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I consider "fundamental quantities" to be those that have dimensions that are are like length, mass, time, temperature, and so on.

"Derived quantities" have dimensions that can be written in terms of the dimensions of fundamental quantities.

Let us say that I have a chemical simulation that takes into account the number of particles of a particular agent -- "moles". There is a relationship between the number of moles and the mass of the particles, so in this scenario I would say that moles are a derived quantity?

What if I am working with a model where the number of particles is a much nicer number to work with than the mass of the particles (for e.g. proteins on the order of hundreds of thousands, but not on the scale of Avagadro's number). Is the number of particles then a fundamental quantity in this context?

More specifically, let's say I am working with a model that considers forces at the level of a cell (say, forces on the order of nanonewtons being exerted by various agents on the cell membrane), while also tracking a small number of proteins.

Would it then make sense for me to have two fundamental quantities -- one being mass in the mechanics calculations necessary for cell level effects, and the other being "number of particles" necessary for "mass law" type ODEs desribing the interaction between proteins?

bzm3r
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    "Number of particles" is...just a number. Why would it have a dimension? – ACuriousMind May 14 '15 at 12:37
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    Interesting that you include temperature among the "fundamental" dimensions. Many treatments would not. Which brings us to a very basic point: systems of units are in many ways optional and elective. These kinds of question have answers about what the conventions actually used say, but they don't have answers that are unarguably correct. – dmckee --- ex-moderator kitten May 14 '15 at 14:49
  • @dmckee Can you point me to a pretty standard resource that does not treat temperature as a fundamental quantity? I am surprised because I just finished reading an account of the supposedly famous "Rayleigh vs. Riabouchinsky" argument. – bzm3r May 14 '15 at 16:31
  • @user89 Recommended reading. – Mark Mitchison May 14 '15 at 23:57

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"Mass" and "number of particles" (henceforth "amount of substance") are in fact unrelated quantities (there's a reason SI defines both the kilogram and the mole as "fundamental units"). The reason for this is that different particles have different masses. Mass and amount of substance are as distinct form each other as mass and volume are; every substance has its own ratio (molar mass and density, respectively) between the quantities in question.

Granted, the analogy isn't perfect - volume of a gas (or any substance really, but it's most noticeable with gasses), and with it density, depend on pressure, but amount of substance, and with it molar mass, does not depend on any easily measured thermodynamic quantity. This fact is what allowed Avogadro to discover his law (namely that, given constant pressure and temperature, the volume and amount of a gas are directly proportional) and with it the concept of the mole.

No Name
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I wouldn't say number of particles is truly a dimension. Sometimes with a quantity like that, making a sort of dimension of it can be a helpful expedient, but I think taking it totally literally can scramble the idea of dimension. Another example of this kind of thing is luminous intensity which is just power (energy per time) weighted according to a function of wavelength that matches (as best we can) the sensitivity versus wavelength of the average human eye. I wouldn't call luminous intesity a true dimension either ... but I have seen it deemed to be one.

AmbretteOrrisey
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The number of particles is a conserved quantity (at large).

The mass unit is derived from the 'number of particles'.
Take the mass unit, the kilogram as a 'bunch of atoms' . The atomic unit is a fraction of a 'bunch of atoms'. It is a recursive definition.
Which means that, as all the 'main' equations of physics are reported to the 'electron mass', the universe can 'scale' thru time.

from A self-similar model of the Universe unveils the nature of dark energy

Consider now mass and charge. The SI unit of mass is the mass of the international prototype of kilogram,which is proportional to the mass of elementary particles; if their mass varies, so will the mass unit; but if that happens, one can expect that the reference atomic energy levels of the time unit will vary as well, and the time unit with them; consequently, the length unit will also vary.

Helder Velez
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  • The "number of particles" is definitely not a conserved quantity. You can find (near) conservation of things like baryon and lepton numbers, but, e.g., the number of photons is obviously not conserved. – ACuriousMind May 14 '15 at 12:37
  • @ACuriousMind: please explain why the mass unit definition is not recursive! It is recursive is my point. I'm not writing about photons, but barionic matter, as deduced by the context. The 'particle' nature of the photon is questionable, imo, see There Are No Pea Shooters for Photons by Marty Green . – Helder Velez May 14 '15 at 13:38
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    And mass is not derived from number of particles. Take a proton: its mass is not 1800 electron masses because it has 1800 electrons. Mass is, essentially, the relationship between the energy and the momentum of a particle. If the mass of the elementary particles would change, the units of mass wouldn' change. – Bosoneando May 14 '15 at 13:41
  • do you have any references more reputable than viXra? – Jim May 14 '15 at 19:35
  • @JimtheEnchanter et al. Now, you can conclude by yourself that the mass unit is the same whatever the absolute size of an atom (because it is recursive !). I know that vixra has a lot of foolish. To read or not to read that is the question that a young cosmologist as you will have to answer. A preliminary version at arxiv-2002 . Downvotes, plenty, scientific counter-arguments 0. – Helder Velez May 14 '15 at 20:53
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    The lack of scientific counter-arguments on this post are not due to their non-existence. It is more likely because your post is so unclear that we are unsure exactly what it is you are claiming. The general flow is certainly misguided, but without clearly knowing the message you are trying to convey, it's very difficult to fashion an appropriate counter-point – Jim May 14 '15 at 20:58
  • Here I can only pinpoint the relation between the 'number of particles' and the mass unit as asked by the OP. By definition the mass of 1 Kg is the mass of X atoms and 1 atom = 1/X Kg is a recursive definition i.e. the weight of an electron is a free parameter (my claim). Because the spectra of a larger atom (of the past as I say) and the one of an atom in motion (receding galaxies) are indistinguishable I will credit 500 points if I'm wrong on this claim – Helder Velez May 14 '15 at 21:52