Note:  The formulas presented in this article are "scratch work", that is, it is very rough development notes.  Part Three of this series provides a more formal description of the foundations and everyone should really begin there.  For a more accurate sense of the math, refer to this post. - 03/07/12

Over the years, I have had many discussions with engineers in regards to a wide range of topics.  I too come from an engineering background, however, I was not trained classically like most engineers.  Trust me to be awkward.  This lack of classical training has led to me butting heads with engineers as to what exactly is possible.  My training began with a focus on physics, so I tend to see things from the perspective of what physics permits, not what current engineering permits.

To most people, especially engineers, they tend to believe that the laws of physics and the laws of engineering are in agreement and thus engineering represents the sum total of our knowledge.  Nothing could be further from the truth.  Further, most engineers believe that stuff like quantum mechanics is something that they can happily ignore when developing their systems.  Whilst this may be true in many cases, if you really wish to push the envelope in your designs, a good grasp of quantum mechanics can reveal an unknown world of possibilities.

What is required is a logical progression from the formulas of electronic and electrical engineering, to the extended formulas and considerations of the quantum world.  From here, we should be able to develop more accurate versions of classical formulas and the processes that govern them.  This will provide engineers with a deeper insight into the laws that govern their circuit design and extend the range of factors that they can consider in precision designs.

Be warned, I am about to walk you off a cliff.  Should you survive the fall, you will have gained an incredible insight into the differences between the viewpoint provided classical engineering and the viewpoint provided by quantum mechanics.

Prepare for rapid descent.

Redefinition

The key to this process is the redefinition of basic formulas learnt in electronic and electrical engineering.  The formulas presented in engineering leave out a significant amount of information that can be used in precision electronic and electrical engineering.  Further, they leave out a lot of information that shows how they relate to physical processes and the insights that brings.

Let's begin by examining the Volt.  We are all familiar with the classical definition of voltage:

A single volt is defined as the difference in electric potential across a wire when an electric current of one ampere dissipates one watt of power.^[2] It is also equal to the potential difference between two parallel, infinite planes spaced 1 meter apart that create an electric field of 1 newton per coulomb. Additionally, it is the potential difference between two points that will impart one joule of energy per coulomb of charge that passes through it.

https://en.wikipedia.org/wiki/Volt#Definition

This is a very naive view of voltage.  From the definition above, the reader is lead to believe that voltage is a singular entity.  The truth is much more complex.  Voltage can be generated by a variety of mechanisms and each of these mechanisms has a range of different factors that serve to change the formula slightly.  In systems that rely on very strict tolerances, these factors can and do become critical.

To demonstrate this, we will look at an Voltage generated by a pure E-field mechanism of relative charges between protons and electrons.  To further complicate matters, I am also going to express this voltage as electrical charge.

I'm sure that last part confused you, isn't the unit of voltage the Volt?  It is if you want it to be, but that's what we call a transform.  We will get to that later, as it will only melt your brain if I try to explain it now.

Voltage(C) = Proton Charge  +  Electron Charge
Elementary Charge (e) =  1.602176565 ×10^−19 C
Proton Charge = 1.602176565×10−19 C
Proton Charge = e
Electron Charge = −1.602176565×10−19 C
Electron Charge = -e

Proof
Voltage (0C) =  1.602176565×10−19 C  +  −1.602176565×10−19 C

Derived Formula
Voltage (e) = (Xe) + (Y(-e))

New Derived Unit
e (Elementary Charge)

Definition 
Voltage is the difference between positive and negative charge distribution.  Voltage is Electrical Charge.

Now, for the astute, I know what you're thinking, a voltage can exist when the overall charge is neutral.  That is entirely correct, but the "mechanism" is different.  So, in a capacitor for example we have the familiar mechanism of charge separation, but we also have the secondary effect of charge imbalance (or polarity).  In classical engineering you may have touched upon this notion when working with Capacitive Matrix, or mutual capacitance.

Can you begin to see how this effect can play a role in capacitor banks or microelectronics?

It would be quite substantial in some environments, yet most engineers have never heard of the effect, at least not at this level.

For now this equation is simple, it does not take into account the distance between those charges and uncertainty in their locations.  Thus, measuring a voltage accurately is not possible and must be defined in terms of probability.  It is mathematically possible for protons (or electrons) in isolation to generate a voltage (and even a current) and not move, however, it has not been proven experimentally (this will make more sense later).  Further, due to conservation of energy, it is not possible to extract useful energy from such an arrangement.  The equation also shows that if you increase the number of electrons, relative to the number of protons, every time the circuit is energized it will experience a form of CEMF if the current carrier is the electron (inverse for protons).  This would also lead to a transient spike due to bunching of electrons and RF emissions.

At this point, it should have occurred to you that we need to relate this new definition of voltage to the Volt.  If we don't, then it would be an arbitrary value with no physical meaning.  To do this, we need to go back to the definition, take a quick look at Ohm's law and the Watt.

A single volt is defined as the difference in electric potential across a wire when an electric current of one ampere dissipates one watt of power.

If we examine Ohm's law, V = IR, we can clearly see that voltage is the same thing as a current.  If we consider a superconductor with no resistance Ohm's law reduces to V = I.  Thus, even Ohm's law demonstrates that voltage is charge.  So, we are off to a good start.

But how can this be?

It must be understood that current and voltage are manifestation, or transforms, of the same thing.  Specifically, they are manifestations of Elementary Charge.

To satisfy the terms of the definition of the Volt, we need to define the Ampere in the same units as our definition of the voltage above.

Ampere (A) = Coulomb per second

Derived Formulas
Electron Ampere (-e/s) = 6.24150965×10^18 -e x 1 s
Proton Ampere (e/s) = 6.24150965×10^18 e x 1 s

New Derived Unit
e (Elementary Charge) per s (second)
e/s

What do we notice about the units?  They are expressed in "per second".  So, for the reduced form of Ohm's law to be correct, V = I, then voltage must also be defined as "per second".  Let's correct that formula here:

Voltage(C) = (Proton Charge  +  Electron Charge) x 1s

Derived Formula
Voltage (e) = ((Xe) + (Y(-e))) x 1s

New Derived Unit

e (Elementary Charge) per s (second)
e/s

Again, the equation for the Ampere has been simplified.  The Ampere has a direction in 3D space and its full description also consists of a vector.  As time is a component of the equation, it is subject to the effects defined by relativity.  Given that V = I, these factors also now apply to voltage.  As with voltage, uncertainty applies and location must be expressed as a probability.

Now that you understand voltage is the same thing as current, ask yourself what a step-up/step-down transformer is doing?  We will cover this when we get to a redefinition of Ohm's law.

Whilst your brain is running out of your ears considering that one, we need to define one more element that will allow us to relate our new definition of voltage to the Volt.  The Ohm.

Ohm = Voltage ÷ Ampere

Derived Formula
Ohm (e/s) = Voltage (e/s) ÷  Ampere (e/s)

New Derived Unit
e (Elementary Charge) per s (second)
e/s

Do you see it?  Well, if V = I and Ohm = I, then charge is the Ohm.  These values appear to be "unifying".  What you need to keep in mind are the concepts of "mechanisms" and "transforms".  Think of a balloon poodle, regardless of which way you look at it you see a balloon (Elementary Charge), but look at it differently and you see a head, body and legs (voltage, current and resistance).

For those familiar with frames of reference, what I have described is a similar notion.

Resistance is a force that opposes the motion of charged particles in the direction of motion.  When read literally, the equation asks how many Amperes per second is lost for this given voltage.  Further, the equation should also contain a vector component(s).  This enables mathematical description of complex interactions such as crosstalk in 3D designs.  Experimental studies in superconductivity shows that temperature plays a role in this equation.  Given that this is material specific, it points to atomic geometry as being the source.  That is, when thermal motion is reduced the alignment of this geometry results in balancing fields and forces in a way that cancels the opposing force.  Finally, given that this formula is derived from Voltage and Ampere, all the notes that apply to them, apply to this value.

So far, so good, the analysis is holding and at this point we can comfortably state that Ohm's law is compatible with the new definitions.  We need to redefine Ohm's law in the new units, which will allow us then to progress to wattage which will allow us to finally confirm the relationship of our new definition of voltage to the Volt.

I = V ÷ R
Current = Voltage ÷ Resistance

Derived Formulas
Current (e/s) = Voltage (e/s) ÷ Resistance (e/s)
Voltage (e/s) = Current (e/s) x Resistance (e/s)
Resistance (e/s) = Voltage (e/s) ÷ Current (e/s)

New Derived Units
e (Elementary Charge) per s (second)
Current = e/s
Voltage = e/s
Resistance = e/s

All the notes that applied to each element of this formula apply here.  Thus, the above relationship is highly simplified and the true formula is extensive.  The more sensitive your circuit design, the more each of these factors will come into play and the more complex the interdependencies become.  Proper circuit analysis of any circuit could quite easily grind any data center to a halt, but certainly worth the time given the ability to run permutations.

We are now able to answer what a step-up/step-down transformer is doing.  It is related to the distribution of charge (voltage vs. current) and the interaction it has with materials.  In this transfer, the physical mechanism that governs the relationship between these aspects of charge (voltage/current) moves charge from one aspect to the other.  In doing so, it lessens or increases the amount of charge carriers (electron/proton) by transferring the charge to/from the voltage.  At this stage, you should be grasping the fact voltage is still the electron/proton but in a different form.

Keep this idea of "unification" and "conversion mechanisms/transforms" in your head.

The last stage in relating our voltage definition is to redefine the Watt in the new units.

W = VA
Wattage = Voltage x Resistance

Derived Formulas
Wattage (e/s) = Voltage (e/s) + Resistance (e/s)
Voltage (e/s) = Wattage (e/s) ÷ Resistance (e/s)
Resistance (e/s) = Voltage (e/s) ÷ Wattage (e/s)

New Derived Units
Wattage = e/s

Now that this is done, we can return to the definition of the Volt and begin the calculation:

A single volt is defined as the difference in electric potential across a wire when an electric current of one ampere dissipates one watt of power.

If we look at the redefinition of the Ampere we can see that there are two formulas, or two types of voltage.  This is because we must account for the polarity of the charges.  I will use the proton as the basis of this formula, to convert it to the electron just replace e with -e.

The relevant formulas are:

V = IR

W = VA

Substituting values using the original units provides the following:

1V = 1A x 1Ohm

1W = 1V x 1A

Replacing the values with the newly derived units we get:

6.24150965×10^18 e/s = 6.24150965×10^18 e/s * 1 e/s

3.89564427110431225e+37 e/s = 6.24150965×10^18 e/s x 6.24150965×10^18 e/s

From this we can list the following conversions:

1 Volt = 6.24150965×10^18 e/s

1 Ampere = 6.24150965×10^18 e/s

1 Ohm = 1 e/s

1 Watt = 3.89564427110431225e+37 e/s

Well, we have done it, we have proven that voltage, current and resistance are nothing more than aspects of Elementary Charge.  Further, we have also proved that electron, protons, voltage and current are the same thing.  We have therefore unified two particles with electric/electrostatic potential energy.

From these basic values, we can now use the relationships they have with other values to express those values in terms of Elementary Charge.  In doing this, we are not obtaining some arbitrary equivalence.  The key to understanding this is that in any unified field theorem, each of these independent values would be required to be composed of the same thing.  In this analysis, we are taking it from the viewpoint of Elementary Charge, but we could just as easily work from the Kilogram, Second, Ohm, etc., and define every value in terms of this.  They are interchangeable because they form part of equation that defines a relationship.

Let's look at this mathematically.  Consider the following:

4d = 2x + 2y

If 4d is divided by either value, the other value will be the result.  Another way of looking at this equation is that 2x and 2y are aspects of 4d.  That is, they are particular transforms and it depends on your frame of reference.  If we now examine Ohm's law, we observe a similar relationship:

V = IR

From the above work and experimental evidence, we know that the concept of current and resistance as being aspects of voltage, or a transform, is indeed quite accurate.

If this applies to one mathematical relationship, it applies to them all.  With this understanding, let's redefine a variety of Standard Units.

We will start with the Siemens:

Siemens = 1 ÷ R
Siemens = Current  / Voltage

Derived Formula
Siemens (e/s) = 1 ÷  Resistance (e/s)
Siemens (e/s) = Current (e/s) ÷ Voltage (e/s)

New Derived Unit
e (Elementary Charge) per s (second)
e/s

 

Worked example for 1 Siemens:

1 e/s = 1 ÷ 1 e/s

1 e/s = 6.24150965×10^18 e/s ÷ 6.24150965×10^18 e/s

I will leave the following for the reader to transform:

Ohm = (meter sq x kilogram) ÷ (second x coulomb sq)
Ohm = joule ÷ (second x ampere sq)
Ohm = (kilogram x meter sq) ÷ (second cubed x ampere sq)
Ohm = (joule x second) ÷ (coulomb sq)

Then try the wavelength, frequency and the speed of light...

Do you see what I have done?  We have unified voltage, current, meter, kilogram and the second in terms of Elemental Charge.  As a result this article also unifies space-time, electroweak force, mass, the electron and the proton.  Further, I have provided a transform that can be used to define all the aspects in which ever unit you choose.  You could even invent a unit of quantum bananas and express all these aspects in those terms.  It doesn't change what it really is, Elemental Charge.

Is this a unified field theory?

I will admit, it is a start.  We really need to dig a little deeper to complete it, such as integrating color charges of quarks, the strong force, spin, neutrinos, neutron, etc.

Well, this has been fun and you should now have a better grasp of the current state of quantum mechanics than most physicists.

I hope you survived the fall.