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News announcements and other topics => News => Topic started by: onepower on September 02, 2020, 07:19:20 PM

Title: The two capacitor paradox debate
Post by: onepower on September 02, 2020, 07:19:20 PM
The two capacitor paradox and moving zero planes.

Background: https://en.wikipedia.org/wiki/Two_capacitor_paradox

I have one charged capacitor with +/- potentials and a difference of 10v. Now I connect an uncharged capacitor, they balance and both capacitors then have 5v on each but somehow I have lost 1/2 the energy... where did it go?.

Most say it was dissipated as heat or radiation but that's a weak explanation at best because it does not define the exact cause of how the energy was dissipated. When I did the experiment I found something quite amazing. We started with two +/- potentials at a difference of 10v with one zero plane dividing them however we ended with four +/- potentials and two zero planes over twice the surface area. So when we divided the energy into two distinct elements having twice the surface area the energy density must be 1/2 because the energy is dependent on the amount of electrical pressure per unit of area is it not?.

It's a chicken and egg dilemma, did the energy dissipate because it was flowing into the second capacitor or did the energy dissipate because it was flowing into the second capacitor which doubled the surface area decreasing the energy density by 1/2?. If the surface area did not increase the energy could not flow into the second capacitor but when it did it lowered the energy density so which mechanism caused the dissipation of energy?... exactly.

Contrary to popular belief the two higher potentials in the first capacitor sensing a path to a lower potential or greater surface area is the first cause not a current flow. As well the doubling of the surface area lowering the energy density by 1/2 is how the supposedly missing energy dissipated not the current flow. The current flow is an effect of the cause not the impetus which drives it.

Now the kicker, I have justified how a doubling of the surface area must reduce the energy density by 1/2 in the the two capacitor paradox which constitutes the cause of the dissipation of energy so if the conductor connecting the two capacitors dissipated energy as well ... then where did it come from exactly?.

You see we have to look at the bigger picture with respect to these problems because it is seldom cut and dry. The solution is actually quite easy so I thought I would throw this out as a brain teaser.

Regards
Title: Re: The two capacitor paradox debate
Post by: v8karlo on September 02, 2020, 07:56:56 PM
If that is true, just raise voltage in cap from 10V to 20V and you will gain extra energy just like that.
If it works in one way, it should work in opposite.


Or maybe something is wrong?
Title: Re: The two capacitor paradox debate
Post by: onepower on September 02, 2020, 08:25:01 PM
Something to think about...
In the Wikipedia link, https://en.wikipedia.org/wiki/Two_capacitor_paradox, all there solutions relate specifically to losses in the conductor and they have completely ignored the source/sink. In which case I suspect they don't actually understand the concept of Energy. What energy is, When it is, Where it is, Why it is and How it is.

There lies the real problem and a majority of people do not understand Energy.

Regards
Title: Re: The two capacitor paradox debate
Post by: v8karlo on September 02, 2020, 08:40:35 PM
Doubling or halfing voltage is done in linear fashion.


Power is calculated in exponential manner.


When our mind tries to connect dots from linear to exponential,
paradox occur, because it is unlogical for us.


Does that means that energy is 4 times smaller with halfing voltage ?
(not power but energy in cap)


So, you see,
everything is correct and
nothing is correct.


Glich in system.

Title: Re: The two capacitor paradox debate
Post by: forest on September 02, 2020, 10:14:13 PM
is that related somehow to charge density ?
Title: Re: The two capacitor paradox debate
Post by: v8karlo on September 02, 2020, 11:01:01 PM
I can only speculate about root of problem.


Charge density depends on charge field which repel each other.


Charge field strength relates to the inverse square law, which is exponential.
When this rule is translated via equations to the power,
it ends that power follow same rule and is exponential.


Just a guess. Never dived into math of power equations to try to find cause.


But I believe that cause is in equations.

Title: Re: The two capacitor paradox debate
Post by: onepower on September 03, 2020, 03:19:12 AM
v8karlo
Quote
Doubling or halfing voltage is done in linear fashion.
Power is calculated in exponential manner.
When our mind tries to connect dots from linear to exponential,
paradox occur, because it is unlogical for us.
Does that means that energy is 4 times smaller with halfing voltage ?
(not power but energy in cap)

Exactly, while the voltage may be 1/2 the energy changes at a different rate which is exponential based on the charge density not the voltage following the inverse square law. More charges in a given area require more force to move them against the force of repulsion/attraction based on the number of charges already present. So energy is never 1+1=2 but 1+1=3, 2+2=9 and so on while the voltage is linear.

Which ultimately begs the question of how we could use this to our advantage given energy is everywhere in everything.

Regards
Title: Re: The two capacitor paradox debate
Post by: v8karlo on September 03, 2020, 04:51:41 PM
P = U * I


Power is product.


Where do you see inverse square law in this simple equation.


Power should not follow inverse square law.
Inverse square law is reserved for strength of field of charges and should not be integrated into power calculations.


Somebody mixed apples and oranges and as result expect only apples.
Which can not be.


Otherwise, just keep adding voltage in cap and soon you will have so much power that you can power the city from capacitor.


Is it like that in reality?

Title: Re: The two capacitor paradox debate
Post by: Lunkster on September 03, 2020, 06:37:26 PM
Doubling or halfing voltage is done in linear fashion.


Power is calculated in exponential manner.


When our mind tries to connect dots from linear to exponential,
paradox occur, because it is unlogical for us.


Does that means that energy is 4 times smaller with halfing voltage ?
(not power but energy in cap)


So, you see,
everything is correct and
nothing is correct.


Glich in system.

Can this problem be simulated by another method like the one in the attached drawing?
Title: Re: The two capacitor paradox debate
Post by: kajunbee on September 04, 2020, 12:51:15 AM
Are you looking for another analogy for capacitors. If so you could replace the liquid  with a compressed gas.
Title: Re: The two capacitor paradox debate
Post by: WhatIsIt on September 04, 2020, 01:43:35 AM
Compressed gas is far more accurate representation
of charges and forces between them, which are calculated
with inverse square law.
Title: Re: The two capacitor paradox debate
Post by: onepower on September 04, 2020, 06:27:16 AM
V8karlo
Quote
P = U * I
Power is product.
Where do you see inverse square law in this simple equation.
Power should not follow inverse square law.
Inverse square law is reserved for strength of field of charges and should not be integrated into power calculations.

Power is simply the rate at which electrical energy is transferred not energy in itself... so what caused the energy to transfer?.   

Quote
Somebody mixed apples and oranges and as result expect only apples.
Which can not be.
Otherwise, just keep adding voltage in cap and soon you will have so much power that you can power the city from capacitor.

I think your confusing power and energy as many do. Energy is the thing which causes something to move and power is only a measure of the rate at which it moved. Energy encompasses everything not only the rate of transfer like power. Can you calculate why your car accelerates or brakes and the energy required based solely on it's velocity in Km/hr?. Well no power is at best a simplistic measure.

Quote
Is it like that in reality?

Yes, no professional uses simple power calculations they always use Energy calculations which why so many seem confused by the two capacitor paradox.

Regards
Title: Re: The two capacitor paradox debate
Post by: lancaIV on September 04, 2020, 11:56:19 AM
Harold " Aspden Notes On Berlin Lecture "

Not full/empty caps but full/full caps dispute !
Title: Re: The two capacitor paradox debate
Post by: v8karlo on September 04, 2020, 01:25:24 PM
V8karlo
Power is simply the rate at which electrical energy is transferred not energy in itself... so what caused the energy to transfer?.   

I think your confusing power and energy as many do. Energy is the thing which causes something to move and power is only a measure of the rate at which it moved. Energy encompasses everything not only the rate of transfer like power. Can you calculate why your car accelerates or brakes and the energy required based solely on it's velocity in Km/hr?. Well no power is at best a simplistic measure.

Yes, no professional uses simple power calculations they always use Energy calculations which why so many seem confused by the two capacitor paradox.

Regards


I said that I can only speculate and try to find reason other than losses.


It seems that you know answer and everything about it,
and I am confused why you opened thread if all of that is known to you?


Did you want to hear others opinions, or to find some victim so you can preach to that person how wrong he is?


Neither you or I are right.
Why?
Because it is still cap conundrum and is not solved.
Once when it will be solved you will know that you were right or wrong.
Until then, all your knowing is just as mine, rant on the moon.


But, been pleasure talking with you.



Title: Re: The two capacitor paradox debate
Post by: v8karlo on September 04, 2020, 03:52:21 PM
Analogy of water, analogy of compressed gas.
Both share one thing.
The molecules will travel from first container to second until are equal.


Lets put 10m of wire between caps.


Electrons are charge carriers and they travel few meters per second through conductor.


So electrons will travel few seconds through 10m of wire.
But caps will equalize in nanoseconds even if wire is 100m long.


Charges can not travel between caps that fast.


That means that same amount of charges are same in both caps all the time.
Only pressure travels between caps, or voltage.


But in equation we calculate that half of charges will remain in first cap,
and half will travel to second.
While actually all charges stay in first cap and same amout of charges will be and was in second cap, just at different pressure, voltage.
So, no changes in charge amount.


But still we calculate half of charges and half of voltage, which means twice half.


Does this make any sense?
Or is just another rant?

Title: Re: The two capacitor paradox debate
Post by: Lunkster on September 04, 2020, 03:54:24 PM
Hi,  In the drawing it placed in this feed, I could have created a video and related the size of the hole in the valve with the amount of time it takes for the liquid to move from glass one to glass two.  I could have had a chart how the volume of liquid moving from glass one decreases with time as it moves from glass one to glass two.  This difference is in how high the liquid is in each glass that changes this rate of transfer.  I could then say that the R/C time constant curve looks the same as the liquid or gas transfer from one glass to the other glass.  The same curve happens as the electrons moving from the plates of one capacitor to the other. 
Now with the transfer of liquid from one glass to the other is the force of gravity is forcing the liquids to be equalized.  WIth gas it would be pressure equalization. But it is not gravity that causes the electrons to move from one capacitor to the other.  So what causes the electrons to take the trip in the first place.  It that the question that is being looked at here?  Is there a pressure that causes the movement? I do not think pressure is the correct word for the movement of electrons.  But is the voltage like the pressure to move the electrons to a lower potential level until both the number of electrons are equal in both capacitors reducing the overall voltage across both capacitors? 

The Lunkester
Title: Re: The two capacitor paradox debate
Post by: kajunbee on September 04, 2020, 04:26:20 PM
The paradox is the energy loss during the transfer of charge. You start with 1 capacitor that has lets say 1 joule of energy. After the charges equalize between two capacitors the calculated energy is half of what you started with. Instead of 1/2 joule on each cap you are left with .25 joules on each one. This adds up to a total of 1/2 joule of energy. Where did the other half go???
Title: Re: The two capacitor paradox debate
Post by: v8karlo on September 04, 2020, 04:33:53 PM
It is a very good question.


Is it pressure?


We all use that term pressure or voltage, but is it really that?
Electricity is not water or gas, and electrons are too slow.


I thought about it many times, and pressure just does not fit exactly.
But without better explanation, I am stuck.


Short answer: I really dont know.


It is like magnetic gears.
If you turn first, second will
turn, and third, and so on.
Even if they turn, they stay on spot, they dont move.


Electrons orbiting atom.
If first atom electrons change orbiting path, it will affect second atom electrons orbiting path, thwn third atom electrons orbiting path and so on, like chain reaction.
When force on first atom electrons stops, they all tend to get back to their usual orbiting paths.
So , nothing really moves, just rearanging orbiting paths of electrons.


And under force, lots of them will jump from their orbitals and become free electrons, which confuses us to think that electrons travel.


Just a thought, I really dont know.

Title: Re: The two capacitor paradox debate
Post by: onepower on September 04, 2020, 08:09:00 PM
V8larko
Quote
I said that I can only speculate and try to find reason other than losses.
It seems that you know answer and everything about it,
and I am confused why you opened thread if all of that is known to you?
Did you want to hear others opinions, or to find some victim so you can preach to that person how wrong he is?
Neither you or I are right.
Why?
Because it is still cap conundrum and is not solved.

I offered a solution of where and why the energy dissipates for debate in the beginning of the thread, you did read it didn't you?. So why are you confused?.
So yes, I did solve it and now I'm looking for opinions on my solutions.

Quote
Is it pressure?
We all use that term pressure or voltage, but is it really that?
Electricity is not water or gas, and electrons are too slow.
I thought about it many times, and pressure just does not fit exactly.
But without better explanation, I am stuck.
Short answer: I really dont know.

I know you don't know but I can help. The electrical pressure relates to the electric field around each electron and while they move slow there are billions and billions of them which produce a very powerful "electron cloud" with a combined field. I remember something from a good book on the subject by A.D.Moore on electrostatics. Moore said if we had a 1 cm cube of aluminum and separated all the positive and negative charges 1 meter apart. The electric field would produce a force of something like 32 million million million pounds. This force is equivalent to the weight of a steel cube 76 miles square.

So you are very much wrong and those tiny electrons in something as simple as a 1cm cube of aluminum can produce unimaginable forces in the right context. The atomic bomb is based on liberating some electrons from a small amount of material which produces a massive amount of energy which can incinerate an entire city... just from moving some little electrons.

So it's probably a good idea to understand what is actually going on because our civilization and every technology we know is based on moving some electrons. Electricity, chemistry, biology, everything revolves around atoms and the electric forces which dictate there action. Kind of important stuff.

Regards




Title: Re: The two capacitor paradox debate
Post by: kajunbee on September 04, 2020, 08:34:11 PM
Your explanation in first post is the conclusion that I came to also. That it is simply the redistribution of charges over a larger area. I had given this quite a bit of thought over the years and was fairly comfortable with this explanation until recently. There are several videos on YouTube now concerning the paradox. In one it was said that if there was not a loss of energy the stored charge would slosh back and forth till the end of time. I’ll see if I can find it again and provide you the link.
Title: Re: The two capacitor paradox debate
Post by: kajunbee on September 04, 2020, 09:33:53 PM
https://youtu.be/4v0YlultV0w

Not sure what this guys credentials are so you might take it with a grain of salt. I can’t envision how this would be possible without some amount of inductance. As far as I know and ideal capacitor has zero resistance and inductance.
Title: Re: The two capacitor paradox debate
Post by: WhatIsIt on September 05, 2020, 04:07:34 AM
OnePower,

What are you talking about.
There is no conundrum at all.

If you look equation for energy in cap then you see that
with doubling voltage, energy is four times larger.

That means that energy in parallel 4 caps of 5 V are equal
to 1 cap of 10V.

If you have only 2 caps of 5V,
it is only half of energy of 1 cap of 10V.

V8 told you that voltage follow linear scale and energy exponential.

What did you not understand?
Title: Re: The two capacitor paradox debate
Post by: WhatIsIt on September 05, 2020, 04:14:49 AM
Real question is

Can cap of 10V perform 4 times of work than cap of 5V,
as energy equation states?
Or is it false?
Title: Re: The two capacitor paradox debate
Post by: kajunbee on September 05, 2020, 01:59:13 PM
Lunkster, another paradox is the energy gain when separating a parallel plate capacitor. You have a capacitor whose plates are separated by a certain distance. Let’s say it’s capacitance is 50 uf and it’s charged to 200 volts. The energy stored would be 1 joule. As you start to separate the plates the voltage will increase and capacitance will decrease. At twice the distance the voltage doubles and capacitance halves. You now have 2 joules of stored energy on the capacitor. Where did the extra energy come from? The explanation you will find is that it required work to separate the plates. In doing so you add energy into the system.

https://youtu.be/ImkQdh8jQ5U
Title: Re: The two capacitor paradox debate
Post by: Jeg on September 05, 2020, 02:46:56 PM
Lunkster, another paradox is the energy gain when separating a parallel plate capacitor. You have a capacitor whose plates are separated by a certain distance. Let’s say it’s capacitance is 50 uf and it’s charged to 200 volts. The energy stored would be 1 joule. As you start to separate the plates the voltage will increase and capacitance will decrease. At twice the distance the voltage doubles and capacitance halves. You now have 2 joules of stored energy on the capacitor. Where did the extra energy come from? The explanation you will find is that it required work to separate the plates. In doing so you add energy into the system.

Nice kajumbee.
What about removing the dielectric which is far lighter than the plate itself...
What about changing the properties of the dielectric material instead of moving anything...
For everything there is a solution. There just need an effort but everything is possible.

Regards
Title: Re: The two capacitor paradox debate
Post by: kajunbee on September 05, 2020, 03:16:44 PM
Jeg, that would be the route to take. Air doesn’t allow you too store a great deal of charge. Changing the property’s  of the dielectric is not something I had considered. No clue how that could be done, but great idea.
Title: Re: The two capacitor paradox debate
Post by: onepower on September 05, 2020, 05:59:47 PM
Kajunbee
Quote
Your explanation in first post is the conclusion that I came to also. That it is simply the redistribution of charges over a larger area. I had given this quite a bit of thought over the years and was fairly comfortable with this explanation until recently. There are several videos on YouTube now concerning the paradox. In one it was said that if there was not a loss of energy the stored charge would slosh back and forth till the end of time. I’ll see if I can find it again and provide you the link.

https://youtu.be/4v0YlultV0w
Not sure what this guys credentials are so you might take it with a grain of salt. I can’t envision how this would be possible without some amount of inductance. As far as I know and ideal capacitor has zero resistance and inductance.

That was an interesting video, thanks.

We could do some thought experiments...
1) We have the two capacitor setup made of superconducting materials with zero resistance, connect them and the electron current sloshes back and forth for an untold amount of time.
2) We have the two capacitor setup with a very high resistance, connect them and it takes and untold amount of time for the voltages to balance.

It would be easy to assume the resistance is the cause of the dissipation of energy however in case 1 it is the inductance which causes the electrons to slosh back and forth not so much a lack of resistance.

In my experiments I added a coil with inductance in between the two capacitors and I measured a dampened alternating current between them. When I removed the inductance there was no alternating current and they balanced immediately. The problem here is that whenever an electron which carries an electric field with it moves it produces a magnetic field. The magnetic field on the conductor gives the electron current a property similar to inertia which then causes it to over run and alternate.

So we could suppose that if we used superconductors in the two capacitor setup and if all the resistance and inductance were removed the electrons would not slosh back and forth for an untold amount of time leaving us back at square one, as you implied. Most are not considering all the factors in my opinion which becomes problematic.

In my opinion the physics dictates that when the initial charge density balances over twice the surface area this is the first cause which dissipates the majority of the energy regardless of what happens in between the capacitors. It also helps that I have seen FE first hand and it was not based on a mysterious energy gain as many suppose but understanding and removing an inherent loss in the system many took for granted. So it is very important to understand exactly what is happening where and why in my opinion.

Regards
Title: Re: The two capacitor paradox debate
Post by: Lunkster on September 05, 2020, 08:38:47 PM
HI,

I WAS WRONG!  My drawing was way off basis because it had the wrong voltages and wrong representation of what is going on.
I AM SO SORRY!  A person my age should not be making mistakes like that.  I think it was a "BRAIN FART"  That stinks!
I AM SO THANKFUL FOR ALL OF YOUR COMMENTS!  If it was not for your comments! I would not see my errors and I would not have a chance to correct them.  I have hopefully made the corrections in the attached drawing that make sense for interesting two cap problem.

The Lunkster
Title: Re: The two capacitor paradox debate
Post by: v8karlo on September 05, 2020, 08:56:29 PM
Lunkster,


In each cap should be 5V, and energy 1/4 , I think.


What do you think, is it real?
By doubling voltage energy grow very rapidly?


All we need to do is raise voltage in cap, and soon energy will be huge.

Title: Re: The two capacitor paradox debate
Post by: kajunbee on September 05, 2020, 09:12:34 PM
V8karlo is correct , there should be 5 volts across each cap. Each cap now has .25 joules stored energy.
Title: Re: The two capacitor paradox debate
Post by: kajunbee on September 05, 2020, 09:23:23 PM
I’m sorry, .25 of the energy on each cap , not .25 joule.
Title: Re: The two capacitor paradox debate
Post by: v8karlo on September 05, 2020, 09:33:23 PM
In one of his videos Don Smith said


Source of FE is high voltage because voltage is squared.


And he was refering to this energy equation.




But, can cap make 4 times of real work with doubling voltage?

Title: Re: The two capacitor paradox debate
Post by: Lunkster on September 05, 2020, 09:42:29 PM
I made the corrections in a way that hopefully makes sense.
Again thank you
I will be slower to respond without checking and rechecking my work. 

The Lunkester
Title: Re: The two capacitor paradox debate
Post by: kajunbee on September 05, 2020, 09:44:34 PM
I asked myself the same question.
Title: Re: The two capacitor paradox debate
Post by: kajunbee on September 05, 2020, 09:50:42 PM
As you see the discharge time is twice as fast but peak power of resistor is 4 times as high.

http://mustcalculate.com/electronics/capacitorchargeanddischarge.php
Title: Re: The two capacitor paradox debate
Post by: WhatIsIt on September 06, 2020, 01:08:38 AM
In one of his videos Don Smith said


Source of FE is high voltage because voltage is squared.


And he was refering to this energy equation.




But, can cap make 4 times of real work with doubling voltage?

And 4 times of energy is needed to charge cap,
So, energy in out is the same.
No free lunch.

What is needed is method to charge cap cheaply,
cheating energy equation, and use difference.

But you know that already.
Title: Re: The two capacitor paradox debate
Post by: lancaIV on September 06, 2020, 01:30:32 AM
The similar "para = against dox= teach" :
Mukherjee generator F1= BIL ,when F2= 1/2BIL we need for compensation 1/2 the voltage and 1/2 the amperage

Fradella generator :1000 rpm gives 1000 rated Watt output

                                      500 rpm gives 0,5x0,5x0,5 = 125 Watt output

                                     100 rpm gives 0,1x0,1x0,1 =       1 Watt output

                              10% rated rotations gives only 1 promille= 0,1% rated energy gain !

                   
Title: Re: The two capacitor paradox debate
Post by: onepower on September 06, 2020, 01:37:12 AM
Kajunbee
Quote
As you see the discharge time is twice as fast but peak power of resistor is 4 times as high.

As expected, which proves what exactly?.

We should offer justification for what we mean and say otherwise it is basically meaningless. So what was your point, where were you going with it, by what reasoning?.

Here is a good example by Iancaiv...
Quote
The similar "para = against dox= teach" :
Mukherjee generator F1= BIL ,when F2= 1/2BIL we need for compensation 1/2 the voltage and 1/2 the amperage
Fradella generator :1000 rpm gives 1000 rated Watt output
500 rpm gives 0,5x0,5x0,5 = 125 Watt output 100 rpm gives 0,1x0,1x0,1 =       1 Watt output
10% rated rotations gives only 1 promille= 0,1% rated energy gain !

It is basically nonsensical gibberish and while it may be factual it has no context anyone can seem to understand. It's like a person writing in Chinese and expecting everyone else to understand it when they cannot read Chinese. Use your words gentlemen, express your idea's and concepts in ways others can understand...that is the way we communicate.

Regards
Title: Re: The two capacitor paradox debate
Post by: lancaIV on September 06, 2020, 02:03:15 AM
" Nonsensical gibberish",probably , for anybody who does not know the right formula application !
 Para-dox or non-linear ~ dynamic


Title: Re: The two capacitor paradox debate
Post by: kolbacict on September 07, 2020, 09:20:32 AM
Hi all.
Now, if a chemical reaction takes place between the charged plates of the capacitor, the equilibrium

will be biased towards the formation of a product with a higher dielectric constant?
Just like our temperature shifts the equilibrium towards exo and endo reactions.

Because with a decrease in the permittivity of the dielectric, the energy of the capacitor

grows (tantamount to the spreading of the plates) and this, as it were, does not fit

. E = U2C / 2. That is, it will appear as if from nowhere.
Am I right ?
Title: Re: The two capacitor paradox debate
Post by: onepower on September 07, 2020, 04:53:41 PM
Lunkster
Quote
I made the corrections in a way that hopefully makes sense.

Thanks for the graphics and it makes more sense when we can see what were talking about.

Another problem with the two capacitor paradox relates to your nice graphics. Here we see two capacitors and when the switch is closed the finite number of electrons present in capacitor 1 redistribute themselves over twice the surface area of cap 1 and 2. In fact all of our electrical systems use a similar principal pumping electrons or raising the electron density then allowing it to redistribute to a lower density.

I like the two capacitor paradox because it is a simplified more transparent version of how our electrical systems actually work without all the complexity. With the two capacitor system we have a finite and know amount of energy in the system based solely on the initial electron density and the final electron density.

This was basically the point I wanted to make when starting this thread. The first cause of the missing energy is the fact that the electron density was reduced to one half when it redistributed over twice the surface area. Any energy radiated as heat or EM waves is an after effect of the motion of the electrons as they redistributed not the cause of the missing energy. You see in all the literature I read they completely ignored the change in electron density and simply said heat or EM waves were generated. They completely ignored the first cause of why the electrons were moving in the first place and what effect this had on the system. This is where our calculations generally fail us because they leave out many of the most important details creating confusion.

So in fact, the only paradox present is that many are using simple calculations and assumptions to replace a real understanding of what is actually happening and why.

Regards