blackholes vs. massless photons

[Pete]

Whilst swan's explanation may be technically incorrect, it still illustrates the correct definitions of the terms; I don't think the answers are geared towards physicists.

I don't believe he was "technically" incorrect per se. I only meant to say that he was incorrect as far as how everyone in the relativity community defines the term mass.

 

There are two ways in which people use the term "mass" in relativity. One is as I've described and the other, i.e. proper mass, is proportional to the square of the magnitude of the particle's 4-momentum. However this is a vauge term since 4-momentum can't always be defined for an object. 4-momentum can only be defined for an isloated object or a pointlike object (no spatial dimensions). But some people use the term mass to refer to proper mass (which is what swan calls rest mass).

 

However it is my opionion that the magnitude of some 4-vectors are best refered to as proper quantities. Thus if

 

dX = (cdt, dx, dy, dz)

 

is a spacelike spacetime displacement then c^2dT^2 = dX*dX where dT is referred to as the proper time interval between the two events. If dX is a spacelike spacetime displacement, then c^2ds^2 = dX*dX where ds is proper distance.

 

Likewise

 

P = (mc, p)

 

is the 4-momentum of a particle whose mass is m and 3-momentum is p.

 

m₀²c² = P*P

 

where m₀ is the particle's proper mass.

 

The terms proper mass and rest mass do not refer to the same thing. Rest mass denotes the value of proper mass when the velocity is zero. However m(0) does not equal m₀ unless dt/dT = 1.

 

For example; In a wide variety of circumstances (i.e. time-orthogonal spacetimes, where g_0k = 0 -- no spacetime dragging) dt/dT is a function of both the particle's speed and the gravitational potential of the particle. dt/dT = 1 only when v = 0 and the gravitational potential also is zero (more on this can be found in Moller's text on general relativity).

 

Pmb

[swansont]

Journal Examples

Apparatus to measure relativistic mass increase' date='[/i'] John W. Luetzelschwab, Am. J. Phys. 71(9), 878, Sept. (2003).

Relativistic mass increase at slow speeds, Gerald Gabrielse, Am. J. Phys. 63(6), 568 (1995).

In defense of relativistic mass, T. R. Sandin, Am. J. Phys. 59(11) 1032 (1991).

A simple relativistic paradox about electrostatic energy, Wolfgang Rindler and Jack Denur, Am. J. Phys. 56(9), Sept. (1988).

An elementary development of mass-energy equivalence, Daniel J. Steck, Frank Rioux, Am. J. Phys. 51(5), May (1983).

A Short Course in General Relativity, Foster & Nightingale, Springer Verlag, (1994).

 

Observed Relativistic Mass Increase for 0.3 eV Electron, G. Gabrielse and H. Dehmelt, Bull., Am. Phys. Soc. 25, 1149 (1980).

 

Yes, as JaKiri surmised, my quick answers were watered down for a mostly non-physicist crowd.

 

But I don't see how you can contend that you are presenting the viewpoint of the "relativity community" with a list of college intro courses, beginner's textbooks and the above list of journal articles - the American Journal of Physics is not a research journal, it is a teaching journal.

 

All you've shown, really, is that some people use it as a teaching tool, or to explain it to the public (e.g the www).

[Pete]

But I don't see how you can contend that you are presenting the viewpoint of the "relativity community" with a list of college intro courses' date=' beginner's textbooks and the above list of journal articles - the American Journal of Physics is not a research journal, it is a teaching journal.

[/quote']And I don't see how you can contend that you're presenting the viewpoint of the "relativity community" by saying that they don't use something which is widely used in the physics literature. I've given you examples from that literature. And these examples are not all from intro college courses. And because the journals I spoke of are teaching journals it can't be taken to mean that they don't reflect the relativity community. In fact it accurately reflects what some relativistists in the relativity people want to relay to students entering the relativity community. I suppose I can go to the research journals but I don't see the point.

 

You say that I've presented a list of college intro courses. That is correct. But that is not the only thing I presented. Many of the texts are quite advanced textbooks. For example if you followed the link to the examples in relativity that I posted they you'll see the following texts listed

 

Relativity: Special, General and Cosmological, Rindler, Oxford Univ., Press, (2001)

Cosmological Physics, John A. Peacock, Cambridge University Press, (1999) [Cosmology text used for MITs graduate cosmology course]

Gravitation, Misner, Thorne and Wheeler, W.H. Freeman & Co., (1973) (MTW)

 

These are advanced special/general relativity texts. I neglected to add

 

General Relativity, Robert W. Wald, University of Chicago Press. This is the GR text which is considered to be the most advanced GR text that is in publication. Note from page 72

However, Posson's equation tells us that

 

del²Phi = 4*pu*rho

 

where rho is the mass (i.e. energy) density of matter ...

One can't call rho mass and also refer to it as energy without it meaning that the mass is relativistic mass.

 

Recall a proof used by MTW on patge 141

Calculate in a specific Lorentz frame. Consider first the momentum density (components T^j0) and the energyt flux (components T 0j). They must be equal because energy = mass ("E = Mc² = M")

 

T^j0 = (energy flux)

 

= (energy density)x(mean velocity of energy flow)j

 

= (mass density)x(mean velocity of mass flow)j

 

= (momentum density) = T^0j

The mass used here is what you call "relativistic "mass." You also neglected to mention that the links I gave are from particle accelerator laboratories, not from intro courses.

All you've shown, really, is that some people use it as a teaching tool, or to explain it to the public (e.g the www).

And you've shown .... what? Why would you think that those research physicists who teach relativity are teaching something that they don't use or expect their students to use? And why would you think that its merely a teaching tool? Simply because its being taught? That could be said about anything that appears in any text. Simply put - a teacher would not teach a student something that they thought to be a bad idea or something that is invalid/meaningless. Also, Jammer's book is on mass from the philosophical point of view. That means it is a book designed to get to the very heart of this topic in physics.

 

You said that the relativity community doesn't use it anymore. It now appears that you mean something different. What is it you mean please? Do you mean that they teach it but don't use it in certain journals?

 

I'd ask you to demonstrate that it doesn't appear in the research literature but that, of course, is an impossible task since one can't prove a negative. Its very important to note that what appears in research journals is quite watered down. By this I mean that you never get to see what thought processes lead research physicists to the end product. The end product rarely, if ever, shows this process, only the end results of the thinking process, not what led the research scientist to his conclusions. It doesn't show what insights he used or where they came from etc.

 

My problem is that I'm disabled at the moment and only gave access to the Am. J. Phys. I'll get to other journals some day and pick through them to see what's there. But whatever it is its quite limited. Research physicists restrict their research to areas like general relativity, cosmology and particle physics. Those areas don't use all the aspects of relativity. I sincelerly doubt that you'd be able to find a journal which discusses the mass of a capacitor. Yet its a legitimate topic. Particle Physicists only deal with objects which can be treated as particles so their use is limited. Plus it is their concern not to study dynamics (where this term is meaningful). They study the inherent properties of particles, such as lifetime, charge, "mass" etc. If you ever see a particle physicist refer to the "lifetime" of a neutron they'll most likely be speaking of the proper lifetime. However proper lifetime and lifetime are two different things which two different meanings and values measured in the lab. But all particle physicists know that the lifetime of a particle is relative whereas the proper lifetime isn't. I see no reason for them to use terms which are inconvenient to them. I expect them to simplify terms. I.e. its simpler to say 'lifetime" so long as everyone unders what it means - proper lifetime. Same with mass. Its simpler to say "mass" rather than "proper mass".

 

Pmb

[Pete]

By the way, some of what I've relayed has come from speaking to research physicists. For example, on this point I once asked a very well-known research physicist if "light has mass" to see his response. He told me that sometimes its useful/helpful to think in those terms. He thinks this stongly enough to teach it to his students in upper level courses at a major "physics university."

 

So let us not neglect how a research physicists thinks and only focus by what appears in his published papers only (not that he leaves it out but I haven't scanned Physical Review D for example for such usage).

 

Pete

[5614]

its amazing how complicated something like 'mass' is, but i think i get it all... thanks

[swansont]

And I don't see how you can contend that you're presenting the viewpoint of the "relativity community" by saying that they don't use something which is widely used in the physics literature.

 

When did I say that I was?

 

And you've shown .... what?

 

Not a whole lot. But I didn't set out to point out a whole lot.

 

5614 asked a question. I gave a quick answer that I thought would help.

 

When I mentioned F=ma' date=' I thought it was implied that I wasn't considering a system where mass was changing. When I mentioned F=GMm/r[sup']2[/sup] I though it was clear that I was looking at things from a classical standpoint. Obviously I was wrong.

 

You want to add to the conversation, great! But there are more constructive ways to do it than to say "that's incorrect" when, in the context I was using, it wasn't incorrect. I also suggest that giving the technically correct answers in terms of tensors and four-vectors isn't going to help as much as you might hope.

 

And when I say that terms like "relativistic mass" aren't generally used, I am basing that on my experience of being a research physicist, because, in my experience, the term isn't used much. If you asked the people with whom I do research what the mass of a photon, is, they'd say, "Zero." Because they take "mass" to be "rest mass"

 

And I see no point in discussing this further.

[YT2095]

Probably all down to Enthusiasm I expect.

 

you`re BOTH very good at your work, and it Shows, Swansont`s been with us a long time and is somewhat more familiar with what terms and levels an answer is expected in.

 

Pmb. although your answers are Great too! and wouldn`t be out of place if Swansont or Jakiri asked them, it`s a little OTT for a basic question

 

 

think Context and Audience, the idea`s to help out and educate, and not Overwhelm

[JaKiri]

"physics university."

 

[Pete]

Pmb. although your answers are Great too! and wouldn`t be out of place if Swansont or Jakiri asked them' date=' it`s a little OTT for a basic question [/quote']I tried to answer a basic question with a basic answer. The first basic question I responded to was

But how can light be influenced by gravity in this way if light, being composed of photons, is massless? Doesn't it require mass to be "heavy"?

And the basic answer I gave was

Light does have mass (aka inertial mass aka relativistic mass). It has zero proper mass (aka rest mass) and that's what you were thinking about.

The second basic question I responded to was

can someone explain the exact difference between:

 

inertial mass' date='

relativistic mass &

rest mass.

[/quote']I responded with the basis answer

The inertial mass of a body is defined as the quantity m such that the quantity mv is conserved in particle collisions as observed from an inertial frame of reference. If you're discussing relativity then some people like to use the term relativistic mass for this same term.

The rest was in response to swan's comments. His responses were about invariants, scalars etc. so II responded to that.

 

Its my experience that people who make the assertions swan did seem to be particle physicists/nuclear/atomic scientists. But such groups have a limited use of relativity, since they rarely do anything which requires speaking of anything other than proper mass. For that reason such groups use only the term "mass" rather than "proper mass" or rest mass and are unaware of what GRists and cosmologists use. I've looked into this one particular subject point in more detail over the years and that research brought me to applications not found in either particle physics, general relativity or cosmology, the main users of relativity.

 

One might have otherwise thought it strange to hear that E = mc² is not always correct. I know that most people would find that fact strange to hear. Yet its true. Its all described in the relativity literature if one knows where to look and it can't be found in particle/GR/cosmology texts etc.

 

I see no point in leaving out interesting points I know of. One can simply feel free to ingore them if they wish.

 

Let me give you an example of certain points I'm refering to; The expression F = ma was not an expression given by Newton. It was given by Euler. For this reason F = ma has been come to be know as Euler's definition of mass. This definition can be used to define what can be called Mach's definition of mass. However Newton's was F = dp/dt. This is the definition used in relativity (the topic of this forum). This yields a definition of mass which has come to be called Weyl's definition of mass. This is the definition I stated above and the one people in relativity use.

 

If a basic question is asked then I'll give a basic response. If that response is objected to or contradicted and I believe that objection/contradiction is incorrect then I'll state so. I see that as the purpose of a discussion forum.

 

Thanks

 

Pmb

[YT2095]

ya know, if I knew anything about Physics, I`de probably come out with something really clever by now, fact is I don`t.

 

HOWEVER... I was appealing to the Diplomatic side in my post. and so... rather that say "Thats Incorrect" wouldn`t it be much nicer to say, yes, and there`s This Also )

 

 

that way we can all get along as one big happy family and stuff

 

 

just an idea

[Pete]

and so... rather that say "Thats Incorrect" wouldn`t it be much nicer to say, yes, and there`s This Also )

When it would apply, sure.

 

I see no reason for someone would take offense at someone saying that something was incorrect. Why would anyone find that offensive???

 

Pete

[Kygron]

I see no reason for someone would take offense at someone saying that something was incorrect. Why would anyone find that offensive???

 

Teasing:

I'm sorry, your question falls beyond the boundaries of GR and I would be unable to answer it in that context. Please post in a more apropriate forum.

[Pete]

Teasing:

I'm sorry' date=' your question falls beyond the boundaries of GR and I would be unable to answer it in that context. Please post in a more apropriate forum.[/quote']

At least it can be said that the question was answered.

 

For those interested in what is actually used you can go to http://www.physicsforums.com and talk to ZapperZ. He is an accelerator physicists at Argonne National Lab who says he uses the so-called relativistic mass. I was wondering how people came to conclude the researches, while they might write about a concept in their text that they don't use it in theor own research. ZapperZ responds

And for whatever it is worth, I used to teach about relativistic mass, and I currently USE relativistic mass for the dynamics in the particle accelerator that I work with. So the assumption that scientists who teach relativistic mass do not use it in their research can be safely thrown out of the window.

 

But then again Steve Carlip (GRist at UC Davis) also claims 'nobody' uses it. sigh!

 

I'll have to wait until I can get to a decent research library and see for myself.

 

Pete

[TrueHeart]

.. they don't reflect the relativity community. In fact it accurately reflects what some relativistists in the relativity people want to relay to students entering the relativity community.

Pmb

That's some impressive relativityping!

[Pete]

That's some impressive relativityping!

What is relativityping?

[TrueHeart]

Typing a message in which every sixth word is some variant of, or akin to, "relativistists". Warning: I'm all caprice, in December!

[Pete]

Typing a message in which every sixth word is some variant of, or akin to, "relativistists". Warning: I'm all caprice, in December!

I see. I this particular case I found it hard not to due to the nature of the subject.

 

Pete

[Pete]

By "physics university" I mean one of the universities which is quite well known for physics. E.g. MIT, Cal Tech, etc.

 

When people say that physicists don't use inertial mass anymore they claim that they use energy instead since "its the same thing". I don't think I gave an example of what that's not true in general. If it was always true that E = m² then one might want to say that this is a definition of inertial mass. But since the correct definition of inertial mass is m p/v then one can defined m as m = E/c² if and only if this expression is true in all possible/concievable cases. If one can give 1 single counter example then such an assertion must be abandoned.

 

A simple example is that of a rod at rest in the inertial frame S'. Let the rod lay on the x' axis and have a force exerted on each end such that the total force is zero. Then the rod does not accelerate in any frame. In this case the realtion E = mc² is invalid. For those of you who understand the math/physics see a related example at

 

http://www.geocities.com/physics_world/sr/rd_paradox.htm

 

I'll make a more explicit example soon and post it.

 

Pete