Can Mass Be Transformed Into Energy?

[yuiop]

Perhaps this is a better way to do the calculation in post #35 ?

Assuming the initial rest mass energy (RE1) of the total system (cannon+batteries+projectiles) is 6m before firing and assuming the total energy (TE) of the system does not change after firing, then the final rest mass energy of the total system after firing (RE2) is:

RE2 = TE - KE = 6m - (2m/0.6 - 2m) = 4.666m

Assuming the rest mass of the projectiles remains constant then the loss of 1.333m in rest mass energy of the system is attributed to the discharge of stored energy in the batteries?

Should the quantity I have been referring to as the "rest mass energy" of the system be formally described as the inertial, invariant or proper mass of the system?

 

[Dale]

I would simply use the conservation of the four-momentum to do this (in units where c=1):
four-momentum of system before firing: (6m,0)
four-momentum of shells after firing: (γm,±γv)
four-momentum of the gun after firing: (6m,0)-((γm,γv)+(γm,-γv)) = (6m-2γm,0)

Note that v must satisfy the condition that 6m-2γm ≥ 0

 

[yuiop]

I would simply use the conservation of the four-momentum to do this (in units where c=1):
four-momentum of system before firing: (6m,0)
four-momentum of shells after firing: (γm,±γv)
four-momentum of the gun after firing: (6m,0)-((γm,γv)+(γm,-γv)) = (6m-2γm,0)

Note that v must satisfy the condition that 6m-2γm ≥ 0

Using the values of v=0.6 and γ=1.666 in the example I gave, then

Invariant mass of the total system before firing = 6m

Invariant mass of the 2 shells before firing = 2m
Invariant mass of the 2 shells after firing = 3.333m (Inertial mass?.. Rest mass?)

Invariant mass of the gun before firing = 4m
Invariant mass of the gun after firing = 2.666m (Inertial mass?.. Rest mass?)

Invariant mass of the total system after firing = 6m

 

[Tachyonie]

I got to read your answers just now.
I asked the question because I felt that pmb_phy was telling me that you cannot convert mass into energy which to me made no sense since I always visioned mass and energy as 2 sides of the same coin as in the E=mcc formula. Now I see that I might have misunderstud.
Its important to state that my knowledge of physics is not very good, and all I know about physics of this magnitude is self-taught since I did not advance that far in school.
As far as I know I ment the invariant mass changing, not the relativistic mass.

 

[pmb_phy]

I got to read your answers just now.
I asked the question because I felt that pmb_phy was telling me that you cannot convert mass into energy which to me made no sense since I always visioned mass and energy as 2 sides of the same coin as in the E=mcc formula. Now I see that I might have misunderstud.
Its important to state that my knowledge of physics is not very good, and all I know about physics of this magnitude is self-taught since I did not advance that far in school.
As far as I know I ment the invariant mass changing, not the relativistic mass.

I think I mentioned that regardless of which mass you're referring to its conserved, for a closed system that is. And conservation of energy always refers to a closed system although some open systems may have a conserved energy.

Pete

 

[Dale]

I would simply use the conservation of the four-momentum to do this (in units where c=1):
four-momentum of system before firing: (6m,0)
four-momentum of shells after firing: (γm,±γv)
four-momentum of the gun after firing: (6m,0)-((γm,γv)+(γm,-γv)) = (6m-2γm,0)

Note that v must satisfy the condition that 6m-2γm ≥ 0

Using the values of v=0.6 and γ=1.666 in the example I gave, then

Invariant mass of the total system before firing = 6m

Invariant mass of the 2 shells before firing = 2m
Invariant mass of the 2 shells after firing = 3.333m (Inertial mass?.. Rest mass?)

Invariant mass of the gun before firing = 4m
Invariant mass of the gun after firing = 2.666m (Inertial mass?.. Rest mass?)

Invariant mass of the total system after firing = 6m

Actually, your numbers are a little off. In units where c=1 and m=1 with v=0.8 we have:
γ=1.667
invariant mass of system before firing: |(6m,0)| = |(6,0)| = 6
invariant mass of each shell after firing: |(γm,±γv)| = |(1.667,±1.333)| = 1
invariant mass of the gun after firing: |(6m-2γm,0)| = |(2.667,0)| = 2.667
invariant mass of the system after firing: |(6m-2γm,0)+(γm,γv)+(γm,-γv)| = |(6m,0)| = 6

Note that the invariant mass of the system after firing (6) is different than the sum of the invariant masses of the parts (4.667). Loosely speaking, this difference (1.333) represents the mass that was converted to energy.

 

[RandallB]

I felt that pmb_phy was telling me that you cannot convert mass into energy.
As far as I know I meant the invariant mass changing, not the relativistic mass.

Just to split hairs a bit,
I believe you did not mean to say “I meant the invariant mass changing” but rather invariant mass is “converting” to energy as it disappears into photons.
I think pmb_phy is telling you that cannot “convert” mass into the energy of a photon because the “mass” is still there as “Inertial” mass in the photon.
I disagree with that as IMO it is only to allow us keep our cake and eat it too;
Just so that a photon still have “zero” mass except for the “Inertial” mass, so the accepted standard of a massless point particle photon is retained, while defining photon “Energy” as a kinetic thing based on mass in the photon.

For me science must pick one or the other; photons either do or do not have mass period. And with the current standard being no mass IMO that means the Energy is a unique thing that can be converted from or into mass.
I suspect that is what you are thinking and IMO represents the approach and descriptions offered by many others (Meitner etc.)

Note the confusion that can from multiple versions of mass.
The DaleSpam and kev discussion on changing values of “invariant mass” for guns and bullets based on changing the relative speeds between them, badly mangles the concept of “invariant mass”.
The term “invariant” means NOT changing:
DaleSpam and kev are actually applying ideas of “Relativistic Mass”, which the modern view considers incorrect and unnecessary and does not apply to this topic of transforming mass.
Although pmb_phy and I disagree on the accepted definition of a photon, I think pmb_phy will agree that these relativistic guns and bullets of changing mass descriptions are misleading at best.

 

[Dale]

The term “invariant” means NOT changing:
DaleSpam and kev are actually applying ideas of “Relativistic Mass”, which the modern view considers incorrect and unnecessary and does not apply to this topic of transforming mass.

"Invariant" means that different reference frames agree on the quantity. I think the term you are looking for is "conserved" which means that the quantity doesn't change over time.

I was correctly using the invariant mass (the Minkowski norm of the four-momentum) and was not referring to relativistic mass (the Euclidian norm of the three-momentum divided by the speed or γ times the invariant mass for particles moving at v<c).

 

[RandallB]

The mass remains the same. The only thing that has changed is the sum of the proper masses. The total inertial mass (aka relativistic mass) remains constant.

I think pmb_phy will agree that these relativistic guns and bullets of changing mass descriptions are misleading at best.

OOPS
I suspect my assumption of agreement here is likely wrong as “relativistic mass” is somehow involved in a way that escapes me.
I also don’t see how I’ll ever reconcile the idea the before and after value of some form of mass for a gun can significantly change after the mass of a pair of bullets depart at 0.6c as the mass of the bullets themselves also change.

If anyone wishes to research these positions further; I believe my position is closest to:
(July 1989). Lev B. Okun
"The Concept of Mass". Physics Today 42 (6): 31–36.

And some of the other positions are likely closer to those of:
(Nov. 1991). T. R. Sandin
"In defense of relativistic mass". American Journal of Physics 59 (11).

I found the published papers referenced under “Mass in special relativity” on Wikipedia.

 

[yuiop]

Just to split hairs a bit,
I believe you did not mean to say “I meant the invariant mass changing” but rather invariant mass is “converting” to energy as it disappears into photons.

Equally, we can say that part of the invariant mass of the gun has been converted into the kinetic energy of the shells.

I think pmb_phy is telling you that cannot “convert” mass into the energy of a photon because the “mass” is still there as “Inertial” mass in the photon.
I disagree with that as IMO it is only to allow us keep our cake and eat it too;
Just so that a photon still have “zero” mass except for the “Inertial” mass, so the accepted standard of a massless point particle photon is retained, while defining photon “Energy” as a kinetic thing based on mass in the photon.

For me science must pick one or the other; photons either do or do not have mass period. And with the current standard being no mass IMO that means the Energy is a unique thing that can be converted from or into mass.

We can have a laser gun version of the thought experiment. A charged battery fires photons in opposite directions until the battery is depleted. The laser gun and battery will weigh less after the battery is depleted. The inertial mass of the gun has been reduced and it would require less energy to accelerate the depleted gun rather than the charged gun. Without being able to assign some form of mass to the photons we can not have a concept of invariant mass for the system as a whole. This is made clearer, if the fuel for the laser gun consists of matter and anti matter. When the the fuel of the gun is depleted, it is very clear the gun weighs less, and without assigning mass to the photons it is very clear that there is no concept of invariant mass for the system as a whole.

THis adaptation of the experiment shows that the loss of mass of the gun (in any version of the experiment) is just as as real as the loss of mass during the annhilation of matter and antimatter into photons.

I suspect that is what you are thinking and IMO represents the approach and descriptions offered by many others (Meitner etc.)

Note the confusion that can from multiple versions of mass.
The DaleSpam and kev discussion on changing values of “invariant mass” for guns and bullets based on changing the relative speeds between them, badly mangles the concept of “invariant mass”.
The term “invariant” means NOT changing:

The gun thought experiment just made clear that invariant mass is only invariant for a closed system. The total (invariant) mass of the whole system was indeed invariant before and after firing. The invariant mass of the individual parts (which are open systems) is not invariant, showing that the expression "invariant mass" can be misleading. Perhaps something along the lines of (Total Inertial mass)^2 = (Total Energy)^2 - (Total Momentum)^2 would be clearer with the understanding that the inertial mass is invariant for a closed system.

DaleSpam and kev are actually applying ideas of “Relativistic Mass”, which the modern view considers incorrect and unnecessary and does not apply to this topic of transforming mass.
Although pmb_phy and I disagree on the accepted definition of a photon, I think pmb_phy will agree that these relativistic guns and bullets of changing mass descriptions are misleading at best.

I think we can all agree that a photon has zero rest mass, and some of us agree that a photon has inertial mass allowing us to assign quantities like momentum to a photon. As mentioned earlier being able to assign inertial (relativistic) mass to a photon allows us to use the concept of invariant mass for a system that includes photons. The energy of a photon is proportional to it momentum (pc) which in turn is proportional to its frequency (hf). The inertial (relatavistic) mass of a photon can be found from mc^2 = hf --> m = hf/c^2.

I was hoping we would avoid descending into an argument about the use of relativistic mass and deliberately avoiding using that term in my previous posts for that reason. It would seem that the term "inertial mass" has crept in as the politically correct replacement for the emotive "relativistic mass". Seeing as how you have brought up the issue of relativistic mass I will quote this passage from the Physics FAQ http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html

=========================================================
A debate of the idea of relativistic mass surfaced in Physics Today in 1989 when Lev Okun wrote an article urging that relativistic mass should no longer be taught (42, June 1989, pg 31). Wolfgang Rindler responded with a letter to the editors defending its continued use (43, May 1990, pgs 13 and 115). In 1991 Tom Sandin wrote an article in the American Journal of Physics arguing very persuasively in favor of relativistic mass (59, November 1991, pg 1032). (Links are provided here, but the articles cannot be downloaded for free.)

An optimistic view would hold that it's a measure of the richness of physics that focussing on different aspects of concepts like mass produces different insights: intuition for the case of relativistic mass in special relativity, and the notion of invariance for the case of tensor language in special and general relativity. But it's also unfortunate that whereas "pro relativistic mass" physicists will happily live with both ideas, "anti relativistic mass" physicists spend a lot of time trying to have relativistic mass outlawed.

Abandoning the use of relativistic mass is often validated by quoting select physicists who are or were against the term. But real science isn't done that way. In the final analysis, the history of relativity, with its quotations from those in favour of relativistic mass and those against, has no real bearing on whether the idea itself has value. The question to be asked is not whether relativistic mass is fashionable or not, or who likes the idea and who doesn't; rather, as in any area of physics notation and language, we should always ask "Is it useful?" And relativistic mass is certainly a useful concept.

==============================================================

 

[yuiop]

The gun thought experiment just made clear that invariant mass is only invariant for a closed system. The total (invariant) mass of the whole system was indeed invariant before and after firing. The invariant mass of the individual parts (which are open systems) is not invariant, showing that the expression "invariant mass" can be misleading. Perhaps something along the lines of (Total Inertial mass)^2 = (Total Energy)^2 - (Total Momentum)^2 would be clearer with the understanding that the inertial mass is invariant for a closed system.

After some further thought, the energy equation

$$m_0^2c^4 = E^2 -P^2c^2$$

after dividing through by $c^4$ to get the mass equation

$$m_0 ^2 = m^2 - m^2v^2/c^2$$

can be expressed as:

$$(Rest Mass)^2 = (Inertial Mass)^2 - (Momentum Mass)^2$$

For a photon inertial mass = E/c^2 and momentum mass = p/c = hf/c^2 are equal and so the rest mass is zero.

The expression for relativistic mass (inertial mass)

$$m = {m_0 \over \sqrt{1-v^2/c^2}}$$

when applied to a photon which has rest mass $$m_o = 0$$ becomes m = 0/0 which is undetermined by this equation but can be found from m = hf/c^2.

Rest mass (also called invariant mass) has the following properties:

1) Rest mass of a particle or closed system is invariant under a Lorentz transformation.
2) Rest mass of a closed system is conserved over time.
3) Rest mass of a particle or part of a system can change over time.

Inertial mass (the mass equivalent of the total energy also called relativistic mass) has the following properties:

4) Inertial mass of a particle or closed system is not invariant under a Lorentz transformation.
5) Inertial mass of a closed system is conserved over time.
6) Inertial mass of a particle or part of a system can change over time.
7) Inertial mass of a system is related to the resistance of the system to being accelerated and is closely related to the active gravitational mass of the system.

Examples:

In the gun experiment the total momentum before and after firing is zero as the shells move in opposite directions. The total energy (and therefore the total inertial mass) of the system is conserved before and after and so is the rest mass.

In the annihilation of a proton and anti-proton, two photons are produced moving in opposite directions to conserve the zero momentum of the system. The inertial mass (total energy) and rest mass of the system as a whole is conserved. Yes.. one photon has zero rest mass, but a system comprising of only two photons moving in opposite directions has non-zero rest mass. Surprising?

In the gun experiment if we consider only the mass of the gun, then the inertial mass and the rest mass of the gun has reduced after firing. This is an example of an object losing rest mass without involving a nuclear reaction. It could be argued that this is not the true rest mass of the gun as the mass lost is due to the loss of energy of the battery. Further rest mass could be “lost” by cooling the gun. It could be argued that the mass of an object that is not at absolute zero temperature with all forms of stored potential energy removed is never representative of the “true” rest mass of the object.
Generally, the rest mass (invariant mass) of an object that is assumed in the equations, is the inertial mass (E/c^2) measured in the inertial reference frame where the object has zero linear momentum, even though it may not truly be at rest due to thermal vibrations, spin, expansion etc. In this respect “proper mass” may be a more intuitive term than rest mass for intrinsic mass.

If we examine a single particle of the proton and anti-proton annihilation, then the rest mass of the single particle is converted to momentum mass while its inertial mass is conserved, The final momentum mass is equal to the inertial mass and the final rest mass is zero because it has become a photon.

A single shell from the double gun experiment has increased momentum mass and increased inertial mass but its rest mass is conserved.

An observer co-moving with one of the shells fired from the double gun sees the inertial mass and the momentum mass of the complete system as being greater than that measured by an observer at rest with the double gun, but both observers see the same rest mass for the system as each other and before and after firing.

A spinning top that comes to rest on a table top which has dissipated its angular motion as heat to its surroundings will have less rest mass and less inertial mass than when it was spinning. Its (linear) momentum mass before and after is zero. While the rest mass of the top as a whole is considered to be less after it has stopped spinning, the "intrinsic" rest mass of the individual elements of the spinning top have not changed over time. The extra weight it had while spinning is the kinetic energy of the elements that that for all purposes "behaves" like additional inertial mass. This is more clearly seen in the example of photon that has no rest mass but has inertial mass purely due to the energy of motion. This inertial mass of the photon is real in the sense that the photon has momentum that it can impart to a massive particle in a collision and it has gravitational mass creating its own little "dent" in the curvature of spacetime.

Having said all that, I can see that only using proper mass and invariant four velocity makes the maths simpler when using tensors and I can also see the desirablity of only having mass associated with matter and treating photons as pure energy. :P

 

[Dale]

It could be argued that the mass of an object that is not at absolute zero temperature with all forms of stored potential energy removed is never representative of the “true” rest mass of the object.

Yes, I agree. That is why I prefer the term "rest energy" for any system of more than one particle. Although based on Pete's earlier post I think "proper energy" is even better. That makes it clear that you are talking about an invariant quantity and that it includes mass due to matter as well as mass due to the energy of the system.

By the way, based on your most recent post I think you understand the difference between "invariant" and "conserved", but just to be clear this paragraph:

The gun thought experiment just made clear that invariant mass is only invariant for a closed system. The total (invariant) mass of the whole system was indeed invariant before and after firing. The invariant mass of the individual parts (which are open systems) is not invariant, showing that the expression "invariant mass" can be misleading.

Should read:

The gun thought experiment just made clear that invariant mass is only conserved for a closed system. The total (invariant) mass of the whole system was indeed conserved before and after firing. The invariant mass of the individual parts (which are open systems) is not conserved, showing that the expression "invariant mass" can be misleading.

 

[pmb_phy]

Although pmb_phy and I disagree on the accepted definition of a photon, I think pmb_phy will agree that these relativistic guns and bullets of changing mass descriptions are misleading at best.

No. I do not agree. I believe just the opposite in fact.

Pete

 

[pmb_phy]

After some further thought, the energy equation

$$m_0^2c^4 = E^2 -P^2c^2$$

after dividing through by $c^4$ to get the mass equation

$$m_0 ^2 = m^2 - m^2v^2/c^2$$

can be expressed as:

$$(Rest Mass)^2 = (Inertial Mass)^2 - (Momentum Mass)^2$$

Perhaps this goes without saying but that is a special case of a closed system. FIf one were to calculate the "rest mass" density and assumes this is true then one is in for a big surprise. For example: Suppose that in the frame S there is a magnetic field. Examine a small element of that field. The element is small enough so that the field may be considered uniform throughout the volume. Let the magnetic field at that point be pointing in the +z direction. Now consider a frame S' which is in standard configuration with S and moving in the +x direction with respect to S. Now evaluate the mass of that volume element. This will have the value one would expect. However consider the same thing but now let the magnetic field point in the +x direction. When you transform these quantities to S' you'll find that the momentum is zero. Thus when you divide by the speed v (of frame S with respect to the zero momentum frame) then the answer you get will equal zero. Its for this reason I prefer not to use terms like "{rest mass" or use "mass" to refer to invariant mass or rest mass. Those terms pply only to special cases and are not valid in all generality. And in my opinion a definition must hold in all possible cases.

Pete

 

[RandallB]

No. I do not agree. I believe just the opposite in fact.

Yes, as you can see from post #44
where I finally came across the Okun vs. Sandin Debate / Controversy
I suspected that to be the case

I question the reasonableness of, as kev puts it, “deliberately avoiding using that term” (relativistic mass) to avoiding addressing Okun opinions when effectively using the principles of relativistic mass, in order to apply different types of mass (rest, momentum, Inertial) to account the constituent parts that make up matter and light.

I find the Sandin position to be inconsistent and confusing, which accounts for inconstant definitions of various forms of mass between practitioners, such as those where you disagree with kev. And since it seems that the total mass “Inertial Mass” is suppose to consist of “Rest Mass” plus “Momentum mass” (Thus the zero ‘rest mass’ photons have a total “Inertial Mass” consisting of “Momentum mass”) such a summary of parts should not have “properties” like the four listed by kev. It should be “Momentum mass” that would be the independent thing to have “properties” to combined with the three properties listed for “rest mass”.

Way to many inconsistencies in the definitions I’ve seen such as:

properties for “rest mass” (invariant mass)
1) Rest mass of a particle or closed system is invariant under a Lorentz transformation.
2) Rest mass of a closed system is conserved over time.
3) Rest mass of a particle or part of a system can change over time.

If this form of mass is “invariant” how does invariant mass of a particle change over time; except by acquiring additional invariant mass to change into a new and different particle; such as an electron that converts into a heavier electron able to maintain a higher energy level.

Personally as I said before I’d rather put photons on having invariant (rest) mass;
But that is not current accepted modern science.
Thus I find the Okun approach much more reasonable. That gives us massless photons carrying a pure form of energy not based on mass.
Energy that can be destructively converted (as in not conserved) into or created from invariant mass. Science becomes a task of understanding the processes of converting between those two things “invariant” masses in particles may or may not be in motion and “pure energy” contained in photons.
But can reliable use an appropriate conversion factor to “conserve” or account for the total of all mass and energy as a whole.

Works for me anyway, if the Sandin doctrine works better for you have at it.

 

[yuiop]

...
Way to many inconsistencies in the definitions I’ve seen such as: If this form of mass is “invariant” how does invariant mass of a particle change over time; except by acquiring additional invariant mass to change into a new and different particle; such as an electron that converts into a heavier electron able to maintain a higher energy level.
...

As far as I know, an invariant quantity in the context of relativity is defined as not changing under a Lorentz transformation, but does not imply the quantity can not change over time. An example of an invariant quantity is transverse length. A vibrating spring in the rest frame has its length continually changing but the length of the vibrating spring at any instant is invariant under transformation to a reference frame that has motion orthogonal to the length of the spring.

The (invariant mass)^2 is simply the quantity that is left when the (momentum mass)^2 is subtracted from the (inertial mass)^2. Inertial and gravitational propeties are related to the inertial mass which is why a photon has those properties, despite have zero rest (invariant) mass. As far as I can tell the only physical property related to rest mass is that non zero mass precludes a particle from moving at the speed of lightand the converse (a particle with zero rest mass can not move at less than the local speed of light). It is also worth noting that the inertial mass of a photon can change under transformation to a different reference frame, because the frequency changes.

 

[pmb_phy]

I question the reasonableness of, as kev puts it, “deliberately avoiding using that term” (relativistic mass) to avoiding addressing Okun opinions when effectively using the principles of relativistic mass, in order to apply different types of mass (rest, momentum, Inertial) to account the constituent parts that make up matter and light.

Each side of the debate that Okun addresses is avoiding using a particular term.

I find the Sandin position to be inconsistent and confusing, ..

Were you yourself confused? If so then what part confused you?

Regarding "parts" of systems - The term rest mass in general has no meaning when it comes to non-closed systems as I mentioned above with the magnetic field example.

PEte

 

[RandallB]

Each side of the debate that Okun addresses is avoiding using a particular term.

?? what part of the Okun position do propionates of it need to avoid using in order to advocate the position.
I read Okun as using one term for mass,
that matter containing mass put in motion relative to other matter can be measured as having a quantity called energy.
And a thing called Energy also exists in massless particles called photons.
And mass can be converted into or from the Energy that makes up the massless photons.
Thus whatever “mass” is; it is not be conserved as parts of can be removed and replaced by conversion into energy in photons.
Likewise energy is not conserved as portions of that can disappear for a closed system as photons are converted into matter with mass.
But the absolute total of Mass and energy must be conserved when combined using an appropriate “exchange rate” to measure total in common units.
The same fixed rate that applies to the conversions; E=mc^2.
There are no Okin terms that propionates need to conceal from the arguments for Okin that I am aware of, they only need one term for mass.

Not so for the Sandin position,
Kev clearly admitted withholding the significance of relativistic mass by not using the term; while clearly it is an important part of the Sandin position defining different forms of mass.

(on Sandin position) Were you yourself confused? If so then what part confused you?

Regarding "parts" of systems - The term rest mass in general has no meaning when it comes to non-closed systems as I mentioned above with the magnetic field example.

No not at all.
It is the Sandin position I find confusing.

Sandin seems unable to establish a consistent meaning to the various forms of mass it proposes (inertial, momentum, invariant, etc.), just as you point out in your examples.

IMO that accounts for why some elements of Sandin (relativistic mass is only one) need to be skirted over in order to advocate for Sandin.
THAT just doesn't work for me.

 

[pmb_phy]

?? what part of the Okun position do propionates of it need to avoid using in order to advocate the position.

Wow. What a confusing question! Okun doesn't like it when people use the term "rest mass" since he believes it is redundant. The whole point of his paper is to do away with any other term expcet "mass" period. However, it should be noted that Okun was not addressing the entire concept of mass as it is used in all generality. He was usinng it to how it pertains to particle physics. In fact Okun never considered the GR portion of Einstein's text The Meaning of Relativity when he wrote that article since in the GR part of that text Einstein does refer to a different use of mass that Okun was speaking about. Einstein used a particular definition of mass which is dependant on the gravitational potential. It was for that reason that he was able to argue the validity of Mach's principle.

I read Okun as using one term for mass, that matter containing mass put in motion relative to other matter can be measured as having a quantity called energy.

But the entire purpose of that paper was to argue that only one term should be used for mass. Okun didn't have a complete understanding of mass when he wrote that paper in fact. He was unaware of the fact that there are situations where E does not equal mc².

Please note that if I don't respond to parts of your posts its not because I'm ignoring them. In those cases I've already said what I had to say one the topic and am trying not to repeat myself, okay? I just wanted to make sure so that you didn't think I was being rude.

By the way, I wrote a paper on this subject which covers all aspects of this debate in fine detail. I would enjoy your feedback if you'd likee to read it? I'm always open to constructive criticism.

Best wishes

Pete