Re: New version of a relativity FAQ

harry wrote:
"Tom Roberts" <tjroberts137@xxxxxxxxxxxxx> wrote in message news:ABz7k.2385$LG4.608@xxxxxxxxxxxxxxxxxxxxxxx
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" ?

One measures it, of course.

My point here was basically for a single, given object (as my example showed) -- it's mass should be an intrinsic property of the object, and should not vary with its position, velocity, or direction, or which observer is looking at it.

The basic notion that mass is an intrinsic property of
an object directly requires that mass be an invariant.
This disqualifies "relativistic mass" as being mass.


Clearly when atoms bind into molecules, LESS mass is present than before they bound but the same amount of particles is present.

Sure. But then, those atoms are DIFFERENT from those molecules made up of the atoms. And when the atoms combine into molecules, energy is released, and we know in relativity that energy and mass are related. Indeed, apply E=mc^2 to the released energy, and as long as both atoms and molecules are at rest that gives the mass difference.


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?

The resistance of an object to acceleration depends on the direction of the applied force relative to its velocity. The webpage mentions this, but then essentially ignores it.


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

Your words are ambiguous. Yes, the mass of a closed system is directly related to the energy contained within. But the mass of an object does NOT depend on that object's velocity relative to an observer (and hence its kinetic energy as measured by that observer) -- this _IS_ the definition of "mass" used by physicists who use relativity daily, regardless of what this FAQ page claims.


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?

Of course not! Proper length is a property of an object, not whatever length that some arbitrary observer might assign to it.


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).

Indeed, "relativistic mass" is the resistance to acceleration only for one specific case: the magnetic force on a charged particle. This does NOT include the cyclotron, in which the RF accelerating field does not obey that.


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!

Not true! There is no "gamma" for null coordinates (i.e. two light-like coords and two spacelike coords). The 3-vectors ESSENTIAL to this usage have no meaning except in inertial frames, and in GR there are no such inertial frames.


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

As I challenged before: write down the Lagrangian for classical electrodynamics in terms of "relativistic mass" and all those 3-vectors. Then do it for QED. THESE are the sort of problems with which theoretical physicists are concerned; indeed, these are SIMPLE and WELL-KNOWN problems, the real point is to use the known symmetries of the world to find NEW theories. "Relativistic mass" completely abandons the underlying symmetry, and is indeed useless for that; the 4-vectors used by mainstream theoretical physicists make the Lorentz symmetry completely transparent (i.e. one can tell at a glance if one's guessed Lagrangian is Lorentz invariant or not).


The LT do stress symmetries, don't they?

Lorentz transforms do no such thing, at least as taught in most elementary treatments. The Lorentz group, however, does.


Tom Roberts
.

Relevant Pages

  • Quantum Gravity 169.7: Accelerative Energy, Mass Creation, and Origin of the Big Bang
    ... Causes mass. ... This suggests that acceleration itself is one of the contributors to ... So suggests that belongs to a class of energy terms, ... energy and acceleration and force have the same dimensions. ...
    (sci.physics)
  • Re: Stuff I didnt know...
    ... If you applied two equal forces to two objects of differing mass, ... key difference will be rate of acceleration. ... is judged quite simply by measuring energy. ... gravity acts with a greater force to make it accelerate at ...
    (rec.sport.rowing)
  • Re: 100 Years of E=mc2
    ... and you will get tha the altogether in mass is exactly as the ... we can say that both m and c are THE components of energy ... The force *causes* acceleration, ... do you accept that general abstract insight ?? ...
    (sci.physics)
  • Re: ON THE CO-DEPENDENCE OF TIME DILATION, SUPERLUMINAL VELOCITIES, AND RELATIVISTIC MASS
    ... Time Dilation, Relativistic Mass, and c as a limit (Superluminal ... THE IMPORTANCE OF SUPERLUMINAL VELOCITIES. ... I thought it was understood as Einstein posed it --- motion is ...
    (sci.physics.relativity)
  • Re: Question on rocket physics & mechanics [redirected from talk.origins]
    ... assume the chopper goes straight up at a uniform acceleration ... To find the energy, multiply the force mby the distance over ... To go from the helicopter problem to the rocket problem and find the ... the complication of changing mass, ...
    (sci.physics)