Re: Did Einstein Repeal Newton's Second Law?

From: Bjoern Feuerbacher (feuerbac_at_thphys.uni-heidelberg.de)
Date: 09/27/04 

Date: Mon, 27 Sep 2004 19:15:59 +0200

Dirk Van de moortel 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second law of motion (F = ma) was "repealed" by one of Einstein's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.
>
> 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

[snip]

Both you are Gregory talk only about Special Relativity, as far as
I can see. But what about General Relativity? It changes Newton's
first law, doesn't it? So, shouldn't the second law also be changed?

Bye,
Bjoern

Relevant Pages

  • Re: Did Einstein Repeal Newtons Second Law?
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  • Re: Did Einstein Repeal Newtons Second Law?
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    (sci.physics)
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