Unraveling the Equivalence of Energy and Mass: A Scientific Perspective

[vin300]

I've always had a problem with the equivalence concept. To begin with, energy is an abstract reality. It keeps changing form, always flowing to counter differences. Mass does the opposite, it concentrates, attracts other masses. An object is motion made up of a specific set of matter, is said to possess, some more mass, but this looks like an incomplete story. If I throw a piece of silver does the extra mass take the form of nuclear energy, some more particles of silver or something else? Everything that looks stupid is because it is done incompletely, as is the case here.

 

[mfb]

f I throw a piece of silver does the extra mass take the form of nuclear energy, some more particles of silver or something else?

There is no extra mass if you throw a piece of silver. Mass corresponds to the energy of the object in its rest frame, which does not change if you move an object. You can increase the mass of a block of silver by heating it. You don't increase the number of silver atoms, you do not even increase the mass of any particle in the block, but you increase the overall mass of the block.

 

[Ibix]

An object is motion made up of a specific set of matter, is said to possess, some more mass

Only in pop-sci presentations and very old textbooks.

 

[vin300]

Only in pop-sci presentations and very old textbooks.

Okay, somebody says it's pop-science, someone else says overall mass does increase. Another thing, when you consider flow of energy, it's almost always associated with entropy increase. Considering motion of mass, I don't think that happens, ball goes up, comes down, it does that lots of times, with nobody bothering about the entropy of the mass maybe because, there's no such thing.

 

[mfb]

Okay, somebody says it's pop-science, someone else says overall mass does increase.

The different answers are for different questions.

Another thing, when you consider flow of energy, it's almost always associated with entropy increase.

I don't think that is true.

Considering motion of mass, I don't think that happens, ball goes up, comes down, it does that lots of times, with nobody bothering about the entropy of the mass maybe because, there's no such thing.

Where is the point?

 

[Ibix]

Okay, somebody says it's pop-science, someone else says overall mass does increase. Another thing, when you consider flow of energy, it's almost always associated with entropy increase. Considering motion of mass, I don't think that happens, ball goes up, comes down, it does that lots of times, with nobody bothering about the entropy of the mass maybe because, there's no such thing.

Really? Why do you think balls don't bounce forever?

Note: this is supposed to be a prompt for thought. You are encouraged to read the PF rules on personal theories before answering.

 

[vin300]

Really? Why do you think balls don't bounce forever?
.

I was trying to equate the flow of energy with that of mass. Energy flowing from one point to another often causes irreversibility, masses making cyclic trips cause no irreversibility. Adding to it, I think balls can very well bounce forever without breaking any laws in the world, pressure of a gas is due to something similar to a ball that has been bouncing forever.

 

[Drakkith]

Adding to it, I think balls can very well bounce forever without breaking any laws in the world, pressure of a gas is due to something similar to a ball that has been bouncing forever.

The gas in a container of gas would only keep bouncing around because the container is at a non-absolute zero temperature. So the gas is hitting molecules and atoms in the container that are themselves moving about and these atoms/molecules are able to transfer energy to a particle of gas. Equilibrium is reached when, on average, the energy transferred from the gas to the container is equal to the energy transferred from the container to the gas. If you lower the temperature of the container, the gas transfers more energy over time to the container than the container transfers to the gas and the gas particles slow down until equilibrium is reached once more.

 

[Ibix]

I was trying to equate the flow of energy with that of mass. Energy flowing from one point to another often causes irreversibility, masses making cyclic trips cause no irreversibility. Adding to it, I think balls can very well bounce forever without breaking any laws in the world, pressure of a gas is due to something similar to a ball that has been bouncing forever.

Bouncing masses lose energy as heat, as Drakkith says - if the Sun went dark we and the atmosphere would cool to -270C and the pressure would drop. The Sun produces an awfully large entropy increase, incidentally providing enough energy to the Earth to allow us to decrease entropy locally. Orbiting masses lose energy to gravitational radiation (very very slowly, it must be said) or collisions with dust and gas particles in space.

May I ask what your point is? This seems more like a personal list of bits of physics you don't understand than a coherent attempt to remedy the holes in your knowledge.

 

[vanhees71]

It is very important to distinguish mass and energy properly. Only in the few years after Einstein's original paper before Minkowski's analysis of the math behind it was justified to confuse things by introducing complicated quantities like "relativistic" mass and even distinguish transverse and longitudinal "mass". Nowadays the concepts are very clear, and the mass is exclusively used in the sense of "invariant mass", i.e., it's a scalar quantity, and energy is the time-like component of the energy-momentum four vector.

 

[pervect]

I've always had a problem with the equivalence concept. To begin with, energy is an abstract reality. It keeps changing form, always flowing to counter differences. Mass does the opposite, it concentrates, attracts other masses. An object is motion made up of a specific set of matter, is said to possess, some more mass, but this looks like an incomplete story. If I throw a piece of silver does the extra mass take the form of nuclear energy, some more particles of silver or something else? Everything that looks stupid is because it is done incompletely, as is the case here.

One of the traditional, pre-relativistic concepts of mass was "quantity of material". I don't recall the exact history of this idea anymore, but it predated Newton.

Energy does not qualify as a "quantity of material" for the reasons you outline above, informally. To try and express what I think the idea behind what you said is, the point is that energy depends not only on the object, but it's frame of reference. Thus if we consider a bullet (minus its shell, just the projectile part) before we fired it from a gun, and the same bullet moving after we fired it, the bullet has more energy when it's moving than when it's still.

Of course, the idea of motion is relative, and frame-dependent. If you consider things from the frame of reference co-moving with the bullet, the bullet is not moving in that frame. So what happens to the energy in this case? The answer is that nothing "happens", energy depends not only the object (the bullet), but what frame of reference the object is in. In any given frame, energy remains the same over time, i.e. it's conserved, but the value of that conserved energy in general depends on which frame of reference you choose. And you're free to choose any frame of reference you like, as long as you stick with it. The operation of changing frames of reference does not yield the same energy of a system, but it's not a physical process, and the fact that the energy is different depending on your choice does not violate the conservation of energy.

As other posters have noted, the idea of "relativistic mass" has fallen out of favor in mainstream science (though it's still quite comon in popularizations, especially old popularlizations, which never seem to die). Instead of giving energy a new name (relativistic mass), most modern texts and papers just call it energy. We have a different concept of mass, called invariant mass, that is more like the original idea of "quantity of material".

However, while invariant mass is more similar to the idea of "quantity of material", it's not exactly the same. Consider taking the above mentioned bullet, and heating it. Heating it adds rest energy to the bullet, and invariant mass can be regarded (in units where c=1) as given by the formula $m^2 = E^2 - p^2$. If you prefer to keep the factors of "c", which are generally just regarded as unit conversions, the formula is $m^2 c^4 = E^2 - p^2 c^2$. If you evaluate these formulae (the first is obviously simpler), adding energy to an object without increasing it's momentum increases its invariant mass. So invariant mass is not a "quantity of material", it does include internal energy such as heat energy.

To summarize, there are two commonly sorts of "mass" defined, and you will encounter both of them on PF. So you really need to be familiar with both to distinguish which one is meant, and if it's important and not clear from context, ask which one is meant.

If you happen to wonder - what sort of mass goes into the formula for Newton's gravity, i.e F = GmM/r^2, the answer is neither one. Newtonian gravity isn't compatible with special relativity, and the sort of gravity that is compatibility with special relativity (General Relativity) does not use either the invariant or the relativistic mass of an object as the source of gravity. What it does use is a topic best left for another thread.

 

[vin300]

So the gas is hitting molecules and atoms in the container that are themselves moving about and these atoms/molecules are able to transfer energy to a particle of gas. Equilibrium is reached when, on average, the energy transferred from the gas to the container is equal to the energy transferred from the container to the gas.

I know. If nothing goes in or out, they're free to go on with their business indefinitely.

Energy does not qualify as a "quantity of material" for the reasons you outline above, informally.

There may be many other reasons as well if people can point out, and as a consequence, I find that they now call relativistic mass an obsolete term.

Of course, the idea of motion is relative, and frame-dependent. If you consider things from the frame of reference co-moving with the bullet, the bullet is not moving in that frame. So what happens to the energy in this case? The answer is that nothing "happens", energy depends not only the object (the bullet), but what frame of reference the object is in.

Yes, it's like different people are able to extract different energies from the same object before reducing it to same state. I think invariance needs freedom from internal stresses, in the process of accelerating and decelerating, some energy may stay absorbed within the material and can cause slight deviations.

If you happen to wonder - what sort of mass goes into the formula for Newton's gravity, i.e F = GmM/r^2, the answer is neither one. Newtonian gravity isn't compatible with special relativity, and the sort of gravity that is compatibility with special relativity (General Relativity) does not use either the invariant or the relativistic mass of an object as the source of gravity. What it does use is a topic best left for another thread.

Gravitational mass is said to be equivalent to inertial by the equivalence principle, which in earlier form said force, mass, acceleration are all equivalent but later said mass is equivalent. The question is energy in some form can be supplied to the body and still kept at rest, light curves under gravity due to its energy, so wouldn't excess energy cause some gravitational effect? Or maybe we can leave it at that.
EDIT: Don't know EFE, but it seems using that, invariant mass has not been defined as the same for everyone.

 

[mfb]

so wouldn't excess energy cause some gravitational effect?

A change in energy changes the effect on gravity, sure.

Invariant mass is called invariant because it is invariant - it does not change with coordinate transformations. In GR there is no general (!) meaningful way to assign a mass to extended dynamic objects, but that should not be relevant here.

 

[Herman Trivilino]

I've always had a problem with the equivalence concept. To begin with, energy is an abstract reality. It keeps changing form, always flowing to counter differences. Mass does the opposite, it concentrates, attracts other masses.

You have drawn a false conclusion. Matter attracts matter via a gravitational interaction, but there are other interactions that cause matter to repel matter.

Mass and energy are properties of matter.

If I throw a piece of silver does the extra mass take the form of nuclear energy, some more particles of silver or something else?

Mass is not a measure of the quantity of matter. Increasing the mass doesn't necessarily mean you've increased the quantity of matter.

There's a fundamental difference between throwing a piece of silver and having pieces of silver move relative to each other. In the former case all you're doing is increasing the energy of the piece of silver relative to you. That does not increase the ordinary mass of the piece of silver. On the other hand, having pieces of silver move relative to each other increases the mass of the collection. In other words, the sum of the masses of the pieces of silver is less than the mass of the collection. The difference being equal to the energy of motion of the pieces relative to their center. This is the true meaning of the equivalence concept.

 

[Drakkith]

Mass is not a measure of the quantity of matter. Increasing the mass doesn't necessarily mean you've increased the quantity of matter.

It doesn't help that there is no formal definition of matter that I know of, and I know of no physical laws that use a term called "matter" as one of their variables.

 

[vin300]

Mass is not a measure of the quantity of matter. Increasing the mass doesn't necessarily mean you've increased the quantity of matter.

I thought mass meant exactly that, didn't expect objection there. Does modernity uproot fundamentals?

There's a fundamental difference between throwing a piece of silver and having pieces of silver move relative to each other. In the former case all you're doing is increasing the energy of the piece of silver relative to you. That does not increase the ordinary mass of the piece of silver. On the other hand, having pieces of silver move relative to each other increases the mass of the collection. In other words, the sum of the masses of the pieces of silver is less than the mass of the collection. The difference being equal to the energy of motion of the pieces relative to their center. This is the true meaning of the equivalence concept.

Anything that you accept as a theory must be applicable once the conditions are satisfied, so one object or a thousand, it must apply to each element.

 

[vanhees71]

In relativistic physics mass is defined by the scalar $m^2 c^2=p_{\mu} p^{\mu}$, where $p^{\mu}$ is the total energy-momentum four-vector of the system. For a composite system it depends on the intrinsic state of the system, e.g., on its temperature. That's the true meaning of the famous but mostly misunderstood formula of physics, $E=m c^2$.

 

[Ibix]

I thought mass meant exactly that, didn't expect objection there. Does modernity uproot fundamentals?

Generally, science is the process of realising that we have no clue what is really fundamental. Models that work ok for creatures sized in metres and timed in seconds fail badly when you start to look outside that range of experience. It's not "modernity" whatever that may be to you. It's broader experimental horizons.

Anything that you accept as a theory must be applicable once the conditions are satisfied, so one object or a thousand, it must apply to each element.

Indeed. And the way energy and mass work in relativity says that there's a difference between one piece of silver going in one direction considered as one system, and many pieces of silver going in many different directions considered as one system.

 

[Drakkith]

I thought mass meant exactly that, didn't expect objection there. Does modernity uproot fundamentals?

From wiki's article on matter: https://en.wikipedia.org/wiki/Matter

Before the 20th century, the term matter included ordinary matter composed of atoms and excluded other energy phenomena such as light or sound. This concept of matter may be generalized from atoms to include any objects having mass even when at rest, but this is ill-defined because an object's mass can arise from its (possibly massless) constituents' motion and interaction energies. Thus, matter does not have a universal definition, nor is it a fundamental concept in physics today.

An empty box is less massive than a box full of light (reflecting continuously off of the mirrored sides). A box at a temperature of 10 k is less massive than that same box at 1,000 k. So mass cannot refer to the amount of matter in an object, as mass can increase or decrease with no loss or gain in particles having invariant mass (not to mention that fact that the term matter is ill-defined anyways).

Anything that you accept as a theory must be applicable once the conditions are satisfied, so one object or a thousand, it must apply to each element.

I think the point that Mister T is trying to get across is that the mass of a system of objects can be greater than or less than the sum of their individual masses. For example, the mass of an atom is less than the sum of the masses that all the protons, neutrons, and electrons composing that atom would have if unbound and measured individually. This is where binding energy comes into play.

 

[Herman Trivilino]

It doesn't help that there is no formal definition of matter that I know of, and I know of no physical laws that use a term called "matter" as one of their variables.

BIPM establishes the mole as the official unit that measures the amount of a substance.

You don't see matter in physical laws because laws are part of the modelling process that is physics. Matter is one of the things being modeled. Mass and energy, on the other hand, are part of the model. Note that mass and energy are human inventions, parts of the models invented by humans. Matter is a naturally occurring phenomenon, not a human invention.

 

[Herman Trivilino]

I thought mass meant exactly that, didn't expect objection there. Does modernity uproot fundamentals?

Einstein's mass-energy equivalence uprooted the notion of mass as a measure of the amount of matter.

 

[Herman Trivilino]

I thought mass meant exactly that, didn't expect objection there. Does modernity uproot fundamentals?
Anything that you accept as a theory must be applicable once the conditions are satisfied, so one object or a thousand, it must apply to each element.

The same definition is used to determine the mass of both a single piece of silver and and a collection of more than one piece of silver. It's the total energy measured in the rest frame. That total energy consists of both the masses of the pieces and any energy they have relative to their center. Thus when you throw that piece of silver you don't alter its mass, and if it's part of a collection of pieces you don't alter it's mass, but you do alter the mass of the collection.

You started this thread by stating you never understood the mass-energy equivalence, and you asked a question about it. Responders have tried to answer and help, but what I see now is you shutting down, and refusing to open your mind to those answers instead of trying to understand them.

 

[Drakkith]

BIPM establishes the mole as the official unit that measures the amount of a substance.

Can you have a mole of photons? If so, does that make them matter?

 

[Herman Trivilino]

Can you have a mole of photons? If so, does that make them matter?

Yes, you can have a mole of photons. I don't know if that makes them matter, but I have seen physicists refer to them as particles of matter in peer-reviewed publications. Another viewpoint is that only the fundamental fermions are the building blocks of matter (quarks and leptons).

I'm not sure how much of this is semantics and how much is physics.

 

[Drakkith]

Yes, you can have a mole of photons. I don't know if that makes them matter, but I have seen physicists refer to them as particles of matter in peer-reviewed publications. Another viewpoint is that only the fundamental fermions are the building blocks of matter (quarks and leptons).

Indeed. There are several viewpoints that I know of, hence the reason why matter isn't well defined.

 

[vin300]

I think the point that Mister T is trying to get across is that the mass of a system of objects can be greater than or less than the sum of their individual masses. For example, the mass of an atom is less than the sum of the masses that all the protons, neutrons, and electrons composing that atom would have if unbound and measured individually. This is where binding energy comes into play.

The same definition is used to determine the mass of both a single piece of silver and and a collection of more than one piece of silver. It's the total energy measured in the rest frame. That total energy consists of both the masses of the pieces and any energy they have relative to their center. Thus when you throw that piece of silver you don't alter its mass, and if it's part of a collection of pieces you don't alter it's mass, but you do alter the mass of the collection

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: 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.

 

[sweet springs]

As for your binary star case, interaction between masses should work, e,g, gravitational, electromagnetic. Minus potential energy in the fields level down energy, i.e. mass of the system.

 

[sweet springs]

Yes, you can have a mole of photons. I don't know if that makes them matter, .

Gamma ray ( photon) turns to be an electron - positron pair. Photons would turn to be material, material would turn to be photons.

 

[vin300]

Bound non self-rotating masses have no greater mass than summation of rest masses, while unbound masses have more than that, is that correct?

 

[sweet springs]

In your case of masses going simply apart, i.e. non binding, kinetic energy contributes so mass of the system is greater than summation of rest masses.
Minus potential energy joins further in bound case ( see #27).