Unraveling the Equivalence of Energy and Mass: A Scientific Perspective

[Drakkith]

Take a system of two masses with the same relative velocity, the difference being in one case the masses behave like binary stars, in the other case they simply move apart. Since the velocities in both cases are same, aggregate rest mass is same, now will the two cases have a different aggregate invariant mass?
EDIT: Take suitable center of momentum so that both cases can be simplified as single body at rest.

If the sum of the potential energy + kinetic energy of each body is the same, then yes, both systems will have the same mass, regardless of what their actual physical arrangement is. Take for example a highly elliptical orbit of binary stars vs those same two stars in circular orbits around their barycenter. As the stars in the elliptical orbits move from their maximum separation distance and approach their minimum separation distance, their kinetic energy greatly increases relative to the center of mass of the system. But at the same time, their gravitational potential energy decreases by an equal amount, leaving no net change in the energy of the system as a whole. At both the maximum and minimum separation, the system will have the same mass as the binary stars in circular orbits.

 

[ZapperZ]

I still think that there is a serious flaw in the whole idea behind this thread, as reflected in the topic. Asking "Energy is mass, is that all?" is similar to asking "Cows are animals, is that all?"

It is as IF that characteristic or categorization ALONE is sufficient to provide the entire description of the entity. It is ignoring that (i)Energy may have momentum; (ii) energy may have angular momentum quantum number; etc...etc.

We have gone through this already in many other threads. An electron simply cannot be taught of as JUST a clump of energy, because of the obvious presence of charge and spin 1/2. So while its mass may be converted into energy, there are OTHER characteristics of an electron that must be taken into account before that can happen to preserve the conservation laws.

The same issue comes in in the reverse process. A photon simply cannot "condenses" into a matter without "help". Anyone who is familiar with pair-production experiments can verify that. There are conservation laws beyond just energy conservation that must be obeyed. These conservation laws are no less important than conservation of energy, and like Glenn Close in "Fatal Attraction", they must not be ignored!

Zz.

 

[Herman Trivilino]

The only way the above appears to mean binding energy to me is if the masses are bound in orbit, that not being mentioned, let me ask one more question:

Right, I didn't refer to the case where the pieces of silver interacted with each other. In that case, in addition to the their kinetic energy one would look at their potential energy, in which case the energy of the system could be less than the sum of the masses of the pieces.

Take a system of two masses with the same relative velocity, the difference being in one case the masses behave like binary stars, in the other case they simply move apart.

Same relative velocity as what? The same relative velocity with respect to what? And when you say "two masses" what do you mean? Do you mean two objects, each object having mass? Mass is not an object, mass is a property of objects. It is this very misconception that prevents many people from understanding the mass-energy equivalence. Mass is not a measure of the quantity of matter. Referring to an object as a mass is a way of speaking that's consistent with the Newtonian notion of mass as a measure of the quantity of matter in an object. It is essentially a way of using mass as a definition of the quantity of matter, something that works only in the Newtonian approximation.

 

[sweet springs]

I still think that there is a serious flaw in the whole idea behind this thread, as reflected in the topic. Asking "Energy is mass, is that all?" is similar to asking "Cows are animals, is that all?"
.

I think energy and mass are two names given to the same phenomena watching the other sides, e.g. twelve and a dozen, salt and sodium chloride, God and the Lord.
Some people say these words are replaceable, others hesitate to do that with subtle but important difference of meanings in their minds.
Watching two sides, energy is massive, mass is energetic.

 

[vin300]

It is as IF that characteristic or categorization ALONE is sufficient to provide the entire description of the entity. It is ignoring that (i)Energy may have momentum; (ii) energy may have angular momentum quantum number; etc...
Zz.

We have not looked at this through the eyes of quantum physicists. Spare me as a layman, but I think the angular momentum quantum number could be directly converted as the corresponding particle energy to equate it to mass. As with partial and integer charges, I'm dumb, not sure whether the field itself has energy or whether energy is transferred only through interactions.

Mass is not an object, mass is a property of objects. It is this very misconception that prevents many people from understanding the mass-energy equivalence. Mass is not a measure of the quantity of matter. Referring to an object as a mass is a way of speaking that's consistent with the Newtonian notion of mass as a measure of the quantity of matter in an object. It is essentially a way of using mass as a definition of the quantity of matter, something that works only in the Newtonian approximation.

At virtually everywhere I've read, they refer to two objects as two masses, irrespective of whether they follow Newton or any other bloke. Even when the objects have no charge, no angular momentum, no thermal energy, no stresses, even with the poorest of objects and men, they all have one thing if they exist: mass. It is fundamental to existence. Add corresponding energy.

 

[Dale]

Personal speculation is not permitted. Thread closed.