Re: Only some energy has mass?

From: Pmb (someone_at_somewhere.com)
Date: 12/06/04 

Date: Mon, 6 Dec 2004 01:57:01 -0500

"Bill Hobba" <bhobba@rubbish.net.au> wrote

> DP wrote and entirely correct and, IMHO, rather good response. Rest mass
is
> invariant and is the M that appears in the free particle lagrangian and
the
> M most physicists mean when they talk about mass in relativity.

I seriously doubt that most physicists mean that. More than 60%? Sure. More
than 80%? I doubt it.

Quantities which appear in relativistic equations such as tensor equations
contain only tensor quantities. Thus you won't see time in a tensor equation
in SR or GR. You'll only see proper time. Particle physicists usually only
speak of proper mass as mass since that's what they study, i.e. the
intrinsic (i.e. proper) quantities of particles. However particle physicists
usually never study anything else except particles. Relativity applies to
everything, not just particles. Therefore they are very limited in their use
of relativity.

Particle physicists also use the term "lifetime" to refer to "proper
lifetime". Proper lifetime is the correct term to use. But its cumbersome.
Since all particle physicists know what each other means by "lifetime" then
its no problem. However if you ask a particle physicist if they believe in
time dilation what do you think they'll say? Therefore they will all use the
term "lifetime" to mean "proper lifetime". Is there any reason to think
they'd do something else for mass? Some still stick with the term "rest
mass". E.g. Thorne and Blanchard use "rest mass" in their new text. I don't
see them use the term "mass" but in the few times they do they mean what you
and others call "relativistic mass". It is also incorrect to assume that
new/modern relativity or new/modern cosmology texts use "mass" only to refer
to proper mass.

There is a common misconception in this newgroup and made by many
physicists - That misconception is to claim that relativistic mass is just
another name for energy. That is incorrect for at least 3 reasons (1) they
represent different things - proportional does not mean identical (2) thing
they are defined differently, thery are merely proprtional in certain cases
as is the energy and frequency of a photon and (3) they are not always
proportional and therefore it fails to meet that criteria of
proportionality, i.e. E = mc^2 = gamma*m_o*c^2 is not always valid. It is
also an error to define the time component of 4-momentum as energy. For that
to be the case it'd have to be true in all cases and it fails to meet that
criteria. This is a noted fact in more complete relativity texts such as
Rindler's Intro to SR text. Its a shame that more authors don't point this
out.

> In fact it
> is the same as the classical mass as required by the fact it reduces to
the
> free particle lagrangian in the non relativistic limit. However in the
> early days of relativity another quantity was defined called the
> relativistic mass - M/sqrt (1 - (v/c)^2) where that M is the rest mass.

As is the case today too.

> It
> is a defined quantity, not something that the physics demands, ...

No branch of science requires any quantity to be given any particular name.
I.e. there is no reason demanded by nature that the proper mass of a
particle is demanded to be "mass".

> ...as physicists
> eventually realized, and its use was abandoned by most if not all
> physicists. Indeed Landau does not even define it in his standard text
The
> Classical Theory of Fields.

That is clearly a bad idea. E.g. take a very simple case of the momentum of
an object subject to external forces. If the object is not a simple particle
then the simple relation E = mc^2 fails to hold if m is proper mass and the
stress in the body due to external forces is non-zero. And the kinetic
energy fails to be K = (gamma-1)mc^2. Although Landau and Lifschitz doesn't
define it doesn't mean that the terminology that they use works in all
cases.

For example: where in that text by Landau and Lifschitz does it tell you
that E = gamma*m_o*c^2 is not always valid? Where do they explain that the
ration p/v is a function of the stress in the rest frame, even when the
total force in the rest frame is not zero?

Pmb

Relevant Pages

  • Re: Only some energy has mass?
    ... >> M most physicists mean when they talk about mass in relativity. ... Particle physicists usually only ...
    (sci.physics)
  • Re: Only some energy has mass?
    ... >> M most physicists mean when they talk about mass in relativity. ... Particle physicists usually only ...
    (sci.physics.relativity)
  • Re: Only some energy has mass?
    ... >> M most physicists mean when they talk about mass in relativity. ... > proper time on clocks of a specific frame of reference. ...
    (sci.physics)
  • Re: Only some energy has mass?
    ... >> M most physicists mean when they talk about mass in relativity. ... > proper time on clocks of a specific frame of reference. ...
    (sci.physics.relativity)
  • Re: Physics and Geometry. / My opinion./
    ... By studying the effect of thermodynamics, physicists came to the ... began to study one individual particle. ... There is no mass in Planck's radiation formula or Einstein's description of the photoelectric effect. ... physicists used Euclidian geometry ...
    (rec.org.mensa)