What exactly is "exact" (was Clean Singleton Docstrings)

[Gene Heskett]

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 — school physics textbook so sorry no link —
> > that in the Newton gravitation law
> > f = -GMm/r²
> >
> > 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 
are going, the more massive you become.  Ergo the rate of the 
acceleration will decrease as the mass builds up.   But the speeds most 
of us deal with are so close to at rest that we do not realize in the 
everyday world around us, that this does apply at the speeds you throw 
that ball while juggling 3 of them.  The effect is quite minimal at our 
everyday speeds, but there is not a set point where it kicks in, its 
always there.  Its just that the difference at everyday speeds, is 
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 
account for 5.3 amps of current thru a klystron amplifier tube, and the 
acceleration voltage speeding the electrons along is 20,000 volts.  That 
beam of electrons is trucking right along at a measurable fraction of c 
speed.  Its also dumping something more than 100KW into the cooling 
water flowing thru the bottom of the tube where the beam lands and is 
absorbed.

This amplifier does not operate by varying the current like a normal 
vacuum tube, it constant current. It is a capacitatively driven tube, 
and the power comes back out by being capacitatively coupled from the 
electron beam.

How many of you can remember the audio buzz in the UHF channels tv sound 
20 years ago?

So I am going to tell you how that buzz became part of the UHF landscape 
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 
1970's when I learned about them, is a long tube, around 5 feet long 
with alternating sections of copper tubeing and ceramic insulators 
separating the copper sections. Typically 4 ceramic sections, each of 
which was sealed to a section of copper equiped with contact rings on 
each end of the copper sections. A tunable box cavity connected the 
copper sections together, bridging the ceramic spacer, so that when the 
tube was "dressed" with these cavity's, and lowered into its focusing 
magnet, (2200 lbs) you could feed about 1 watt of signal into the top 
cavity, which either retarded the velocity of the beam slightly, or 
accellerated it a bit. The beam then passed out of that cavity and on 
into the next one, tuned a couple megahertz lower, then passed thru the 
third cavity normally tuned about 4.2 megahertz higher.  Each cavity it 
passed thru reinforced this small velocity change until one could 
visualize the electrons traveling in little balls by the time it enters 
the last cavity, and this cavity has a coupling loop to extract the 
amplified signal, 30 kilowatts of it, all because that last cavity is 
ringing  like a bell because of the capacitative coupling between these 
bunched up electrons and the cavity.

The buzz that was so annoying is directly related to the relativistic 
effects being modified by the video signal. The electrons gain more mass 
as they speed up, so the speed up does not match the slowdown because 
they lose mass thereby slowing more, so the net effect is that the tube 
gets longer at the high power levels of the synch signal, inventing an 
FM signal that is not there in the drive.

Then, since most tv transmitters before digital were actually two 
transmitters, one for the video, and one for the audio, and the audio 
ran at a constant power level since it was an FM signal, so the aural 
was not similarly effected.  The old tv's also used the difference 
frequency, here in the US of 4.5 megahertz as their aural detection 
system.  So this FM component to the visual became mixed with the 
unaffected audio, injecting this darned buzz into the audio IN your tv.

And relativity, in the form of e=mv2 was the culprit.  Not even the FCC 
had that figured out.

I had that pointed out to me by a blown water pump breaker, and the lack 
of cooling water blew the bottom out of the collector bucket on the 
visual tube. About 50 milliseconds after the pump went locked rotor from 
the phase failure.  After replacing the breaker, I wheeled the aural 
tube out of its cubicle and put it into the visual transmitter and tuned 
it up for picture service, old tube, got about 80% power out of it.  
Then I rigged a cable of aural drive over to the visual and fed about 
100 milliwatts of aural drive just to get back on the air while Varian 
was building me a new klystron which takes several weeks.  At home that 
night, checking to see if the viewers might notice, the pix looked ok 
but something told me to crank up the sound. Zero buzz, because both 
signals were being amplified in the same tube, and subjected to 
identical amounts of this distortion, there was no difference to be 
detected in the tv itself.  The distortion was absolutely in lock step 
and totally inaudible to the tv's.  With both tubes running normally, 
that buzz was only down about 53db at best.

So relativity applies, even to the baseball being thrown by a little 
leager.  We just do not have the precision to measure it when the effect 
is hundreds of digits to the right of the decimal point.

Cheers, Gene Heskett
-- 
"There are four boxes to be used in defense of liberty:
 soap, ballot, jury, and ammo. Please use in that order."
-Ed Howdershelt (Author)
Genes Web page <http://geneslinuxbox.net:6309/gene>