What is the meaning of matter in physics? By defining matter in terms of mass and mass in terms of matter in physics, are we not forming circular definitions? Please give a meaning of "matter" in Physics that circumvents this circularity.

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    $\begingroup$ what is the context? For what particular experiment are you asking this? $\endgroup$ – aaaaaa May 6 at 16:36
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    $\begingroup$ This is very google-able. For example, en.wikipedia.org/wiki/Matter $\endgroup$ – aquirdturtle May 6 at 22:53
  • $\begingroup$ Mass is not defined in terms of matter in physics (it is defined, roughly, as the energy remaining when something is not moving), so no need to worry about circularity. $\endgroup$ – Rococo May 7 at 4:32
  • $\begingroup$ Mass can be defined gravitationally or inertially, and while no measurement has yet demonstrated a difference between the two, I'm not aware that current theories require them to be equal. $\endgroup$ – chepner May 7 at 14:01

What is the meaning of "matter" in physics?

It doesn't matter. Sometimes matter means "particles with rest mass". Sometimes matter means "anything that contributes to the stress-energy tensor". Sometimes matter means "anything made of fermions". And so on. There's no need to have one official definition of the word "matter", nothing about the physical theories depends on what we call the words.

Discussing this any further is just like worrying about whether a tomato is really a fruit or a vegetable. A cook doesn't care.

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    $\begingroup$ +1 Definitely agree with the way you answered the way you interpreted the question, but a more interesting interpretation is: what gives matter mass? This question seems much more fundamental and meaningful to me. $\endgroup$ – Joe Iddon May 6 at 10:50
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    $\begingroup$ @JoeIddon then you should ask your own question. $\endgroup$ – Solar Mike May 6 at 11:04
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    $\begingroup$ @JoeIddon not to disregard your curiosity, but that is what 10000 scientists at CERN are figuring out $\endgroup$ – aaaaaa May 6 at 16:35
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    $\begingroup$ @aaaaaa Not really. Just because something gives mass to electrons doesn't mean it also gives mass to protons (and we're pretty sure they're completely unrelated, beyond the general "mass is just the energy of a system"). $\endgroup$ – Luaan May 6 at 19:59
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    $\begingroup$ "Knowledge is knowing a tomato is a fruit. Wisdom is knowing not to put tomato into fruit salad." $\endgroup$ – Cort Ammon May 7 at 0:51

Please give a meaning of "matter" in Physics that circumvents this circularity.

In modern physics, mass is definitely not defined in terms of matter, and there is no circularity.

What we classically called mass was really a definition of its effects on and by other objects. We saw this as an intrinsic quality of an object, and definitional in that statement is that different types of matter had different masses - a 1m sphere of steel is more massive than a 1m sphere of water. We saw that as "obvious", different types of matter have different amounts of mass and that just makes sense.

Critically, the mass of an object defined its gravitational effect. That is, gravity was something caused by mass. This made mass "a thing", and objects with mass were "matter". Compare this to, for instance, a water wave. This clearly exists but is not of itself material, it's simply the water that was already there moving up and down. A body of water would cause a certain amount of gravity, and adding waves, which are "non-material", would not change that.

With the introduction of General Relativity in the early 20th century, this definition was seen to be incorrect. Earlier, Einstein concluded that E=mc^2, which means that mass is (although this terminology is very misleading) "another form of energy". Pondering this, a number of contemporary physicists helped develop GR, in which any and all energy causes gravity (though a mathematically complex system). So in GR, adding waves to water does increase its gravity, because the system has more energy. A shotput will have a certain gravity, and that will change if you heat it. Etc.

At this point, the link between mass and matter was broken. Mass was previously "that thing that causes gravity", but in GR, that was gone. Matter was previously "those things with mass", and while one could change that to be "rest mass" and still have a reasonable definition, we no longer needed it, there is no real need to have a definition of matter.

This is not a theoretical issue - it one "weights" an electron it will have higher "mass" if it's moving faster. Nothing in the electron changed, the change was what we thought we were actually measuring, not some intrinsic property of the object, but its total energy.

In QM, these definitions are further blurred. Particles, energy, fields, mass, all of it is "flexible" and not trivial to pin down. One can have a "mass-like concept" in QM which would be "the total internal energy of an object", but such a definition no longer serves a purpose. Another definition might be that matter is the class of particles called fermions, as opposed to bosons, but both cause gravity and have "mass like effects", because, under them, there's no real "mass".

This may sound confusing, but this true of most modern physics. Even simple things you think you understand, like "spinning", look very different today.

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    $\begingroup$ "Even simple things you think you understand, like "spinning", look very different today." I presume you mean the 'spin' measurement of a particle. I'm not sure it makes sense to say 'spinning' is something different that we typically think given that the term 'spin' was based on an incorrect model of what was really happening. It's kind of like asserting that the general understanding of 'charm' or 'strange' is wrong because it doesn't consider how the properties of the types of quarks that bear those names. $\endgroup$ – JimmyJames May 6 at 18:11
  • $\begingroup$ "given that the term 'spin' was based on an incorrect model of what was really happening" - exactly. $\endgroup$ – Maury Markowitz May 6 at 20:15
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    $\begingroup$ I don't want to give you too hard a time here because it's good answer overall, it's just that picking the wrong word for a phenomena doesn't mean the word means something else. A good example is 'lead': there's the metal and there's the kind in your pencil (graphite). That doesn't mean we are confused about what lead really is. It's just a misnomer applied to pencils. What mass is or isn't is a far more substantial question. It's not just semantics. $\endgroup$ – JimmyJames May 6 at 21:42

One way matter is sometimes defined is that it has mass and takes up space. I'm not sure if this really makes sense in quantum mechanics, but it is related to one particle physics definition: Fermions follow the Pauli Exclusion Principle which says that no two identical fermions can have all the same quantum numbers while they occupy the same quantum system(which corresponds roughly to our notion of "place"). This is why only two electrons can occupy the same orbital in an electron. Sometimes, matter is defined as fermions.

On larger scales most of what we think of as matter is made of atoms. Atoms tend to repel other atoms if they get too close. (According to Andrew Lenard and Freeman Dyson, this is also because of the Pauli Exclusion Principal. https://aip.scitation.org/doi/abs/10.1063/1.1705389) This property of ordinary matter leads to the "normal force" in classical physics, and is why particles in gases bounce off each other.

One good definition for mass is that it is a property of matter which determines it's motion according to certain equations. In classical mechanics, these are:

  • Newton's Second Law: $F=ma$
  • Newton's Law of Universal Gravitation $F_g=G\frac{m_1m_2}{r^2}$

(You can find explanations for these easily.)

Sometimes m in the first equation is called "inertial mass", and m in the second equation is called "gravitational mass", but the two are always proportional (ie. equal with the right choice of the constant G)

Einsteins Theories of Special and General Relativity caused some reinterpretation of the concept of mass and introduced some new (more accurate) equations relating mass to motion. Νotably it is necessary for inertial and gravitational mass to be equal for the general theory of relativity to be true.

For some definitions of mass, it might interest you to start looking at the Wikipedia page if you haven't already: https://en.wikipedia.org/wiki/Mass#Definitions

  • $\begingroup$ I don't know if it's wise to propagate the "matter = fermions" definition, since even at the subatomic scale it's violated by lots of things that we normally call matter. In particular, according to your definition, all mesons are not matter, because they are all bosons with integral spin. $\endgroup$ – probably_someone May 7 at 8:39

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