Re: New version of a relativity FAQ


"Tom Roberts" <tjroberts137@xxxxxxxxxxxxx> wrote in message
news:ABz7k.2385$LG4.608@xxxxxxxxxxxxxxxxxxxxxxx
Pmb wrote:
A new version of the FAQ "Does mass increase with speed?" was written and
is now online at
http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html

This is a well written article on this whole relativistic mass thing. The
author makes a great point
-------------------------------------------------------------------------------
A common argument against the use of relativistic mass is the fact that
the equation E=mc^2 says that a body's relativistic mass equals its total
energy, so why should we use two terms for what is essentially the same
quantity? We
should just stay with energy, and use the word "mass" to refer only to
rest mass. But this argument neglects the definitions of the words mass
and energy. Mass is a property of a body that we have an intuitive feel
for;
its definition as a resistance to acceleration is very fundamental.
Energy, on the other hand, is defined in physics in rather ad hoc ways.
Neither concept is even remotely understood by modern physics.
-------------------------------------------------------------------------------

I think we're going to have to review changes to the FAQ more carefully.
This page now just mentions a few straw-man objections to "relativistic
mass", and does not discuss at all the actual reason why "mass" is best
considered to be an invariant. And worse: it is internally inconsistent in
just this area.

For instance, I would not say "[mass's] definition as a resistance to
acceleration is very fundamental", I would say its definition as "how much
'stuff' is present" is more fundamental. "relativistic mass" does not obey
this, but the usual terminology does.

And how would you decide ""how much 'stuff' is present" ? Clearly when atoms
bind into molecules, LESS mass is present than before they bound but the
same amount of particles is present. I agree that it may be useful to put in
your argument but of course with the counter argument.

In the physics 101 I took many years ago, the example given
was to differentiate mass from weight, as the former should
not vary with position, but for a given object the latter
diminishes at the top of a mountain or in orbit. Having
"mass" vary with velocity is equally inappropriate, as is
having it vary with direction.

Why would it vary with direction? Did you mean "position" perhaps?

"How much stuff is present"
is CLEARLY independent of such variations.

See above - nobody uses a mass definition that doesn't change with energy.

A more serious objection is that the author says "Mass is a property of a
body" (which I agree with), but "relativistic mass" IS NOT A PROPERTY OF A
BODY (it varies with the body's motion and its physical situation). This
article is internally self-inconsistent.

Hmm, he more or less defines what he means with that between the brackets.
Would you say that (relativistic) length is a property of a body? If yes,
why? If no, why not, and why would this be self-inconsistent with its use?

Another inconsistency: "resistance to acceleration" is dependent on the
direction of the applied force, but "relativistic mass" is not direction
dependent. The author has abandoned his own "very fundamental" definition.

Indeed: he should clarify somewhere that relativistic mass only is a measure
for resistance to acceleration when it remains constant, such as in a
cyclotron (which was the preferred definition of Feynman).

Like PMB, tears come to my eyes from this page :-). But not
because of its relationship to my personal beliefs (which PMB
calls "quality of writing"), but rather because it is internally
inconsistent and therefore wrong.

Just tell him about the errors; if you are convincing, I'm sure he'll
improve it. :-)

And it is wrong in subtle
ways that can easily confuse its target audience. That is
diametrically opposed to the purpose of a FAQ page.

The old version was wrong in subtle AND not-so-subtle ways...

The first paragraph ends "which concept is more useful?", but the article
only mentions elementary uses and never touches on the real issue: the
relationship between kinematics and dynamics.

Perhaps you want to add that?

The underlying question is: What is the best way to generalize terminology
and concepts from Newtonian physics to relativity? Note I said
"relativity", not "SR", and that is an important aspect of this.

The fact that c is not a universal constant as in SRT makes the relationship
E=m*c^2 more meaningful.

There are two very different generalizations:

The one which has become standard:

Term Newton SR GR
------- ------------ ---------- ----------
velocity 3-vector 4-vector 4-vector
momentum m*v m*V m*V
mass invariant invariant invariant
force 3-vector 4-vector 4-vector
acceleration 3-vector 4-vector 4-vector

And the one that article advocate:

Term Newton SR GR [*]
------- ------------ ---------- ----------
velocity 3-vector 3-"vector" (none)
momentum m*v gamma*m*v (none)
mass invariant gamma*m (none)
force 3-vector 3-"vector" (none)
acceleration 3-vector "matrix mess" (none)

[*] These are not discussed at all, and I base them on the
fact that in GR any coordinates are equally valid.

I would be surprised if that is right - almost certainly all equations can
be written in terms of gamma*m!

Note, please, that these terms are those that appear in the DYNAMICS of a
physical theory, but their definitions are KINEMATICAL. The whole point of
kinematics is to make the dynamics simpler by making fundamental
symmetries be incorporated into the terminology and notation.

Hmm... that reminds me of some articles by Harvey Brown, such as:
http://philsci-archive.pitt.edu/archive/00001385/01/9908048.pdf

This second table completely abandons that.

It is your table. ;-)

I challenge advocates of this second table to write down the Lagrangian of
classical electrodynamics using those quantities, and compare to the
standard formulas. Then for extra credit try the Lagrangian of QED (this
will be exceedingly perverse, and I'll be surprised if it fits on one
page).

Comparing these tables shows why the standard terminology has become
standard. "Relativistic mass" and the other entries in the second table
are of use ONLY pedagogically, and ONLY in teaching elementary SR. They
are essentially useless in advanced SR

?? Please give an example of a real-world problem where relativistic mass is
"essentially useless".

and in real physical theories like QED and GR, beause those definitions do
NOT reflect the underlying kinematical symmetry (local Lorentz
invariance); the standard meanings do reflect it, which is at base why
they are so much better. And I challenge the pedagogical use of
"relativistic mass" -- IMHO stressing symmetries is an EXTREMELY important
part of teaching physics.

The LT do stress symmetries, don't they?

Remember in Newtonian mechanics different 3-vectors
transform differently under boosts, but in SR all 4-vectors
transform identically. This gets amplified in the differences
between the two tables, and the "matrix mess" for acceleration
is truly perverse compared to the transformation of
4-acceleration. But that is minor compared to the complexity
of writing dynamical equations using the second table, and
the difficulty of generalizing them to GR....

At the turn of the last century J.W. Gibbs went on a crusade to establish
the 3-vector notation we all use today. My arguments are quite similar to
his: the notation should reflect the underlying symmetry. Gibbs obviously
won that dispute; I have no doubt about a similar ultimate result of this
terminological and notational dispute. For the same reasons.

I think this page needs to be re-written again. It should discuss the
origins of the terms "mass" and "relativistic mass", and why the latter
has gone out of favor in research and advanced classrooms, and why the
current terminology is better -- it simplifies the DYNAMICS of any
relativistic theory by making the KINEMATICAL relationships obey the
underlying symmetry. As is, it takes a rather superficial and elementary
viewpoint.

As long as the old errors are not reintroduced (or new errors!), that's fine
of course. :-)

Cheers,
Harald


.

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