quoted text -
>
> > - Show quoted text -
>
> Abusing that mathematical truth is important for you to not get away
> with. You do so at your own peril.
>
> Mitch Raemsch

I am simply pointing out there is a relationship to matter and aether
and what we define as 'energy' is the physical effects matter
transitioning to aether has on the neighboring matter and aether. In
this regard:

A=Mc^2 where A is aether and M is matter.

From: mpc755 on 7 Apr 2010 00:57

On Apr 6, 12:47 pm, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote:
> mpc755 wrote:
> > On Apr 6, 10:29 am, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote:
> >> Normally we apply the word "mass" to OBJECTS, not to collections of unbound
> >> objects. In the initial state the electron and the positron EACH have a mass,
> >> and the total mass is 1.022 MeV/c^2. In the final state the gammas each have
> >> zero mass, and the total mass is 0. The total energies of the initial and final
> >> states are the same. The total kinetic energy of the initial state is 0, but the
> >> total kinetic energy of the final state is 1.022 MeV. These units have c=1, and
> >> it is obvious that mass was indeed converted to kinetic energy.
>
> > Stating the 'total mass is 0' is misleading. The mass still exists.
>
> No. I am using these words with their standard meanings in modern physics.. There
> is no mass in that final state.
>

http://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence

"According to the theory of relativity, mass and energy as commonly
understood, are two names for the same thing, and neither one is
changed or transformed into the other. Rather, neither one appears
without the other. Rather than mass being changed into energy, the
view of relativity is that rest mass has been changed to a more mobile
form of mass, but remains mass. In this process, neither the amount of
mass nor the amount of energy changes. Thus, if energy changes type
and leaves a system, it simply takes its mass with it. If either mass
or energy disappears from a system, it will always be found that both
have simply moved off to another place."

What is being described in the paragraph above is matter transitioning
to aether.

From: Now that is one happy monkey. on 7 Apr 2010 01:49

On Apr 6, 9:57 pm, mpc755 <mpc...(a)gmail.com> wrote:
> On Apr 6, 12:47 pm, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote:
>
> > mpc755 wrote:
> > > On Apr 6, 10:29 am, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote:
> > >> Normally we apply the word "mass" to OBJECTS, not to collections of unbound
> > >> objects. In the initial state the electron and the positron EACH have a mass,
> > >> and the total mass is 1.022 MeV/c^2. In the final state the gammas each have
> > >> zero mass, and the total mass is 0. The total energies of the initial and final
> > >> states are the same. The total kinetic energy of the initial state is 0, but the
> > >> total kinetic energy of the final state is 1.022 MeV. These units have c=1, and
> > >> it is obvious that mass was indeed converted to kinetic energy.
>
> > > Stating the 'total mass is 0' is misleading. The mass still exists.
>
> > No. I am using these words with their standard meanings in modern physics. There
> > is no mass in that final state.
>
> http://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence
>
> "According to the theory of relativity, mass and energy as commonly
> understood, are two names for the same thing, and neither one is
> changed or transformed into the other. Rather, neither one appears
> without the other. Rather than mass being changed into energy, the
> view of relativity is that rest mass has been changed to a more mobile
> form of mass, but remains mass. In this process, neither the amount of
> mass nor the amount of energy changes. Thus, if energy changes type
> and leaves a system, it simply takes its mass with it. If either mass
> or energy disappears from a system, it will always be found that both
> have simply moved off to another place."
>
> What is being described in the paragraph above is matter transitioning
> to aether.

Check out "heretical" aether-friendly views in "Galilean
Electrodynamics" and "Physics Essays", two obscure journals

From: PD on 7 Apr 2010 09:17

On Apr 6, 10:33 pm, Tony M <marc...(a)gmail.com> wrote:
> On Apr 6, 3:22 pm, PD <thedraperfam...(a)gmail.com> wrote:
>
>
>
> > On Apr 6, 7:58 am, Tony M <marc...(a)gmail.com> wrote:
>
> > > On Apr 5, 2:40 pm, PD <thedraperfam...(a)gmail.com> wrote:
>
> > > > On Apr 5, 1:35 pm, "Sue..." <suzysewns...(a)yahoo.com.au> wrote:
>
> > > > > On Apr 5, 2:18 pm, PD <thedraperfam...(a)gmail.com> wrote:
>
> > > > > > On Apr 4, 12:53 am, Koobee Wublee <koobee.wub...(a)gmail.com> wrote:
>
> > > > > > > On Apr 3, 10:23 pm, Tom Roberts wrote:
>
> > > > > > > > Tony M wrote:
> > > > > > > > > As per the mass-energy equivalence, can I assume the following is
> > > > > > > > > valid?
>
> > > > > > > > In relativity, which I assume is the context for your question, mass and energy
> > > > > > > > are not "equivalent" in the manner you seem to think. They are in certain
> > > > > > > > circumstances inter-convertible, but are most definitely not the same.
>
> > > > > > > This is unbelievable. Self-styled physicists came up with (E = m
> > > > > > > c^2). Now, they are walking away from it and speak with a forked
> > > > > > > tongue. These clowns are very liberally interpreting the scripture
> > > > > > > according to their religion. That's what you get for liberal-art
> > > > > > > schools, I guess. <shrug>
>
> > > > > > E=mc^2 in no way implies that mass and energy are equivalent, any more
> > > > > > than F=ma implies that force and acceleration are equivalent.
>
> > > > > > The equation relates the quantitative values of two distinct physical
> > > > > > variables. That's what equations do.
>
> > > > > > If you cannot read an equation, then perhaps you should read some
> > > > > > sentences that precede and follow the equation where it is presented.
>
> > > > > <<...an electron and a positron, each with a mass
> > > > > of 0.511 MeV/c2, can annihilate to yield 1.022 MeV of energy.>>http://en.wikipedia.org/wiki/Electronvolt
>
> > > > > Sue...
>
> > > > Yes, indeed. There is the numerical equality I was talking about. Note
> > > > that a processes where the collision of two objects with mass produces
> > > > a predictable amount of energy does not imply that mass and energy are
> > > > equivalent. Perhaps you have the same difficulty that KW is having.- Hide quoted text -
>
> > > > - Show quoted text -
>
> > > I think you're right PD, mass and energy are not the same thing. Maybe
> > > "equivalence" is not the best word, "duality" is probably better. The
> > > way I see it, mass and energy are two sides of the same coin, one
> > > cannot convert mass to energy and vice-versa. For a certain amount of
> > > energy in a system there will always be a corresponding amount of
> > > mass, as per E=mc2.
>
> > > Sue's example of electron-positron "annihilation" can be a bit
> > > misleading, making one believe that mass gets converted to energy,
> > > when that's not the case. The isolated system consisting of the
> > > electron and positron has the same total energy and corresponding mass
> > > before and after the "annihilation", except now instead of electron
> > > and positron we have gamma photons (and maybe some other particles).
>
> > One must be a little bit careful about the meaning of mass here.
> > The invariant mass of the system (m^2 = E^2 - p^2) is indeed ...
> > well ... invariant, but you'll notice this quantity is not the
> > summative mass, namely the sum of the rest masses of the particles
> > involved. Where mass-energy conversion takes place, it is summative
> > mass that is usually being referred to.
>
> Yes PD, one must be careful about the meaning of mass, especially when
> talking about "rest" or "invariant" mass. This will surely confuse a
> lot of people. One must keep in mind that there is ONLY ONE MASS. The
> problem is that the VALUE of that one mass is observer dependent. In
> order to provide a common ground for all the observers scientists have
> defined these standard frames of reference. If everyone measures the
> mass in the same standard frame of reference then they will all get
> the same value. For the "rest" mass (which applies to one particle)
> the frame of reference is at rest with that particle. The "invariant"
> mass applies to systems of particles and is defined in the frame of
> reference in which the system is at rest, even though individual
> particles in the system are not. But we know there is no preferred
> frame of reference in relativity, and it's postulated that all the
> laws of physics are the same in any of them, so these standardized
> frames are no more special than the infinite number of other frames of
> reference one can choose. (I'm talking about inertial frames in SR
> here.) The equation E = m c^2 IS the general form for the TOTAL ENERGY
> in any arbitrary frame of reference, where m is the relativistic mass
> in that frame of reference.

Well, perhaps this is being pedantic, but I would quibble with your
claim that there is only one mass and that that one mass is the
relativistic mass. This is precisely what has gone out of disfavor in
recent decades.