relativistic mass
Joshua C. Sierles
and the FAQ informed that the "relativistic mass" concept, that mass increases
in a movingobject, relating to m=E / c^2, is obsolete and somewhat popularist.
I have seen no indication that Einstein's equation does not show that mass
increases with, say, increasing velocity.What exactly is the reason for
teaching E=mc^2 if the standard definition of mass isa non-variant one? I
speculate that there is no definite answer to this, but as many as possibleare
appreciated. :)
Erik Max Francis
> I have a question regarding the recently posted FAQ. I am a first year physic
> and the FAQ informed that the "relativistic mass" concept, that mass increase
> in a movingobject, relating to m=E / c^2, is obsolete and somewhat popularist
> I have seen no indication that Einstein's equation does not show that mass
> increases with, say, increasing velocity.What exactly is the reason for
> teaching E=mc^2 if the standard definition of mass isa non-variant one? I
> speculate that there is no definite answer to this, but as many as possiblear
> appreciated. :)
I'm no expert, but I'd be perfectly happy to speculate.
Relativistic mass seems often to be taught as an easy-to-understand
introduction to special relativity. It goes something like this:
"You know that m we always used in our equations? Well, it turns out
that it's in fact dependent on velocity, v. So instead of using m,
use u (the relativistic mass), and now you know special relativity."
[I use 'u' for relativistic mass because it tends not to look like a
mass.]
Unfortunately, this doesn't work. The naive substitution of u for m
in the equations of Newtonian mechanics works in a few limited cases,
but generally does not -- K = (1/2) m v^2 or F = m a (vector form) are
obvious examples. The matter of this confusion is very evident in
recent discussions on sci.physics concerning the different and
interrelation of (rest) mass, momentum, and energy.
With special relativity, there's a lot more to learn than just new
equations; relativity involves an entirely new mindset, one which a
mere upgrading of Newtonian mechanics won't provide.
In my opinion it's much better to simply yank the rug and start over
with special relativity. The relativistic mass only serves to
confuse, and additionally serves no useful purpose; it's just another
name for energy. Don't say p = m v, say p = m v gamma. Don't say F =
m a, say F = dp/dt.
Erik Max Francis, &tSftDotIotE ...!uuwest!alcyone!max m...@alcyone.darkside.com
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Joe Lavelle
>name for energy. Don't say p = m v, say p = m v gamma. Don't say F =
>m a, say F = dp/dt.
you much, is that the force law is F= dp/dt, not F= ma.
In view of the relativity of simultanaety, newton's third law doesnt hold.
Mike Kelsey
|> Erik Max Francis <m...@alcyone.darkside.com> writes:
|>
|> >name for energy. Don't say p = m v, say p = m v gamma. Don't say F =
|> >m a, say F = dp/dt.
|>
|> In my view, this is a wise response. The reason relativistic mass won't help
|> you much, is that the force law is F= dp/dt, not F= ma.
Right. Although, technically, the force law is F = dp/dt in Newtonian
mechanics as well -- remember the rocket equation? There, you have both v
_and_ m varying with time, so the force law goes F = m dv/dt + (dm/dt) v.
|> In view of the relativity of simultanaety, newton's third law doesnt hold.
Not true. Newton's third law (action and reaction) is a statement about
opposing forces at a point, or contact forces. It says nothing about forces
which are separated by a distance. A contact force-pair (you pushing down
on the floor, the floor pushing up at you), is always simultaneous in any
frame, since the force-pair is "generated" at a single event point, so the
interval "between" the forces is identically zero, component by component.
-- Mike Kelsey
--
[ My opinions are not endorsed by SLAC, Caltech, or the US government ]
"I've seen things you people wouldn't believe. Attack ships on fire
off the shoulder of Orion. I've watched C-beams glitter in the dark
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Olaf Deppe
: Mass increases with velocity... This is because, as an object
: increases its velocity, it also increases its kinetic energy.
: As we all know, from E=mc^2 , mass and energy can be converted
: into one another... The KE the object pics up is converted
: into mass: this is where the delta-m comes from.
Joshua Sierles <j...@mcs.com> writes:
: I have a question regarding the recently posted FAQ. I am a first year physic
: and the FAQ informed that the "relativistic mass" concept, that mass increase
: in a movingobject, relating to m=E / c^2, is obsolete and somewhat popularist
: I have seen no indication that Einstein's equation does not show that mass
: increases with, say, increasing velocity. What exactly is the reason for
: teaching E=mc^2 if the standard definition of mass isa non-variant one? I
: speculate that there is no definite answer to this, but as many as possiblear
: appreciated. :)
The thing is fairly simple: E=mc^2 describes the _rest_ energy of a
particle. If the particle is in motion with respect to you, its
momentum must be added to the energy in quadrature: E^2 = (mc^2)^2 + (pc)^2
Ok, E=mc^2 says that energy and mass are actually the same. But its a
good convention, to call only the rest energy mass (in high energy physics
you usually set c=1, yielding E^2 = m^2 + p^2), since this quantity we
need to connect the energy of a particle with its momentum.
Olaf
George B. Haff
Mass increases with velocity... This is because, as an object increases
its velocity, it also increases its kinetic energy. As we all know, from
E=mc^2 , mass and energy can be converted into one another... The KE the
object pics up is converted into mass: this is where the delta-m comes from.
<i am pretty sure>
<sorry if i'm wrong>
-George
John Palkovic
George> Mass increases with velocity... This is because, as an object
George> increases its velocity, it also increases its kinetic energy.
George> As we all know, from E=mc^2 , mass and energy can be converted
George> into one another... The KE the object pics up is converted
George> into mass: this is where the delta-m comes from.
Tis a far, far better thing when mass is a Lorentz invariant quantity.
Unbelieving amateurs should read the sci.physics FAQ Item 28, it is
right on (kudos to Scott Chase and Matt Austern). If you are not
swayed by the FAQ, then look up the reference by Prof. Okun that it
gives.
As others have said, why make mass velocity dependent? It serves no
useful purpose.
George> <sorry if i'm wrong>
You are.
-John
--
palk...@desy.de Deutsches Elektronen-Synchrotron, Relativity Engineering
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Matt McIrvin
Erik Max Francis <m...@alcyone.darkside.com> wrote:
>In my opinion it's much better to simply yank the rug and start over
>with special relativity. The relativistic mass only serves to
>confuse, and additionally serves no useful purpose; it's just another
>name for energy. Don't say p = m v, say p = m v gamma. Don't say F =
>m a, say F = dp/dt.
Or, even better, say p = mv and F = ma, where p, v, F, and a are
the relevant four-vectors!
--
Matt 01234567 <-- Indent-o-Meter
McIrvin ^ Harnessing tab damage for peaceful ends!