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From: Gene Heskett <gheskett@shentel.net>
Newsgroups: comp.lang.python
Subject: Re: What exactly is "exact" (was Clean Singleton Docstrings)
Date: Tue, 19 Jul 2016 01:22:55 -0400
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On Monday 18 July 2016 23:16:32 Steven D'Aprano wrote:

> On Tue, 19 Jul 2016 10:36 am, Rustom Mody wrote:
> > I recollect =E2=80=94 school physics textbook so sorry no link =E2=80=94
> > that in the Newton gravitation law
> > f =3D -GMm/r=C2=B2
> >
> > there was a discussion about the exponent of r ie  2
> > And that to some 6 decimal places it had been verified that it was
> > actually 2.000002
>
> Because gravitational forces are so weak, it is very difficult to
> experimentally distinguish (say) an exponent of 1.999999 from 2.000002
> from 2 exactly.
>
> Most physicists would say that an experimental result of 2.000002 is
> pretty good confirmation that the theoretical power of 2 is correct.
> Only a very few would think that the experiment was evidence that both
> Newtonian and Einsteinian gravitational theory is incorrect.
>
> (Newton, for obvious reasons; but also general relativity, since
> Newton's law can be derived from the "low mass/large distance" case of
> general relativity.)
>
> But it's an interesting hypothetical: what if the power wasn't 2
> exactly?
>
I do not believe it is. The theory of relativity says that the faster you=20
are going, the more massive you become.  Ergo the rate of the=20
acceleration will decrease as the mass builds up.   But the speeds most=20
of us deal with are so close to at rest that we do not realize in the=20
everyday world around us, that this does apply at the speeds you throw=20
that ball while juggling 3 of them.  The effect is quite minimal at our=20
everyday speeds, but there is not a set point where it kicks in, its=20
always there.  Its just that the difference at everyday speeds, is=20
likely a few hundred digits to the right of the decimal point.

Now, trade those 1 lb balls in on a few quintillion electrons, enough to=20
account for 5.3 amps of current thru a klystron amplifier tube, and the=20
acceleration voltage speeding the electrons along is 20,000 volts.  That=20
beam of electrons is trucking right along at a measurable fraction of c=20
speed.  Its also dumping something more than 100KW into the cooling=20
water flowing thru the bottom of the tube where the beam lands and is=20
absorbed.

This amplifier does not operate by varying the current like a normal=20
vacuum tube, it constant current. It is a capacitatively driven tube,=20
and the power comes back out by being capacitatively coupled from the=20
electron beam.

How many of you can remember the audio buzz in the UHF channels tv sound=20
20 years ago?

So I am going to tell you how that buzz became part of the UHF landscape=20
for so many years, so bear with me as I have a story to tell.

This klystron amplifier, a new one of which was north of $125,000 in the=20
1970's when I learned about them, is a long tube, around 5 feet long=20
with alternating sections of copper tubeing and ceramic insulators=20
separating the copper sections. Typically 4 ceramic sections, each of=20
which was sealed to a section of copper equiped with contact rings on=20
each end of the copper sections. A tunable box cavity connected the=20
copper sections together, bridging the ceramic spacer, so that when the=20
tube was "dressed" with these cavity's, and lowered into its focusing=20
magnet, (2200 lbs) you could feed about 1 watt of signal into the top=20
cavity, which either retarded the velocity of the beam slightly, or=20
accellerated it a bit. The beam then passed out of that cavity and on=20
into the next one, tuned a couple megahertz lower, then passed thru the=20
third cavity normally tuned about 4.2 megahertz higher.  Each cavity it=20
passed thru reinforced this small velocity change until one could=20
visualize the electrons traveling in little balls by the time it enters=20
the last cavity, and this cavity has a coupling loop to extract the=20
amplified signal, 30 kilowatts of it, all because that last cavity is=20
ringing  like a bell because of the capacitative coupling between these=20
bunched up electrons and the cavity.

The buzz that was so annoying is directly related to the relativistic=20
effects being modified by the video signal. The electrons gain more mass=20
as they speed up, so the speed up does not match the slowdown because=20
they lose mass thereby slowing more, so the net effect is that the tube=20
gets longer at the high power levels of the synch signal, inventing an=20
=46M signal that is not there in the drive.

Then, since most tv transmitters before digital were actually two=20
transmitters, one for the video, and one for the audio, and the audio=20
ran at a constant power level since it was an FM signal, so the aural=20
was not similarly effected.  The old tv's also used the difference=20
frequency, here in the US of 4.5 megahertz as their aural detection=20
system.  So this FM component to the visual became mixed with the=20
unaffected audio, injecting this darned buzz into the audio IN your tv.

And relativity, in the form of e=3Dmv2 was the culprit.  Not even the FCC=20
had that figured out.

I had that pointed out to me by a blown water pump breaker, and the lack=20
of cooling water blew the bottom out of the collector bucket on the=20
visual tube. About 50 milliseconds after the pump went locked rotor from=20
the phase failure.  After replacing the breaker, I wheeled the aural=20
tube out of its cubicle and put it into the visual transmitter and tuned=20
it up for picture service, old tube, got about 80% power out of it. =20
Then I rigged a cable of aural drive over to the visual and fed about=20
100 milliwatts of aural drive just to get back on the air while Varian=20
was building me a new klystron which takes several weeks.  At home that=20
night, checking to see if the viewers might notice, the pix looked ok=20
but something told me to crank up the sound. Zero buzz, because both=20
signals were being amplified in the same tube, and subjected to=20
identical amounts of this distortion, there was no difference to be=20
detected in the tv itself.  The distortion was absolutely in lock step=20
and totally inaudible to the tv's.  With both tubes running normally,=20
that buzz was only down about 53db at best.

So relativity applies, even to the baseball being thrown by a little=20
leager.  We just do not have the precision to measure it when the effect=20
is hundreds of digits to the right of the decimal point.

Cheers, Gene Heskett
=2D-=20
"There are four boxes to be used in defense of liberty:
 soap, ballot, jury, and ammo. Please use in that order."
=2DEd Howdershelt (Author)
Genes Web page <http://geneslinuxbox.net:6309/gene>