A relativistic thought-experiment on energy

[Reiyuki]

A relativistic thought-experiment on energy.

One day, we find ourselves standing on a very interesting planet.  This planet is far, far from Earth, and orbits VERY close to a black hole.  As such, their perception of time and energy is very different from the rest of the universe.

To solve their world's energy problem, the people on this planet launched a very special satellite in a highly-eccentric orbit.  This satellite comes very close to the planet during a small part of the year, and quickly slingshots far away for the rest of the year.  It is in its own stable orbit and requires no additional energy once launched.


When the satellite is close, they charge its internal capacitors with almost no losses.  The satellite absorbs over 1 megajoule of energy.

Now, as the satellite flies away from the planet, it experiences strong relativistic effects.  Because it is further from the gravitational well of the black hole, the rate-of-time on the satellite changes, and from the point-of-view of the planet, it appears to speed-up substantially.

When the satellite is a long way from the planet, it begins beaming focused microwaves toward the planet at 10ghz.

Due to the nature of special relativity, these waves become refracted as they approach the planet, which causes them to upshift in frequency manyfold.  This formerly 10ghz microwave signal has now been up-shifted to 500thz, and is received on the planet as visible light.


Because this blue-shift has increased the energy of the incoming waves thanks to relativity, the planet is now able to use much more power than it transmitted to the satellite in the first place.  Naturally, they set aside a small amount of power to recharge the satellite when it is back near periapsis.

A few crazy inventors on that planet are hard at work trying to recreate the same effects with simple circuits, since relativistic shifts in frequency are much easier to create using coils and capacitors rather vs expensive, bulky satellites.  One of them was occasionally heard muttering that frequency *is* energy, while another went crazy complaining about kings and electrons...



Hopefully this story will convey the concepts intended.

[PhysicsProf]

A relativistic thought-experiment on energy.

One day, we find ourselves standing on a very interesting planet.  This planet is far, far from Earth, and orbits VERY close to a black hole.  As such, their perception of time and energy is very different from the rest of the universe.

To solve their world's energy problem, the people on this planet launched a very special satellite in a highly-eccentric orbit.  This satellite comes very close to the planet during a small part of the year, and quickly slingshots far away for the rest of the year.  It is in its own stable orbit and requires no additional energy once launched.


When the satellite is close, they charge its internal capacitors with almost no losses.  The satellite absorbs over 1 megajoule of energy.

Now, as the satellite flies away from the planet, it experiences strong relativistic effects.  Because it is further from the gravitational well of the black hole, the rate-of-time on the satellite changes, and from the point-of-view of the planet, it appears to speed-up substantially.

When the satellite is a long way from the planet, it begins beaming focused microwaves toward the planet at 10ghz.

Due to the nature of special relativity, these waves become refracted as they approach the planet, which causes them to upshift in frequency manyfold.  This formerly 10ghz microwave signal has now been up-shifted to 500thz, and is received on the planet as visible light.


Because this blue-shift has increased the energy of the incoming waves thanks to relativity, the planet is now able to use much more power than it transmitted to the satellite in the first place.  Naturally, they set aside a small amount of power to recharge the satellite when it is back near periapsis.

A few crazy inventors on that planet are hard at work trying to recreate the same effects with simple circuits, since relativistic shifts in frequency are much easier to create using coils and capacitors rather vs expensive, bulky satellites.  One of them was occasionally heard muttering that frequency *is* energy, while another went crazy complaining about kings and electrons...



Hopefully this story will convey the concepts intended.

" This planet is far, far from Earth, and orbits VERY close to a black hole.  As such, their perception of time and energy is very different from the rest of the universe."

    OK, the black hole causes a blue-shift - so effectively, the black hole's gravity is the source of the energy - right?
    But - can you do something like this on planet earth?

[Reiyuki]

" This planet is far, far from Earth, and orbits VERY close to a black hole.  As such, their perception of time and energy is very different from the rest of the universe."

    OK, the black hole causes a blue-shift - so effectively, the black hole's gravity is the source of the energy - right?
    But - can you do something like this on planet earth?

What fun synchronicity PhysicsProf, I was writing a follow-up just as you posted

Yes, in this case the blue-shift is the source of the increased energy, and the black-hole's gravity is the source of the blue-shift.  The satellite is the 'modulation' between a low and high energy state.


What we are doing is cycling between a high and low density environment and synchronously adding/removing energy at certain points of this cycle.
* Energy is added to the satellite at a low-point in the cycle (without changing its mass)
* Satellite proceeds to a higher-orbit
* Satellite beams the same energy back
* Blue-shift refraction causes the frequency (and thus energy) to increase.

--------------------------------

Dimensionally, we would do the same thing on earth by cyclically varying inductance/capacitance of a system while adding/removing at certain points of the cycle.

Imagine a lossless LC tank circuit consisting of an inductor and variable air capacitor.  We add 1 unit of energy and it shuttles between dielectric and magnetic domains at a certain frequency (standard LC resonance).

Now if we decrease the capacitance of this circuit, the same energy is now resonating at a higher frequency (as if it had been blue-shifted ).  This change in C does not necessarily take any energy, as this parameter can be changed at the point in the cycle when the capacitor is nearly empty (or physically switching between series+parallel).

To gauge the amount of change in total energy, we would use:
*  E=HF to compare the min+max frequencies of the system
*  the initial amount of energy that was added to the circuit
*  and the phase-angle of modulation to the charge/discharge cycle.

Now if such a system were ran in reverse (starting with a high-frequency oscillation and increasing capacitance), one would instead red-shift the resulting EM wave and decrease the total energy contained in the system.

-----------------------------

Hopefully some of this makes sense?

[Reiyuki]

By-the-way, I expect two major criticisms to arise from this thought-experiment:

-------------------------------------

Critical Response 1 - The mass of the satellite increases at it is being charged, causing its orbit to decay and preserve CoE. (E=MC^2)

  - Does a charged capacitor weigh more than an uncharged capacitor?   Has anyone checked?
  - Does a charged inductor weigh more than an uncharged inductor?
  - Does a permanent magnet lose mass as it transitions past its curie point?
  - Does a sealed battery gain/lose mass as it is charged/discharged?

If the answer to any of these is no, then the thought-experiment is still valid as the satellite's mass does not change during the cycle.

If the answer is yes, then we are instead provided with a new means of extracting 'free energy' by gating the gravitational field of the earth with electricity:

Two capacitors balanced on a seesaw are alternate their charge between each-other.  This is done with superconductive cables and is thus lossless.  When one capacitor is charged, its mass is increased, causing the seesaw to tip in that direction.  The energy is shuttled back the other way, and the seesaw tips in the opposite direction.  We hook up a generator to the see-saw and extract free power as long as the gravitational field exists.
In this example, gravity is a constant source of energy and is being 'gated' by shuttling electricity back-and-forth.

-------------------------------------

Critical Response 2:  Redshift/blueshift causes a wave to absorb/dump energy to preserve its relativistic energy content.

- Individual photons experience redshift/blueshift, a wave-group is not necessary. One would have to explain how groups of photons shed energy while individual photons do not.
- One would also be forced to ask whether this energy is dumped into the refractive body or simply disappears.
- Planck's Constant (E=HF) would have to be rewritten/reinterpreted to account for the gain/loss in energy.

[TinMan]

By-the-way, I expect two major criticisms to arise from this thought-experiment:

-------------------------------------

1 - The mass of the satellite increases at it is being charged, causing its orbit to decay and preserve CoE.

  - Does a charged capacitor weigh more than an uncharged capacitor?   Has anyone checked?
  - Does a charged inductor weigh more than an uncharged inductor?
  - Does a permanent magnet lose mass as it transitions past its curie point?

If the answer to these is no, then the thought-experiment is still valid as the satellite's mass does not change during the cycle.

If the answer is yes, then we are instead provided with a new means of extracting 'free energy' by gating the gravitational field of the earth with electricity:

Two capacitors balanced on a seesaw are alternate their charge between each-other.  This is done with superconductive cables and is thus lossless.  When one capacitor is charged, its mass is increased, causing the seesaw to tip in that direction.  The energy is shuttled back the other way, and the seesaw tips in the opposite direction.  We hook up a generator to the see-saw and extract free power as long as the gravitational field exists.
In this example, gravity is a constant source of energy and is being 'gated' by shuttling electricity back-and-forth.

-------------------------------------

2:  Redshift/blueshift causes a wave to absorb/dump energy to preserve its relativistic energy content.

- Individual photons experience redshift/blueshift, a wave-group is not necessary. One would have to explain how groups of photons shed energy while individual photons do not.
- One would also be forced to ask whether this energy is dumped into the refractive body or simply disappears.
- Planck's Constant (E=HF) would have to be rewritten/reinterpreted to account for the gain/loss in energy.

An interesting thought about charge having weight.

I have 6x 500 farad caps ,so maybe tonight i will weigh them discharged,and then again charged.
With a total of 3000 farads,you would think we would see any slight change in weight,as we will go from 0 up to 11,000 joules of stored energy--right
Well i don't think so,as the energy is always in the cap,only when the cap is discharged,the stored energy is now balanced on the two plates of the capacitor.

So when a cap has 0 volts across it,that means the amount of electrons on each plate is equal.
When you !charge! a cap,you take the electrons from one plate,and transfer them to the other plate.
So the weight will remain the same,as the electron volume never changes within the cap.


Brad

[forest]

too complicated. How about this one : a resonating tank circuit with a antenna , basically radio transmitter.
what IF we short at peak of current in tank circuit and create feedback to create free oscillating at higher frequency of antenna with it own capacitance. Is the radiated radio wave of higher frequency is energy gain Tesla did such experiments but I don't know the results

[Reiyuki]

An interesting thought about charge having weight.

I have 6x 500 farad caps ,so maybe tonight i will weigh them discharged,and then again charged.
With a total of 3000 farads,you would think we would see any slight change in weight,as we will go from 0 up to 11,000 joules of stored energy--right
Well i don't think so,as the energy is always in the cap,only when the cap is discharged,the stored energy is now balanced on the two plates of the capacitor.

So when a cap has 0 volts across it,that means the amount of electrons on each plate is equal.
When you !charge! a cap,you take the electrons from one plate,and transfer them to the other plate.
So the weight will remain the same,as the electron volume never changes within the cap.

Brad

Thanks for the input Brad, I'd be really curious how the experiment turns out

And I agree that the net coulomb charge is probably static in a single-capacitor situation. (resulting in zero mass-change)


Forest: you might be onto something; personally I'm focused on proof-of-concept models rather than energy-producing devices (better to understand steam engines before building jet turbines).
If the concept is valid (that symmetry breaks down when conveying energy between reference frames), there would be many, many ways to model and exploit it.

[lost_bro]

What fun synchronicity PhysicsProf, I was writing a follow-up just as you posted

Yes, in this case the blue-shift is the source of the increased energy, and the black-hole's gravity is the source of the blue-shift.  The satellite is the 'modulation' between a low and high energy state.


What we are doing is cycling between a high and low density environment and synchronously adding/removing energy at certain points of this cycle.
* Energy is added to the satellite at a low-point in the cycle (without changing its mass)
* Satellite proceeds to a higher-orbit
* Satellite beams the same energy back
* Blue-shift refraction causes the frequency (and thus energy) to increase.

--------------------------------

Dimensionally, we would do the same thing on earth by cyclically varying inductance/capacitance of a system while adding/removing at certain points of the cycle.

Imagine a lossless LC tank circuit consisting of an inductor and variable air capacitor.  We add 1 unit of energy and it shuttles between dielectric and magnetic domains at a certain frequency (standard LC resonance).

Now if we decrease the capacitance of this circuit, the same energy is now resonating at a higher frequency (as if it had been blue-shifted ).  This change in C does not necessarily take any energy, as this parameter can be changed at the point in the cycle when the capacitor is nearly empty.

To gauge the amount of change in total energy, we would use:
*  E=HF to compare the min+max frequencies of the system
*  the initial amount of energy that was added to the circuit
*  and the phase-angle of modulation to the charge/discharge cycle.

Now if such a system were ran in reverse (starting with a high-frequency oscillation and increasing capacitance), one would instead red-shift the resulting EM wave and decrease the total energy contained in the system.

-----------------------------

Hopefully some of this makes sense?

Good day Reiyuki

Hmm.... this sounds very similar to parametric resonance. 
OK, Capacitance is inversely proportional to potential, so if the capacitance 'C' is decreased (Increase in Frequency >> Blue-Shift analogy) by 1/2 then  the original Voltage (V1) now becomes double, V1*2 == V2.
Since Q=C*V;  during the above process, the quantity of Charge (Q) has been conserved (assuming lossless) and is the same as when the process started.
Now, the Energy (stored on cap) = 1/2Q*V; and since V1(original voltage) is now V2(the double of V1), the Energy stored by the cap has increase (either by expanding inter-plate distance-or by switching a second cap in series w/ the first cap) because the starting voltage V1 has doubled in the process.
External energy applied to the system is required to physically separate the plates, but what would happen if ZVS or ZCS is used to switch in and out a series capacitor identical to the original one in the circuit?  This would effectively cut the original 'C' in half while doubling the circuit 'V' and modifying the Energy of the circuit likewise. Only thing left to do would be to synchronized the output (loading of the circuit) w/ the ZVS switching of the series capacitor.
Maybe run it all using photovoltaics............

take care, peace
lost_bro

[F6FLT]

By-the-way, I expect two major criticisms to arise from this thought-experiment:

-------------------------------------

Critical Response 1 - The mass of the satellite increases at it is being charged, causing its orbit to decay and preserve CoE. (E=MC^2)

  - Does a charged capacitor weigh more than an uncharged capacitor?   Has anyone checked?
  - Does a charged inductor weigh more than an uncharged inductor?
  - Does a permanent magnet lose mass as it transitions past its curie point?
  - Does a sealed battery gain/lose mass as it is charged/discharged?

If the answer to any of these is no...

The answer is yes in any case.
See https://www.overunityresearch.com/index.php?topic=3796.msg77408#msg77408 that I wrote before reading your post here.

[Reiyuki]

F6FLT,
If a capacitor gains mass when it is being charged, where is this excess mass coming from?

The same number of coulombs is present inside the capacitor whether it is charged or not, they are merely displaced to one side or the other.
So it cannot be coming from the Coulomb field....

The same question would apply to a magnetic coil.  Does a large superconducting coil gain/lose mass when it is energized?  Where is the additional mass coming from?  Do webers posses mass, and if so what is the value?


As stated in the other thread, there appears to be a potential symmetry-break granted to us by relativity.  The 'loophole' appears to stem from the fact that EM waves/photons can convey force despite not gaining/losing mass themselves.

[TinMan]

F6FLT,
If a capacitor gains mass when it is being charged, where is this excess mass coming from?

The same number of coulombs is present inside the capacitor whether it is charged or not, they are merely displaced to one side or the other.
So it cannot be coming from the Coulomb field..

The same question would apply to a magnetic coil.  Does a large superconducting coil gain/lose mass when it is energized?  Where is the additional mass coming from?  Do webers posses mass, and if so what is the value?


As stated in the other thread, there appears to be a potential symmetry-break granted to us by relativity.  The 'loophole' appears to stem from the fact that EM waves/photons can convey force despite not gaining/losing mass themselves.

One could also ask if a wound up spring(which now stores energy) weighs more than that same spring unwound(which stores no energy).
As the mass of the spring never changes,then it's weight also must remain the same.


Brad

[Reiyuki]

One could also ask if a wound up spring(which now stores energy) weighs more than that same spring unwound(which stores no energy).
As the mass of the spring never changes,then it's weight also must remain the same.

Brad

EXACTLY!!   There seems to be a surprising disconnect between potential energy and kinetic energy in cases like this.

Good day Reiyuki

Hmm.... this sounds very similar to parametric resonance. 
OK, Capacitance is inversely proportional to potential, so if the capacitance 'C' is decreased (Increase in Frequency >> Blue-Shift analogy) by 1/2 then  the original Voltage (V1) now becomes double, V1*2 == V2.
Since Q=C*V;  during the above process, the quantity of Charge (Q) has been conserved (assuming lossless) and is the same as when the process started.
Now, the Energy (stored on cap) = 1/2Q*V; and since V1(original voltage) is now V2(the double of V1), the Energy stored by the cap has increase (either by expanding inter-plate distance-or by switching a second cap in series w/ the first cap) because the starting voltage V1 has doubled in the process.
External energy applied to the system is required to physically separate the plates, but what would happen if ZVS or ZCS is used to switch in and out a series capacitor identical to the original one in the circuit?  This would effectively cut the original 'C' in half while doubling the circuit 'V' and modifying the Energy of the circuit likewise. Only thing left to do would be to synchronized the output (loading of the circuit) w/ the ZVS switching of the series capacitor.
Maybe run it all using photovoltaics............

take care, peace
lost_bro

Thank you for the very engineerable description lostBro.  I see you are starting to get to the real points I am alluding to in this thought experiment.  The nice thing is that the process it is extremely engineerable and falsifiable.

* In the EM world, energy and frequency are directly proportional via Planck's Constant.   (E=HF)
   (This can also be described in the EE world with EMF and MMF, where change in coulombs/webers per-unit-time determines the amount of energy conveyed per-unit time.)
* Frequency is described by impedance (dimensional between cause and effect).
   In the case of astrophysics, gravity is an impedance.  In the case of electrical engineering, it is determined by Inductance and Capacitance.
* Impedance can be dynamic and does not necessarily require expenditure of energy.  In the case of my first post, gravity presents as an impedance that can be varied with altitude.  In orbit, the energy required for this variation approaches zero.


I actually started this thread as an abstract way of describing/understanding Dollard/Steinmetz mathematics concerning parametric variation of LC.
It's one thing to see a set of equations or computer simulation but another to actually see the process in a completely different context.


Best of luck all

[Reiyuki]

A practical envisioning of this thought experiment would involve a circuit that varies its inductance/capacitance at twice its fundamental frequency.
When modeling the resulting hysteresis curve, one will note a region in which the curve is folded back over itself.  Since hysteresis losses are derived from the total area of this diagram, the region that is folded-over would be considered a negative hysteresis region.

Since EMF and MMF are both derived by change in Coulombs/Webers over time, a greater change per-unit time represents a greater EMF produced.  The time constant of this is determined by the inductance/capacitance at each point in time.  This could also be conventionally described as a blue-shift or a change in frequency.

Another possible way to utilize may be to charge an inductive coil with one impedance, and with a diode, redirect the flyback across a different impedance..

-------------------------->>

"Use a damn Alexanderson Mag-amp, not mechanical rotors, etc. Use harmonics of line frequency on the control winding.
Use a car alternator or other machine to generate them, not solid state. Tune the control winding with a series condenser (watch for high voltage)"
http://www.energeticforum.com/159983-post470.html

Chris Carson Built the Rotary Electrostatic Converter. His design was based entirely on my electrical theory and math. It was designed to demonstrate and validate the concept of  Synchronous Parameter Variation and the Four Quadrant Theory of  Electricity. The device worked well . It had to spin up to around 10,000 RPM. This unit took Chris months to complete; to get all of the parts together, and to get it perfectly balanced and operational.
Chris determined that it was starting to exhibit the effects of synthesis of  electrical energy from the electrostatic field.
This is a result of  the variation of capacitance (C in Farrads) with respect to time (T in seconds) which results in a negative conductance G (in Siemens).
Hence the generation of electric energy.
http://www.tuks.nl/pdf/Eric_Dollard_Document_Collection/Eric%20Dollard%20-%20%20Posts%20on%20EnergeticForum.pdf

"Consider energy, flowing straight and level down the proximity of a transmission line. The energy does not know the width of the channel through which it is passing. If the energy reaches a point where the dielectric changes (but not the geometry), some of it will continue on and some of it will reflect. If the energy reaches a change in the width of the transmission line some will reflect and some will continue as well. The energy current will not know whether:

(a) the dielectric is changing, or
(b) the geometry is changing.

Energy current does not have directional inertia, so that (a) is equivalent to (b). Energy current does have an aspect ratio. If the aspect ratio is forced to change, some of the flowing energy will reflect in order to assure that its total aspect ratio remains constant."
http://rexresearch.com/sweet/1nothing.htm

"The essence of the effect lies in the fact that the addition of electromagnetic fields (constants and variables) are added no energy, and the field amplitude.
The field energy is proportional to the square of the amplitude of the total electromagnetic field. As a result, the simple addition of the energy fields of the total field can be many times the energy of the initial fields separately. This property of the electromagnetic field is non-additivity of the energy field.
For example, when added to a stack of three flat circular permanent magnet energy of the total magnetic field is increased to nine times! A similar process occurs with the addition of electromagnetic waves in the feeder lines and resonance systems.
Total energy of a standing electromagnetic wave can be many times greater than the energy of waves and the electromagnetic field to add."
http://www.hyiq.org/Downloads/Melnichenko/Andrei_Melnichenko_Inventions.pdf

[F6FLT]

F6FLT,
If a capacitor gains mass when it is being charged, where is this excess mass coming from?

It comes from the energy needed to change the capacity.
If you move the plates apart from each other of a charged capacitor, you exert a force against the Coulomb force, so you spend work.
It is very easy to calculate that this work plus the initial energy of the capacitor is equal to the final energy gained E=C.U²/2.

EXACTLY!!   There seems to be a surprising disconnect between potential energy and kinetic energy in cases like this.
...

Energy depends on the referential, it's not absolute. Therefore an energy analysis must always be made in only one referential, preferably inertial.
With a spring, it is an elastic potential energy, we can keep its center as the origin of the referential and easily calculate its mass variation, it is 1/2 * k x²/c² where x is the elongation or shortening.
With the potential energy of gravity or kinetic energy, it is necessary to take either a referential independent of the two objects whose movements are relative or that of the object that remains at rest. The energy gained or lost and therefore the mass is not located in each object but in the system of both objects as a whole.

[Reiyuki]

It comes from the energy needed to change the capacity.
If you move the plates apart from each other of a charged capacitor, you exert a force against the Coulomb force, so you spend work.
It is very easy to calculate that this work plus the initial energy of the capacitor is equal to the final energy gained E=C.U²/2.

The work expended to change a parameter like capacitance can indeed be decoupled from the work performed.

* In the case of mechanical or electrical switching, this is a fixed quantity that is in no way related to energy imparted by the capacitors.  A 1mfd or 10farad capacitance can be mechanically switched using the same amount of energy.  See attached.
* In the case of dynamic variation (Rotary Electrostatic Converter), the parameter can is varied while is has no/little charge placed on it.

In both cases, it is the mathematical equivalent of moving the capacitor plates closer/further.

The same rules apply to inductors.


Thanks F6FLT, I do appreciate your diligence in critiquing the concept, as any good theory needs to stand up to honest scrutiny.


Edit: the cap switching example is not an example of OU, but an example of dynamic variation of C.
the total number of Coulombs is conserved in both states.

[Smudge]

Here is a paper I wrote some years ago dealing with induced inertia effects, and in particular the possibility of using the Earth's scalar magnetic potential.  I posted this elsewhere on one of the many TPU threads but I can't remember which one.  As it touches on some of the thinking here on this thread I thought I would re-post it.
Smudge

[Smudge]

The work expended to change a parameter like capacitance can indeed be decoupled from the work performed.

* In the case of mechanical or electrical switching, this is a fixed quantity that is in no way related to energy imparted by the capacitors.  A 1mfd or 10farad capacitance can be mechanically switched using the same amount of energy.  See attached.
.........it is the mathematical equivalent of moving the capacitor plates closer/further.

Beware of that simplistic statement.  Charging capacitors in parallel then switching them in series can seem to offer OU when the capacitor values are widely different.  The capacitance value changes from (C1+C2) to (C1*C2)/(C1+C2) and the voltage goes from V to 2V.  But you do not end up with a capacitance value of (C1*C2)/(C1+C2) charged to 2V.  When you discharge the series combination into a load the smaller capacitance quickly discharges, then with current still flowing in the same direction the smaller capacitance charges up in the opposite polarity.  When the current drops to zero you have zero voltage cross the two capacitors, but they are not fully discharged, they are simply charged to the same small voltage but in opposite polarity.  You then need further switching to discharge both.  The net result is you get out all the energy you put in.  There is no OU.  That situation is completely different to having the series combination charged up to 2V while they are in series.  But misguided OU presenters don't go into that detail, they just assume that the math tells them that charging in parallel and discharging in series can lead to OU.
Smudge 

[Reiyuki]

Beware of that simplistic statement.  Charging capacitors in parallel then switching them in series can seem to offer OU when the capacitor values are widely different.  The capacitance value changes from (C1+C2) to (C1*C2)/(C1+C2) and the voltage goes from V to 2V.  But you do not end up with a capacitance value of (C1*C2)/(C1+C2) charged to 2V.  When you discharge the series combination into a load the smaller capacitance quickly discharges, then with current still flowing in the same direction the smaller capacitance charges up in the opposite polarity.  When the current drops to zero you have zero voltage cross the two capacitors, but they are not fully discharged, they are simply charged to the same small voltage but in opposite polarity.  You then need further switching to discharge both.  The net result is you get out all the energy you put in.  There is no OU.  That situation is completely different to having the series combination charged up to 2V while they are in series.  But misguided OU presenters don't go into that detail, they just assume that the math tells them that charging in parallel and discharging in series can lead to OU.
Smudge

Whoops, I should have been more specific.
I was pointing out an example where the capacitance is varied with respect to time.  The potential energy contained of course is conserved in either case (but both will have different R/C time constants when charging/discharging).

Of course, if OU was so simple it would have already been done this way.
It is far more likely that such a system would not work in a static state.

I thoroughly enjoyed your paper, thanks; there seems to be much overlap in terms of how we approach these esoteric systems.

[F6FLT]

The work expended to change a parameter like capacitance can indeed be decoupled from the work performed.
...

That's false.
For example, the work for spacing capacitor plates depends on the charge. I don't see the point in denying the Coulomb law.

* In the case of mechanical or electrical switching, this is a fixed quantity that is in no way related to energy imparted by the capacitors.
...

A switch is NOT a parameter change. If you have a charged capacitor C in series with a short-circuited capacitor of the same capacity, you have still an equivalent capacitor C. If you switch off the shorted capacitor so as to divide the capacity by two to increase the energy, you have C/2 at the end, but the charge is always only in the first capacitor while in the second, you have zero. No energy is gained. With capacitors in parallel, it's the same thing.

"Of course, if OU was so simple it would have already been done this way. "   

[Reiyuki]

That's false.
For example, the work for spacing capacitor plates depends on the charge. I don't see the point in denying the Coulomb law.

I think you misunderstand.  Coulomb's law applies to the capacitor plates themselves, but notsomuch to the circuit that surrounds it.
When capacitance of a circuit is changed via manual switching (for example, changing two identical capacitances between parallel and series), the total coulomb charge remains the same, but the voltage and capacitance change proportionally to balance the equation.
(However the RC time constant does indeed change....)

A switch is NOT a parameter change. If you have a charged capacitor C in series with a short-circuited capacitor of the same capacity, you have still an equivalent capacitor C. If you switch off the shorted capacitor so as to divide the capacity by two to increase the energy, you have C/2 at the end, but the charge is always only in the first capacitor while in the second, you have zero. No energy is gained. With capacitors in parallel, it's the same thing.

I did not said energy changes simply by switching capacitance, it is only one half of the solution.  What does change is the RC time-constant, and thus the ElectroMotive force at various parts of the cycle.

In a static state, the total number of coulombs is indeed a conserved quantity, and the voltage changes to meet this inequality in the same way that Boyle's Law applies to gases.
Volts = Coulombs / Farads
Farads = Coulombs / Volts


For physical variation of capacitance (ie: varying plate distance), one must also consider the charge at every point in the cycle, since variation will cost energy and some will return it (much the same way that a spring is stretched and relaxed).


Steinmetz covers this interaction quite well:
http://www.tuks.nl/pdf/Reference_Material/Steinmetz/Reaction%20Machines%20chapter%20in%20Alternating%20Current%20Phenomona.pdf

[F6FLT]

...
I did not said energy changes simply by switching capacitance, it is only one half of the solution. 
...

You said "The work expended to change a parameter like capacitance can indeed be decoupled from the work performed."

That's false when the parameter change results in an energy gain, which is the goal.
In this case the change of parameter requires energy, the one that will be "gained" (minus losses).

[Reiyuki]

You said "The work expended to change a parameter like capacitance can indeed be decoupled from the work performed."

That's false when the parameter change results in an energy gain, which is the goal.
In this case the change of parameter requires energy, the one that will be "gained" (minus losses).

Varying capacitance by itself does not result in energy gain.  It is merely a dimensional transformation.
I should have been more clear.  'work performed' is referring to the natural EMF/MMF during the charge/discharge cycle and not cyclic variation of C by itself.

When varying plate distance, the same number of coulombs is present in a capacitor in both cases, but the voltage and capacitance have changed (along with the RC time-constant )

Varying the plate distance cyclically does not require net energy, as the energy required to pull the plates apart is equal to the energy returned when the plates are pulled together (minus intermolecular losses).
This is akin to pushing/pulling a spring;the energy spent to compress the spring is returned on extension.


The 'work performed' discrepancy lies in the change in time-constants for the charge/discharge cycle(re: frequency).
https://www.onlinemathlearning.com/charge-circuits.html
The same amount of energy is returned, but at a different frequency.

[F6FLT]

...
When varying plate distance, the same number of coulombs is present in a capacitor in both cases, but the voltage and capacitance have changed (along with the RC time-constant )

Varying the plate distance cyclically does not require net energy
...

That's true, but you don't produce energy.
Similarly, cyclic movement of a mass at variable speeds also requires no energy when deceleration and acceleration are balanced.
But if system energy is used, then changing the parameter will require energy over a cycle.
In the case of the charged capacitor, the spacing of the plates increases its energy and their next convergence restores it, but if you consume part of the energy produced in the first phase, the restored energy will not enough and you will have to provide the same additional energy to modify the capacity in the next cycle.

[Reiyuki]

That's true, but you don't produce energy.
Similarly, cyclic movement of a mass at variable speeds also requires no energy when deceleration and acceleration are balanced.
But if system energy is used, then changing the parameter will require energy over a cycle.

We're dealing with a dimensional relationship, so a better analogy would be varying the density of an object with respect to time while lifting/dropping it.   Or changing the spring constant of a mass-spring system while it is being compressed/expanded.

Remember that cause and effect are no longer occurring at the same time due to hysteresis (lest we violate causality:P).

Altering the parameter of L or C can indeed be varied in a manner that requires a purely fixed amount of energy.
- In the case of capacitance, capacitors can be physically switched into series/parallel configurations without succumbing to plate attraction via Coulomb's law.
- In the case of inductors, inductance can be physically varied using saturable reactors (Magnetic Amplifier)
https://www.youtube.com/watch?v=DBX1-POuJMw
In both cases, the act of variation is effectively decoupled from the action of the rest of the circuit and could thus be considered a reactive variation.


In the case of variation of potential, current, capacitance, or inductance with respect to time, the following pair handles the geometric coefficients:
Farad per second      (Siemens)
Henry per second      (Ohms)
(see: http://www.gestaltreality.com/energy-synthesis/eric-dollard/energy-defined )

Note that these both relate directly to frequency as in:
        F= 1/(2pi Sqrt(L*C)   (LC frequency formula)
and    E=HF                      (Planck's Constant)

Also note that if L or C is varying with respect to time, so is the frequency of the waves circulating within it.


Now the question is to validate such methods of parametric variation expressed by the likes of Dollard, Steinmetz, and Alexanderson generate the nonlinear solutions suggested by the mathematics.  Many means should be possible, and in fact many credible inventions of recent history will often make more sense when viewed through this lens.


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http://www.borderlands.de/net_pdf/NET0107S26-28Det.PDF

http://aias.us/documents/uft/UFT382.pdf