Re: where does newtons laws fail
- From: "Harry" <harald.vanlintel@xxxxxxx>
- Date: Fri, 23 Sep 2005 19:59:10 +0000 (UTC)
<markwh04@xxxxxxxxx> wrote in message
news:1127253670.841926.51930@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> jaan wrote:
> > iam really searching for the answer where does newtons laws fail.
>
> The infrastructure underlying Newton's Laws fails -- that is: the
> structure of its spacetime.
I'm not sure what is meant above with "Newton's spacetime", but in fact,
*apparent* ("observed") space and time in Newton's theory fail at high
speeds. One should not confuse transformation rules for observation with the
underlying concepts about possible causes.
The deviation between observation and prediction was corrected by Lorentz,
and with that correction (leading to the Lorentz transformations), Newton's
concept of hidden absolute space and time(=process durations) seems to work
perfectly well for non-quantum events.
About his laws:
With the post-Einstein concept of relativistic mass increase it's not
necessary to retrofit Newton's force law F=d(m*v)/dt to Minkowski spacetime,
as with m=gamma*m_0 it works fine as it stands (that's how I learned it,
from the physics text book of Alonso&Finn, 1978). Relativistic mass implies
choosing Newton's dynamic definition of mass as the definition of mass.
There is a never settled debate about Newton's third law. It's often assumed
to fail, but experimental confirmation is lacking.
Thus with the Lorentz transformations and a convenient definition of mass,
Newton's laws of physics work for any speed in any inertial frame just as
they did for low speeds with the Galilean transformations.
Perhaps Newton's laws fail in quantum mechanics, but I'm not knowledgable on
that subject.
Best regards,
Harald
> Use the word "event" in the following to denote that which is
> characterized by a position and time -- a point-instant.
>
> Newton's laws presume a spacetime amongst whose features includes the
> following ones of significance:
>
> * Spacetime has the form of a sequence of 3-dimensional snapshots, each
> representing "space" at a given "time"
>
> * The past of any event is ALL of space on all the snapshots preceding
> that which the event lies on
>
> * The future of any event is ALL of space on all the snapshots
> preceding that which the event lies on
>
> * A hypothetical object travelling at an infinite speed in one frame of
> reference would be doing so in all frames of reference. Infinity is an
> invariant speed. All finite speeds are relative.
>
> * To say the same thing another way: two events simultaneous in one
> frame of reference are simultaneous in all frames of reference.
>
> * To say the same thing a third way: for a given event, the
> neither-past-nor-future of the event comprises a 3-dimensional space --
> namely, the snapshot the event lies on.
>
> * To say the same thing a fourth way: if A, B, C are events and A is
> neither past nor future of B, B is neither past nor future of C, then A
> is neither past nor future of C.
>
> The contrast to Relativity is this:
> * The past of any event is a sphere (and its inside) that contracts
> down at light speed to the event, itself -- the past light cone of the
> event.
>
> * The future of the event is a sphere (and its inside) that expands at
> light speed from the event, itself -- the future light cone of the
> event.
>
> * The invariant speed is FINITE. Not all finite speeds are relative,
> which makes the name "Relativity" of the theory entirely inappropriate,
> as Einstein pointed out early on.
>
> * Infinity is NOT an invariant speed, it's relative.
>
> * The neither-past-nor-future of a given event is a FOUR dimensional
> continuum -- namely the outside of the past and future light cones of
> the event.
>
> * It is possible for A, B, C to be events with A neither before nor
> after
> B, B neither before nor after C, but A before C. (Example: A = the
> Earth at a specific time, C = the Earth 1 second later; B = the Moon at
> one of a specific range of times within the approximate 2 second window
> of its existence that lies outside the light cones of A and C).
>
> The two spacetimes are known, respectively, as Galilean and Minkowski
> spacetime.
>
> In the process of trying to retrofit Newton's Laws to Minkowski
> spacetime, this forces the concepts of energy and momentum to be
> unified into a single entity -- the 4-momentum. The law of inertia has
> to be suitably modified and extended; with the additional condition
> that a quantity, U, of energy must be associated with a mass equal to
> U/c^2, where c is light speed.
>
> In Newtonian spacetime, the two separate concepts of kinetic energy
> (Lagrangian and Hamiltonian) for a body are equal, the equivalence
> expressed by L = H; where L and H are related by the Legendre transform
> H = pv - L, and the momentum and velocity by the relation p = mv.
>
> This implies that L = mv^2/2; H = p^2/2m.
>
> In Relativity, these two concepts split. The Hamiltonian is larger
> than the Lagrangian, since it also includes the contribution provided
> by the mass equivalent of the total energy of the Hamiltonian, itself.
> So, they lie in a ratio, H/(m + H/c^2) = L/m, where m is the rest mass
> of the body.
>
> Likewise, the momentum carries this additional contribution: p = (m +
> H/c^2) v.
>
> Since L and H are related by the Legendre transform, H = pv - L, this
> implies that
> H/(m + H/c^2) = L/m; L = (m + H/c^2)v^2 - H
> whose solution is
> L = mv^2/(1 + (1 - (v/c)^2)^{1/2})
> = mc^2 - mc^2 (1 - (v/c)^2)^{1/2}
>
> H = p^2/((p/c)^2 + m^2)^{1/2} + m)
> = mc^2/(1 - (v/c)^2)^{1/2} - mc^2.
> So, it's natural to identify mc^2 as the rest energy of the body and
> equate the total kinetic energy to H + mc^2, which is
> E = H + mc^2 = mc^2/(1 - (v/c)^2)^{1/2}.
> The momentum is thus
> p = mv/(1 - (v/c)^2)^{1/2}
> and (E, p) form the components of the momentum 4-vector.
>
.
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