Is mass a number?

Ghost:

Your basic misunderstandings of Newton's 3rd law are really a topic for a different thread. But we should be able to correct them in one post. If you still don't understand after this, then a separate thread for educating you on this particular topic may be required, but let's try.
The very fact that I accelerated the ball is evidence to the fact that the net force was greater than zero. So the ball did not "push back" with the same force as I pushed it. The net is the difference.
The net force on the ball is non-zero, so the ball accelerates. But the ball's push back on your hand is a not a force that acts on the ball; it is a force that acts on your hand.

If you want to examine your hand as the system of interest, then you can do an F=ma analysis for that. Determine all the forces acting on your hand (including the push-back force from the ball, of course). Add up all those forces. If there is a net force on your hand, then your hand will accelerate.

Here's where the learning happens in one sentence: A "Reaction" force in Newton's 3rd law always act on a different system from the force to which the reaction force applies.

Example: Your hand (system 1) pushes on a ball (system 2). The force of your hand on the ball is a force acting on the ball. By Newton's 3rd law of motion, the ball exerts an equal an opposite "reaction" force. The reaction force is a force that acts on your hand. Notice: force of hand on ball acts on system 1. Reaction force of ball on hand acts on system 2.

Learning should now be complete. Homework exercise: Choose some other examples where two objects or systems interact. Try to identify the action-reaction force pairs and the objects/systems on which they act.
Sorry, Newton was wrong, and I proved that decades ago!
Claims like that make you look like an uneducated fool, given that it is clear from your post that you haven't understood Newton's 3rd law prior to now. You should probably avoid extravagant self-serving claims in future. They may make you feel good about yourself, but they risk making you look like a fool to others when they are unjustified.
Measuring mass? Measuring a number?
I know. It's ridiculous. But that's what you said you were doing.

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I know. It's ridiculous. But that's what you said you were doing.

We'll set aside Newton for now and stick to the topic of mass.

You claim mass is just a number.

So you have a ball. Good so far?

Now, what are you measuring concerning the ball, in order to arrive at a mass number?

Are you measuring the volume of the ball and arriving at a mass number?
Are you measuring the color of the ball and arriving at a mass number?
What are you measuring about the ball in order to claim you measured the mass of the ball?

If you claim mass is just a number, then what is it that you measured, a number? What did you measure in order to arrive at that number?

arfa brane:

I've thought about it, and all I can say is, if you invented a measurable property that is based on the length of your right arm, then you didn't invent the length of your right arm, you just decided it's a unit of length.

So what? I can choose arbitrary names for pre-existing physical properties too.
Arminess is not a pre-existing property. It is not the same as length, obviously. A ball has non-zero length (diameter, if you like), but it has zero arminess. In fact, most things in the universe turn out to have zero arminess, even though they have non-zero length.

Arminess clearly cannot be put into a one-to-one correspondence with the notion of the length of an object. The Jarm is not a unit of length.
Yes, any change of terminology for a physical thing like length or time, doesn't change the fact it was there before you change the name, and after!
There was a time before the word "length" was invented. Indeed, there was a time before the concept of length was invented. So arminess is not on a fundamentally different footing from length.

If length is something that is inherent in an object, then so is arminess.

Strange that two days ago nothing in the universe had arminess. Now everything has it! Wow! A new physical property has come to light, that has been inherent in every object yet unrecognised before now. (Am I a genius, or am I a genius?)
But it doesn't explain how mass is a number. I don't think you've managed that one yet
Clearly you didn't understand the relevance of my example. That's a pity, since it directly addresses an objection that you raised. Well, maybe you'll cotton onto it in a month or two. You'll be having a shower and something will suddenly click and you'll have that "Aha!" moment that I love to see in students. I look forward to that, even though I won't be there to see yours.
A density of matter with mass m, at a distance R from an axis of rotation, even when it isn't rotating and has no angular momentum, has a moment of inertia. If there is no cause needed for actual rotation, what "causes" the existence of R and the inertia tensor? Is that why it's a scalar (0,2) object?
Moment of inertia, like most quantities in physics, has a particular mathematical definition. What ultimately "causes" it is that human beings invented the concept and defined it. That, of course, is a very different question to "why is it useful?"

Given your problem understanding that mass and energy are concepts, do we really need to add yet another physical quantity into the mix - one that is even more abstracted from common-sense intuition?

Can you bottle moment of inertia?

More of the thinking I've done about the "mass is a number" argument James is determined to keep using.

After admitting that it has units. So it's not a number, it's a number of units. It's a number "with" units if that's what you mean to say.
Yes. Wasn't that clear?
Physics however, will be brutal about it. James wants to answer the question: when did mass first appear in the universe? So he can answer the one about what humans measure, or how they measure it, or what they call a unit of length.
Mass first appeared in the universe when some human being started to use a word like "mass" to denote a particular concept. Early ideas about mass were probably pretty vague. In fact, I don't think the idea really solidified until Newton came along in the 1600s. So, if you want to put a date on it, you might say that mass first appeared in the universe around 1610 CE.

arfa wants to ask the question: when did matter first appear in the universe? James R's answer to that is: around 13.7 billion years ago.

You agree that mass and matter are not the same thing, don't you? I trust that you've kept up with the discussion about this that I had with Motor Daddy Ghost, above. (Pay special attention to the bits about ambiguous use of language before you comment.)
Perhaps, along the way we can answer the one about when did a meaningful distance first appear?
I guess we need to ask: meaningful to whom?

Ghost:

We'll set aside Newton for now and stick to the topic of mass.
How rude. You should acknowledge that I helped you to understand Newton's third law, at the very least. Or, alternatively, you could tell me that you still have a shaky grasp of the topic and you need more help. Or whatever.

I'll wait until you do that before helping you again. Where are your manners?

You agree that mass and matter are not the same thing, don't you?
I do. I thought we'd done that one. I thought I'd also point out, again, that transparency and glass aren't the same thing.

As to where mass came from, it didn't appear when matter first appeared, because it's a human concept? I can tell two different weights apart, but not their masses?
I can tell two colors apart but not . . . something something.

I do. I thought we'd done that one.
So did I. But I get the impression you're still struggling. You've given little sign so far that you've understood or accepted what I have said. You also seem to keep repeating points that I have previously addressed.
I thought I'd also point out, again, that transparency and glass aren't the same thing.
I thought we did that one, too. Transparency, like mass, is a property that a glass object has. Both mass and transparency are, fundamentally, concepts.

You can't show me a bottle full of transparency, can you, any more than you can show me a bottle full of energy?

One more thing, while we're (still) at it: previously I used gravitational potential energy as an example. You did not comment at all on that. We sometimes say things like "A ball raised to height h above the ground has potential energy U=mgh". Here's the important question for you: where is the potential energy in this example?

I am under the impression (please correct me if I'm mistaken) that you believe that properties like energy and mass are somehow "built into" objects. You would say, I assume, that it is impossible to separate a ball from its mass, because the mass is somehow contained within the ball (or, equivalently (?), its atoms). Is that correct? Is that why you think the idea of having a bottle of the ball's mass - without the ball itself - is a nonsensical idea?

If this is a correct explanation of your view, then I want you to tell me where the exactly potential energy is in a ball lifted above the ground. Where would we look for the energy? Is it in the ball? Is it in the ground? Is it in the air between the ball and the ground? Where? And how will we know when we've found the right location? Will we see the energy there?

Or do you perhaps think that potential energy is somehow fundamentally different to kinetic energy, or rest mass energy, or similar?

Of course, if you have already understood my position by now, and you have come to accept it, I'd be pleased to hear that, too. It would be friendly way to wind up this conversation - nice a change from your customary arrogance and snideness.
As to where mass came from, it didn't appear when matter first appeared, because it's a human concept?
Yes. That's what I wrote in my previous post.

This doesn't, by the way, mean that it is meaningless to talk about the masses of things that existed before human beings came along and invented the concept of mass.
I can tell two different weights apart, but not their masses?
I can tell two colors apart but not . . . something something.
You're the one trying to tell things apart. Surely you're the person most aware of your own capabilities.

A question for whoever thinks they know: which is more fundamental, mass or inertia? Is there a way to prove they are both physically real, or only one is, or maybe neither?

Using well known mathematical techniques, of course.

I would say mass is more fundamental, but as I also said inertia comes along too. It's just a law of physical, material objects that they have a mass and a volume. To say they have matter is sort of a given. To say it has a density, or even an average density, like wood say, is saying what, James?

How does mass also occupy the same volume as the matter? Numbers don't go into bottles. By saying the distribution of matter is the distribution of its mass, at an atomic level, the answer is, the thing we call mass is equivalent to the matter, in a volume.

I thought we did that one, too. Transparency, like mass, is a property that a glass object has. Both mass and transparency are, fundamentally, concepts.
No, that's just wrong. We have concepts and label them with words, but they are part of the real world we see, hear, feel, etc.
Mass is something to do with a field or a mechanism, for particles in the Standard Model at rest. How did your mass-is-a-number idea fit in to that?

A question for whoever thinks they know: which is more fundamental, mass or inertia?
More fundamental to what?
Is there a way to prove they are both physically real, or only one is, or maybe neither?
Perhaps now would be a good time for you to work up a definition of the term "physically real".

What are the necessary and sufficient conditions for something to be "physically real", according to you?
I would say mass is more fundamental, but as I also said inertia comes along too. It's just a law of physical, material objects that they have a mass and a volume. To say they have matter is sort of a given. To say it has a density, or even an average density, like wood say, is saying what, James?
Density is defined to be mass per unit volume. It's a measure of how tightly matter is packed into a space, roughly speaking.
How does mass also occupy the same volume as the matter?
Mass is just a number. Numbers don't take up any space, unless you count brainspace.
Numbers don't go into bottles.
Right!
By saying the distribution of matter is the distribution of its mass, at an atomic level, the answer is, the thing we call mass is equivalent to the matter, in a volume.
A distribution of "stuff" (matter) is not the same as a distribution of numbers (mass).

No, that's just wrong. We have concepts and label them with words, but they are part of the real world we see, hear, feel, etc.
How's your answer to my question about potential energy coming along? Is it almost ready for publication, or do you need more time to think about it or write it up?
Mass is something to do with a field or a mechanism, for particles in the Standard Model at rest. How did your mass-is-a-number idea fit in to that?
Are you thinking of the Higgs field? Can you detect the Higgs field? Or is it more of a ... concept?

Mass is just a number. Numbers don't take up any space, unless you count brainspace.
Mass is equivalent to the amount of matter in a volume. This quantity is not "just a number", a mass density is not just a number.
A distribution of "stuff" (matter) is not the same as a distribution of numbers (mass).
A distribution of matter is not even a distribution of numbers. Matter is not a number and nor is the mass of matter a number.
I'm not confused about the distinction between a number and a number of kilograms, or a number of particles of matter.
Are you thinking of the Higgs field? Can you detect the Higgs field? Or is it more of a ... concept?
Is the facility that discovered the Higgs boson a concept? High energy physics is a concept? Did the LHC detect the Higgs boson or did it detect a concept?

Your idea that mass is a human concept and the idea that it's a number are a semantic gutterball.
Matter is made out of massive particles. Atoms have an atomic weight and since mass is additive, if you have a large number of atoms or molecules in a solid object they add up to something a human can see or test the weight of. If it's a small rock, or some grains of sand say. A handful of sand weighs more than a few grains because of the summation over the "graining of matter". Ultimately the graining is determined by particles in the Standard Model.

Or, so they tell us. But no, according to James, mass is a number. Well, no, it just isn't.

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Ghost:

How rude. You should acknowledge that I helped you to understand Newton's third law, at the very least. Or, alternatively, you could tell me that you still have a shaky grasp of the topic and you need more help. Or whatever.

I'll wait until you do that before helping you again. Where are your manners?

You did not help me understand squat! I told you I proved Newton wrong decades ago, and I stand by that. That is a separate topic, so I am sticking with the topic at hand, which is your claim that mass is just a number.

I know you, James. I once posted a topic here about something, with a link supporting my claim. You claimed I was trolling! I expect the same of you here. If I was to ramble on about how wrong Newton was, and why, you would ban me for posting alternative theories in the science section. I can not win with you, because you have a ban button ensuring I never can win!

...and you FORGOT to answer my questions. You made a big stink about me being rude, to divert from answering the questions in that post. What are you measuring, a number?

Density is defined to be mass per unit volume. It's a measure of how tightly matter is packed into a space, roughly speaking.

So the definition of density talks about mass and volume. Where did you get "matter is packed into a space" from that definition?

According to the definition, there is mass and volume. No mention of matter.

Matter is made out of massive particles.

So matter is just a bunch of mass. Got it!

So matter is just a bunch of mass. Got it!

The periodic table is a list, ordered by atomic weight. Atoms of different elements have different weights.

Think of atoms like grains of matter, matter is volume, with inertia. Inertia implies mass. Those are all the terms we need for an ansatz.
An ansatz is a choice of a tool, roughly. So make some sand into a solid disc and find its moment of inertia, being that device that sums all the grains together. It needs an x and a y coordinate for each grain; in fact the summing over small volume elements only needs two parameters, a way to address each one and is why it's a (0,2) tensor construction.

For a disc, both mathematically and physically, one dimension is suppressed, it's flat so doesn't have much extent in the third dimension. So Pythagoras says any radius R has two coordinates--wherever you choose to construct them on the disk--and the square of R is the sum of the two squares of the sides. So all the R's that you index have an x and a y index and you square the x and the y and add them to get R. This is just a way to address elements of the volume, with a pair of indices. So it\s a tensor. that inputs two scalars and outputs each R, or any R, or all R. When R is fixed, that is, and the mass is distributed in the form of a disk.

But the inertia tensor also uses (measures) the total mass, a calculation needs this too. Because it can be calculated, does that mean inertia is a number? I don't see how you get there, or anywhere near there. There is no there, there.

The periodic table is a list, ordered by atomic weight. Atoms of different elements have different weights.

The term "atom" is an object, like the term "solar system" is an object.

An atom has a nucleus, comprised of protons and neutrons, and the nucleus is surrounded by electrons.
A solar system has a nucleus, which is our Sun, and the Sun is surrounded by planets and such.

An atom and a solar system are both objects that are comprised of smaller components, which are also comprised of smaller components, etc ....

Of course, an atom is a component of a solar system, and a solar system is a component of a galaxy, which is a component of a universe, which is a component of a multiverse etc....

All of those objects are massive objects, comprised of smaller massive objects.

It is all motion, so small it is beyond our scope to measure and observe, and so large it is beyond our scope to measure and observe. It is all matter, comprised of massive objects, extending infinitely in scale, small and large. "Turtles all the way, UP AND DOWN!"

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If this is a correct explanation of your view, then I want you to tell me where the exactly potential energy is in a ball lifted above the ground. Where would we look for the energy? Is it in the ball? Is it in the ground? Is it in the air between the ball and the ground? Where? And how will we know when we've found the right location? Will we see the energy there?
The potential is relative to the distance to wherever the potential is zero.
The zero potential is where you say, or choose it to be. But since you know the ball will hit the ground, it might as well be the ground.
Or dig a hole and increase the potential. Locally you can gauge where the potential is zero.
Don't forget the vertical displacement is there because work was done; information about this is available from the displacement (which represents) an output.

According to James' "it's just a number" concept, time is just a number, because you can't bottle it.

But ask James what stops things from happening all at once and he will tell you time.

He is playing a word game. We know there is a real phenomena known as "time", but according to James, if you can't bottle it then it's just a number!

In James' world, everything that can't be bottled is a number.

The periodic table is a list, ordered by atomic weight. Atoms of different elements have different weights.

.

On one point of detail, the periodic table is ordered, not by atomic mass, but by the number of protons (and thus electrons) in the atom. It is the number of electrons that determines the chemical properties that define each element, cf. Aufbauprinzip. For example the mean atomic masses of Ar, K and Ca are 40, 39 and 40 respectively.

But of course it is true that the atomic mass generally tends to increase as the number of protons increases, especially since nuclei are most stable when they contain similar numbers of protons and neutrons.

I've seen the argument that mass can be considered as a coefficient of matter.

So the general form for inertia in solid bodies \$\$ I = MK^2\$\$ relates inertia to the mass coefficient as the square of the radius of gyration. Or to the inverse square the in the inverse sense.

In the sense of relations