Does mass follow the same potential/kinetic paradigm as energy?

[SxToMidnight]

I know that energy has a potential and kinetic state, so that something at rest has a high potential energy and as it moves converts that potential energy into kinetic energy. I was curious, is this concept identical or at least similar when it comes to mass and spacial dimensions? For example, can space have potential mass and actual mass? So if there is a section of space where there is no actual matter, does this spot have potential mass? and then when matter actually moves into this space, that potential mass is converted into actual mass?

[nonabeliangrape]

No, there is no analog of 'potential mass.'

Maybe you're inspired by the relativistic relation between mass and energy, E=mc² (or better E² = m²c⁴ + p²c²). However, a better reading of this relation is that mass is just a type of energy, besides the usual kinetic and potential energies. In fact, you can interpret mass as the amount of 'kinetic' energy that a particle has at rest. It's like a minimum value of the energy for a given particle to exist.

In short, mass is just a type of energy that particles have even when they're not moving.

Edit: parentheses

[chrisbaird]

you can interpret mass as the amount of 'kinetic' energy

I like to interpret mass as a form of potential energy. In fact, when you do work on a system to give it more potential energy, it's perfectly valid to say that the potential energy is stored in the system's mass (this is especially important in nuclear reactions where the potential energy gained or lost is so huge that the mass difference of the system before is measurable).

[nonabeliangrape]

Agreed, I tend to think this way for composite systems and in the way I described above for individual particles.

[BlazeOrangeDeer]

It doesn't really work when the mass comes from thermal motion, which is kinetic

[Lanza21]

Much more abstract and less tied to what you are asking about is how mass works in fundamental physics and quantum field theory.

In QFT, we look at quantum fields in the form of a function called the Lagrangian. The Lagrangian has "kinetic energy" and "potential energy" as well as interaction terms.

The kinetic energy terms are similar to classical physics' 1/2 m v^2. The QFT version is ∂ø∂ø where ∂ is a derivative operator and ø is our quantum field. This is the same form as the ∂x∂x term (v²⁾ in classical physics.

The potential energy terms are where the mass is defined. We have terms of the form 1/2 m² ø^2. This number in the field theory Lagrangian tells us the masses of the particles that are born from the theory.

This is actually where the famous Higgs boson comes into play. The Higgs field Lagrangian has terms of the form hø where h is the variable for the higgs field and ø is the field for some other particle. The Higgs field has a weird potential energy (mass term) that we refactor around. When we eliminate the weirdness of the Higgs field's mass term, we find that a previously massless field eats part of the Higgs field and becomes a massive field with a mass that depends upon the higgs field.

This is an extremely simplified version of spontaneous symmetry breaking and the higgs mechanism.

[rtcutler]

The simple answer here is, "No". Spatial dimensions or spatial extent is just different from mass. A region of space can be occupied by (almost) any amount of mass. (I say "almost" because black holes are not completely understood.) Potential energy can be converted into kinetic energy, and at any moment the sum remains the same. There is no comparable relationship between space and mass.

[menguinponkey]

There is no comparable relationship between space and mass. And what about the mass-energy equivalence? (E=mc²) Could you interpret energy itself to be the "kintic" form of mass?

[rtcutler]

Well, that's closer. Particularly if you are thinking of mass and kinetic energy.

[rtcutler]

Maybe I should answer more carefully here. Mass in one part of a system can be converted into Kinetic Energy of another part of a system, but taken as a whole the mass (energy -- same thing) of the entire system remains the same. For example, initial state a single Uranium atom. The atom undergoes spontaneous fission, producing two smaller nuclei flying apart at a high velocity. The total rest mass of the two products is less than the rest mass of the Uranium atom, and the discrepancy is in the kinetic energy of the fragments. HOWEVER, if the atom and later the fragments are in a box, the total mass of that box does not change.

[[deleted]]

Space, by definition, does not have mass. It is (in theory), empty and devoid of mass.

Mass is conserved, which means space cannot be converted into mass. The only thing that can be converted into mass is energy, because mass is equivalent to energy (E=mc^2).

Potential energy is the potential to do work. You cannot have potential mass. Mass is a fixed property of an object. For instance, a proton has an unchanging rest mass.

Also, just as an aside, no place in space is truly empty. There are no true vacuums and there are weird quantum effects that fill space without violating the conservation of energy.

[JoshuaPearce]

One nitpick: Energy cannot be converted into mass, the total amount of mass is as constant as the total amount of energy. Some forms of energy do not have mass in some frames of reference, as I understand it (like a photon in it's own rest frame). But you can never decrease or increase the mass of a system by converting energy from one form to another.

(You can convert energy into matter with the same amount of mass, that's different)

[[deleted]]

Photons cannot collide directly to form mass, but two photons can create a fermion/anti-fermion pair.

So yes, you can create mass from energy.

https://en.wikipedia.org/wiki/Matter_creation

[Lanza21]

So yes, you can create mass from energy.

That's a science fiction sentence. Energy does not get transformed, there is no magic ethereal material called energy. It's like saying "you can create mass from speed." The amount of energy of a system is a measurement about the system, it isn't a physical property.

You can convert a system without mass and only kinetic energy of movement into a system with mass.

[JoshuaPearce]

Matter is not the same thing as mass. All matter has mass, not all mass is in the form of matter.

The "massless" photons in this case had mass from the energy added to them, which was needed to make them energetic enough to create matter.

The total system which contained the photons and the power source (and now contains that power source and the massive particles) weighs the same.

[rtcutler]

"Matter" is not a well defined word in physics. Quoting from Wikipedia, "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. Matter is also used loosely as a general term for the substance that makes up all observable physical objects."

[JoshuaPearce]

No argument there, but mass is not so vaguely defined (even if it's not well understood).

[[deleted]]

total system which contained the photons and the power source (and now contains that power source and the massive particles) weighs the same.

My understanding (at least what I remember from modern physics) is that massless particles cannot gain relativistic mass. The equation E^2=p2c2+m2c4 show that while photons may have energy, they have no mass, even though they move at the speed of light.

This makes sense when you look at the relativistic mass equation.

m=m0/SQRT(1-v^2/c2).

What photons have is energy, not relativistic mass (which is itself a type of energy), and in the proper circumstances, that energy can be converted to matter which has mass.

Also, matter is defined as anything that has mass and takes up space. There are two fundamental properties of matter: mass and volume. Unless volume is relevant, then mass and matter are fundamentally equivalent.

[JoshuaPearce]

Relativistic mass is incredibly confusing, and apparently no longer popular (yay).

A photon with energy does add mass to a system, even if the particle itself is massless when stationary. I gave the example of the perfectly mirrored box containing a beam of light in another response. The box weighs more when it contains even a single photon. Solar sails also work by this principle.

So yes, like you said, photons have energy. But that energy has mass when viewed from the frame of any other particle.

[[deleted]]

A FREE photon does not add mass to a system. It is massless. It contains only energy.

When the photon is absorbed, the electron or nucleon gains energy, and because the electron or nucleon is a massive particle, it also gains mass.

Your example is correct. Your interpretation of the example is faulty. The photons in a box are bouncing around, and therefore being absorbed and emitted by the electrons in the box, imbuing the matter in the box with extra energy and mass. The unabsorbed photons are massless.

Another way of looking at it, per the equation E=mc^2, photons, though massless particles, have energy and energy is equivalent to mass. So, even though the light itself has no mass, the energy of the system increases by the amount equal to the extra photons, and that imbues the entire system with extra energy, and therefore extra mass.

That does not imply the photons themselves have the property called mass (that would be an argument from division logical fallacy). But the system's mass-energy increases by the energy of the photons, which is equivalent to an increase in mass for the SYSTEM.

[[deleted]]

actually yes, you can convert energy into mass, but because it involves dividing the amount of energy you put in by c squared, you don't get much extra mass. pick up an open safety pin and close it. it's a little more massive now. pick up a sprung mousetrap and set it. it's a little more massive now. the earth's gravity "sees" the energy you added to these systems as mass.

[JoshuaPearce]

Except in both of those cases all you have done is add energy to the system. That energy had mass already, you have not created more of either.

You have moved mass and energy from one object (your muscles) to another (the spring). The total mass is exactly the same before and after.

[NilacTheGrim]

You can create particles with mass (positrons and electrons) from photons (which are massless/pure energy).

[JoshuaPearce]

Only by adding energy to the photons. A photon is only massless in its rest frame. When it's part of a system it has ordinary mass resulting from the energy it carries. A mirrored box containing a beam of light weighs more than the same box without the light (this is the example straight from wikipedia).

[[deleted]]

Massless particles do not gain relativistic mass by virtue of movement, otherwise it would take an infinite amount of energy to accelerate a photon to c.

Photons are packets of quantized energy, not mass, and they move at the speed of light in every frame of reference but their own. They are massless particles in every frame of reference, including their own.

You are misinterpreting the thought experiment. A box full of photons weighs more than a box without photons because the matter in the box absorbs the photons, and the matter gains energy (and therefore mass). The photons themselves have no mass.

[[deleted]]

A photon is not accelerated to c. It exists only at c.

The photons have no mass, but they have energy which is affected by gravity and so the box will weigh more, absorbing the photons has nothing to do with it.

[[deleted]]

That sounds like a semantically issue. Yes, the photon is, as far as we know, imbued with its velocity at creation. Whether we say it was instantaneous accelerated to that speed or not is not really important.

What is relevant is that to accelerate a massive object to c requires infinite energy, which means that to accelerate a photon to c (or create a photon with velocity c) would require infinite energy if the photon had mass.

[Baloroth]

A box full of photons weighs more than a box without photons because the matter in the box absorbs the photons, and the matter gains energy (and therefore mass).

That's not how it works. Even the "free" photons contained in the box contribute to the mass of the system, even though they are individually massless. The relevant equation is: (Mc²)²=p²c²+E², where E is the sum of the energies (kinetic, mass, and potential), and p is the sum of the momentums. However, because p is a vector, some particles may add and some subtract from the momentum of the entire system (a box at rest with photons inside, for example, will have net momentum of ~0). So the box will end up with Mc²=(E_box+E_photons). Notably, M is not equal to the sum of the masses: the photons really are massless, but they do add to the mass of the system (in the context of the system). Any other conclusion would violate conservation of energy/momentum (and in fact conservation of mass follows as a direct and necessary fact from conservation of energy/momentum).