The weight of capacitance :-)

Calculate how much mechanical energy is stored in the spring, and apply Einstein's equation. It won't be much more than the relaxed spring, because there are almost 1e17 joules per kilogram.

--

John Larkin                  Highland Technology Inc 
www.highlandtechnology.com   jlarkin at highlandtechnology dot com    

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Wellllll......

A 1M solar mass black hole (galactic-center-sized) has an event horizon of

2.953e6 km radius, or a capacitance (assuming flat space; I don't have a clue how the notion of capacitance changes in GR :) ) of:

C = 8 pi e_0 G m / c^2

*+8+*+pi+*+electric+constant+*+gravitational+constant

0.329 F

Now if you wanted to know farad*ays*, you could suppose the black hole swallowed only electrons (assuming gravity overcomes electric repulsion -- it probably can't, this would be a serious case of galactic hair-standing-on-end!), so its mass is entirely due to electrons (and the energy of packing them in!).

Supposing the energy is due entirely to electric energy (probably a good bet, the electrons inside will be hyperrelativistic pretty quickly):

E = 1/2 C V^2 = m c^2 m c^2 = 4 pi e_0 G m V^2 / c^2

m cancels out, so it's independent of mass (and size). Cool!

V = c^2 / (2 sqrt(pi e_0 G))

= 1.043e27 volts

And as we can see, the electrons will be essentially like photons, since it takes ~1e27 eV to accrete each electron (electron RME ~ 511keV, insignificant).

(Incidentally, replacing e_0 with mu_0 gets you the respective magnetic result, 2.77e24 amperes. Obviously, the ratio is the impedance of free space, sqrt(e_0 / mu_0).)

An interesting result is -- if you can compress a poor electron hard enough in the first place -- it doesn't matter how many you rub together, they all push with the same gravitoelectric constant. It's a very well regulated, extremely high voltage storage battery, but do try to keep it away from all those protons you freed up in the process!

Back to the charge, our 1MSol black hole will hold a charge of about

3.56e21 faraday (3.43e26 C), or 0.0059 moles of moles of electrons. You'll use up, what, about a star's worth of electrons building it?

Weight is indeed the force exerted by an accelerated mass. And if you want a more fundamental definition, you can replace force with potential energy, exchange particles or so on. I suppose my choice of "weight" is as ambiguous as saying "mass", since all we can measure is the apparent mass of anything.

Who knows if anything is really...there, man?.. Besides matter being mostly puffy electrons and so on, of course. Modern particle physics tells us everything is really fields and symmetry (ping-pong ball particle physics is more of a geometric "I hit something" placeholder, though despite its mechanical analogy, is still surprisingly relevant and effective), and certain states of those fields result in things we call matter. Specifically, "drag" from the Higgs field results in mass. This imposition is going to be yet another quantity in terms of energy, so maybe it's a correct statement to paraphrase, "nope, it's energies all the way down!" In that case, then, it shouldn't matter what scale you measure the mass (or weight) of an object on: it will always be a true statement that it "weighs" so-and-so, including its internal energy state. This really shouldn't be surprising to anyone, because conservation of momentum is really the only thing Einstein imposed in his equations; there's no conservation of mass anymore, only mass-energy.

Tim

--
Deep Friar: a very philosophical monk. 
Website: http://webpages.charter.net/dawill/tmoranwms

[snip]

Through the short around to the other side of the cap.

-- Paul Hovnanian mailto: snipped-for-privacy@Hovnanian.com

------------------------------------------------------------------ Some people are like Slinkies; they serve no specific purpose, but they bring a smile to your face when you push them down the stairs.

[snip]

I'd measure it. But I don't think I could get my DVM probe back from the black hole.

-- Paul Hovnanian mailto: snipped-for-privacy@Hovnanian.com

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--
Photons can have no rest mass, but if, as you say, 

     E = mc²,  

then 
  
          E 
     m = ----, 
          c² 

and it follows that if E increases, m must also increase. 

Consequently, an ultraviolet photon - being more energetic than an 
infrared photon - will also be more massive.

The constant that converts mass to charge is 1.758820150(44)×10^11 C/kg.

That's a lot a' electrons...

--
Les Cargill

"coloumb equivalent" then.

--
Les Cargill

The same amount as a soul.

--

John Larkin                  Highland Technology Inc 
www.highlandtechnology.com   jlarkin at highlandtechnology dot com    

Precision electronic instrumentation 
Picosecond-resolution Digital Delay and Pulse generators 
Custom timing and laser controllers 
Photonics and fiberoptic TTL data links 
VME  analog, thermocouple, LVDT, synchro, tachometer 
Multichannel arbitrary waveform generators

What? Of course they have mass. Read any physics text that covers relativity. All energy has mass.

Rick

That's why I think it would weigh more. Mikek

Hey, one thing you can weight is the magnetic field gradient.

If you weight a little permenant magnet (keeping it away from the scale with maybe a styrofoam cup or something.) and then flip the magnet over, the difference in weight tells you something about the vertical component of the field gradient. You've got the measure the magnetic moment of the magnet to get any real numbers.

George H.

When the two capacitors were charged to different voltages, on each capacitor, a different number of electrons were moved from one plate to the other, enough in each case to account for the charged voltage. When they were discharged, each capacitor returned to equilibrium, with the same number of electrons on each plate. The energy involved in the charging was lost to a combination of dissipation (resistance during discharge), and radiation (due to the movement of the electrons).

--
John

Photons have momentum, but no mass. They do not interact gravitationally.

--

John Larkin         Highland Technology, Inc 

jlarkin at highlandtechnology dot com 
http://www.highlandtechnology.com 

Precision electronic instrumentation 
Picosecond-resolution Digital Delay and Pulse generators 
Custom laser drivers and controllers 
Photonics and fiberoptic TTL data links 
VME thermocouple, LVDT, synchro   acquisition and simulation

trons.

pty it

here

Oops, don't tell that to Eddington.

(what makes a black hole black?)

George H.

ed text -

--
Could you be a little less specific?

Was I unclear? Read the first four words in the first paragraph of my link.

"The photon is massless"

--

John Larkin         Highland Technology, Inc 

jlarkin at highlandtechnology dot com 
http://www.highlandtechnology.com 

Precision electronic instrumentation 
Picosecond-resolution Digital Delay and Pulse generators 
Custom laser drivers and controllers 
Photonics and fiberoptic TTL data links 
VME thermocouple, LVDT, synchro   acquisition and simulation

electrons.

it

A black hole warps space. That doesn't mean that photons participate in the gravitational force.

--

John Larkin         Highland Technology, Inc 

jlarkin at highlandtechnology dot com 
http://www.highlandtechnology.com 

Precision electronic instrumentation 
Picosecond-resolution Digital Delay and Pulse generators 
Custom laser drivers and controllers 
Photonics and fiberoptic TTL data links 
VME thermocouple, LVDT, synchro   acquisition and simulation

It's full of liberals? ;-)