Adonis Diaries

Now that’s news to me: Energy is in Inertia. “Work” is simply “a transfer of inertia”.

Posted on: May 18, 2022

Kieran D. Kelly

Feb 23, 2022

A Simple Explanation for Energy…

Einstein published a paper that asked the question “Does the inertia of a body depend upon its energy-content?”

The received message was “Mass is also a form of Energy”;

All energy is inertia. And all “work” is simply “a transfer of inertia”.

The quantity of inertial mass “GENERATED” is determined by the speed of spatial oscillation.

A few explanatory equations in this valuable article:

c = (ωₘₐₓ)(rₘᵢₙ). (r-min) being the minimum “radius of twist”)

u = (ω)(rₘᵢₙ)

the speed of light (c) equates to the maximum linear speed of angular oscillation.

E-max is the maximum allowable energy containable in an elementary spatial oscillation.

E = (mₘₐₓ u c) or E = (mₘₐₓ u uₘₐₓ)

(c)² = (uᵣₑₗ)² + (vᵣₑₗ (rel. means relative to observer. V is linear speed)

(uᵣₑₗ/c) = SQRT (1 – (vᵣₑₗ/c)²)= 1/γ

TIME is not really a thing in itself, NOR is it a “fourth” dimension. TIME is but an emergent property of oscillating 3D-Space.

(Δvₘₐₓ)² = (c)² – (u. (Maximum change in velocity (delta-v-max). Knowing that “change in velocity” is absolute and Not relative as velocity to the observer)

½mv² = (Δm c c)

This equation says that an absolute change in Kinetic Energy equates to an absolute change in Mass

What is Energy?

I have always found the scientific definition of energy highly unsatisfactory.

The scientific definition of energy states that “Energy is the Ability to do Work”. So what is Work then?

Well, the scientific definition of work states that “Work is a measure of Energy Transfer”.

So A is defined by B, and B is defined by A. That’s clearly not very useful, but we will come back to this later.

It is safe to say that everyone has a “feel” of what “Energy” is: it is just hard to put your finger on it.

Amplitude and Frequency

We know that energy often travels in waves (of particles?). Water waves and sound waves are common examples of this.

Waves are simply a series of oscillations. The amplitude of any oscillation is simply the maximum displacement of an event from its equilibrium position. In general the amplitude of the wave, tells us how much energy is in a wave.

In the case of water waves, higher amplitude means taller waves. And, in the case of sound waves, higher amplitude means louder sound.

Amplitude, however, is not the only factor that determines the amount of energy transfer in a wave.

The “Frequency” of a wave tells us how many amplitudes are transferred per second.

And so taken together we can say that the amount of energy in material waves is a product (Not necessarily a product, but two factors entering into the equation) of the intensity of the waves (as given by the amplitude), times, the number of waves per second (as given by the frequency).

In 1802, Thomas Young suggested that the energy in “Light” also travels in waves.

And , in 1865 James Clerk Maxwell’s work on electromagnetism not only seemed to confirm this idea, but further suggested that these waves are in fact, “Electromagnetic” waves.

Electromagnetic waves are considered part of classical physics. The classical relationship between amplitude and intensity is therefore said to extend to light; and so in the case of light waves, higher amplitude means brighter light.

However, unlike all other waves in classical physics, the rate of energy transfer is said to be independent of the frequency, and consequently the energy in a beam of light is said to be determined solely by the amplitude, or the “brightness”, of the light.

This belief in the independence of intensity from frequency ultimately led to some considerable confusion when, in December 1900, Max Planck made a mathematical discovery that seemed to imply that the amplitude of light was, in fact, “Quantized” by frequency — meaning that the amplitude of light, could ONLY rise and fall in increments of a minimum value of energy, defined by the frequency itself.

This “quantization of energy” was a significant break with classical physics, and would ultimately lead to the strange new world of “Quantum” physics.

I am suggesting that this drastic break with classical physics was somewhat misguided.

In my work, I am suggesting that the concept of “energy quantization” was a misinterpretation of the underlying physics of light.

I suggest that a more likely explanation is that: what is normal for classical material waves is simply reversed for classical EM waves.

I am suggesting that while the energy in material waves is defined by the intensity per wave (as given by the amplitude), times, the number of waves per second (as given by their frequency); the energy in EM waves , by contrast, is defined by the intensity per photon (as given by the frequency), times, the number of photons at a given moment in time — and the size of this “group of photons” is what is being measured as the “amplitude” of the EM wave.

This idea could be summarized in a fashion below:

  • Sound Wave Energy (E) ∝ Intensity per wave (i.e. amplitude/loudness) x Number of waves per second (i.e. frequency).
  • Light EM Energy(E) ∝ Intensity per photon (i.e. frequency) x Number of instantaneous photons (i.e. amplitude/brightness).

This reimagining of the nature of light leads to some very interesting results.

First — A Quick Recap

In the previous post “The Amplitude IS the Frequency” I addressed the idea that EM Waves, and the Speed of Light, might in some way be related to the “Rate of Change of CURL (circulating field)”…

In his work on classical electrodynamics, James Clerk Maxwell had introduced the concept of “Curl” to explain “Circulating” electric and magnetic fields.

Maxwell defined curl as “a circulation, per unit area, over an infinitesimal path, around a point in space”.

In the previous post, we asked the question what if there is no such thing as a “zero-dimensional point” in space? What if space is actually “quantized” into tiny “ Infinitesimal Volumes”?

If this were to be the case then the concept of curl would have to relate NOT to a zero-dimensional point in Space, but to an infinitesimal three-dimensional “Element of Space”.

And, in this scenario Maxwell’s description of curl as being a “Circulation per Unit Area”, would equate to the concept of “Twisting the Cross-Sectional-Area” of an infinitesimal-volume about its remaining third dimension.

And THAT possibility led to a very important consequence, because twisting any cross-sectional area of a cube comes up against a physical restriction, in the form of: a maximum amount of twist.

It is impossible to twist a 2D square more than 90 degrees; and we used this simple geometric fact to reason that if there exists a maximum quantity of twist (θₘₐₓ = π/2 radians), then there must also exist a minimum turning circle, with a minimum “radius of twist” (r-min).

And if there exists a (r-min) then, thanks to the fixed speed of light (c), there must also exist a maximum angular frequency (ω-max).

From these simple foundational steps, we were able to render an alternative version of the famous Planck-Einstein Relation (E=hf)—which in the previous paper was given by

Equation (1.9) _________ E = (hfₘₐₓ)(θ/θₘₐₓ)

(Two limiting factors: fₘₐₓ and θₘₐₓ)

This equation is saying that the amount of energy in an oscillating quantum volume is a function of its frequency, which itself is a function of the angular amplitude of displacement and oscillation, theta.

We will use this equation as the starting point for the following work…

Speed of Oscillation

Equation (2.1) ________ E = (hfₘₐₓ)(θ/θₘₐₓ)

In this equation (f-max) is the maximum frequency of oscillation, and its value is 2.9521 x 10⁴² Cycles per Second.

This equation can also be written in its alternative form as

Equation (2.2) ________ E = (ħωₘₐₓ)(θ/θₘₐₓ)

In this equation, the Planck Constant (h) has been replaced by the “Reduced Planck Constant” (h-bar) which has a value of (h/2π), and (ω-max) is the maximum “angular” frequency of oscillation, and its value is 1.8549 x 10⁴³ Radians per Second.

Using the equality (θ/θₘₐₓ) equals (ω/ωₘₐₓ), from the equation (1.6), we can convert equation (2.2) to

Equation (2.3) ________ E = (ħωₘₐₓ)(ω/ωₘₐₓ)

Since (ω-max) is a constant, what we have here, in equation (2.3), is one of the traditional forms of the Planck Einstein Relation that says that the energy in a photon of light is determined by its angular frequency (ω).

Now, one of the earliest developments in the science of physics was Galileo’s insight that “angular frequency” is, in fact, the same thing as “angular SPEED”.

And so if we multiply (r-min) by an angular frequency we will get a linear speed.

We have already seen that the product of the constants omega-max and (r-min) gives us the speed of light (c).

Equation (1.4) _________ c = (ωₘₐₓ)(rₘᵢₙ)

And so now, if we were to multiply the variable omega by this same quantity (r-min) we will clearly get a speed which is clearly less than (c) which we will label as “(u)”.

Equation (2.4) __________ u = (ω)(rₘᵢₙ)

Using this notation equation (2.3) can now be written as

Equation (2.5) _________ E = (ħωₘₐₓ)(u/c)

Now, clearly (u) represents the linear speed associated with the angular speed of oscillation, which means that

the speed of light (c) equates to the maximum linear speed of angular oscillation.

This is interesting because, to date, there is no provable or, for that matter, even credible explanation for why there should exist a maximum speed in the universe. But the very existence of any sort of physical maximum implies that something physical must be limiting behavior.

Consequently it seems not unreasonable to suggest that maybe the speed of light (c) could, actually be the result of the physical upper-limit that simple geometry places on the “angular speed” of an angular oscillation of a quantum unit of space. We will elevate this idea to a postulate of this work, and write it as

Equation (2.6) ____________ c = uₘₐₓ

Now, we believe that this is more than just a wild guess, because this postulate leads to some interesting results that seem to explain a large swathe of Modern Physics.

The ratio of (u) over (c)

The first of these is that since (c)is a constant, then what we have in equation (2.5) is a form of the Planck Einstein Relation that says that the energy in a photon of light is determined solely by its own “speed of oscillation”. Which is interesting…

A second result is that we can now see that (θ/θₘₐₓ), (ω/ωₘₐₓ), (f/fₘₐₓ), and (u/uₘₐₓ) are, in fact, all different forms of the dimensionless quantity (u/c).

Eq. (2.7) ________ (u/c) = (θ/θₘₐₓ) = (ω/ωₘₐₓ) = (f/fₘₐₓ) = (u/uₘₐₓ)

This means that each of these values (associated with an elementary spatial oscillation) can be expressed as a fraction of their maximum value.

Equation (2.8) ___________ θ = (θₘₐₓ)(u/c)

Equation (2.9) __________ ω = (ωₘₐₓ)(u/c)

Equation (2.10) __________ f = (fₘₐₓ)(u/c)

Equation (2.11) _________ u = (uₘₐₓ)(u/c)

And a third result is that the quantity (ħωₘₐₓ) clearly equates to the maximum energy of a photon (E-max) which means that equation (2.5) can also be written as

Equation (2.12) _________ E = (Eₘₐₓ)(u/c)

Given the values of (h-bar) and (ω-max), E-max has a value of 1.9561 x 10⁹ Joules.

This quantity is already known to Physics as the so-called “Planck-Energy”, and so equation (2.14) now tells us what this mysterious quantity of energy actually represents. 

E-max is the maximum allowable energy containable in an elementary spatial oscillation.

These are all interesting results. But there is more…

Special Relativity

The connection between (u-max) and (c) points to a similar connection between the domain of Quantum Physics, and the domain of Special Relativity.

We know that the Planck Energy is related to the Planck Mass in the following way

Equation (2.13) _________ Eₘₐₓ = (mₘₐₓ cc)

And so if we combine equations (2.12) and (2.13) we get an equation for energy written in terms of both, the Planck Mass, and the Speed of Oscillation

Equation (2.14) ________ E = (mₘₐₓ cc)(u/c)

And by cancelation this reduces to

Equation (2.15) __________ E = (mₘₐₓ u c)

Alternatively, using equation (2.6), we could also write this equation as

Equation (2.16) _________ E = (mₘₐₓ u uₘₐₓ)

Now, for an observer moving with the oscillating photon there is no perceived linear motion to this oscillation, so the “SQUARED” version of equation (2.16) can be written as

Equation (2.17) _________ E² = (mₘₐₓ u uₘₐₓ

However, as we all know, speed is relative, and consequently the squared version of equation (2.16) is NOT the same for all observers.

Any observer outside the frame of oscillation will see the total energy content as being DISTRIBUTED between a speed of oscillation, and a speed of linear motion.

Consequently, the general form for the energy within an oscillation (from the point of view of ALL observers) must be written as

Eq. (2.18) ____ E² = (mₘₐₓ u uᵣₑₗ)² + (mₘₐₓ u vᵣₑₗ (rel means relative to observer)

This is the full equation for the energy contained in an oscillation from the point of view of ANY observer in ANY frame of reference.

Distribution of energy content (between oscillatory and linear motion)
Distribution of energy content (between oscillatory and linear motion)

This is another significant result for it suggests that:

Although the energy content of the photon is the same for all observers, the distribution of that energy content can be different for different observers.

Moreover, if we equate equations (2.17) and (2.18) and divide both sides by the quantity (mₘₐₓ u) we get

Eq. (2.19) _________ (uₘₐₓ)² = (uᵣₑₗ)² + (vᵣₑₗ

And using equation (2.6) from above, we can rewrite this as

Eq. (2.20) __________ (c)² = (uᵣₑₗ)² + (vᵣₑₗ

This equation suggests that: although the speed of light (c) is indeed constant for all observers (as Einstein postulated in 1905), the distribution of that fixed speed is, in fact, “relative”.

Moreover, equation (2.20) can be rearranged as follows

Eq. (2.21) __________ (uᵣₑₗ)² = (c)² – (vᵣₑₗ

Eq. (2.22) _________ (uᵣₑₗ) = SQRT (c² – vᵣₑₗ²)

Eq. (2.23) _________ (uᵣₑₗ/c) = SQRT (1 – (vᵣₑₗ/c)²)

And this quantity (u-relative over c) is the inverse of gamma (γ), a quantity that is ubiquitous in Special Relativity.

We write this relationship as

Equation (2.24) _____________ uᵣₑₗ/c = 1/γ

It should be noted here that: the quantities (u) and (u-rel) are different quantities.

The quantity (u) determines the energy content, and the quantity (u-rel) reflects the observers measurement of the distribution of that energy content (measured as a distribution between two different forms of motion — oscillatory motion and linear motion)..

Without having to dive into all the gory details of Special Relativity, it is clear to see that this relative distribution of energy can explain the true nature of TIME .

Time is a relative quantity; not because the speed of light (c) is fixed, but because the distribution of (c) is relative; and so “Observed-Time” is always relative to the observers relative motion.

Einstein was right to believe that Time is Relative, that it is a subjective quantity. And here we can clearly see why that is the case.

Time is really just a consequence of the fact that:

while all spatial oscillations have an angular cycle, not all angular cycles are created equal (some have more radians than others)

It also means that TIME is not really a thing in itself, NOR is it a “fourth” dimension. TIME is but an emergent property of oscillating 3D-Space.

This is another important result of this work. However, there is more…

Energy-Momentum Relation

It is clear to see that (mₘₐₓ u) can also be written as (mc), so this means that we can convert equation (2.18) to

Eq. (2.25) ___________ E² = (m c uᵣₑₗ)² + (m c vᵣₑₗ

And since the quantity (m vᵣₑₗ) represents “relative momentum”, we can write equation (2.25) as

Eq. (2.26) ____________ E² = (m c uᵣₑₗ)² + (pᵣₑₗ c)²

If this equation appears familiar, it is because this equation is reminiscent of the traditional “Energy-Momentum Relation” in which both Energy (E) and Momentum (p) are considered “relativistic” quantities.

In equation (2.26), however, momentum is relative, but energy is NOT.

The reason being is that although “observed” momentum is relative, so too is the “observed” speed of oscillation; and so the value of this relative momentum has no effect on the value of energy (E), but merely on the “Observed Distribution” of energy (E-squared).

Equation (2.26) shows that different observers see different distributions of Rest Energy and Momentum Energy.

This is another important result of this work. However, there is more…

Maximum Speed

While, velocity may be relative, a change in velocity is absolute.

Therefore given the existence of a maximum energy (allowable per unit volume), then there must also be a maximum allowable change in velocity for a given value of (u) — regardless of the observer’s own frame of reference.

To calculate this maximum allowable change in velocity, we will start with the observation that, for any change in energy, the following equation will hold true.

Equation (2.27) __________ E = (u/u)E

Since we know that there is a limit to the quantity of energy allowable per unit volume, the equation for a maximum change in energy is therefore given by

Equation (2.28) _________ Eₘₐₓ = (uₘₐₓ /u)E

This equation tells us that the maximum change in energy is determined solely by the current value of (u-1), and thus we can use (u-1) to calculate the maximum change in velocity (delta-v-max).

Eq. (2.29) _________ (Δvₘₐₓ)² = (uₘₐₓ)² – (u

Eq. (2.30) __________ (Δvₘₐₓ)² = (c)² – (u

Eq. (2.31) __________ Δvₘₐₓ = SQRT (c² – u²)

So here we see that: the maximum speed a particle can achieve is determined by its own internal speed of oscillation. Consequently, only things that have very low energy (such as light) are capable of travelling close to the universe’s maximum speed (c).

This is another important result of this work. But, there is one more thing worth looking at…

Kinetic Inertia

Associated with any absolute change in velocity, is an absolute change in Kinetic Energy. Thus we can express a change in energy in an alternative way from before.

Equation (2.32) ___________ E = E + ΔE

Now, we can replace (delta-E) with a quantity representing a Change in Kinetic Energy

Equation (2.33) __________ E = E + ½mv²

And, we can rearrange this equation, to get

Equation (2.34) ___________ ½mv² = E – E

And using equation (2.27) from above, we can rewrite this equation as

Eq. (2.35) ___________ ½mv² = (u/u)E – E

And this can be rewritten as

Eq. (2.36) __________ ½mv² = E ((u – u)/u)

Which can be rewritten as

Eq. (2.37) ____________ ½mv² = E (Δu/u)

And, using equation (2.15), this can be rewritten as

Eq. (2.38) _________ ½mv² = (mₘₐₓ u c)(Δu/u)

And this can be rewritten as

Equation (2.39) ___________ ½mv² = (mₘₐₓ Δu c)

Which can be rewritten as

Equation (2.40) _____________ ½mv² = (Δm c c)

This equation says that an absolute change in Kinetic Energy equates to an absolute change in Mass…

This is probably the most important take-home message of this work on energy, because it concerns the very nature of energy itself.

We all know that the faster something moves the harder it is to stop, and here we see that the faster something moves, the more massive it becomes, which makes it not only harder to stop but also harder to accelerate further. These two facts taken together suggests that energy is really just a form of “INERTIA”.

Summary & Conclusion

Before Einstein, the concept of energy was always simply associated with the concept of motion (or, the potential for motion).

But then everything changed when Einstein published a paper that asked the question “Does the inertia of a body depend upon its energy-content?”

The received message of this famous paper is that “Mass is also a form of Energy”;

However, it seems possible that the true message has never been fully appreciated (not even by Einstein himself).

If the supposition that it is Space that is quantized (NOT energy) is the correct interpretation of Planck’s work, then this conjecture must ultimately lead us to the conclusion that ALL ENERGY (both rest energy and momentum energy) is simply a form of INERTIAL MASS; and consequently, contrary to what is taught, there can be no such thing as “massless energy”. All energy is inertia. And all “work” is simply “a transfer of inertia”.

This conjecture also suggests that Inertial Mass is not really a thing in itself, but an emergent property of the dynamics of Quantum 3D-Space, which can be clearly shown by rewriting equation (2.14) as follows

Equation (2.41) _________ mcc = (mₘₐₓ cc)(u/c)

Equation (2.42) ___________ m = (mₘₐₓ)(u/c)

Here we see that the quantity of inertial mass “GENERATED” is determined by the speed of spatial oscillation; (and how and why this should come to be so, we will come to next)…

© Kieran D. Kelly

This is Post #3 in the series on NeoClassical Quantum Theory

Note: The processes in Nature leave the mass intact by decomposition. Only human species managed to “exhaust” Earth mass.

My conjecture is that a Star explodes when its Mass can no longer sustain the required energy needed in its processes.

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