Re: Did Einstein Repeal Newton's Second Law?

From: Gregory L. Hansen (glhansen_at_steel.ucs.indiana.edu)
Date: 09/28/04 

Date: Tue, 28 Sep 2004 01:49:09 +0000 (UTC)

In article <qEX5d.258879$dW1.13375555@phobos.telenet-ops.be>,
Dirk Van de moortel <dirkvandemoortel@ThankS-NO-SperM.hotmail.com> wrote:
>
>"Donald Macnaughton" <donmac@matstat.com> wrote in message
>news:iTW5d.1930$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 second law of motion (F = ma) was "repealed" by one of Einstein's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.

Now here's something I don't like about relativistic mass. Suppose you
weren't accelerating something. Suppose you had a sequence of lights
programmed to turn on and off to look like something was accelerating.
Keep the time and distance short so we can define a rest frame valid for
the process, but watch it from a moving frame.

There's no masses, no forces involved, but you still have to be able to
transform it to the moving frame, and a' is not equal to a! You cannot
have a mechanics if you can't get the basic description of motion right,
and if you can transform the acceleration, you don't need relativistic
mass. Relativistic mass gives you a way to pretend your lab-frame system
is really Newtonian. 

-- 
"And don't skimp on the mayonnaise!"

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 ... >and still defined defined momentum p as mass times velocity, ... and if you can transform the acceleration, ...
    (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)
  • 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)
  • 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)
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