Duration of The Cycle
Time Dilation on the Scale of a Single Cycle
Maxwell’s Electromagnetic Wave Equation is traditionally read as a three-dimensional wave equation containing a fixed speed of light. An alternative way to read the mathematics is that
Maxwell’s 3D Wave Equation contains a Fixed 3D Speed.
NeoClassical Relativity (NCR) is based on this interpretation of Maxwell’s mathematics.
In the two previous posts, I introduced the two postulates of NeoClassical Relativity.
The first postulate is that: The Speed of Light is a three-dimensional combination of the Speed of Oscillation and Speed of Linear Travel. Mathematically, this postulate can be written as the “3D Speed Equation”
Equation (1) _________________ c² = u² + v²
{Where u is the speed of oscillation in two spatial dimensions, and, v is the speed of travel in the third.}
The second postulate states that: The Oscillation-Length of a 3D Cycle is a Fixed Quantity. Mathematically, this postulate leads to the “3D Length Equation”
Equation (13) ___________ (λ-c)² = (λ-min)² + (λ-v)²
{Where, λ-c is the cycle-length, λ-v is the wave-length, and λ-min equals 2π times the Planck Length — which equates to a length of 1.0155 x 10⁻³⁴ meters.}
In the previous post, we discussed Einstein’s “Light-Clock” thought experiment and highlighted the fact that while different observers, in different frames of reference, can all agree that they all observe the same single up and down cycle of light, what they cannot agree on is the length of that cycle.
We went on to show that the reason for both agreement and disagreement is that while the observed distance travelled (λ-v) is a variable and depends on the observer’s frame of reference, the observed oscillation-length (λ-min) is fixed and therefore independent of an observer’s frame of reference.
The relationship between the fixed and variable lengths, of a single cycle of light, is given by equation (13) above.
It is worth noting that the difference between the squares of the variable cycle-length (λ-c) and the variable wave-length (λ-v), must always equal the square of the fixed quantity lambda-min {as the table below shows}.
So given the fact that the speed of light is a constant, and having just established that no cycle-length (λ-c) can be less than a minimum distance (λ-min), the question naturally arises as to whether there is a corresponding minimum amount of time associated with the three-dimensional cycle.
The Passing of Time
As we can see from the table above, at very high speeds the cycle-length and the wave-length (λ-v) are virtually indistinguishable from each other, but as we move to slower speeds, the deeply hidden difference between the cycle-length and the wave-length begins to emerge.
As speeds slow down the wavelength begins to reduce much more than the cycle-length, and the divergence of these two lengths brings to the surface the deeply hidden fact that different frequencies of light move at different speeds (even in a vacuum, despite what is traditionally taught).
The reason that this fact is so important to pay attention to is that: it is, in reality, the frequency of the three-dimensional cycle that ultimately determines the passing of time…
T-min
The “frequency” of light is always expressed in cycles per second, and is therefore just another way of talking about the time interval or “duration” (T) of a single cycle. Accordingly, there is an inverse relationship between duration and frequency, which is given by
Equation (16) ______________ T= 1/f
This means that the relationship between the duration of a cycle and its cycle-length can be written as
Equation (17) _____________ T= (λ-c) / (c)
Given that c is a constant, this equation effectively tells us that as the duration goes down, so too does the cycle-length. But we know, from equation (13) above, that the cycle-length can never go to zero, which means that the duration can never go to zero. Consequently, when the cycle-length is set to its minimum value equation (17) becomes
Equation (18) __________ T-min = (λ-min) / (c)
Thus, we can now see that a further consequence of the second postulate of NCR is that no cycle duration can be less than a “minimum duration” (T-min).
And, given that (λ-min) equals (2π) times the Planck Length, the minimum duration of any cycle must therefore be equal to (2π) times the Planck Time.
[Note 1: This equates to a time of 3.38742 x 10⁻ ⁴³ seconds.]
[Note 2: I will show at a later date that T-min is the smallest unit of time, not the Planck Time as is widely believed.]
Thus, having previously established that no cycle-length can be less than a minimum distance, we now see that that fact requires that every cycle must also have at least a minimum duration.
With this concept in mind, let us now look at what this tells us about cycle duration in general.
Duration of The Cycle
First, we need to recall equation (12), from the previous post
Equation (12)____________ u = f (λ-min)
Using equation (16) above we can rewrite this as
Equation (19) ____________ u = (λ-min)/T
And when we rearrange this we get
Equation (20) ____________ uT = λ-min
Next, by rearranging equation (18) we get
Equation (21) ____________ c (T-min) = (λ-min)
And so now we have two equations for lambda-min (20 & 21), which means that we can equate the two
Equation (22) ___________ u T = c (T-min)
And, if we rearrange equation (22) we get
Equation (23) ____________ T = (c/u)(T-min)
This equation is the “Duration Dilation Equation”. The factor (c/u) is commonly known as “gamma” (γ). Thus, this equation is effectively Einstein’s time dilation equation on the scale of a single cycle.
This equation tells us that the “duration of a cycle” increases as a thing moves faster; meaning that: the lower the frequency of a thing the more “Time” it will experience per cycle…
The Nature of Time
So what does all this tell us about the “Nature of Time”?
Well, fundamentally it tells us that “Time” is merely a physical cycle, and a physical cycle is simply a quantity of physical “Change”.
Equation (23) tells us that: while different cycles might have different durations, all cycle durations can be quantified in terms of “a minimum duration (T-min)” — a minimum quantity of change that we perceive as “Time”.
It tells us that the passing of this “Time” depends on the physical length of a thing’s cycle; because that is what ultimately determines the speed of its clock…
So ultimately, the duration dilation equation tells us that:
There is no such thing as “Universal Time”.
Time is simply a “Quantity of Change”.
And the Speed of Oscillation determines the Speed of Change…
© Kieran D. Kelly
This is Post #3 in the series on NeoClassical Relativity Theory
