New definition of mass

[arfa brane]

Even though the equations Einstein introduced in 1915 concern the curvature induced by massive objects, the theory does not offer a simple or standard way of determining what the mass of an object is. Angular momentum — a measure of an object’s rotational motion in space-time — is an even harder to define concept.

Some of the difficulties stem from a feedback loop that is built into general relativity. Matter and energy curve the space-time continuum, but this curvature becomes a source of energy itself, which can cause additional curvature — a phenomenon sometimes referred to as the “gravity of gravity.” And there is no way to separate an object’s intrinsic mass from the extra energy that comes from this nonlinear effect. Moreover, one cannot define momentum or angular momentum without first having a firm grip on mass.

Einstein recognized the challenges involved in quantifying mass and never fully spelled out what mass is or how it can be measured. It was not until the late 1950s and early 1960s that the first rigorous definition was proposed. The physicists Richard Arnowitt, Stanley Deser, and Charles Misner defined the mass of an isolated object, such as a black hole, as viewed from almost infinitely far away, where space-time is almost flat and the object’s gravitational influence approaches zero.

Although this way of calculating mass (known after its authors as “ADM mass”) has proved useful, it doesn’t allow physicists to quantify the mass within a finite region. Say, for instance, that they are studying two black holes that are in the process of merging, and they want to determine the mass of each individual black hole prior to the merger, as opposed to that of the system as a whole. The mass enclosed within any individual region — as measured from the surface of that region, where gravity and space-time curvature might be very strong — is called “quasilocal mass.”

==https://www.quantamagazine.org/mass...t-ambiguous-by-einstein-get-defined-20220713/

Mass is not yet a thing that anyone can say they know what it is.

Ok? You know who this is aimed at, don't you?

 

[exchemist]

The mass "of an object", i.e. mass is a property of objects. And "the challenges involved in quantifying mass", and how it can be "measured", so a quantitive property.

This all seems fairly uncontentious.

The issue the article addresses is the "gravity of gravity" i.e. the extra mass/energy an object has by virtue of the curvature it creates. So a conundrum in general relativity.

GR deals in relationships between a number of quantitative (numerical) properties of systems: mass, energy and momentum, none of which can be said to exist independently of the systems they are properties of.

 

[James R]

Mass is not yet a thing that anyone can say they know what it is.

Issues with quantifying (measuring) mass do not mean that nobody knows what mass is.

You might have trouble measuring the length of a bacterium, but that doesn't mean you don't know what length is.

 

[arfa brane]

You might have trouble measuring the length of a bacterium, but that doesn't mean you don't know what length is.

Are you saying you know what length is? and if you do know, that means you know what mass is?

I guarantee you can't explain what it is you know about either mass or distance, or for that matter any other 'numerical' physical quantity.

But have at it. Maybe you can invent a windmill to tilt at.
Of course, you will say, everyone knows what distance is. It's that thing between two separate points, eh?
Further, since physical quantities are numerical, how does that make mass, or charge, a number? How does it make distance a number?
Or are only some physical quantities actually numbers, some aren't? What rule gets applied?

Or perhaps the idea that a numerical quantity is a number is flawed somehow. In the sense it just isn't true?

 

[Beaconator]

Are you saying you know what length is? and if you do know, that means you know what mass is?

I guarantee you can't explain what it is you know about either mass or distance, or for that matter any other 'numerical' physical quantity.

But have at it. Maybe you can invent a windmill to tilt at.
Of course, you will say, everyone knows what distance is. It's that thing between two separate points, eh?
Further, since physical quantities are numerical, how does that make mass, or charge, a number? How does it make distance a number?
Or are only some physical quantities actually numbers, some aren't? What rule gets applied?

Or perhaps the idea that a numerical quantity is a number is flawed somehow. In the sense it just isn't true?

Mass is fundamentally related to pi. Which explains how relatively even numbers such as the table of elements end up with close to even masses. The closest one dimensional demonstration of this is rolling a wheel with a diameter of one along the table of elements and noticing the columns intersect at 1/3 marks.

 

[Dywyddyr]

Mass is fundamentally related to pi.

Nonsense.

 

[exchemist]

Mass is fundamentally related to pi. Which explains how relatively even numbers such as the table of elements end up with close to even masses. The closest one dimensional demonstration of this is rolling a wheel with a diameter of one along the table of elements and noticing the columns intersect at 1/3 marks.

This is appalling ballocks, even for a certified nutcase like you.

 

[James R]

arfa brane:

Useful quantities in physics typically have operational definitions. An operational definition says "To measure the X of a thing, follow these steps: 1. blah blah blah; 2. blah blah blah; etc." Note that following the "recipe" is what defines the quantity X; this is different from having some abstract definition of X and then trying to work out ways to determine it after the definition is established.

In the case of mass, one operational definition might look something like this:
1. Apply a known force F to an object.
2. Measure the resulting acceleration of the object.
3. The ratio F/a is the mass, m, of the object.

In light of that...

Are you saying you know what length is? and if you do know, that means you know what mass is?

Yes, I can give you operational definitions of both length and mass. Therefore, I know what they are.

I guarantee you can't explain what it is you know about either mass or distance, or for that matter any other 'numerical' physical quantity.

Well, you're wrong again. Or still wrong, as it may be.

Of course, you will say, everyone knows what distance is. It's that thing between two separate points, eh?

You did a bad job of trying to predict what I would say. Maybe give that up. You might learn more.

Further, since physical quantities are numerical, how does that make mass, or charge, a number?

Er... numbers are numerical. Aren't they?

How does it make distance a number?

If you tell me you're 5 feet tall, I'd say that the "5" in there is a number. Wouldn't you?

Or are only some physical quantities actually numbers, some aren't? What rule gets applied?

A simple rule of thumb is: look for the numbers. There is no "5" in the colour "blue", for instance, but there is a "5" in "5 feet tall". It's not very hard to spot numbers.

Or perhaps the idea that a numerical quantity is a number is flawed somehow.

You think it's flawed? Tell me how its flawed, and what your superior solution is to this hard problem of numbers that you've discovered.

 

[arfa brane]

Useful quantities in physics typically have operational definitions. An operational definition says "To measure the X of a thing, follow these steps

Yes. I know that James. I also know that a definition necessarily assumes things.
I also know that the phrase "physically real" you've been so keen to have me ah, define, is just a pair of words. What they might mean or how they are defined, by who and for what reason, isn't really all that relevant.

Except if a need is perceived to use definitions. I trot out the obvious "betweenness" of distance between two points, and you're off again.
This time you accuse me of anticipating or predicting what the Great James, is going to pronounce next. Because it's all about you and what you think is important, eh James?

If you tell me you're 5 feet tall, I'd say that the "5" in there is a number. Wouldn't you?

Of course the 5 is a number, well, strictly speaking it's a symbol that we all are supposed to interpret as the value of . . . I just know there's something else goes here . . . "a number" perhaps . . .

I would also say the number is still there when you have 5 feet, but feet aren't a number, wouldn't you say?
Which is the main reason I say a numerical quantity is not a number, and the idea, your idea that it is, is flawed. Unsupportable.

Numbers don't influence each other, masses and charges do though. Have you spotted that?

 

[arfa brane]

I can give you operational definitions of both length and mass. Therefore, I know what they are.

Well sure you do. Except for the little problem of having to assume the existence of . . . (I'll let you fill in the blanks here)

 

[Beaconator]

This is appalling ballocks, even for a certified nutcase like you.

It’s still an interesting exercise… figuring out the differences between distance traveled and mass.

I think hydrogen is at1.1 and the diameter is .75 or so right off the top of my head from ten years ago

 

[arfa brane]

Why James the Great Thinker, is just wrong to say he knows what mass is.
He contradicts Feynman; if he knows what mass, and what distance are, let's assume he thinks he knows what time is too, then he must know what energy is; energy has physical units:- mass units, distance units, and time units, energy is not a number because numbers are not a mixture or mashup of anything except other numbers.

But let's leave an out for the poor guy and assume knowing what time is, is not possible, it just won't ever make any kind of sense, if you apply an accepted definition of "know"; which I might assume means having to store certain information, and be able to recall it. You can't do this with time, it seems. Time really can't be put in any kind of bottle.

Ahem. I hereby deny any perceived attempt to claim any unique or particular, or even enlightening, knowledge of time or what it really is.
And yes, it does depend what really, . . . really means.

 

[James R]

I also know that the phrase "physically real" you've been so keen to have me ah, define, is just a pair of words.

Then, can I assume you won't be using that term in future?

This time you accuse me of anticipating or predicting what the Great James, is going to pronounce next. Because it's all about you and what you think is important, eh James?

You literally wrote "Of course, you will say, everyone knows what distance is. It's that thing between two separate points, eh?"

I'd say my "accusation" is clearly supported by your words. Don't you agree?

That you follow up with an attempted insult is also something I have come to expect from you. You can't help yourself.

I would also say the number is still there when you have 5 feet, but feet aren't a number, wouldn't you say?

"feet", in this context, is a unit of measure.

Which is the main reason I say a numerical quantity is not a number, and the idea, your idea that it is, is flawed.

I have already accepted that many physical quantities have units.

It remains the case that you can't put "5 feet" in a bottle. You can't see "5 feet". You can't eat "5 feet". You can't smell "5 feet". "5 feet" can't talk to you or make you a cup of coffee. "5 feet" is just a number and a unit. It is, of course, typically associated with measuring a distance or length. That has never been a matter of disagreement.

Unsupportable.

When will you work out that mere assertion is not an argument? What you need, if you're serious, is some kind of reason why you think "5 feet" is something other than a number and a unit. Otherwise, you're just giving us your opinion for the nth time, and that's not worth any more than it was the first time.

Numbers don't influence each other, masses and charges do though. Have you spotted that?

Masses and charges don't influence each other.

Two objects can attract each other gravitationally, or electrically if you like. But you can't produce two masses that will attract one another. You can't bottle mass. Mass won't make your coffee.

 

[James R]

Why James the Great Thinker, is just wrong to say he knows what mass is.

Unevidenced assertion, as usual.

He contradicts Feynman;

How so? Where? What did Feynman say that's different from what I said? Quotes, please.

... if he knows what mass, and what distance are, let's assume he thinks he knows what time is too, then he must know what energy is; energy has physical units:- mass units, distance units, and time units, energy is not a number because numbers are not a mixture or mashup of anything except other numbers.

Units, just like numbers, are concepts. You can't bottle units. There's no such thing as a bottle of kilograms, or a bottle of Joules.

Sheesh. How hard is this for you? Seriously. Are you really unable to distinguish a concept from a physical object? Or is this just some kind of time-wasting game you're playing?

But let's leave an out for the poor guy and assume knowing what time is, is not possible, it just won't ever make any kind of sense, if you apply an accepted definition of "know"; which I might assume means having to store certain information, and be able to recall it. You can't do this with time, it seems. Time really can't be put in any kind of bottle.

No bottle of time. Right. And therefore... ?

 

[arfa brane]

Yes, I can give you operational definitions of both length and mass. Therefore, I know what they are.

This is why your logic is fried, James.

You believe that an operational definition, is the same as knowing what is being defined "really" is. Right?
A definition cannot avoid making assumptions. Usually these are motivated by, well, some thing or other.

 

[arfa brane]

What you need, if you're serious, is some kind of reason why you think "5 feet" is something other than a number and a unit.

What you need is an explanation of why a number and a unit, (two things) is a number (not two things). Why is this "unit" there? What is it?
Does anyone know--does "it's a concept" do the trick?

 

[arfa brane]

Masses and charges don't influence each other.

According to who?

Two objects can attract each other gravitationally, or electrically if you like. But you can't produce two masses that will attract one another.

You say in the first sentence that objects can attract each other; then if I assume you mean the conventional quantity of matter (somehow without explanation now different in the second sentence because . . . well, never mind). But the first sentence contradicts-- what you say is wrong with what I say. Charges influence each other, mass is a kind of charge objects have, because atoms have it too. Sentence 1 agrees with what I say, and you claim it's wrong. All over again

Just woolly stuff. Mass is a charge, matter is charged or "has" mass and other kinds of charge

 

[James R]

arfa brane:

Are you unable to acknowledge the distinction between a concept or property and a physical object to which that concept or property applies, or just unwilling to acknowledge the distinction?

I notice that you keep skipping over the core of our disagreement, to talk instead about irrelevancies. Mass and length are properties of things, not things in and of themselves. Mass is not a "thing" that does anything of its own accord, or which can cause anything to happen. Mass is a concept in your head. A tennis ball is a thing that you can put in a bottle. We can associate a concept (a number), called mass, with a thing called a tennis ball. But the mass of the tennis ball is not the tennis ball. The tennis ball can fall on your head. Its mass cannot.

Do you disagree with any of this? Do you have any thoughts at all on any of this? Are you able to bring yourself to think about any of this? Are you able to express an opinion that is on topic on any of this?

Now, we can also deal with the irrelevancies, but you should really try to engage with the core rather than insisting on messing about at the periphery all the time.

You believe that an operational definition, is the same as knowing what is being defined "really" is. Right?

Not necessarily. Does it matter?

A definition cannot avoid making assumptions.

Okay.

Usually these are motivated by, well, some thing or other.

Okay.

So what?

What you need is an explanation of why a number and a unit, (two things) is a number (not two things). Why is this "unit" there? What is it?
Does anyone know--does "it's a concept" do the trick?

Units are signposts, pointing us towards the kind of thing that the number is representing. 5 kilograms tells us that we're dealing with mass. 5 kilometres tells us that we're dealing with distance or length. Also, units always have a reference. To talk meaningfully about 5 kilograms, we have to already have a well-defined concept of what 1 kilogram is. For 5 kilometres to be useful, we need to know what 1 metre is.

Units are concepts. 1 metre, for instance, is defined to be the distance travelled by light in a vacuum in 1/299792458 seconds. That is a conceptual definition. You can't bottle 1 metre. You can't open a jar of metres or have 1 metre hit fall on your head.

You say in the first sentence that objects can attract each other;

Do you accept that objects can attract each other gravitationally or electrically? If you do not, then we have a lot more issues to work through with you than I thought.

But the first sentence contradicts-- what you say is wrong with what I say.

No. I have not contradicted myself. Nor have you been coherent enough to even attempt to point out a contradiction.

Charges influence each other, mass is a kind of charge objects have, because atoms have it too.

Charges don't influence each other. How can a number influence another number? Can concepts collide? Can a concept hit you on the head?

Just woolly stuff.

You're failing to engage. Try harder. Concentrate on the core issue, which is your confusion between concepts and objects. The two are not the same thing. Once you understand that, everything might become clearer for you.

Mass is a charge, matter is charged or "has" mass and other kinds of charge

By "charge" we usually mean electrical charge, and that is what I assumed you meant. I am happy to accept that mass is a kind of charge, that relates to gravity rather than electomagnetism, if you like. It's a nit picky irrelevance to your core confusion.

 

[arfa brane]

Mass and length are properties of things, not things in and of themselves.

Oh sure. The distance between me and the TV is a concept. It isn't a thing in and of itself.
Riiiii . . .

Units are signposts,

. . .ght.
Whatever unit "of" distance I choose to measure the distance to the TV, they're signposts? What you're saying is the unit distances I use to measure a larger distance, is one big signpost? That's unfathomable.

1 metre, for instance, is defined to be the distance travelled by light in a vacuum in 1/299792458 seconds. That is a conceptual definition.

Yes, and a physical definition. The speed of light is physically real, as real as an electric field, right? So this conceptual definition is based on "physically real" observations--measurements, right?

Measurements are what kind of object, James?

 

[James R]

Oh sure. The distance between me and the TV is a concept. It isn't a thing in and of itself.

A distance is not an object. Do you agree, or not?

Whatever unit "of" distance I choose to measure the distance to the TV, they're signposts? What you're saying is the unit distances I use to measure a larger distance, is one big signpost? That's unfathomable.

I'm sorry to see you struggling so mightily with what I think is a very simple concept.

Here's what I wrote: "Units are signposts, pointing us towards the kind of thing that the number is representing. 5 kilograms tells us that we're dealing with mass. 5 kilometres tells us that we're dealing with distance or length."

I'm happy to answers specific questions. Tell me what you can't fathom in that statement of mine and perhaps I can put it in simpler language you can understand.

The speed of light is physically real, as real as an electric field, right?

I thought we agreed that you would stop using the term "physically real", because you're unable to define what that means.

If you think you can define it, then tell me what it means to you for a speed to be "physically real"? What is required for a speed to become physically real, as opposed to being conceptual? What is required for an electric field to become physically real, as opposed to conceptual?

Once again, I notice that you completely skipped over the concept/object distinction that I pointed out at the start of my previous post. Why is that? Mental block? Blind spot? Too hard for you?

So this conceptual definition is based on "physically real" observations--measurements, right?

Tell me what "physically real" means, then I'll try to give you an answer.

Measurements are what kind of object, James?

They aren't objects. Making a measurement is a process. The result of a quantitative measurement is a number. Numbers are conceptual. (Although, maybe "physically real" includes numbers, for you, which might make numbers "physically real" as well. I can't tell what you think unless you tell me.)