E=mc^2 vs. ZPE
Date: Sunday, November 02, 2003 @ 23:26:00 UTC Topic: Science
In a recent post on the Yahoo free_energy list vcrepair wrote: Energy of mass per Einstein's E=MC^2
Everyone knows the famous equation Energy = mass * velocity of light squared. But what do the units come out as in standard terms? For 1 gram of mass and light velocity 3 * 10^8 meters per second?
If 1 Joule or Watt second is equivalent to 1 Kilogram Meter^2/second^2 or
1 NewtonMeter then how many Joules per gram of mass?
1 Newton accelerates 1 kilogram 1 meter per second per second
1 kilowatt hour is 3.6 million Joules, (3600 seconds X 1000)
So would that be; 1 gram * (3 *10^8 meters/second)^2
= 1 gram * (9 * 10^16 meters^2/second^2) or
9 * 10^13 kilogrammeter^2/ sec^2 or 9 * 10^13 Joules or wattseconds?
Since a kilowatt hour is 3.6 * 10^6 Joules then 1 gram of mass would yield 9*10^13/3.6*10^6 = 2.5*10^7 Kilowatt hours or 25000 Megawatt hours.
At 10 cents per kilowatt hour that would be $2,500,000 worth of electric power…

Vcrepair’s final result is correct (even though “gram” is not the standard unit for mass).
Let’s see now how much energy is assumed to be in 1 millimeter cube (mm^3 – another nonstandard unit for volume but… you’ll understand why) of space, according to the Quantum Electrodynamics (QED) theory.
I shall quote here from the paper “ZPV Background” by Prof. Jordan Maclay, Quantum Fields LLC (http://www.quantumfields.com/ZPV.htm or see “A few general comments on vacuum energy” in our “editorials” section):
“If you have a hot body in equilibrium with its surroundings, it is radiating and reabsorbing photons (quantized bundles of electromagnetic radiation) of all wavelengths. The energy of a photon of frequency f is Planck's constant h times the frequency hf . The energy distribution of these photons is given by the Planck blackbody equation. If you imagine cooling the body and surroundings to absolute zero, you would find that a temperature independent electromagnetic field remained. This electromagnetic field, which is always present even if no matter or charged particles are present and the temperature is absolute zero, represents the lowest state of the electromagnetic field. The corresponding fluctuating electromagnetic field is called the zeropoint (ZP) field of the electromagnetic field. The presence of this zeropoint field is predicted by QED (Quantum Electrodynamics). QED is the most precise physical theory we have; its predictions have been verified to 1 part in 10 billion!
The zeropoint field is the "ground state" of the electromagnetic field. In this ground state, the equations indicate that no ordinary physical photons are present, yet electromagnetic energy is present. The energy for a given frequency is 1/2 hf, one half of the usual energy of a photon. Sometimes the zeropoint field is described as consisting of "virtual" or very shortlived photons, that appear and disappear before it is possible to detect them. The presence of zeropoint fluctuations has been verified experimentally with very accurate measurements of the Lamb Shift, other atomic energy level shifts, the magnetic moment of the electron, and the Casimir force. QED predicts that the number of ZP quanta (1/2 hf) of frequency f is proportional to the square of the frequency. This gives an energy density for the vacuum that goes as the cube of the frequency.
Special relativity requires that any observer going through space cannot tell how fast she is going in an absolute sense. Thus the zeropoint fluctuations must look the same, independent of her velocity as she travels through space. Therefore the Doppler shifted frequency spectrum must look the same as the unshifted frequency spectrum. This requirement of special relativity results in an energy density of the zeropoint fluctuations identical to that predicted by QED, namely an energy density proportional to the cube of the frequency. Summing over all the frequencies present, gives a total energy density in the vacuum of which is proportional to 1/(L)^4 where L is the shortest wavelength of the ZP fluctuations allowed. If we take L as zero, then we obtain an infinite energy. Applying quantum principles to general relativity (geometrodynamics) suggests that at lengths shorter than the Planck length (10^35 m), the nature of spacetime fluctuates, and therefore no meaning can be ascribed to a length shorter than the Planck length. Thus we could use the Planck length as a cutoff.
The energy density of the ZP fluctuations in empty space (according to QED) is about 10^114 joules/cubic meter if we use the Planck length (10^35 m) as a cutoff. “

(This is just oneway of looking at this question – see how bizarre and embarrassing for the current well verified and accepted theories of physics things can get, by reading the rest of Maclay’s paper).
Consequently, since 1kWh = 3.6*10^6 Joules and 1 m^3 = 10^9 mm^3 then 10^114 Joules/cubic meter = ~ 3*10^98 kWh of ZPenergy in one millimeter cube of vacuum.
To put it in perspective, the total world energy consumption in 2001 was 404 QuadBtu (one Quadrillion British thermal units = 10^15 Btu = ~ 3 *10^11 kWh) or (just ;)~10^14 kWh/year.
But hey…the Universe was created in a Big Bang from a point in the Nothingness …or so the story goes!

