Re: The planet orbiting Algol.

In sci.physics.relativity, HW@..(Henri Wilson)
<HW@>
wrote
on Sat, 19 Nov 2005 21:46:48 GMT
<7f6vn15t64pn1l3451m1coperalopn8upq@xxxxxxx>:
> On Fri, 18 Nov 2005 03:30:33 GMT, The Ghost In The Machine
> <ewill@xxxxxxxxxxxxxxxxxxxxxxx> wrote:
>
>>In sci.physics.relativity, Paul B. Andersen
>><paul.b.andersen@xxxxxxxxxxxxxxxx>
>
>>> If c is the initial speed of the photon and c' is the speed
>>> when it has fallen a distance h, then we according to NM have:
>>>
>>> c'^2 - c^2 = 2gh
>>> (c'/c)^2 = 1 + 2gh/c^2
>>> c'/c = sqrt(1 + 2gh/c^2) = ca. (1 + gh/c^2)
>>>
>>> But what is the frequency?
>>> In your (correct) calculation you assumed that the frequency
>>> of the photon is defined by E = hf.
>>
>>Hm...yes, I did assume that. I guess at the time I figured
>>that it was far easier to measure the energy of a photon
>>than its frequency.
>>
>>Or something.
>
> Nobody has ever associated an intrinsic frequency with a single photon.

OK.

In any event, I'm not sure I care all that much about the
frequency; the energy is much more useful. It's
what knocks out the electrons in various experiments
and in our eyeballs as we watch TV, for example.

>
>>
>>> But Henri claims that the BaTh predicts a Doppler shift
>>> f' = f(c+v)c = fc'/c,
>>
>>I could see a Newtonian theory predicting changes in
>>*wavelength*, though I'm not sure about the frequency.
>
> No Ghost. Wavelength remains the same under the BaTh.
> Frequency is a measure of the 'number of wavecrests arriving per second' at an
> observer.
>
>>Of course v = lambda * nu or w * f anyway (I use 'w' instead
>>of 'l' for readability; damned ASCII); if one assumes
>>f'/f = c'/c, then w' = w by necessity.
>
> No it doesn't.
> w is constant. Use my 'sawblade' model.
> the faster you move the saw, the higher the frequency of
> teeth passing a point.
> ..but the tooth separation doesn't change.
>
>>
>>Now consider the static curve
>>
>>y = sin (2 * pi * x / w)
>>
>>which is of course a curve that oscillates around the X axis,
>>impacting it at 0, w/2, w, etc.
>>
>>If one introduces a third dimension, one gets a moving curve, perhaps:
>>
>>y = sin(2 * pi * (x-ct)/w)
>>
>>which is basically having the curve move at lightspeed (which
>>for purposes of this exercise is an arbitrary speed c).
>>
>>And now for the coordinate shift. If we take the Galilean transform
>>
>>x' = x - vt
>>y' = y
>>t' = t
>>
>>the equation becomes
>>
>>y' = sin(2 * pi * (x' + vt' - ct')/w)
>>
>>which is clearly a curve of wavelength w and velocity c-v.
>>
>>Hmmm. OK, I'm wrong, I admit it. :-) The wavelength
>>did not change at all.
>
> good.
>
>>
>>I'm tempted to throw the Lorentz at this curve but it
>>will probably only make a mess... :-)
>>
>>But now let's look at the frequency. If we set x = 0,
>>we should get a good measurement, and it turns out
>>
>>y_0 = sin(-2 * pi * ct/w)
>>
>>which means that for the original curve the frequency is c/w.
>>If we take the shifted equation, we get
>>
>>y_0' = sin(-2 * pi * (c-v)t/w)
>>
>>which means that the frequency is (c-v)/w, and f'/f = (c-v)/c.
>>
>>Of course, one can reverse v, and get f'/f = (c+v)/c in that
>>case -- Henri's equation.
>
> Good.
>>
>>
>>> and has then implicitly defined the frequency of
>>> a photon as being proportional to its speed.
>>> With this definition, we get the BaTh to predict:
>>> f' = f(1 + gh/c^2).
>>>
>>> The big problem with this definition is of course
>>> that then the energy of a "BaTh photon" must be:
>>> E = const*sqrt(f).
>>
>>Since in Newtonian mechanics E = 1/2 m v^2, where m is
>>a rather abstract quantity in the case of light,
>>E'/E would have to be proportional to the square
>>of the new velocity over the old were energy solely dependent
>>on wavelength and speed (since the wavelength is unchanged
>>in this theory). In other words,
>>
>>E'/E = (c+v)^2/c^2
>
> No there is still an 'h.c/w' term.
> I would say energy of light moving at c+v goes something like
> [h.c/w + (some function of v^2)]

OK, E = hc/w + f(v^2), where f() is a function. SR contends that
f(v^2) = 0. Did you want to define f()?

>
>>
>>If energy be solely dependent on frequency and speed,
>>E'/E = (c+v)^2/c^2 * (c/(c+v)) = (c+v)/c = f'/f.
>
> Don't use 'frequency' Ghost. The correct equation is E=hc/w

The correct equation (if there is one using this particular
form -- but remember that light is not traveling at speed
c in this theory) is E = h(c+v)/w. In SR v = 0, of course.
It gets more complicated since E also is equal to 1/2 m (c+v)^2.
This means of course m = 2E/v^2 = 2h/((c+v)w), giving that light
photon a variable mass.

If one goes with E = hc/w one gets m = 2hc/(w(c+v)^2) and it's
*still* a variable mass.

If one goes with E = hc/w + f(v^2), one gets
m = 2hc/(w(c+v)^2) + 2f(v^2)/v^2. Since f(v^2) is a function
call I can draw no conclusions about m's variability here.

I suppose one might show this as very weak evidence of a
back-EMF of some sort but this is getting a tad ridiculous.

>
>>Since E = hf anyway, the latter is consistent with SR
>>and experimental measurement. Unfortunately it
>>leads to that pesky 2 factor in the Pound-Rebka experiment.
>
> Paul said it didn't. You were wrong.

Ah, you're right; there's no falsifying the BaTh *this* way.

>
>>
>>> This is not in accordance with experimental evidence.
>>>
>>> So the BaTh is falsified either way.
>>>
>>> That is of course no problem for Henri, his laws
>>> of nature change according to which phenomenon
>>> he is explaining away. :-)
>>
>>There are times I wish I could do that to my bank account. :-)
>
> Paul cannot understand why I am always right....

Neither can I. But never mind that; all you need do is compute
the following parameters correctly and we'll forgive you. :-)

[1] Distance from Sol to Algol.
[2] Distance from Algol to Algol's planet.
[3] Mass of Algol's planet.
[4] Radius of Algol.

[.sigsnip]

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#191, ewill3@xxxxxxxxxxxxx
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