> On Aug 28, 12:03 pm, Tom Roberts wrote:
>

>> Sanny wrote:

>>> What is the proof the Mass is always conserved?

>

>> There can be no such proof, because mass is quite clearly not conserved
>> for many known situations.

>
> It depends on how you interpret the mass to be.  
>

>> Under certain general circumstances, energy is conserved, and momentum
>> is conserved, and angular momentum is conserved, but not mass.

>
> The conservation of energy is very much in the bag according to the
> Noether’s theorem.  However, the conservation of the angular momentum
> is not a sure thing especially in a binary system.  
>

>>> Its just happens that mass do not get destroyed or created.

>

>> This, too, is simply not true.

>

>> The most obvious counterexample is the reaction:

>

>>         \gamma + A => A + e- + e+

>

>> The \gamma on the left has zero mass, but the e+ and the e- on the right
>> each have a clearly non-zero mass of 511 keV/c^2.

>
> Since gamma rays have momentums, the most appropriate interpretation
> is to model them with mass where this mass is a function of speed.  Of
> course, anyone can choose to define the mass only at rest.  In doing
> so, you are just making a deeper fool of yourself in the long run.
>
>

>> There are literally thousands of other examples -- just look up ANY
>> chemical or nuclear reaction, and with sufficient accuracy you'll find
>> the masses on the two sides are not equal. Nuclear reactions typically
>> have a mass difference on the order of a few MeV/c^2; chemical reactions
>> typically have a mass difference on the order of a fraction of an
>> eV/c^2, and it is exceedingly difficult to measure such small
>> differences. The mass deficits in nuclear reactions are well established.

>
> All these thousands of examples can easily be demystified if the mass
> is defined as energy divided by the speed of light squared.  
>
> Why have you guys never thought about that?  Yes, mysticism is the key
> to your survival.  
>

>>> In Nuclear Fusion Mass is converted into energy.
>>> E= m* c2;
>>> I think this do not violate that principle of Conservation of Mass?

>

>> There is no such principle. This example CLEARLY shows that mass is not
>> conserved (it's converted into energy, which is not mass).

>

>> Energy is conserved in nuclear fusion, but that's a different topic.

>
> No, it is not a different topic.  Your interpretation allows you to
> flip-flop to the winning side whenever the situation comes into your
> favor, and this is not science.  The only interpretation to mass is,
> once again, energy divided by the speed of light of the observer.
>
>

>>> People say [...]

>

>> People say lots of things. Many of them are not true.

>
> Please stay with the topic.  People (most physicists) say the only
> interpretation to mass is the rest mass.  That is perfectly OK.
> However, in doing so, you are just adding more problems for
> yourselves. Once again, the best way to interpret what mass is is
> proportional to energy.  Msss is energy, and energy is mass.  Believe
> me.  In that case, mathematics get a lot simpler.
>
> For example, the Schwarzschild metric demands the conservation of
> energy.  You (plural) just would not go there because interpreting
> mass solely as the rest mass does not allow you to do so.  In doing
> so, you have no explanation why energy is conserved after declaring
> that no such entity as the potential energy.  From the geodesic
> equations, the energy of an object with rest mass of m under the
> curvature of spacetime manifested with mass M (add all other
> requirements such as M >> m, etc) can be expressed as follows.
>
> E = m c^2 sqrt(1 – 2 U) / sqrt(1 – B^2)
>
> Where
>
> **  U = G M / c^2 / r
> **  B^2 c^2 = (dr/dt)^2 / (1 – 2 U)^2 + r^2 (dO/dt)^2 / (1 – 2 U)
> **  dO^2 = dLongitude^2 cos^2(Latitude) + dLatitude^2
>
> The conservation of the overall mass, m sqrt(1 – 2 U) / sqrt(1 – B^2),
> results in the conservation of energy as well.  Under very special
> circumstance such as weak gravitation (1 >> 2 U) and low speed (1 >>
> B^2), the above equation reduces into the Newtonian equation
> describing the conservation of energy in orbital mechanics below.
>
> E – m^2 c^2 = m B^2 c^2 / 2 – m U c^2
>
> Where
>
> **  m B^2 c^2 / 2 = Kinetic energy
> **  m U c^2 = Potential energy
>

>> Timberwoof said:

>>> There is no "proof", but beginning with Lavoisier, a French tax
>>> collector who applied strict principles of accounting to his
>>> observations of chemical reactions, the observationthat under ordinary
>>> conditions, mass is neither created nor destroyed, has always been
>>> confirmed.

>

>> His measurements were insufficiently accurate to detect the mass
>> differences. Indeed even today it is quite difficult to measure the mass
>> deficits of chemical reactions; general theoretical arguments show they
>> must be present (molecules are bound). Particle physicists measure mass
>> deficits in nuclear (and sub-nuclear) reactions all the time.

>
> Give me a break.  Justifying your interpretation of mass based on a
> crude 19th century (or earlier) is totally groundless.  
>

>> The Timelord said:
>>  > [proof mass is conserved] comes from the continuity equation [...]

>

>> That equation is valid only in classical mechanics. It is not valid in
>> relativity, nor in the world we inhabit.

>
> This is nonsense.  The Euler-Lagrange equation (geodesic equation)
> associated with spacetime shows so time after time that the energy
> must be conserved according to Noether’s theorem.    This, of
> course, includes your binary systems which you (plural) have claimed
> gravitational radiation without trying to justify, qualify, and
> understand the mathematics of geodesic variations.  
>

>> Mass conservation remains APPROXIMATELY valid in many circumstances,
>> including our everyday lives. In certain circumstances it is possible to
>> have mass conservation: if one had a truly closed system then the mass
>> of the system as a whole would be constant. This is not possible in the
>> world we inhabit (radiation always leaks in or out). In many cases,
>> however, the mass transfer due to the radiation is below one's
>> measurement resolution, and for most practical purposes the mass of the
>> system can be considered to be conserved.

>
> Any Lagrangian that you can derive and qualify does not indicate a non-
> conservation of energy.  Just because you (plural) can squeeze out a
> wave equation from the crack in the geodesic variation equations, you
> still have to show a violation in Noether’s theorem to justify your
> gravitational radiation.