# What is the difference between mass and energy?

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I think mass and energy are proportional only when momentum is zero. I doubt it if there is a satisfactory definition of mass or energy in GR that works in all cases.

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I doubt it if there is a satisfactory definition of mass or energy in GR that works in all cases.

That is absolutely correct. Energy and mass are equivalent via $E = mc^{2}$, so talking about a total mass of total energy of a space-time is also equivalent.

Different notions of energy/mass are useful in different situations. In general there is no definition of energy/mass. This is due to energy being tied in with temporal translations.

Without any details, either the space-time has the property of temporal translation symmetry, ie. is stationary then we more or less have the usual definition of energy as a conserved charge via Noether's theorem. This is the Komar mass. If the space-time is only asymptotically flat then one can use the "symmetries at infinity" to define momentum and energy. Depending on how you do this you get the Bondi or ADM quantities.

Without these symmetries it is difficult to know what to do.

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Mass is a type of energy. Energy is conserved in inertial frames including in special relativity, but general relativity deals with accelerating frames.

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So then mass is energy meaning that there is no difference? So is everything made up of energy? or is energy made of matter? Is matter really anything more than an explanation for what we can't explain? I'm not sure where I was going with this.

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Mass is a type of energy. Energy is conserved in inertial frames including in special relativity, but general relativity deals with accelerating frames.

IOW, if spacetime is flat, energy is conserved, but once you have to go to another frame of reference (because of curved spacetime), energy will not be conserved — it is not invariant between frames.

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Mass is only one of many forms energy can take. It can be photons, heat, kinetic energy, potential energy, electrical energy, etc. Do you think there is a difference between these? But they can convert one to the other, and only energy is conserved.

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So energy makes up everything and since energy cant be destroyed, it changes into different things. Energy makes up all the things you mentioned already. So then is energy the same as mass but mass isn't the same as energy?

Edited by ScaryPirateMan
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It is more of a subclass than an equivalence. All dogs are mammals, but mammals are not equivalent to dogs, nor are dogs equivalent to mammals.

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Got it. I think I'll just leave it alone and just read what the people who actually understand all this say. Thanks

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Mass is a type of energy. Energy is conserved in inertial frames including in special relativity, but general relativity deals with accelerating frames.

FAQ: Does special relativity apply when things are accelerating?

Yes. There are three things you might want to do using relativity: (1) describe an object that's accelerating in flat spacetime; (2) adopt a frame of reference, in flat spacetime, that's accelerating; (3) describe curved spacetime. General relativity is only needed for #3.

A prohibition on #1 is particularly silly. It would make SR into a trivial theory incapable of describing interactions. If you believed this, you would have to stop believing, for example, in the special-relativistic description of the Compton effect and fine structure in hydrogen; these phenomena would have to be described by some as yet undiscovered theory of quantum gravity.

#1 often comes up in discussions of the twin paradox. A good way to see that general relativity is totally unnecessary for understanding the twin paradox is to pose a version in which the four-vector equation a=b+c represents the unaccelerated twin's world-line a and the accelerated twin's world-line consisting of displacements b and c. The accelerated twin is subjected to (theoretically) infinite accelerations at the vertices of the triangle. The triangle inequality for flat spacetime is reversed compared to the one in flat Euclidean space, so proper time |a| is greater than proper time |b|+|c|.

#2, accelerated *frames*, is less trivial. It's for historical reasons that you'll see statements that SR can't handle accelerated frames. Einstein published special relativity in 1905, general relativity in 1915. During that ten-year period in between, nobody really knew what the boundaries of applicability of special relativity were. This uncertainty made its way into textbooks and lectures, and because of the conservative nature of education, some students are still hearing, a century later, incorrect assertions about it.

In an accelerating frame, the equivalence principle tells us that measurements will come out the same as if there were a gravitational field. But if the spacetime is flat, describing it in an accelerating frame doesn't make it curved. (Curvature is invariant under any smooth coordinate transformation.) Thus relativity allows us to have gravitational fields in flat space --- but only for certain special configurations like uniform fields. SR is capable of operating just fine in this context. For example, Chung et al. did a high-precision test of SR in 2009 using a matter interferometer in a vertical plane, specifically in order to test whether there was any violation of Lorentz invariance in a uniform gravitational field. Their experiment is interpreted purely as a test of SR, not GR.

http://arxiv.org/abs/0905.1929

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Mass is only one of many forms energy can take. It can be photons, heat, kinetic energy, potential energy, electrical energy, etc. Do you think there is a difference between these? But they can convert one to the other, and only energy is conserved.

Isn't it photon a massless?

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Got it. I think I'll just leave it alone and just read what the people who actually understand all this say. Thanks

!

Moderator Note

I don't think you've gotten bad information here, so if you are feeling frustrated with the concept, please don't take it out on others

Isn't it photon a massless?

Yes; that's not being contradicted here. Mass is a form of energy. Photons are something else that can have energy.

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IOW, if spacetime is flat, energy is conserved, but once you have to go to another frame of reference (because of curved spacetime), energy will not be conserved it is not invariant between frames.

Isn't it energy is not frame-invariant in Newtonian mechanics, but it is conserved? Isn't it conservation and frame-invariance are two different things?

I think the issues involved in curved spacetime are both qualitatively different from and much more complicated than what you're saying.

Edited by needimprovement
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Isn't it energy is not frame-invariant in Newtonian mechanics, but it is conserved? Isn't it conservation and frame-invariance are two different things?

I think the issues involved in curved spacetime are both qualitatively different from and much more complicated than what you're saying.

Yes, they are different things. I meant energy conservation does not apply between frames or with multiple frames, since it is not an invariant quantity.

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Does the mass of a particle ultimately caused by the energetic relations of its components or some inherent mass in those components or a combination of the two? Sometimes I think all particles consist of counterbalancing fields resulting from infinite levels of sub-particle/processes. Other times I wonder if there's not some particles that are ultimately irreducible to underlying energy-relations. Is this a pointless issue or do you think that all particles will ultimately be explained in terms of interacting energy fields? Or are they already and I just don't get the theory (i.e. string theory, etc.)?

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I meant energy conservation does not apply between frames or with multiple frames, since it is not an invariant quantity.

I think in GR, 4-divergence, or contract of covariant derivative, of energy stress tensor is zero at anywhere in space-time and in any frame of reference which means energy and momentum is locally conserved.

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!

Moderator Note

I don't think you've gotten bad information here, so if you are feeling frustrated with the concept, please don't take it out on others

I wasn't. I literally meant what I said. I got it as much as I can and would like to just read and learn from everyone else. I apologize for appearing angry or something.

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I wasn't. I literally meant what I said. I got it as much as I can and would like to just read and learn from everyone else. I apologize for appearing angry or something.

OK. Sorry for the misunderstanding.

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• 9 months later...

I realize that this is an old thread, but it's the first one I could find that fits the subject of my question. Basically, I'm wondering if quarks are ever destroyed. In this sense I'm thinking of the gamma rays produced by the mutual annihilation of an electron-positron pair.

The vast majority of proton-antiproton events are mediated by the strong interaction, i.e. from a quark theory point of view, they involve only rearrangements of quarks, and like-flavor quark pair creation or destruction. This results primarily in various mesons, primarily pions, and kaon pairs are also observed.[3] Rarer events include a photon. (Of course, many of the primary decay products, notably neutral pions, later decay into gamma-ray photons.) Unlike in electron-positron annihilation, proton-antiproton annihilation to two photons is expected to be extremely rare; one sensitive search for such events[4] saw an excess of signal-like events but did not claim this as a direct detection.

This passage from the cited Wikipedia article seems to indicate that quarks can be directly or indirectly converted into energy (photons), but that such events are rare.

Conversely, the Wikipedia article on color confinement seems to be saying that separating quarks is pretty much impossible:

The color force between quarks is large, even on a macroscopic scale, being on the order of 100,000 newtons.[citation needed] As discussed above, it is constant, and does not decrease with increasing distance after a certain point has been passed.

When two quarks become separated, as happens in particle accelerator collisions, at some point it is more energetically favorable for a new quark–antiquark pair to spontaneously appear, than to allow the tube to extend further. As a result of this, when quarks are produced in particle accelerators, instead of seeing the individual quarks in detectors, scientists see "jets" of many color-neutral particles (mesons and baryons), clustered together. This process is called hadronization, fragmentation, or string breaking, and is one of the least understood processes in particle physics.

What I'm having trouble with is, if quarks can't be separated without spontaneously creating a new quark-antiquark pair, how do they manage to decay to (ultimately) leptons and/or photons?

Chris

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Quarks creating leptons would have to be a rare event, since quarks are baryons; I am unsure of the details that would allow this (something about chiral symmetry). AFAIK having more quarks than antiquarks is part of the baryogenesis problem, which is still unanswered.

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Quarks creating leptons would have to be a rare event, since quarks are baryons; I am unsure of the details that would allow this (something about chiral symmetry). AFAIK having more quarks than anti-quarks is part of the baryogenesis problem, which is still unanswered.

Initially I thought that quarks and leptons were two entirely separate "horses of a different color". After reading about pions and muons, though, I'm not sure:

Pions are bosons with zero spin, and they are composed of first-generation quarks. In the quark model, an up quark and an anti-down quark make up a π+, whereas a down quark and an anti-up quark make up the π, and these are the antiparticles of one another. The uncharged pions are combinations of an up quark with an anti-up quark or a down quark with an anti-down quark, have identical quantum numbers, and hence they are only found in superpositions. The lowest-energy superposition of these is the π0, which is its own antiparticle...

--and--

The π±mesons have a mass of 139.6 MeV/c2 and a mean lifetime of 2.6×10−8s. They decay due to the weak interaction. The primary decay mode of a pion, with probability 0.999877, is a purely leptonic decay into a muon and a muon neutrino:

π+μ+μ

πμ-μ

The second most common decay mode of a pion, with probability 0.000123, is also a leptonic decay into an electron and the corresponding electron neutrino. This mode was discovered at CERN in 1958:

π+ e+e

πe-e

Also,

About 10,000 muons reach every square meter of the earth's surface a minute; these charged particles form as by-products of cosmic rays colliding with molecules in the upper atmosphere...

-and-

When a cosmic ray proton impacts atomic nuclei in the upper atmosphere, pions are created. These decay within a relatively short distance (meters) into muons (their preferred decay product), and neutrinos...

Quarks seem to rather easily change into leptons.

Chris

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I misunderstood what you meant by creating a lepton and quark decay, which is why I mentioned baryogenesis (and thought I typed leptogenesis as well). When a meson decays into a mu or electron and its associated antineutrino, the lepton number hasn't changed. Creating a particle and creating a particle/antiparticle pair are distinct issues; in the former the baryon or quark number changes and in the latter it does not. The first is rare and the second is not. Sorry for the confusion.

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Maybe I'm misunderstanding the question as well. Can quarks be destroyed, ie annihilate with their anti-particles ?

Well obviously we cannot isolate quarks to test this out ( yet ). But QCD is renormalizable, and, to me, that implies the creation of virtual pairs of quarks and their bosons ( gluons ) in their immediate vicinity to explain their interactions. Can we make the jump and assume that since virtual quarks and gluons are created and annihilated, then so are 'real' quarks ?

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Maybe I'm misunderstanding the question as well. Can quarks be destroyed, ie annihilate with their anti-particles ?

This is essentially what I'm wondering about, also.

Each meson has a corresponding antiparticle (antimeson) where quarks are replaced by their corresponding antiquarks and vice-versa. For example, a positive pion (π+) is made of one up quark and one down antiquark; and its corresponding antiparticle, the negative pion (π−), is made of one up antiquark and one down quark.

What happens when, for instance, a positive pion collides with a negative pion?

Do the quarks annihilate and produce leptons and (perhaps) photons?

Chris

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