Re: Einstein's Doppler equation wrong?
From: sal (pragmatist_at_nospam.org)
Date: 10/31/04
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Date: Sat, 30 Oct 2004 22:51:59 -0400
On Sat, 30 Oct 2004 03:19:49 +0000, Androcles wrote:
>
> "sal" <pragmatist@nospam.org> wrote in message
> news:pan.2004.10.30.02.22.31.661633@nospam.org...
> : Just a few odds and ends.
> :
> : On Thu, 28 Oct 2004 13:13:26 +0000, Androcles wrote:
> :
> : > "sal" <pragmatist@nospam.org> wrote in message
> : > news:pan.2004.10.28.01.58.30.58603@nospam.org...
> : > : On Wed, 27 Oct 2004 22:07:57 +0000, Androcles wrote:
> : > :
> : > :
> : > : > : If pressure impulses in air did that, we wouldn't be able to
> : > : > : understand each other when we talked!
> : > : >
> : > : > They do. An organ pipe resonates.
> : > :
> : > : That's not _quite_ the same effect, though, I think.
> : >
> : > I'll refer you to Christiaan Huyghens. Take ANY point ...
> :
> : Hmmm .... you may be right. This deserves more thought than I'm
> likely to
> : give it...
>
> Well, give thought to this.
> 'j' is used as the sqrt(-1) to avoid confusion with 'i' which represents
> current, and you've done a pretty good job at confusing it. 'j' is NEVER
> current.
Right -- it's current _density_, not current. Here are a couple of
references; I'm just quoting the definitions, but trust me, I'm not "quote
mining" here:
Griffiths, Intro to Electrodynamics, p. 212, second paragraph
" ... we describe it by the volume current density, J, defined as
follows..."
This J, the volume current density, is the J in Maxwell's equations, which
are also discussed at length in Griffiths.
Purcell, Electricity and Magnetism (from the Berkeley Physics Series),
inside back cover where the units are defined:
...
CURRENT DENSITY J (esu/sec)/cm^2, defined by I = integral(J da)
...
Purcell's definition makes it more explicit that I is current, and J is
current density.
Dorf, The Electrical Engineering Handbook, CRC Press, 1993, page 1132,
under "Dielectrics and Insulators", second paragraph,
" ... sigma is equal to the leakage current density J_l ... "
Finally, I'll mention that this is not universal -- some texts use I for
the current density. But it seems to be very common. Of the first four
places I looked, three of them used J for current density; the fourth used
I.
Again, Maxwell's equations have a J in them, but it's current density.
There are no imaginary numbers in dear old Maxie.
If you prefer to go on believing otherwise, without looking it up to
actually check the definitions of the symbols in any textbook that lays
them out, I can't very well change your mind, of course. I know perfectly
well you won't be convinced by quotes I choose. :-)
> I agree with Maxwell, and Maxwell says the current is phase shifted,
> leading 90 degrees from the voltage, whatever the assistant professor, the
> fumble mumbler, yourself or anyone else says. Say "uncle":-)
>
>
> : [ ... ]
> :
> : > :[SAL, on transmission line echoes:]
> :
> : > : Again, it's the bounce from the end that gives the echoes.
> Terminate
> : > : it properly, so there's no "bounce", and the signal comes out
> the
> : > : other end perfectly "clean".
> : >
> : > I disagree. I consider there to be two boundaries, one at each
> end, with
> : > a resonant standing wave between antenna and "resistor". In
> reality we
> : > do not use a resistor anyway, we use an impedance. That is known
> as
> : > "terminating properly". Just because the units of impedance are
> the same
> : > as the units of resistance does not imply a terminating resistor
> is
> : > employed.
> :
> : Ever done anything with ethernet, using the old thinnet drop cables?
> If
> : you unplug the computer, you _must_ plug in a terminator in its
> place (or
> : somebody from network operations comes and yells at you). The
> terminator
> : consisted of a connector with a small resistor tying the core and
> shield
> : of the coax together. At least in the ones I've seen, it really was
> just a
> : simple resistor; I think it was either 50 or 75 ohms.
> :
> : Without the terminator, the thinnet cable spits back echoes into the
> : network, and the whole segment either goes dead or gets really slow
> as a
> : result of errors and "ghost" collisions. With the terminator,
> packets run
> : down to the end of the cable and just vanish.
> :
> : A dead short at the end would act just like an open, as far as
> scrambling
> : the network goes, except that the echoes would come back "reversed",
> with
> : the voltage inverted versus the outbound signal.
> :
> : (The vampire taps didn't have the same problem, of course -- pull
> out the
> : needle and you're all set, no terminator required.)
> :
> : Similarly, a SCSI bus needs to be terminated to avoid echoes.
> Nowadays
> : the termination is active and involves a hunk of circuitry. In the
> "old
> : days", fifteen years ago, passive terminators were typically used:
> it was
> : just a resistor pack, plugged onto the second SCSI connector on the
> last
> : device in the chain. (I don't know what the values were.)
>
> Something needs looking into, because a 100 kW transmitter doesn't use a
> resistive load, the signal still goes up a pipe to the antenna at the top
> of a ruddy great tower and we are talking about the same frequency as the
> receiver is tuned to.
Well, sure -- a resistive load would melt! :-)
The current and voltage are in phase going into the antenna and the power
goes out into the aether ... ER oops I mean onto the air ... anyway it
goes away from the antenna.
With the ethernet and SCSI examples, I was just pointing out a couple
cases where a resistive load is used.
> 50 ohms resistance at 100 kW is gonna be a stinking
> hot coil of metal radiating 100 kW of heat, not FM, whichever end of the
> pipe you place it, and your reciever had better be close to the tower,
> not 100 miles away. Where is that current going? Up one side of the pipe
> and down the other.
>
> Capacitors are added to inductive loads in industry to reduce current in
> the cables and switchgear leading to the motors.
Right -- the caps get the current back in phase with the voltage, so it's
actually doing something useful rather than just heating the wires. Don't
they use something like that in long transmission lines, too?
> Motors use minimum
> resistance or energy is wasted as heat.
>
>
>
> : [ ... ]
> :
> : > Kitchen science:
> : > Add a few drops of vegetable oil to a saucer of water, then add
> dish
> : > washing liquid and watch what happens.
> :
> : I think I know the answer but I may try it anyway.
> :
> : > Here's another. Dice a carrot and potato. Mix. Now separate the
> carrot
> : > from the potato. No, not by hand. Do it the easy way.
> :
> : Uh .... Drop them in a bowl of water, and one of them will float but
> not
> : the other?
>
> Yep. Carrots float. Potatoes sink.
> Just thought you might like to amuse your youngster.
> Salt and sand, of course, everyone knows that one.
>
>
> : If that doesn't work, offer the whole mess to a rabbit. After a
> while
> : only the potato will be left on the plate.
> :
> : If it's not either of those then I really don't know.
> :
> :
> : --
> : I can be contacted through http://www.physicsinsights.org
> :
> :
-- I can be contacted through http://www.physicsinsights.org
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