Phineas T Puddleduck wrote:


For non-relativistic objects

Paddlebutt, you and PD just make up physics as you go
along, doncha? Pray tell us, quick before the Stooges
gallery jumps to help you, what it is you're calling "non-
relativistice objects".

I know what relativistic objects are: figments of your
combined imaginations from the SR subset of relative
motion. Are you saying "non-relativistic objects" are
those real things that we can empirically research?

Newton defined momentum, given the symbol p, as
the product of mass and velocity -- p = m v. When speed becomes
relativistic, we have to modify this definition -- p = gamma (mv)

And just when does speed become relativistic, PQuack?
When it's in your head?

Notice that this equation tells you that for any particle with a non-zero mass,
the momentum gets larger and larger as the speed gets closer to the speed of
light. Such a particle would have *infinite* *momentum* (SNICKER) if it could
reach the speed of light. Since it would take an infinite amount of force (or a
finite force acting over an infinite amount of time) to accelerate a particle
to infinite momentum, we are forced to conclude that a massive particle always
travels at speeds less than the speed of light.

Some text books will introduce the definition m0 for the mass of an object at
rest, calling this the "rest mass" and define the quantity (M = gamma m0) as
the mass of the moving object.

So you're saying here that anyone can arbitrarily make a real
massive object into a massless object at will? I always knew
that Mandrake could do that, but not that physicists or teachers
have the same magical powers.

This makes Newton's definition of momentum still
true provided you choose the correct mass.

Of course, but what if you choose the wrong mass?
Can you fix that with a wave of your Mandrakian wand?

In particle physics,

Oh, you're narrowing your studies to that, are you?

when we talk
about mass we always mean mass of an object at rest and we write it as m and
keep the factor of gamma explicit in the equations.

Which is the same as saying, "We ignore the energy
accruing to the object due to its motion, since it and us
are at constanct velocity wrt each other, and the speed
gamma cancels out." Or, "There is no such thing as an
object at rest, but we can imagine there is some such by
comparing the motion of objects that are moving at the
same speed and direction as we are." There is nothing
invalid about that, unless you claim it represents reality.

Much more dramatically, in modern particle accelerators very powerful electric
fields are used to accelerate electrons, protons and other particles. It is
found in practice that these particles become *heavier* *and* *heavier* as the
speed of light is approached, and hence need greater and greater forces for
further acceleration. Consequently, the speed of light is a natural absolute
speed limit. Particles are accelerated to speeds where their mass is thousands
of times greater than their mass measured at rest, usually called the "rest mass"

Now shall we make it SPNAK 4 for you TG, or are you gonna admit your ignorance.

What ignorance? That has already been covered long
before you got here. It's new to you since you just began
to read about it, but it's old hat to regular poster here. I
would not advise you to waste our time by posting stuff
you just learned.

BTW, how can those particles get heavier and heavier if
they are massless? Oh, that's right - you Stooges have
magic wands!

I think we both know the answer. You can't shut up.

But you can, right?