Distinctions among the concepts: mass, matter, energy

[Buzz Bloom]

I started this thread because I was much confused by the post

https://www.physicsforums.com/threads/first-energy-or-mass.923809/page-2#post-5831139​

in a thread which was closed before I could seek clarification there. I am hopeful that @PeterDonis, and/or others, will help me here.

Peter responded the following:

Which means that first you need to define what you mean by "matter" and "energy". (Also, the OP did not say "matter"; he said "mass". They're not the same.)​

to a response I had made to the OP:

You want to understand the earliest state of the universe in terms of the matter and/or energy present at that time.​

I had previously posted the following which in it’s context I thought would serve as a definition for “matter”.

1. Two photons will collide with each other, and each collision will produce a pair of some other kind of particle: (a) matter particles, i.e. particles with mass; (b) particles without mass that are carriers of some other form of energy than EM, e.g. gluons. The pair will be the anti-particles of each other.​

Let me clarify my intended definition of “matter” here.

Matter consists of particles which have mass.​

Is this a definition which professional physicists would find acceptable? If not, why not?

Since the mass of each particle does not vary with velocity, given a specific volume of space at a fixed time, the total quantity of mass in a volume of space is the sum of all the individual masses of the particles in that space. Is this correct? If not, why not? (Before answering, please read the following.)

I am aware of a possible ambiguity. Wikipedia says

A proton is a subatomic particle, symbol p or p+, with a positive electric charge of +1e elementary charge and mass slightly less than that of a neutron.​

Now I may well be mistaken about the following.

A proton consists of three quarks together with some gluons so that the combination is stable. Quarks have mass (although Wikipedia does not give any specific mass) but at the present time it is accepted that gluons have zero mass (although Wikipedia gives a experimentally determined maximum mass of 1.3 MeV/c²).​

If this is correct, then I would expect that the mass of a proton would equal the mass of the quarks plus the mass equivalent of the energy (relative to the rest frame of the proton) carried by the quarks and gluons. If this is correct then the definition of “the total quantity of mass in a volume of space” would need to be modified as follows:

The total quantity of mass in a volume of space is the sum of the individual masses of all the fundamental particles in that space.​

In the closed thread I gave the following definition for “fundamental”.

By fundamental, I mean that each of these particles does not consist of any combination of smaller particles.​

Regarding the definition of “energy”.
I understand that a word may well have a different meaning in a different context. Merriam-Webster gives four definitions

https://www.merriam-webster.com/dictionary/energy​

of which only the third seems to be a common usage in physics.

a fundamental entity of nature that is transferred between parts of a system in the production of physical change within the system and usually regarded as the capacity for doing work​

Wikipedia gives

In physics, energy is the property that must be transferred to an object in order to perform work on, or to heat, the object. It can be converted in form, but not created or destroyed.​

Personally I find here that Merriam-Webster is more useful than Wikipedia. Perhaps someone can provide a reference that gives a definition for “energy” that would be acceptable to all professional physicists.

In the following parts of the referenced post, I think Peter misunderstood that I was attempting to describe the matter-energy nature of the stuff present in the early universe, and specifically did not want to “ignore” the fact that the quantity of matter was negligible compared to the quantity of energy.

Buzz Bloom said: I think it reasonable to also say that a photon is a non-matter particle that is the carrier of electromagnetic energy (EM).​

This is reasonable, but it is also reasonable when talking about the early universe to ignore the matter/non-matter distinction altogether and just talk about the various particles and their properties. This is particularly relevant in the early universe since the key distinction that makes cosmologists adopt the term "matter" only for certain particles in the present universe--the fact that "matter" is cold (i.e., its kinetic energy is negligible compared to its rest energy)--is not present in the early universe (see below).​

Buzz Bloom said: The mass equivalent of the average EM energy carried by a photon during this period is greater than than the largest mass of any of the other particles. The way you are stating this is misleading.​

A better statement would be that the average temperature of the universe (which means the average energy of everything, not just photons) was much larger than the rest mass of any of the particles. Which means all of the particles can be treated as highly relativistic and their rest masses can be ignored in most calculations. (Even this glosses over some important issues like the electroweak phase transition.)​

Buzz Bloom said: I think the most reasonable way to describe this early universe environment with respect to matter and energy is that the universe contained both matter and energy. It never consisted of only one or the other.

I think it's even more reasonable to just say the early universe contained a lot of relativistic particles, all of which carried energy, without even bothering about the matter/non-matter distinction. See above.​

 

[Drakkith]

Let me clarify my intended definition of “matter” here.
Matter consists of particles which have mass.Is this a definition which professional physicists would find acceptable? If not, why not?

You can use it in that way, sure. But the problem is that there is no single definition of "matter". It's one of those terms which isn't clearly defined. Which isn't usually a problem because any time scientists need to be specific, such as in published papers, they usually use more specific terminology. And if not that, then the context usually tells you how they're using the word as long as you're familiar with the terminology of the field.

Since the mass of each particle does not vary with velocity, given a specific volume of space at a fixed time, the total quantity of mass in a volume of space is the sum of all the individual masses of the particles in that space. Is this correct? If not, why not? (Before answering, please read the following.)

If this is correct, then I would expect that the mass of a proton would equal the mass of the quarks plus the mass equivalent of the energy (relative to the rest frame of the proton) carried by the quarks and gluons. If this is correct then the definition of “the total quantity of mass in a volume of space” would need to be modified as follows:
The total quantity of mass in a volume of space is the sum of the individual masses of all the fundamental particles in that space.In the closed thread I gave the following definition for “fundamental”.
By fundamental, I mean that each of these particles does not consist of any combination of smaller particles.

You'd need to include the energy of the particles within that volume as well as their mass. The total mass would be the sum of the masses of the individual fundamental particles plus any mass-energy present (mass-energy being the amount of mass calculated according to the mass-energy equation). So the mass of a hot gas cloud is more than a cold gas cloud consisting of an equal number of gas particles in an equal volume, as the hot gas particles have more kinetic energy on average.

Regarding the definition of “energy”.
I understand that a word may well have a different meaning in a different context. Merriam-Webster gives four definitions
https://www.merriam-webster.com/dictionary/energyof which only the third seems to be a common usage in physics.
a fundamental entity of nature that is transferred between parts of a system in the production of physical change within the system and usually regarded as the capacity for doing workWikipedia gives
In physics, energy is the property that must be transferred to an object in order to perform work on, or to heat, the object. It can be converted in form, but not created or destroyed.Personally I find here that Merriam-Webster is more useful than Wikipedia. Perhaps someone can provide a reference that gives a definition for “energy” that would be acceptable to all professional physicists.

They're both perfectly fine descriptions of energy. Note that I used "description" and not "definition" here on purpose. Definitions are inherently limited in their ability to describe phenomena because they are often short in length and broad in scope. If you want to understand what a "dog" is, then looking at the definition is not that helpful. You would only be able to understand a very small amount about their look, behavior, and other properties based on the definition. The same is true for energy. The definition does not tell you the full story. It doesn't tell you all the intricacies involved, such as how many types of energy there are and how they are related and used in science.

Also, you can state the same thing using different words, so definitions of something from more than one source may seem to conflict with each other when they actually don't. Or they sometimes do conflict with each other, which is why it's important to understand all the details of a topic and not just look at the definition.

Buzz Bloom said: I think the most reasonable way to describe this early universe environment with respect to matter and energy is that the universe contained both matter and energy. It never consisted of only one or the other.

I think it's even more reasonable to just say the early universe contained a lot of relativistic particles, all of which carried energy, without even bothering about the matter/non-matter distinction. See above.

That's fine if you don't care about the matter/non-matter distinction. But since photons are almost never considered to be matter then the distinction can be useful.