Re: Did Einstein Repeal Newton's Second Law?

From: Bill Hobba (bhobba_at_rubbish.net.au)
Date: 09/27/04 

Date: Mon, 27 Sep 2004 21:20:31 GMT

"Dirk Van de moortel" <dirkvandemoortel@ThankS-NO-SperM.hotmail.com> wrote
in message news:qEX5d.258879$dW1.13375555@phobos.telenet-ops.be...
>
> "Donald Macnaughton" <donmac@matstat.com> wrote in message
news:iTW5d.1930$tT2.384584@news20.bellglobal.com...
> > I'm a statistician, not a physicist. In an essay I'm writing
> > about scientific reasoning I would like to say whether Newton's
> > second law of motion (F = ma) was "repealed" by one of Einstein's
> > two theories of relativity. However, although I've done some
> > digging, I haven't found a good discussion of this topic. So I
> > have the following questions:
> >
> > 1. Does one of Einstein's theories repeal (or modify) Newton's
> > second law? If so, how? If not, do Einstein's theories take
> > Newton's second law as a given?
>
> A partial answer:
>
> Actually Newton's second law does not give force as mass
> times acceleration,
> F = m a
> but as the time derivative of momentum,
> F = dp/dt
>
> Newton defined momentum p as mass times velocity
> p = m v
> and velocity v as
> v = ds/dt
> hence, when mass is invariant or constant, the force is given by
> F = m dv/dt
> = m a
>
> Einstein treated mass M as dependent on the so-called rest-mass m
> and the velocity v:
> M = gamma m
> where
> gamma = 1 / sqrt( 1 - v^2/c^2 )
> so he kept Newton's second law
> F = dp/dt
> and still defined defined momentum p as mass times velocity,
> p = M v
> = gamma m v.
>
> So we could say that Einstein did not change Newton's second law,
> but he used another defintion of mass.

Interesting take and I see your logic. However modern treatments use the
lagrangian approach. In that approach as espoused by Landau - Classical
Theory of Fields page 24 the most geranial lagrangian consistent with SR is
L = alpha sqrt (1 - v2) (units c =1). When one takes the classical limit
(ie L = alpha - alpha v2/2) it turns out that alpha = -M to be consistant
with the classical lagrangian Mv2/2. Thus from that point of view it could
be argued exactly the same definition of mass was used.

Thanks
Bill

>
> The force is now given by
> F = d(M v)/dt
> = m d(gamma v)/dt
> = m d(gamma v)/dt
> = m [ gamma dv/dt + v d(gamma)/dt ]
> = m gamma [ 1 + gamma^2 v^2 ] a
> = m gamma^3 a
> This is only valid when the acceleration has the same direction
> as the velocity. [For other direction, see article below].
>
> Nowadays this "relativistic mass" M is a bit out of fashion, and
> momentum is *directly* defined as
> p = gamma m v.
>
> You will find a very good read in this FAQ article:
>
http://hermes.physics.adelaide.edu.au/~dkoks/Faq/Relativity/SR/mass.html
>
> Hth,
> Dirk Vdm
>
> >
> > 2. If Newton's second law is repealed, does the repeal depend on
> > the assumption of the equivalence of inertial and gravita-
> > tional mass? If we no longer make this assumption, do things
> > change?
> >
> > 3. Is it possible to build viable models in which Newton's second
> > law always holds and viable models in which the law sometimes
> > doesn't hold? (The type of model might be controlled by con-
> > trolling the order in which physical concepts are introduced
> > in a formal development.) If so, which type is preferred?
> >
> > Citations of books or articles about these ideas are also wel-
> > come. Thank you.
>
>
>

Relevant Pages

  • Re: Did Einstein Repeal Newtons Second Law?
    ... > Newton's second law as a given? ... Actually Newton's second law does not give force as mass ... Newton defined momentum p as mass times velocity ...
    (sci.physics)
  • Re: Did Einstein Repeal Newtons Second Law?
    ... > Newton's second law as a given? ... Actually Newton's second law does not give force as mass ... Newton defined momentum p as mass times velocity ...
    (sci.physics.relativity)
  • Re: Did Einstein Repeal Newtons Second Law?
    ... >> Newton's second law as a given? ... > Actually Newton's second law does not give force as mass ... > and still defined defined momentum p as mass times velocity, ... Theory of Fields page 24 the most geranial lagrangian consistent with SR is ...
    (sci.physics.relativity)
  • Re: Did Einstein Repeal Newtons Second Law?
    ... >> Newton's second law as a given? ... > Actually Newton's second law does not give force as mass ... > Newton defined momentum p as mass times velocity ... > and still defined defined momentum p as mass times velocity, ...
    (sci.physics)
  • Re: Feynman Lectures and Physics Teaching.
    ... bits of cheese - we can combine them together to create double the mass and ... so check Newton's second law. ... Lagrangian that yields the field equations is accepted for the face ... circular under the current interpretation to GR. ...
    (sci.physics.relativity)