Is mass a number?

[arfa brane]

Moderator note: This thread was originally split from two unrelated threads titled "arfa's musings on elastic surfaces" and "Time and information". A conversation about whether mass is a number came up in both of those threads. Here is is consolidated in one place.

I'm sure that at some stage in the future you'll tell us all the secret about why [energy] is given the physical units it has. When will you do that, exactly?

After you, James.
What I'm actually interested in is why mass, distance and time are convenient abstractions when you compose them in a certain way and call it energy.
Of course, mass is something you can put in a bottle. Or maybe that depends on how you abstract what a bottle is, whether you can say a bottle is real. Maybe it's down to whether anything is real, or whether physics is about anything real or whether real is an appropriate concept. Time is an abstraction, right? Distance is real though, or maybe just really an abstraction which is useful. Maybe physics is just one big abstraction; the moon abstractly orbits the earth. The sun abstractly outputs light and heat. Yeah . . .

You're lucky to get any of my attention at this point.

Oh thankyou so much, James. I get to discuss the important ideas with someone as important as you. I feel so privileged.

Oops,
I'm wrong again. So when is feeding time?

 

[arfa brane]

Without context, it's very difficult to agree to such a general statement. What information? What system are you talking about? How are you defining/measuring the information?

Physical information, James. Let's call the observable universe the system I'm talking about, or that Leonard Susskind or Seth Lloyd talk about. They even give lectures at universities about it.

How is information defined/measured at a black hole event horizon? How is it measured or defined in a brain or any other physical system not in equilibrium? Assuming a brain in thermal equilibrium is a dead brain, say. Or assuming someone who can conceive that the information in their own brain isn't physical, then tries to explain how that can be physically possible. Someone like you, say.

 

[James R]

After you, James.

You can't tell me why energy has the units it has?

What I'm actually interested in is why mass, distance and time are convenient abstractions when you compose them in a certain way and call it energy.
Of course, mass is something you can put in a bottle.

No. Mass is not something you can put in a bottle. Mass is a number that measures the resistance an object/particle or similar has to being accelerated. You can put a ball in a bottle, but you can't put its mass in there. Its mass isn't "stuff" that can be bottled.

Come on, arfa brane. This isn't a hard concept to get your head around. Why don't you stop pretending not to understand? Stop trying to dance around the simple point I keep putting to you and face it head on. You're the smart guy out of the two of us, aren't you? Do you understand the point I'm making, or not? If you understand and still disagree, then you'd better tell me straight out why I'm wrong and you're right.

Or maybe that depends on how you abstract what a bottle is, whether you can say a bottle is real. Maybe it's down to whether anything is real, or whether physics is about anything real or whether real is an appropriate concept. Time is an abstraction, right? Distance is real though, or maybe just really an abstraction which is useful. Maybe physics is just one big abstraction; the moon abstractly orbits the earth. The sun abstractly outputs light and heat. Yeah . . .

Start from the start. Consider the bottle and the number six, say. Is there any fundamental difference between the "reality" of the bottle and the "reality" of the number six? To help you to answer this quesiton, go to the cupboard and get out a bottle. If the number six is in the cupboard, you can get that out as well.

Now, if there's some time in the cupboard, please put it in the bottle. Take a photo for us and post it here. That might show that it isn't an abstraction.

Can you put some distance in your bottle, too?

How about the moon and the sun? (Hint: you might need a bigger bottle.)

Oh thankyou so much, James. I get to discuss the important ideas with someone as important as you. I feel so privileged.

Good.

 

[arfa brane]

No. Mass is not something you can put in a bottle.

That's confusing
If the bottle is made of glass, which is matter, then the bottle has mass.
Where is the bottle's mass? Hint, it's in the matter the bottle is made of.

Say the bottle is a planet, then it has mass, and again the mass is in the planet.

As to whether I understand your point, no I don't.
A number is a number. A kilogram isn't.

You can weigh a bottle, you can't weigh a number.

 

[James R]

You can weigh a bottle, you can't weigh a number.

Now you're getting it! Great!

If the bottle is made of glass, which is matter, then the bottle has mass.
Where is the bottle's mass? Hint, it's in the matter the bottle is made of.

Okay. So, it should be possible to separate the mass from the matter and put them in separate bottles. Right? Can you do that? Take a photo of just the mass by itself, maybe?

Once you've done that, can you get a photo of a bottle of energy?

 

[arfa brane]

Okay. So, it should be possible to separate the mass from the matter and put them in separate bottles. Right?

Why should that be possible? It's not right. Not at all.

You're the one claiming mass is a number, though. It isn't a number. Though.

 

[James R]

You're the one claiming mass is a number, though. It isn't a number. Though.

Looks like a number to me.

 

[arfa brane]

Looks like a number to me.

That's nice.
Physics doesn't care what it looks like to you. Though.

Besides, what kind of number does it look like? Does it look like an integer or maybe a real number?
A complex number? An octonion perhaps?

So what does a number look like, to you?

 

[James R]

Physics doesn't care what it looks like to you. Though.

The same applies to you, too. Though. Physics doesn't care what you think mass is, either.

Good that we're both clear on that.

So, any ideas as to what mass is, if not a number? Did you get that photo of mass in a bottle yet?

 

[arfa brane]

The same applies to you, too. Though. Physics doesn't care what you think mass is, either.

I know, right?

But you seem to be confused about putting mass in a bottle made of matter, when there is already mass in a bottle made of matter, or anything made of atoms of matter. You say it can't be done, but it's already done. What the hell is that?

Am I trying to discuss physics with a moron here?

And answer the question: what does a number look like? No idea?
Me either.
Where did you get the idea that it should be possible to separate the mass from the bottle and put it in a different bottle? How different do these bottles have to be from each other to do this (obviously ridiculous) thing? What the hell are you talking about? No idea?

 

[James R]

But you seem to be confused about putting mass in a bottle made of matter, when there is already mass in a bottle made of matter, or anything made of atoms of matter.

The example I gave was putting a ball into a bottle. You say the mass of the ball is somehow contained within the ball, but also that mass is not the same as the matter in the ball. Therefore, it follows that you ought to be able to separate the matter in the ball from the mass in the ball, and put both of them into separate bottles. After all, you say that mass and energy are both, effectively, substances. Don't you? We can bottle substances.

Where are your photographs of mass in a bottle and energy in a bottle?

[Note: for clarity, since you seem to be struggling to make the distinction between a thing in a bottle and the bottle itself, I acknowledge that bottles are made of matter, which has its own associated mass. I emphasise, however, that the mass of a bottle - or any other object - cannot be bottled separately from the object, or indeed at all. I hope this is now clear to you.]

Am I trying to discuss physics with a moron here?

That's one possibility. Another possibility is that I'm trying to discuss physics with a moron. Dunning Kruger, you know.

And answer the question: what does a number look like? No idea?

It doesn't look like anything. Numbers are ideas, concepts. Do you have a bottle full of numbers anywhere? Of course you don't.

But wait a moment! You say that energy is not a number. What does energy look like, then? No idea?

Where did you get the idea that it should be possible to separate the mass from the bottle and put it in a different bottle?

From you!

 

[arfa brane]

What I'm actually interested in is why mass, distance and time are convenient abstractions when you compose them in a certain way and call it energy.
Of course, mass is something you can put in a bottle.

I said mass is something you can put in a bottle. Add some more matter, like water to this bottle.
This abstraction that I'm using here, is that mass is additive. Newton I think called it the "ponderable quantity" of an object.
I'm saying ponder this, if you have an empty bottle, is it easier to lift it after you fill it with water?

So he's saying I also think that by lifting a weight you can compare it to another, lifted weight. Or object with mass, if you like.

Notice how the word weight is an abstraction of this Newtonian idea, of lifting weights.

 

[arfa brane]

After all, you say that mass and energy are both, effectively, substances. Don't you? We can bottle substances.

Where do I say that?

 

[arfa brane]

It doesn't look like anything. Numbers are ideas, concepts. Do you have a bottle full of numbers anywhere? Of course you don't.

Aha. If I can say I do have, and it's in my head when I think about numbers, can you prove I can't call it numbers in a bottle?

Can you prove mass is a number? Please show me how it's done.

 

[arfa brane]

No. Mass is not something you can put in a bottle. Mass is a number that measures the resistance an object/particle or similar has to being accelerated. You can put a ball in a bottle, but you can't put its mass in there. Its mass isn't "stuff" that can be bottled.

And then I say mass already is "put in" a bottle.
I also say you can put a ball in a bottle, which means the mass goes in as well. A direct contradiction--see that?, right there.

Newton said a few centuries ago that all he had to say about what mass is, is that it's a ponderable quantity.
I say mass is not a number, because you can't weigh a number, numbers don't arrive equipped with inertia. Numbers don't occupy a volume.

The idea that mass or energy are "just numbers" is a useless idea.

Richard Feynman said "nobody knows what energy is", James R is saying "energy is a number". Which one is right?
What is a mass ansatz, and why would it be useful, or . . . not?

 

[James R]

Can you prove mass is a number? Please show me how it's done.

It might be easier if you can provide a counter-example.

Can you show me a mass that isn't a number?

 

[Motor Daddy]

It might be easier if you can provide a counter-example.

Can you show me a mass that isn't a number?

Go outside and pick up a rock. That is a massive object. All objects have mass, and we measure the mass using numbers and units. Mass is a physical thing, not just a number.

The amount of matter an object has is called mass, and we can quantify that mass using numbers and units.

Mass evolves to space!

 

[James R]

I also say you can put a ball in a bottle, which means the mass goes in as well. A direct contradiction--see that?, right there.

The ball's mass isn't in the bottle. It's in your head.

How many times do we need to go around on this before the penny drops? Or do you have some kind of block?

I say mass is not a number, because you can't weigh a number, numbers don't arrive equipped with inertia. Numbers don't occupy a volume.

You can't weigh a mass. Mass is what you get in your head when you weigh an object. You say something like "That milk carton has a mass of 1 kg". You didn't weigh its mass; you weighed the carton itself. The mass is that "1 kg" you have in your head, after you read it off the display of the set of scales.

The idea that mass or energy are "just numbers" is a useless idea.

Better than thinking of energy as a mysterious glowing substance that flows from one object to another, which is a hopelessly misleading notion.

The "mass" thing is mostly harmless, because the issue mostly never comes up as to where the mass that is associated with a given object actually is. You associate the object and its mass in your head. You're so used to doing that, that now you actually believe that the mass and the object are one and the same.

When it comes to energy, the problem is similar, but worse. Energy tends to "flow" from one thing to another, but that "flowing" is only really in your head. Energy is not "stuff", but your mental image compensates by imagining it to be like "stuff". That's fine, if all you need is a superficial understanding of what energy really is, but in physics you quickly run into problems almost immediately with that naive concept.

Let me give you an example. Lift a ball to height h above the ground. We say there is "gravitational potential energy" of mgh associated with this, where m is the mass of the ball (a number!) and g is the acceleration due to gravity. So, where is this energy located exactly? Is it in the ball? No. Where, then?

Richard Feynman said "nobody knows what energy is", James R is saying "energy is a number". Which one is right?

Feynman understood that it's a number, same as me; probably he even says that in his Lectures (I'd have to go back and check). The "nobody knows what it is" thing was a rhetorical flourish.

What is a mass ansatz, and why would it be useful, or . . . not?

You tell me.

 

[James R]

Go outside and pick up a rock. That is a massive object. All objects have mass, and we measure the mass using numbers and units. Mass is a physical thing, not just a number.

You're coming to this discussion late. Perhaps start by reviewing the earlier posts in the thread. That way, you won't be rehashing points that have previously been addressed.

The amount of matter an object has is called mass, and we can quantify that mass using numbers and units.

Great! You got it!

Maybe you can explain it to arfa brane. He's struggling.

 

[Motor Daddy]

Great! You got it!

I agree with you about energy being just a calculated number, using units of course.

Mass is not just a number, mass is a word for matter. You could just as easily say an object has x amount of matter instead of saying the mass is x.

Mass is a word meaning matter, and we measure it using numbers and units. A rock is a massive object that we can use numbers and units to measure its mass.

Mass is matter. Quantifying mass is quantifying matter. We use numbers and units to do that.

So saying mass is just a number is not correct. Mass is matter.