1. Originally Posted by Copernicus
I could be wrong, but if the inductance of the transformer is not high enough for certain types of capacitors that are not linear with voltage, you can get all sorts of kinds of nonlinearity in the ramp up.
As Geo Kaplan said, what transformer? And nobody's saying real capacitors are ideal. Leakage means very low currents won't charge the capacitor beyond a certain point, dielectric "constants" can vary with electrical field strength, plates can physically move closer to each other under electrostatic forces, etc...

Regardless, the behavior of real capacitors is very far from what we'd see if this theory were correct...capacitance in general is essentially independent of current or voltage over a very wide range, but if the theory were correct, capacitance measured using the time constant of a RC circuit would appear to be inversely related to the voltage. We're not talking about being off by just a bit...capacitance when charged to 100V would be 1/100th that when the same capacitor is charged to 1V. Capacitors usually aren't high precision components, but the tolerance is generally on the order of 5-20%, not 10000%. Even the simplest oscillators and filters would give results wildly different from those expected.

2. ... (and are also avoiding answering our questions) ...
Transpower, the Rules require that you defend your ATM proposal by answering all direct, pertinent questions. You haven't really done this so far. You need to start doing it.

Now.

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It seems to me that you have entirely skipped part one of the tag line below. Could you please cite one observation that time is quantized? Please, no assertions, no speculations, just a real observation, confirmed and repeatable, that there is a smallest unit of time. Realize that if there is no such observation, then your theory is speculation at best.

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Originally Posted by cjameshuff
As Geo Kaplan said, what transformer? And nobody's saying real capacitors are ideal. Leakage means very low currents won't charge the capacitor beyond a certain point, dielectric "constants" can vary with electrical field strength, plates can physically move closer to each other under electrostatic forces, etc...

Regardless, the behavior of real capacitors is very far from what we'd see if this theory were correct...capacitance in general is essentially independent of current or voltage over a very wide range, but if the theory were correct, capacitance measured using the time constant of a RC circuit would appear to be inversely related to the voltage. We're not talking about being off by just a bit...capacitance when charged to 100V would be 1/100th that when the same capacitor is charged to 1V. Capacitors usually aren't high precision components, but the tolerance is generally on the order of 5-20%, not 10000%. Even the simplest oscillators and filters would give results wildly different from those expected.
I am sorry for the confusion. I was referring to high dielectric capacitors in 10000 range where the capacitance can diminish as much as 80 percent depending on AC voltage applied. The waveforms on the oscilliscope can be very odd with tremendous spikes in voltage.

5. Originally Posted by Copernicus
I am sorry for the confusion. I was referring to high dielectric capacitors in 10000 range where the capacitance can diminish as much as 80 percent depending on AC voltage applied. The waveforms on the oscilliscope can be very odd with tremendous spikes in voltage.
This is because real components do not behave like ideal ones. The real behaviour can still be modelled (to any chosen degree of accuracy) by modelling the departures from ideal with parallel and serial resistance and inductance, the non-linearities of the components, etc. (Using standard physics of course, not some broken theory which, by its own admission, does not match reality.)

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Originally Posted by Copernicus
I am sorry for the confusion. I was referring to high dielectric capacitors in 10000 range where the capacitance can diminish as much as 80 percent depending on AC voltage applied. The waveforms on the oscilliscope can be very odd with tremendous spikes in voltage.
Yes, capacitors made with nonlinear dielectrics will act...nonlinearly. PZT is a wonderful dielectric, for example, but the way you get high dielectric constants is to have a high polarizability. Those dipoles can only stretch/rotate so far, though, so you must operate at well below breakdown voltage (both AC and DC, not just AC) to avoid saturation of the polarization. Beyond that, the capacitance rapidly approaches that of vacuum. These materials are also piezoelectric and temperature sensitive (indeed, they can be pyroelectric). These behaviors are precisely why high-K dielectrics generally aren't used in ramp generation circuits. In any case, none of this is at all relevant to what cjameshuff's point was.

7. Originally Posted by Copernicus
I am sorry for the confusion. I was referring to high dielectric capacitors in 10000 range where the capacitance can diminish as much as 80 percent depending on AC voltage applied. The waveforms on the oscilliscope can be very odd with tremendous spikes in voltage.
Enough. No more derailment from Copernicus' post about transformers or other topics. This thread is for Transpower to explain his idea and answer questions about it; that's it. It is not for any other side discussion. If you anyone wishes to discuss related topics, start your own thread.

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The very simple DC circuit I'm discussing includes a constant voltage source, V, a resistor, R, and a capacitor, C, in series. I'm not discussing a current source. I gave the equations above, from both the Reciprocal System and the conventional theory, for the voltage across the capacitor as a function of time. The Reciprocal System predicts faster charging and discharging of capacitors than conventional theory. Tuma (p. 223 in Handbook of Physical Calculations) says very clearly, "Theoretically, after an infinite time the current I becomes zero. In practical cases, it is a matter of seconds." He thus discounts the conventional expression.

In the original publication on the Reciprocal System by Dewey B. Larson in 1959, he predicted that large, external galaxies would be moving away from other galaxies (outside their gravitational limits) at faster and faster speeds the farther the distance. This was, of course, contrary to conventional theory, but recently has been proven observationally. For the computational details, see my paper "Calculation of the Gravitational Limits and the Hubble Constant for the Local Group" at http://transpower.wordpress.com.

Getting back to ordinary electrical currents: they are neutral of course, but conventional theory says that the negative charges of the electrons are counter-balanced by the positive charges of the protons. The Reciprocal System says that the electrons are neutral. If they were charged, they would repel one another to the surface of the conductor--this would be static electricity; the Reciprocal System identifies static charges as charged electrons. So, electrons come in two flavors: charged and uncharged. There are no charged electrons on the surface of ordinary conductors, so we know that the electrons in the currents are uncharged.

From the famous experimental physicist, P. W. Bridgman (The Thermodynamics of Electrical Phenomena in Metals and a Condensed Collection of Thermodynamic Formulas, p. 3): "The electron theory came crowding on the heels of the formulation of the field equations, with its thesis that the properties of all matter could be explained in terms of the motion of concealed discrete electrical particles, and that the motion of these particles was controlled by the field equations, extrapolated to microscopic dimensions hopelessly beyond direct experimental verification, and before their validity had been checked even over the entire experimental domain. And finally, crowding on the heels of electron theory, is wave mechanics, forced on us by the new experimental facts of atomic physics, in which we give up the idea of discrete electrical particles with individuality, but retain the concept of the electrodynamic field to control the motion of what replaces the electron, and determine the magnitude of this field (as, for example, in the neighborhood of the nucleus of an atom) in terms of a fictitious discrete elementary charge acting after the fashion of the charges of large scale experience. In the face of a historical development like this it would not be surprising if points had been missed, and it seems to be worth while that at least one physicist should attempt a critical review and record somewhere his findings." That's exactly what Dewey B. Larson and I have done. The results are in our books and papers.

9. Transpower, in my last post I asked you to start answering questions in accordance with BAUT Rules. Can you please point out which questions are addressed in your latest post, #38?

Oh, and I killed your live link. We don't care too much for overt self-promotion here. Repeatedly posting links to your paper, when you have been told to present your arguments here, looks like an attempt to boost your Google rating. Anyone interested knows by now where to find it.

10. Originally Posted by Transpower
In the original publication on the Reciprocal System by Dewey B. Larson in 1959, he predicted that large, external galaxies would be moving away from other galaxies (outside their gravitational limits) at faster and faster speeds the farther the distance. This was, of course, contrary to conventional theory, but recently has been proven observationally.
It is irrelevant how many random predictions it makes that appear to be roughly correct (even a broken clock can be right twice a day); the theory is trivially falsified by producing incorrect results, as you described earlier:

Originally Posted by Transpower
At 5 volts, which is typical, the Reciprocal System and conventional theory give the same energy result. The differences become great then the voltage is << 5 or >> 5.

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Originally Posted by Transpower
The very simple DC circuit I'm discussing includes a constant voltage source, V, a resistor, R, and a capacitor, C, in series. I'm not discussing a current source.
Yes, we know this, and you know that we know this. Cjameshuff's post -- and what it means -- is clear to anyone with "ordinary skill in the art." So, given your lofty academic credentials (at least as you've represented them), we must conclude that you're deliberately choosing to ignore cjameshuff's post. One needn't look too hard to infer why, for from your persistent avoidance of answering the simplest of questions, it's clear that you simply don't have the ability to refute our arguments. In lieu of debate, you just want to preach to us. I for one have no expectation that you will change your established pattern of behavior, despite repeated warnings from the mods to play by the rules.

So it's summary time. Sprinkled among adverts for your site, you made the assertion that energy in a capacitor is linearly proportional to voltage, rather than to the square of voltage. It is one of the few times that you ventured to offer a specific, testable claim of your grand theory. Many of us pointed out that this claim has been shown wrong (both theoretically and experimentally), at least from the order of a volt (the realm of low-power consumer electronics) to the order of a megavolt (the peak voltage of long-distance power transmission lines). I note for the record that this dynamic range of voltages extends well beyond the risible "5V limit" that you pulled out of the air. We have experimental support for the mainstream view (which is precisely WHY it's the mainstream), and you have nothing but a pile of papers. Papageno's dismissive reference to them as "pathetic" may be painful to hear, but it captures the essence honestly.

12. Originally Posted by Transpower
The very simple DC circuit I'm discussing includes a constant voltage source, V, a resistor, R, and a capacitor, C, in series. I'm not discussing a current source.
In your criticism of my counterexample, the circuit you refer to is a capacitor charging from a constant current source or discharging through a constant current load. You can not dismiss my argument by pretending the circuit is something else.

Now. The example is a capacitor charging or discharging at constant current, to or from some arbitrary maximum voltage. This is not negotiable. You may not substitute an example from one of your papers, you may not change it to use a constant voltage source. In your reply to this message, you must consider this circuit. Now, as nicely numbered and initialed formal questions:

CJH1: What is the voltage waveform across the capacitor?
CJH2: What is the power waveform, given that the current through the capacitor is constant?
CJH3: How much energy is transferred while changing state between fully discharged and half-charged, compared to the energy transferred to fully charge or discharge the capacitor?
CJH4: How much energy is transferred while changing state between half-charged and fully charged, compared to the energy transferred to fully charge or discharge the capacitor?
CJH5: Given the claim of your theory that stored energy is directly proportional to voltage, what would your theory predict for the answers to CJH3 and CJH4?

CJH6: What precisely is "nonsensical" about the notion of electromagnetic radiation resolving the "paradox" you keep referring to?
CJH7: What voltages are common in audio gear, tube radios, modern computers, etc?
CJH8: What force moves "neutral electrons" around and confines them in a capacitor in your Reciprocal System?
CJH9: What evidence do you have that charge is not strictly conserved, or that anything like "neutral electrons" exists?
CJH10: What is the origin of the electrical field around a charged capacitor, if it serves as a repository for neutral electrons as you claim?
CJH11: What is the origin of the mechanical forces on the plates of charged capacitors?

Originally Posted by Transpower
I gave the equations above, from both the Reciprocal System and the conventional theory, for the voltage across the capacitor as a function of time. The Reciprocal System predicts faster charging and discharging of capacitors than conventional theory.
And since real capacitors produce results in agreement with conventional theory, allowing us to build RC oscillators, filters, charge pumps, dynamic memories, etc that actually work, this is a failure of the Reciprocal System.

Originally Posted by Transpower
Tuma (p. 223 in Handbook of Physical Calculations) says very clearly, "Theoretically, after an infinite time the current I becomes zero. In practical cases, it is a matter of seconds." He thus discounts the conventional expression.
The theory involves simplifications that treat motion of large numbers of quantized charges as continuous and considers components to be ideal and circuits to be in isolation. Real circuits move real electrons around through non-ideal components and are subject to random thermal motions of atoms and electrons, external interference, and so on. This is not a failure of mainstream theory.

Originally Posted by Transpower
Getting back to ordinary electrical currents: they are neutral of course, but conventional theory says that the negative charges of the electrons are counter-balanced by the positive charges of the protons. The Reciprocal System says that the electrons are neutral. If they were charged, they would repel one another to the surface of the conductor-
Absurd. You even mentioned the reason this doesn't happen...the positive charges of the protons. Why would electrons move toward the surface and leave a huge positive charge in the center? Consider that question CJH12.

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Originally Posted by John Mendenhall
It seems to me that you have entirely skipped part one of the tag line below. Could you please cite one observation that time is quantized? Please, no assertions, no speculations, just a real observation, confirmed and repeatable, that there is a smallest unit of time. Realize that if there is no such observation, then your theory is speculation at best.

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Originally Posted by Transpower
In the original publication on the Reciprocal System by
Dewey B. Larson in 1959, he predicted that large, external
galaxies would be moving away from other galaxies (outside
their gravitational limits) at faster and faster speeds the
farther the distance. This was, of course, contrary to
conventional theory, but recently has been proven
observationally.
Edwin Hubble discovered that relationship between speed
and distance of galaxies in 1929. A theoretical description
of the relationship came even earlier: It was worked out by
Alexander Friedman in 1922.

-- Jeff, in Minneapolis

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As a service to people finding this thread at some later date, here's the mainstream -- and correct -- solution to the "two-capacitor 'paradox'" for future reference:

First, the problem statement, as typically found in Physics 101 classes:

Without loss of generality, consider two capacitors of value C. Assume that one initially has no charge, and that the other is initially charged to a voltage V. At time t=0, a switch connects these two capacitors. A quick calculation based on charge conservation shows that the final voltage should be V/2.

Now, the initial energy is CV^2/2, while the final energy is CV^2/4. Energy seems not to have been conserved. This apparent failure is the starting point for Transpower's ATM claim. Rather than consider the likelihood that his own ignorance is the real problem, he chooses instead to ignore the vast body of quantitative evidence in favor of mainstream physics and develops an elaborate "solution" to a non-existent problem.

But where is the missing energy? Given the large accounting discrepancy -- half the energy seems to be missing -- how can mainstream theory not be wrong?

There is indeed a problem, and it stems from the appearance of infinite currents that flow for an infinitesimal time. Now, infinities require special handling, so we must be very careful in working out the math. One of several (perhaps many) ways to do this is to eliminate the infinities at the outset. Here's what I mean: Postulate the existence of a non-zero resistance in the circuit (to bound the currents to finite values), compute the energy loss due to the resistor, and then consider what happens as the resistance goes to zero.

As Transpower himself has stated (several times, in fact, as he desperately dodged cjameshuff's post on constant-current charging of capacitors) the voltage across a charging capacitor will vary exponentially with time in this configuration. In our case, the voltage between the capacitors (which is the same as the voltage across the resistors) will have the form

V(t) = V*exp(-2t/RC).

The instantaneous power dissipated in the resistor is just the square of that voltage, divided by R. The total energy, Er, lost due to the resistor, is simply the integral of that power:

Er = (1/R)*∫[V*exp(-2t/RC)]^2 dt = CV^2/4.

Note that the energy lost is precisely the amount needed to fix the energy accounting ledger. Also note that the energy lost is independent of the resistor's value. A large resistor just loses the energy more slowly than a small one. And a zero-valued resistor loses this energy in zero time. ETA2: If radiation is permitted by boundary conditions, the effect of that energy loss is again represented by a resistance (known, appropriately enough, as the radiation resistance), but the value of that energy loss is unchanged, thanks to the result's independence of the precise value of the resistance. It all contributes to universal warming.

So we see that there is actually no paradox, and thus there is no paradox to be resolved. Further we see that any solution that "corrects" this apparent paradox must actually be wrong.

Whether Transpower's paper on the two-capacitor problem is pathetic or not, it is certainly completely wrong. And therefore so is the Reciprocal Scaling Theory (or whatever the heck RST stands for) on which that paper is based.

ETA: Transpower/Satz makes a big deal about simplicity, arguing that RST is superior in that regard. I note for the record that the mainstream solution to the two-capacitor problem is compact enough to include in a single post (even though it's wordier than necessary). Satz's goofy paper occupies something like 10 pages, and it's hopelessly, unsalvageably, horribly and absurdly wrong. So in this case, the mainstream approach is simpler, on top of being correct.

Once again, game over for RST. Stick a fork in it. It's done.
Last edited by Geo Kaplan; 2012-Jan-05 at 06:16 PM. Reason: grammar; ETA: PS on simplicity; fixed missing right-parenthesis in integral; ETA2: ref to radiation

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From Post #25 and before:

Tensor1 Then show us the calculations that you would use in RS, to predict the decay of the orbit of PSR 1916+13. And show how those calculations match observations

From post #9:
Tensor2 QED has been calculated to more than 10 decimal places(another error about conventional theory). It matches observation to 10 decimal places. If RS can't, it's less correct than QFT, no matter how you spin it.
Provide the calculations from RS that can match observations to 10 decimal places.

Also from post #9
Tensor3 I asked specifically for you to show where current experiments disagree with theoretical predictions. There must be many such examples if current theory is as wrong as you claim it is.

Tensor4 Yeah, but according to you current theory is so bad that they shouldn't work at all, right?

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Let's consider a simple mechanical analogy to the electrical situation I've described. Suppose we have two cylindrical vats, one filled with a liquid and the other empty. A pipeline is connected between them with a valve. At time zero, the valve is opened. Obviously, the liquid will flow from the filled vat to the other vat. If they are the same size, the final height will be the same for both. The original potential energy of the first vat is, partially, converted to kinetic energy of the fluid to the second vat. This kinetic energy is transformed to potential energy in the second vat. After this process, the combined potential energy of the two vats will be equal to the potential energy of the liquid in the first vat at the start of the vat, minus any possible losses in the connecting pipe, valve, and wall friction, which should be small.

Now try to understand the two capacitor problem. Electrons in the first capacitor have energy (voltage = energy/electron), while the second capacitor (in parallel) is empty of electrons. The switch is closed, and electrons move from the first capacitor to the second capacitor. The voltage drops from what it was in the first capacitor, and the two capacitors come to the same voltage (or "pressure" or "force" in the mechanical analogy). There is no loss of energy in this process (other than that due to resistance of the connecting wire, which should be very small). Therefore energy is conserved. The electrons are not charged in this process--they are neutral, and all capacitors are neutral. Charges are easily created and destroyed, as any kid knows from running across a carpet in a dry room and touching a door knob. The "charge conservation" of "modern physics" is bogus. Conventional physicists keep charge conservation but are ready to ditch energy conservation. They have it backwards.

CJH1: What is the voltage waveform across the capacitor? [I gave the equation in a previous post.]
CJH2: What is the power waveform, given that the current through the capacitor is constant? [The current is not constant--it obvioiusly decays to zero.]
CJH3: How much energy is transferred while changing state between fully discharged and half-charged, compared to the energy transferred to fully charge or discharge the capacitor? [It's the integral of v x i over dt. See the paper.]
CJH4: How much energy is transferred while changing state between half-charged and fully charged, compared to the energy transferred to fully charge or discharge the capacitor? [See the paper.]
CJH5: Given the claim of your theory that stored energy is directly proportional to voltage, what would your theory predict for the answers to CJH3 and CJH4? [Already have done that. See the referenced paper.]

CJH6: What precisely is "nonsensical" about the notion of electromagnetic radiation resolving the "paradox" you keep referring to? [Because it's handwaving. There is no evidence of this, and it's not negligible.]
CJH7: What voltages are common in audio gear, tube radios, modern computers, etc? [It ranges of course. See Guidebook of Electronic Circuits. In the PC, and most circuit boards, it's 5 volts.]
CJH8: What force moves "neutral electrons" around and confines them in a capacitor in your Reciprocal System? [A voltage source of course. A voltage is simply energy/electron. So if there is a higher energy/electron in one part of a circuit compared with another, there will be a flow. In the very simple DC series circuit, the current flows from the voltage source to the capacitor until the capacitor reaches the same voltage, at which point the current ceases.]
CJH9: What evidence do you have that charge is not strictly conserved, or that anything like "neutral electrons" exists? [Because if we were really dealing with charges, they would repel themselves to the surface of the conductor--in fact they might even leave the conductor.]
CJH10: What is the origin of the electrical field around a charged capacitor, if it serves as a repository for neutral electrons as you claim? [Moving electrons (whether charged or not) do, of course, create an electric field.]
CJH11: What is the origin of the mechanical forces on the plates of charged capacitors? [Voltage in the Reciprocal System has the same dimensions as force, t/s^2.]

Tensor1 Then show us the calculations that you would use in RS, to predict the decay of the orbit of PSR 1916+13. And show how those calculations match observations

From post #9:
Tensor2 QED has been calculated to more than 10 decimal places(another error about conventional theory). It matches observation to 10 decimal places. If RS can't, it's less correct than QFT, no matter how you spin it.
Provide the calculations from RS that can match observations to 10 decimal places.

Tensor3 I asked specifically for you to show where current experiments disagree with theoretical predictions. There must be many such examples if current theory is as wrong as you claim it is. [I have a whole Database of Reciprocal System calculations of the properties of matter. The nuclear theory is full of holes: the negatively-charged electrons should spiral right down and neutralize the positively-charged protons; the protons should repel one another explosively; neutrons are unstable every where we work with them. The Bohr orbits are purely hypothetical; the strong force is purely adhoc (like the demons of our ancestors).]

Tensor4 Yeah, but according to you current theory is so bad that they shouldn't work at all, right? [The empirical relations of physics are accepted and explained by the Reciprocal System. We do accept, of course, Newton's Law of Gravitation (suitably modified at high speed), Newton's Laws of Motion (ditto), Ohm's Law, Hess's Law, Kirchoff's Laws, Maxwell's equations (suitably interpreted), Faraday's Law, Avogadro's Law, Pascal's Law, the laws of optics, and the law of the conservation of energy. We also accept Planck's theory of the quantum of radiant energy, Einstein's extension to the photoelectric effect, the Lorentz transformations, and E=mc^2.]

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Originally Posted by Transpower
Tensor1 Then show us the calculations that you would use in RS, to predict the decay of the orbit of PSR 1916+13. And show how those calculations match observations

Originally Posted by Transpower
From post #9:
Tensor2 QED has been calculated to more than 10 decimal places(another error about conventional theory). It matches observation to 10 decimal places. If RS can't, it's less correct than QFT, no matter how you spin it.
Provide the calculations from RS that can match observations to 10 decimal places.

Originally Posted by Transpower

Tensor3 I asked specifically for you to show where current experiments disagree with theoretical predictions. There must be many such examples if current theory is as wrong as you claim it is. [I have a whole Database of Reciprocal System calculations of the properties of matter. The nuclear theory is full of holes: the negatively-charged electrons should spiral right down and neutralize the positively-charged protons;

Originally Posted by Transpower
the protons should repel one another explosively;

Originally Posted by Transpower
neutrons are unstable every where we work with them.

Originally Posted by Transpower
The Bohr orbits are purely hypothetical;

Originally Posted by Transpower
the strong force is purely adhoc (like the demons of our ancestors).]

You have not provided any experiments that do not agree with current theoretical predictions. What you have provided is nothing more than unsupported assertions. Either provide such experiments, or retract your claims.

Originally Posted by Transpower
Tensor4 Yeah, but according to you current theory is so bad that they shouldn't work at all, right? [The empirical relations of physics are accepted and explained by the Reciprocal System. We do accept, of course, Newton's Law of Gravitation (suitably modified at high speed), Newton's Laws of Motion (ditto), Ohm's Law, Hess's Law, Kirchoff's Laws, Maxwell's equations (suitably interpreted), Faraday's Law, Avogadro's Law, Pascal's Law, the laws of optics, and the law of the conservation of energy. We also accept Planck's theory of the quantum of radiant energy, Einstein's extension to the photoelectric effect, the Lorentz transformations, and E=mc^2.]
Gee I ask a simple yes/no answer and I get a bunch of observations, all of which can be derived from current theory. So I guess current theory isn't so bad. Thank you for reaffirming current quantum theory.

19. Originally Posted by Transpower
The electrons are not charged in this process--they are neutral, and all capacitors are neutral. Charges are easily created and destroyed, as any kid knows from running across a carpet in a dry room and touching a door knob. The "charge conservation" of "modern physics" is bogus.
Provide evidence. Your supposed example of breaking charge conservation is easily shown to only be an example of charge separation (just look at any of a wide range of electrostatic generators), and your statement about capacitors remaining neutral shows only that you misunderstand capacitors...they remain neutral in mainstream theory as well.

Originally Posted by Transpower
Conventional physicists keep charge conservation but are ready to ditch energy conservation. They have it backwards.
Except the model in conventional physics conserves energy, and your theory fails to do so. My constant current example makes it irrefutably clear that the energy expended or extracted is proportional to the square of the voltage at maximum charge. If your theory predicts that charging from a voltage source requires energy directly proportional to that voltage, then it predicts that you could build a free energy machine by charging capacitors from a voltage source and discharging them through a constant current load, or make energy vanish into nothing by doing the opposite.

Originally Posted by Transpower

CJH1: What is the voltage waveform across the capacitor? [I gave the equation in a previous post.]
Where? All I see is you refusing to even consider the waveform under these conditions.

Originally Posted by Transpower
CJH2: What is the power waveform, given that the current through the capacitor is constant? [The current is not constant--it obvioiusly decays to zero.]
Re-stating part of the setup is not answering the question. What is the power waveform of a capacitor charging or discharging at constant current?

Originally Posted by Transpower
CJH3: How much energy is transferred while changing state between fully discharged and half-charged, compared to the energy transferred to fully charge or discharge the capacitor? [It's the integral of v x i over dt. See the paper.]
CJH4: How much energy is transferred while changing state between half-charged and fully charged, compared to the energy transferred to fully charge or discharge the capacitor? [See the paper.]
CJH5: Given the claim of your theory that stored energy is directly proportional to voltage, what would your theory predict for the answers to CJH3 and CJH4? [Already have done that. See the referenced paper.]
I will not go to the paper. You are required to answer these questions, and to do so here. This is extremely simple to do, and I have in fact already done it in post 11, which you keep trying to ignore.

Originally Posted by Transpower
CJH6: What precisely is "nonsensical" about the notion of electromagnetic radiation resolving the "paradox" you keep referring to? [Because it's handwaving. There is no evidence of this, and it's not negligible.]
There's no evidence for electromagnetic radiation? Or thermal dissipation in real world components? How is it handwaving when the missing energy is precisely that predicted by more detailed calculations?

Originally Posted by Transpower
CJH7: What voltages are common in audio gear, tube radios, modern computers, etc? [It ranges of course. See Guidebook of Electronic Circuits. In the PC, and most circuit boards, it's 5 volts.]
Yes, it ranges...over what range?
And aside from being irrelevant to a wide variety of electronic devices, your statement about PCs is simply wrong. It's mostly 3.3V these days, a lot of it is 1.8V, some of it is 1.2V, 1V, or even lower. It's been many years since 5V logic has been dominant.

Originally Posted by Transpower
CJH8: What force moves "neutral electrons" around and confines them in a capacitor in your Reciprocal System? [A voltage source of course. A voltage is simply energy/electron. So if there is a higher energy/electron in one part of a circuit compared with another, there will be a flow. In the very simple DC series circuit, the current flows from the voltage source to the capacitor until the capacitor reaches the same voltage, at which point the current ceases.]
But what force is being exerted on these neutral electrons? And why do capacitors retain their charge when removed from a voltage source?

Originally Posted by Transpower
CJH9: What evidence do you have that charge is not strictly conserved, or that anything like "neutral electrons" exists? [Because if we were really dealing with charges, they would repel themselves to the surface of the conductor--in fact they might even leave the conductor.]
Why would they repel each other, given the presence of an approximately equal number of positive charges in the material? I even asked this in the post you're replying to (as CJH12). You have also failed to give any evidence of neutral electrons (that somehow can still be electrically manipulated, and should be trivial to detect).

Originally Posted by Transpower
CJH10: What is the origin of the electrical field around a charged capacitor, if it serves as a repository for neutral electrons as you claim? [Moving electrons (whether charged or not) do, of course, create an electric field.]
What moving electrons? We're talking about a charged capacitor here.

Originally Posted by Transpower
CJH11: What is the origin of the mechanical forces on the plates of charged capacitors? [Voltage in the Reciprocal System has the same dimensions as force, t/s^2.]
This does not come close to answering the question.

I have to say, you are not scoring well. A big pile of unsubstantiated statements, half answers, and attempts to avoid giving an answer. None of my questions are particularly difficult to answer. Addressing my point about capacitors charging or discharging under constant current requires only the most elementary math, yet you constantly refuse to even consider it.

20. Originally Posted by Transpower
CJH7: What voltages are common in audio gear, tube radios, modern computers, etc? [It ranges of course. See Guidebook of Electronic Circuits. In the PC, and most circuit boards, it's 5 volts.]
That is so wrong. Very few components in a PC run at 5V. Especially not modern high performance microprocessors, for which many thousands of hours of highly accurate analog simulations are performed using standard physics. And, you know what, we have never had to make some sort of fudge because we are using the "wrong" theory at voltages other than 5V.

So how does that work? Or is your theory falsified yet again?

21. Originally Posted by Transpower
Let's consider a simple mechanical analogy to the electrical situation I've described. Suppose we have two cylindrical vats, one filled with a liquid and the other empty. A pipeline is connected between them with a valve. At time zero, the valve is opened. Obviously, the liquid will flow from the filled vat to the other vat. If they are the same size, the final height will be the same for both. The original potential energy of the first vat is, partially, converted to kinetic energy of the fluid to the second vat. This kinetic energy is transformed to potential energy in the second vat. After this process, the combined potential energy of the two vats will be equal to the potential energy of the liquid in the first vat at the start of the vat, minus any possible losses in the connecting pipe, valve, and wall friction, which should be small.
Actually, the same math applies, and even the same "paradox". The energy required to force a given quantity of fluid into a vat (starting at ground level) is proportional to how full it is...that quantity of fluid has to be raised by a height proportional to the fullness of the vat. When you integrate this, you find that the energy stored in the vat is proportional to the square of the fluid height. Letting it equalize with another vat of the same capacity will obviously lead to the height halving, leaving two vats with a total of half the stored energy of the one original vat. The remaining energy was lost to heat and noise.

You can also just integrate the potential energy of the vats. The potential energy of each layer of liquid is directly proportional to its height, plotted versus height it makes a ramp. The potential energy of the fluid in the vat (area under the ramp) is again proportional to the square of the height.

...what were you trying to show, again?

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Originally Posted by Transpower
Let's consider a simple mechanical analogy to the electrical situation I've described. ... {snip}
I am impressed by one of your abilities, I must admit. To be able to write so much without actually saying anything right is remarkable.

Cjameshuff has already beaten me to the punch in pointing out that the water tank analogy possesses precisely the same characteristics as does the two-capacitor problem. At least you are consistent in not understanding either one while simultaneously using both in your attempt to overturn all of physics.

You have still failed to answer nearly all questions that have been pending, including GK1 and GK2. I add the following:

GK3: Show the error in my solution to the 2-capacitor problem. Do not simply assert that it is wrong, as you are in the bad habit of doing. You must show specifically where the mathematics in my solution is wrong. If you cannot, withdraw your claim and concede that there is, in fact, no actual paradox.

GK4: Similarly, conventional physics says that the very analogy you offered -- that of the water tanks -- exhibits the same "paradox" as does the two-capacitor problem. Show specifically where conventional physics is wrong (again, do not merely assert that it is wrong; you must show specifically, mathematically where it is wrong). If you cannot, concede that conventional physics is correct.

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Originally Posted by Transpower
Conventional physicists keep charge conservation but are ready to ditch energy conservation. They have it backwards.
You continue feebly to shout this wrong assertion over and over. Yet, who are these benighted "conventional physicists?" I've already pointed out that the very reference you cited -- Sears and Zemansky -- specifically state that both charge and energy are conserved. I show it in my post. You continue to ignore both (and we know why, now, don't we). Perhaps your university was populated by a bunch of physicists made of straw, but the rest of us actually studied the subject.

In the PC, and most circuit boards, it's 5 volts.
Microprocessors used in PCs have not run on 5 volts in almost two decades. Modern microprocessors operate much closer to one volt. Yet, CPU designers are still able to predict power consumption to a high accuracy; no discrepancy of the type you have steadfastly asserted have appeared. That is, hundreds of millions of chips have behaved precisely in accord with a quadratic dependency of energy on voltage, not a linear one, in a voltage regime well below your 5V limit. Before you attempt to move the goalpost to 2 (or something else), I caution you that many experimental CPUs have operated at a few-tenths of a volt, and the power once again behaves exactly as conventional theory predicts.

You -- and RST -- are simply wrong. Hundreds of millions of chips -- indeed, billions when we include the many support chips and memory devices that comprise a PC -- mock your predictions every second.

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[I have a whole Database of Reciprocal System calculations of the properties of matter. The nuclear theory is full of holes: the negatively-charged electrons should spiral right down and neutralize the positively-charged protons; the protons should repel one another explosively; neutrons are unstable every where we work with them. The Bohr orbits are purely hypothetical; the strong force is purely adhoc (like the demons of our ancestors).]
Um... Do you actually know any quantum physics?
1) electrons and protons cannot 'neutralise' each other. They are totally different beasts. One is a composite hadron, the other a lepton. There are properties other than charge that are conserved.
2) electrons don't orbit the nucleus. They exists as a cloud around it. Again QM gives a good and consistent picture of how this works.
3) the strong force is not ad hoc. It explains a lot of things (like hadronic jets in colliders). It works. Do you dismiss the Weak force as ad hoc too?
4) unbound neutrons are unstable. And again we have a good handle on why this happens. Bound neutrons are not. And again, we have a good theory for why this is the case. It is sonsistent with the body of knowledge we have and with observations.
5) the Bohr orbits as mainstream physics are more than fifty years out of date. Probably nearer a hundred now.

So basically it looks like you have either not kept up with real physics and continued to bash circa 1900 interpretations of it, or are building a series of strawmen. Either way I suggest you don't do that here. The people on this board generally understand the physics and are quite capable of spotting these issues with your arguments. It discredits you and your ideas in their eyes. If you need to update your physics we can recommend some good resources. If you are building strawmen then it is not a valid way to prove your theory.

What tends to work here are:
1) worked examples showing how your theory reproduces the validated predictions of current theories
2) worked examples showing where your theory differs in its predictions from current theory
3) evidence or proposals for experiments that would validate your theory over current theory.

25. transpower, it is time that you start actually give REAL answers to the questions that are put to you.
DO NOT put your answers directly behind the questions between [ ], that makes it impossible to see where an answer starts.
Please GIVE some evidence for your claims that there are e.g. "uncharged electrons." and how "uncharged electrons" can create an electric field.

Giving non-answers next time will get you infracted.

26. Originally Posted by Transpower
Let's consider ...
Sorry, should have said this earlier. Transpower has received an infraction for being unresponsive.

27. This has been a fun thread for me. It has been decades since I have studied dielectrics, and the changes in materials and material properties are amazing. Nice work, guys.

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Tensor: PSR 1916+13 a binary pulsar. Just as there may be one or more planets created in a supernova explosion (according to the Reciprocal System of theory), there may be one or more white dwarfs or pulsars. Usually, of course, a supernova explosion will result in a binary star system. White dwarfs result from a supernova explosion in which the stellar thermal limit is reached (Type I or A); pulsars are produced from a supernova explosion in which the stellar age limit is reached (Type II or B); see The Universe of Motion for details. Pulsars have a translational speed which white dwarfs don't. They are miniature quasars, and like most quasars, they will eventually leave our half of the universe and move to the other, inverse half, where space and time are interchanged.

As for "10 decimal places", see the RST calculations for interatomic distance--something that Quantum Mechanics cannot do (it cannot even do calculations of He.) Also QM does not even, after a 100 years, have a workable theory of ferromagnets--but the Reciprocal System does! (See one of my papers above.) The neutrons that we know of are not stable; the nuclear theory of the atom assumes they become stable in the "nucleus." The protons we know of repel one another, but somehow, in the nuclear theory of the atom, there is an ad hoc demon that keeps them together. Assumption after assumption is piled on, completely contrary to our actual experience. U supposedly has 92 electrons and 92 protons. Really? In the Reciprocal System, U has rotational spin numbers 4-4-6. I'll take a simpler, more accurate theory every time.

Ah, the old "cloud" theory; we don't know where the hypothetical electrons are, so therefore they must be smudged out (somehow). This is such obvious nonsense (violates the logic of A = A)--is the electron a wave or a particle? Is the photon a wave or a particle? Conventional theory is very confused; the answers are in the Reciprocal System.

Electrostatic generators do make use of electrical charges, but capacitors do not.

CJamesHuff: You say “If your theory predicts that charging from a voltage source requires energy directly proportional to that voltage, then it predicts that you could build a free energy machine by charging capacitors from a voltage source and discharging them through a constant current load, or make energy vanish into nothing by doing the opposite.” Not so at all; there is no free energy machine; the energy comes from the voltage source. Jeez. Eventually the constant voltage source will decline to nothing.

GeoKaplan: You say, “There is indeed a problem, and it stems from the appearance of infinite currents that flow for an infinitesimal time.” Buddy, if you get infinities in a theory, you should know you’re wrong and give up. There are no infinite currents in the Reciprocal System. But thanks for showing that according to conventional theory of the two capacitor problem, half the energy is lost. Please try to capture that energy! HaHa.

CJamesHuff: You say, “The energy required to force a given quantity of fluid into a vat (starting at ground level) is proportional to how full it is...that quantity of fluid has to be raised by a height proportional to the fullness of the vat. When you integrate this, you find that the energy stored in the vat is proportional to the square of the fluid height.” C’me on, man, the energy is proportional to the mean height, as in mgh Or consider the pressure head, the height of a column of homogeneous fluid that will produce a given intensity of pressure. The pressure heads in the two vats will equalize. h = p/w or p = h x w.

Shaula: If a charged electron and a charged proton are close together, their charges will neutralize. This happens regardless of the disparity in their masses. My papers provide numerous worked examples of RST and the comparison with theory.

Here’s an experiment that Rutherford failed to do and thus set in motion the many mistakes of the nuclear theory of the atom and the electrical theory, including the problem with capacitors. Rutherford used charged helium atoms (alpha particles) from Po-210 to bombard a gold foil, and he observed the scattering. From these results he concluded that there must be a central nucleus of the atom, consisting of protons, repelling the alpha particles. What he should have done next was to neutralize the alpha particles and run the experiment again. The Reciprocal System predicts the same scattering—because in this theory the atoms are not normally charged, and the repulsion is due to a different, non-electrical cause. The conventional theory would or should predict something quite different.

29. Originally Posted by Transpower
Electrostatic generators do make use of electrical charges, but capacitors do not.
Repeating a claim does not provide support for it. You have outstanding questions relating to this particular claim which you have repeatedly avoided answering...examples being CJH9, CJH10, and CJH11.

Originally Posted by Transpower
CJamesHuff: You say “If your theory predicts that charging from a voltage source requires energy directly proportional to that voltage, then it predicts that you could build a free energy machine by charging capacitors from a voltage source and discharging them through a constant current load, or make energy vanish into nothing by doing the opposite.” Not so at all; there is no free energy machine; the energy comes from the voltage source. Jeez. Eventually the constant voltage source will decline to nothing.
Except that according to your reciprocal theory, the capacitor will only require energy proportional to its voltage to charge, and it's clear that it can deliver energy proportional to the square of its voltage to a constant-current load. If a part of the energy removed from the capacitor is used to replenish the voltage source that charges it, then there's no reason for it to dwindle to nothing.

Originally Posted by Transpower
CJamesHuff: You say, “The energy required to force a given quantity of fluid into a vat (starting at ground level) is proportional to how full it is...that quantity of fluid has to be raised by a height proportional to the fullness of the vat. When you integrate this, you find that the energy stored in the vat is proportional to the square of the fluid height.” C’me on, man, the energy is proportional to the mean height, as in mgh
We're talking about a liquid, not a solid object that only varies in height as a unit and can't be separated into its parts. The stored energy is not proportional to the height, it is equal to the total potential energy of each little bit of liquid in the vat added together. By your math, the potential energy of a full tank (mean height 0.5*h) is only double that of a half tank (mean height 0.25*h), yet the upper half of the contents of a full vat (mean height 0.75*h) has 3x the potential energy as the lower half.

Your claim implies that it takes exactly as much work to fill a tank from half way to full as it does to fill it from empty to half full, despite having to push the liquid upwards an ever increasing distance as you pump it in. Once again, you're failing basic math and physics.

Originally Posted by Transpower
Or consider the pressure head, the height of a column of homogeneous fluid that will produce a given intensity of pressure. The pressure heads in the two vats will equalize. h = p/w or p = h x w.
Okay, lets consider the pressure head!
What's the plot of pressure at the bottom over time of a vat draining from full to empty at a constant flow rate? A linear ramp.
What's the plot of mechanical power? Power = flow rate*pressure...another ramp. Hmm.
What's the energy released from the draining tank? The integral of power over time, the area under the mechanical power plot...a triangle. Proportional to the square of the initial fluid height.

Does this remind you of anything?

And a reminder, you are required to answer the other outstanding questions. Your previous posts do not qualify as answers.

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Originally Posted by Transpower
GeoKaplan: You say, “There is indeed a problem, and it stems from the appearance of infinite currents that flow for an infinitesimal time.” Buddy, if you get infinities in a theory, you should know you’re wrong and give up. There are no infinite currents in the Reciprocal System. But thanks for showing that according to conventional theory of the two capacitor problem, half the energy is lost. Please try to capture that energy! HaHa.
Once again we see your inability to answer a straightforward question, coupled with a persistent dishonesty. Tsk, tsk.

For the umpteenth time, I point out that conventional theory has no problem accounting for all of the charge and all of the energy. Both charge and energy are conserved. You continue to claim falsely that "conventional physicists" are willing to abandon energy conservation. I have shown mathematically that both charge and energy are conserved in the two-capacitor example. Your failure to show an error in the derivation is noted. We therefore see that your claim is false.

It is also amusing that you assert -- characteristically without any support -- that the mere appearance of infinities automatically invalidates a theory. It's amusing because you evidently fail to recognize that even RST theory must have infinities. An ideal, lossless capacitor of the type considered in the two-capacitor example must produce an infinite current for an infinitesimal time when short-circuited with a superconductor. Your own equations show this (remember, you were the one who brought exponentials into the situation; all you have to do is let the resistance approach zero in the equation you yourself provided, and there you have infinities). If infinities automatically falsify a theory (they don't), then RST is also automatically wrong. Your reasoning is indeed feeble.

Next, "recapturing" energy is by no means a requirement in conventional theory, if by "recapturing" you mean to imply that all energy must be available for doing work. There's this thing called the second law of thermodynamics. People who have studied physics know what this is. You may wish to add the study of thermo to your list of things to do.

Are all RST-adherents as lacking in awareness of the theories they propose to overturn?

Finally, I note for the record that you have not answered any of my outstanding questions (you've replied, but not answered). When might I expect actual answers, free of your usual evasions and empty assertions?