[JP]

I'm just taking issue your one line above that I quoted.

I smell a debate about proper mass vs rest mass in the air. That's when I must leave the room. Methinks it be bad juju!

I wasn't the one telling posters that proper mass has little or nothing to do with the definition of mass!  I'm content to call them "invariant/proper mass" and "inertial/relativistic mass" and skip the arguing phase over which meets the definition of mass.

[Pmb]

I'm just taking issue your one line above that I quoted.

I smell a debate about proper mass vs rest mass in the air. That's when I must leave the room. Methinks it be bad juju!

I wasn't the one telling posters that proper mass has little or nothing to do with the definition of mass!  I'm content to call them "invariant/proper mass" and "inertial/relativistic mass" and skip the arguing phase over which meets the definition of mass.

Don't get me wrong.I wasn't blaming anyone for anything about that. More later. Gotta go to pain clinic.

[lightarrow]

Perhaps the solution should be to elect me the President of Physics

[]

and I'll rewrite all the textbooks to clear this up?   

I like your kind of humour.

[lightarrow]

I've already explained in simple terms why you can't localize a photon, but you don't accept it because, you say, it works only for photons described in quantistic sense; I tried to show you that this is the only description for the term "photon" and so we are in a loop...
I sincerely don't know what else I could say.

If that is your response then you weren't paying attention to what I was saying. You consistently keep forgetting the approximation and what it would mean to put the photon's position vector inside the area of uncertainty according to how the wave function would average the position. I gave you an example of a pixel of 0.001 mm in width a length and when it detects the photon then its localized in that area and the location of the photon is the location of the pizel) e.g. geometric center.

Ah, yes, localized after detection, of course. The problem is, and this is not the first time I write it, I was talking of localizing it in flight, between source and detector.

You youy insist on ignoring every single thing I've said regarding approximation then there is no use to continue this conversation. Why should I post something I know you're going to igore?
While you're at it it wouln't hut you to finally state what it is you mean by saying something can or can't be localized. E.g. find a QM texbook and quote the definition of "localized" or "localize" so you won't be vauge anymore.

Have a look also here:

http://stochastix.files.wordpress.com/2008/05/what-is-a-photon.pdf

<<What is a photon?
Rodney Loudon
University of Essex, Colchester, UK>>
...
<<A one-photon excitation in such a mode again carries an energy
quantum ¯hω distributed over the entire interferometer,
including both internal paths. Despite the absence of any localization
of the photon, the theory provides expressions for
the distributions of light in the two output arms, equivalent to
a determination of the interference fringes.>>

[lightarrow]

Sorry, but I don’t know what a Fock state is.

In any case, that’s not what I meant by a “classical photon.” Recall the definition that I used.

Do you mean it's a definition invented by you? It's just a question.

A classical photon is a particle whose inertial energy

"inertial energy"? Sorry but I've never read this term; it's not another of "your definitions", isnt'it?

is related to its momentum by E = pc and interacts with charges via the electromagnetic interaction. There is no associated wavelength since that’s a quantum property just as a classical electron has no wavelength. By this definition it moves on a classical trajectory, has a position vector, etc.

Ok. What you have described here is simply a classical pulse of light: an electromagnetic wavepacket. Why do you call it "classical photon"? Well, if I will find it in books of physics, I will conform to it, no problem; don't see any problem in using that term, as soon as it will be defined.

This is what they use in the derivations for the mass-energy equivalence relationship where they use the conservation of the center of momentum. It’s also what relativists use when they draw a worldline of a photon.

If they use the term "photon" it's a misuse and they could simply talk of an electromagnetic wavepacket. I suspect some relativists don't actually now what "a photon" exactly is; I don't mean I know it well, but it's a lot of time I discuss this specific subject with physicists, at university, first and in the forums.

[lightarrow]

Put a kilogram of matter and one of antimatter into an impregnable box, like a Schrödinger cat box, and the mass of the box (any category of mass you care to choose) will not change when the contents annihilate each other. Even if the box only contains light, the mass(es) will not change.

Correct, but it doesn't confirm your statement.
By the way, there is no need of matter and antimatter and not even of light in a box,  two photons are enough, because such a system have a non-zero mass (I mean invariant mass, not relativistic mass), I have already showed it in a recent thread and in several others, during the years.

It's both correct and does prove my statement.

If you say so...

[lightarrow]

Forget what he's been saying. He has a way of confusing the poperties of mass with those of proper mass.

[]  Sorry, I wasn't.

There are three aspects of mass given three names and each are merely just called "mass" because they all have the same value
(1) inertial mass - m = p/v. The higher the inerial mass the harder it is to change its momentum.
(2) passive gravitational mass - The property of matter to respond to a gravitational force.
(3) active graivtational mass - The property of matter to generate a gravitational field.
proper mass (i.e. what lightarrow is always referring to when he sees the word "mass") has little or nothing to do with the defining characteristics of mass. A photon has zero proper mass but has inertial mass, passive gravitational mass and active gravitational mass.

Just "Four" kinds? My God, where has gone your creativity? From you I expected at least a hundreds kinds  []
You still have a lot of work to do, if you want to write since-fiction books  []

[yor_on]

This one does a nice job of explaining the history of mass, and how the idea of passive and active mass came to be. The Equivalence Principle: A Question of Mass 

[lightarrow]

This one does a nice job of explaining the history of mass, and how the idea of passive and active mass came to be. The Equivalence Principle: A Question of Mass 

History is interesting, but once physics has established the equivalence of those masses, there is no need to talk about them any longer, there is just one.

[yor_on]

I think the point of it has to do with light quanta. "A photon has zero proper mass but has inertial mass, passive gravitational mass and active gravitational mass." The 'passive' being what is acting on it, the 'active' being the way it will act on other, the inertial mass being its resistance to change, all as I think of it. But if it is a field then? How many degrees of freedom would be needed to create a static field in where you have the illusion of a arrow, waves/particles, gravity and motion, and all of it being observer dependent?

[yor_on]

Because if you consider it from observer dependencies it seem to me that you either have to assume 'something' unchanging, being the platform from where observer dependencies are created, or else make a assumption that all observers have a own 'universe'. And that, it its turn, comes from the fact that we use repeatable experiments to define 'reality'. That's the way we set it up physically. And if that thinking is correct, that your experiments will tell you what is true and what is wrong. Then the universe I see, and experimentally verify as me having a certain distance to some other body for example, will differ from yours according to relativity.
==

Locally I would say that we all have a equivalent arrow, as proved when being in a same frame of reference with what you measure. From a point of locality we're all 'equal' regarding the arrow. The same goes for distances. From that point of view the universe consist of one unchanging base, same for us all, observer dependencies created through 'c' (combined with energy/mass/'motion'). But the fact is that your reality is defined through your experiment, so finding someone else's watch to go slower than yours relativistically and experimentally must be true to/for you.

So locality is where we're all equal as I see it. And where all arrows are equivalent.
And one more thing, accelerations.

The weirdest example, and proof, of a 'change' that I know. Everything that exist seems to me to somehow (be able too?) accelerate? What is a virtual particle? If it is not there, but then is, can you see that as a 'acceleration' from a probability into a 'outcome' ('real' particle) ?

[Pmb]

I wasn't the one telling posters that proper mass has little or nothing to do with the definition of mass!

Inertial Mass - Defines momentum. Quantifies resistance to changes in momentum.
Passive Gravitational Mass - The property on which gravity acts
Active Gravitational Mass - That which generates a gravitational field.

Those are what characterizes mass, by definition. How does invariant mass simply fit in there? We all know that it does, but in what direct manner?

[JP]

Mass is the length of the energy-momentum four vector, no matter how fast you're going.  This satisfies F=ma and p=mv (with some problems with photons, I believe), and reduces beautifully to classical mass in the relativistic limit when three of the vector's components become negligible.  There's something to be said for the elegance of this concept.

The last two of your points have to do with general relativity, so I'd add that relativistic quantum mechanics uses invariant mass, in the place of where mass would enter in the non-relativistic equations, mostly because of the simplicity with which it enters the equations in place of non-relativistic mass when promoting 3-vectors to 4-vectors.  This isn't as elegant or long-standing as "it generates gravity," but that's because we happened to be born into a world where we experience gravity daily, and not because it's any less fundamental.  If we were born as quantum objects, we'd find it very fundamental indeed!

[waytogo]

I'm sorry if this is a dumb question but physics is not really my area. I've been listening to the CBC Massey lectures by physicist Neil Turok, which I quite like. Anyway, when he talks about mass increasing at higher speeds, how does that happen? Is there actually an increase in the amount of matter or atoms or particles? Or does it just take more force to accelerate it? I had always thought that mass and matter were the same thing.

Hi there, Its NOT a dumb question, I still have no answer of that. Anyway, you have to consider that its just a ancient theory and new ones should be replaced in next decades.

[Pmb]

Mass is the length of the energy-momentum four ..

That is merely an equality relating inertial energy, momentum and proper mass. It's not a definition of mass, at least it shouldn't be. The onlyway you can arrive at that relationship is by relating inertial mass to velocity of an isolated system. It doesn't work in general by the way. It only works for competely isolated systems. It wouf fail for a drop of water in an electric field. The definitions are as I gave them above. They are what characterize mass.

[Pmb]

I'm sorry if this is a dumb question but physics is not really my area. I've been listening to the CBC Massey lectures by physicist Neil Turok, which I quite like. Anyway, when he talks about mass increasing at higher speeds, how does that happen? Is there actually an increase in the amount of matter or atoms or particles? Or does it just take more force to accelerate it? I had always thought that mass and matter were the same thing.

Hi there, Its NOT a dumb question, I still have no answer of that. Anyway, you have to consider that its just a ancient theory and new ones should be replaced in next decades.

Its hardly ancient since its found in even the most recently published textbooks.

[JP]

The definitions are as I gave them above. They are what characterize mass.

Ah, the old "I chose to characterize mass by these definitions, therefore they characterize mass" argument.  That works for the definition I gave, too.   

I thought up another interesting question about invariant vs. inertial mass, though.  I don't understand the Higgs mechanism enough to give a definite answer, but from the descriptions I've heard of it by scientists, it explains inertial mass in terms of a field, and the strength of a particle's inertial mass by the coupling to that field.  That could mean a coupling constant would probably be the best definition of inertial mass, which seems like invariant mass.  The Higgs mechanism could provide a means to explain inertial mass in terms of a single constant plus a field of nature.  If that's true, invariant mass is presumably more fundamental than inertial mass, which is another good reason to consider it a definition of mass.  This is speculation, so take it with a large grain of salt unless a Higgs specialist on the forum wants to confirm or refute it.  :p

This horse, however, has been beaten to a fine paste at this point.  Arguing our opinions on the internet doesn't change the fact that all these definitions  are valid extensions of the concept of classical mass, and all find widespread use, albeit in different fields of study.  I guess we'll keep on arguing until someone figures out quantum gravity and ties all the concepts of mass into one fundamental definition.

[Pmb]

Ah, the old "I chose to characterize mass by these definitions, therefore they characterize mass" argument.  That works for the definition I gave, too.   

Not really. It was never I who chose them. They've been around long before I was born, and still are.

[Pmb]

I wasn't the one telling posters that proper mass has little or nothing to do with the definition of mass!

I just realized that you misquoted me here. I never said that. What I said was that proper mass has little or nothing to do with the defining characteristics of mass.

I would never say that it had nothing to do with mass, never! The reason being, that it’s simply not true. Did you miss that part or were you confused? [we all have our days ] I think you mistook me for saying that proper mass has nothing to do with the definition of mass. That’s now what I said simply because I don't believe it to be. The  defining characteristics being the whole point I was making.

If you'll notice, I do my best to avoid getting into discussions about the definition of mass. There's just way too much to the concept than can be gotten to in a discussion in a discussion forum. In fact it was for just that reason that wrote that article on the subject. Everything I believe regarding the concept of mass is in the paper at http://arxiv.org/abs/0709.0687

I recommend that you read it. I’d enjoy your feedback and any comments or constructive criticism that you might have on it.

I can pretty much guarantee that every aspect about mass that you could come up with are tell me about mass is contained in that paper, including the most obvious notion that the “mass” of a particle is the magnitude of the particle’s 4-momentum. If you read the paper you’ll find what I consider to be a much better definition of proper mass, i.e. as the quantity m such that the quantity P = mU (where P = 4-momentum and U = 4-velocity) for a system of particles which interact only by contact forces, is conserved.


Note: What's with this stupid editor? Everytime I try editing in this window it keeps popping up to the top so I have to keep scrolling down to see what I'm editing!

[JP]

Ah true, I did misquote you.  Sorry for that.

My point still stands in roughly the same form.  If you list a bunch of defining characteristics of mass that preclude another definition of mass, then of course it has little or nothing to do with those characteristics.  Though I would argue that the use of invariant mass does meet the kinematical characteristics of mass, since classically, inertial mass in Newton's second law, F=ma, can be replaced in the four-vector version with invariant mass, and it's particularly elegant to view the transition to special relativity geometrically in terms of 4-vectors. 

The horse is still very dead, though.  We all agree (I hope!) on the physics involved, and that describing it requires 4-vectors and/or tensors.  In the end, we're arguing about a single scalar value pulled out of these equations, so of course there's multiple ways to do that!  Similar debates come up a lot in physics, where one has vectors/tensors and tries to use a single scalar to describe the physics.  It's always insufficient and very often just as contentious (look up degree of entanglement in quantum mechanics for a similar debate), and obscures the fact that everyone involved agrees on the physics.  I imagine this argument over mass will go on unless, some day, a unified theory comes along that does involve a single scalar value in the place of mass (for example, a coupling constant to some field describing inertial and gravitational masses) from which all other definitions follow.

I'll check out your paper when I have a chance.  I've got a backlog of reading to do at the moment.