Re: De Broglie's Mistake
- From: "srp" <srp@xxxxxxxxxxxx>
- Date: Tue, 16 Aug 2005 22:32:03 GMT
"OsherD" <mdoctorow@xxxxxxxxxxx> a écrit dans le message de news:
1124204971.502300.304630@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> >From Osher Doctorow mdoctorow@xxxxxxxxxxx
>
> COPYRIGHT NOTICE
> De Broglie's Mistake
> Copyright By Owner Osher Doctorow Ph.D.
> First Published 2005
>
> Prince Louis de Broglie is considered to have given the major impetus
> to quantum theory beyond Planck and Einstein with his equation:
>
> 1) lambda = h/p
>
> where lambda is the wavelength and p the momentum of a particle.
> Wavelength is also known as period (T), or time for one complete cycle
> or vibration of wave motion. However, from the circular representation
> of harmonic motion, the period T is an angle theta made by a moving
> point moving with constant angular velocity w along a circle in the x-y
> plane, the angle being that between the radius vector and the positive
> unit x-axis vector, and the frequency f or number of complete
> vibrations per unit time is:
>
> 2) f = 1/T
>
> or in the quantum theory (e.g., for light), writing f = nu (which I'll
> abbreviate to v):
>
> 3) v = c/T
>
> The circular representation shows that the angle T or theta is related
> to a displacement and to a position x on the x axis with the circle
> centered at the origin, namely position x is the projection of the
> point on the circle onto the x axis immediately below it, and x moves
> to left or right as the point on the circle moves counterclockwise or
> clockwise respectively for example along the circle. Calling the
> moving point on the cicle Q and the projection at x P, P makes one
> complete "vibration" (back and forth motion) for each revolution of Q,
> and so v or f is also the number of such vibrations as horizontal (x)
> displacements represented by position x, as well as the number of
> complete revolutions T per unit time.
>
> The above construction is well known, but it is usually not realized
> that x as position is as accurate a description as x as displacement
> with the circle centered at the origin. If w is the angular velocity,
> we have:
>
> 4) T = theta = wt
> 5) x = R cos(wt), R radius of circle
>
> If we cumulate or add /x/ as the total distance travelled by P, this
> total distance increases linearly proportional to time t, and hence it
> is "arbitrary" whether we consider that time or distance is involved,
> and if the distances are cumulatively strung along the x axis
> successively, it is also arbitrary whether time or position is involved
> in regard to the latter scenario. This is despite the fact that:
>
> 6) w = v = 2pi f
> 7) x = R cos(2pi f)
>
> since there are 2pi radians in a complete revolution.
>
> Let's write x for position rather than using some symbol for cumulative
> /x/ as above, in which case De Broglie's equation (1) becomes:
>
> 8) x = k/p
>
> or:
>
> 9) xp = k
>
> where k is a positive constant which is very small. This is the Weak
> Heisenberg Uncertainty Principle that I defined in my last few threads.
>
>
> Why didn't anybody notice this? The objects or "wave-particles"
> involved are not visual for us as macroscopic observers! Microscopic
> or quantum physics is one step removed from direct observation!
> Moreover, the "convention" that there is no real trajectory even though
> harmonic and trigonometric machinery is used almost impels one to
> ignore displacement and distance in the above scenario! Finally, it
> could be argued that there is something less "real" about x or /x/
> cumulated than about t, but this is silly since time is even less
> directly "observed" than space at the quantum level if not equally!
>
> Isn't projection one step removed from circular motion, and isn't
> circular motion one step removed from simple harmonic or general wave
> motion? This is irrelevant since the question is whether spatial (x
> axis) or time scales should be used. The point is that a spatial scale
> for x is as "valid" as using time t in de Broglie's equation.
>
> Osher Doctorow
>
I am wondering as to where you see a mistake by de Broglie here.
Could you elaborate?
It seems to me that as long as you use p, you are really using m_0 and
v_bohr,
the product of which is a constant by definition.
It also seems to me that what really matters with the de Broglie equation
is that an electron with the energy induced in the ground state, even if it
is
free moving, will move at velocity lambda_bohr * f, which is 2187691.252 m/s
if you calculate classical, or alternately 2187647.561 m/s if you calculate
relativistic.
André Michaud
.
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