|Stitching the Measurement Space Together - I
29th June 2019
Earlier we were discussing the topological space underlying the measurement space for Aku the amoeba, a macroscopic observer. The measurement space description is dependent upon the observer's (Aku's) measurement capability. The upper limit for the measurement capability is defined by the fine structure constant α. What α tells us is, that if we shake an electron on average 137 times, the electron spits out one photon. In fact the value of α represents the efficiency of the manifold wrapped around the topological space. It is the efficiency of this manifold, we are trying to improve. If we could improve the efficiency even to ~1/134, it will be a huge accomplishment.
δi ≡ ∞j .
And it is characterized by the time-independent j-space constant jML defined as:
where mo is the rest mass for elementary particles, and λCompton is Compton wavelength. However Aku lives in a dynamic world, dynamism which is the consequence of the entropy inherent in the nature of the discrete measurement space. How do we visualize the j-space and the resulting universe for Aku?
What we would like to do in next few blogs, is to develop a multifaceted fabric in discrete measurement space, a fabric in which physical structures can be introduced. The physical structures here, could be elemental or cosmic. Usually the measurements are defined for a point in space-time. When we speak of stitching together a discrete measurement space, we are discussing how the measurements corresponding to different points in space-time, are to be combined together.
1. Resources are needed even for the Simplest measurement:
The time-independence of action is assumed only when we write wave-equations in Aku's measurement space using t, for a conservative system. However any conservative system is a very small subset of any discrete measurement space. The concept of a conservative system is extremely useful for developing a mathematical structure for an observed physical phenomenon, but it also has fairly limited prediction capability.
We can not simply reverse the process described above, by lumping all the details together and then start sorting out the different types of objects from a big gigantic blob of information1. We will be stuck in a quagmire of sheer madness. No decision making will be possible, which is actually all nature wants to do with minimum or no hassles, the process inherent in nature we can call "continuation". The "continuation" is defined as the progression through successive zero-entropy measurements. Going around in circles, does not count as continuation. Nature does not repeat itself, an observer does. We will discuss "continuation" in detail later on.
Notice that the direction of the tangential component t , remains the same, however the direction of the normal component n, changes across locations in the space-time grid in j-space. The unit vectors n and t , are similar to the fundamental dyad of a metric tensor gμν . We will discuss the geometrical significance of having a normal vector in j-space, and why we need tensors in j-space a little later.
Let us sum up:
To be continued..
1. Actually we sort of can, by assuming various Symmetries and forming Groups etc. (aka matrix formulation), then describe measurements in corresponding fields by Differential Equations and Boundary Conditions (aka wave formulation). But then nobody understands what is really happening inside M-elephant. Clearly in this case, the circuits can not be completed in j-space and hence the precision in the description will be missing. For example, one may end up with a wooden basket with 6.2 red colored oranges and 3.8 orange colored apples with one leg each, sitting on a wicker table with no legs. That will still be okay perhaps, if the number of dimensions turns out to be 26.
2. Imagine a phase space with a single cell at t = 0j. This single cell will contain all the information about δi. It is called the initial state represented as <t = 0j>. As the entropy of the system increases, we can think of this single phase space cell, dividing and multiplying as time t progresses, according to observer's or system's capability (v << c), while combined phase space still has the same information content, i.e. δi. The combined phase space has its own clock τ, which stays frozen for Aku's reference frame S, hence the assertion that the universe is equivalent to a single zero-entropy measurement.
Sigma-z and I
Rationale behind Irrational Numbers
The Ubiquitous z-Axis
Knots in j-Space
Cauchy and Gaussian Distributions
Discrete Space, b-Field & Lower Mass Bound
The Cat in Box
The Initial State and Symmetries
Discrete Measurement Space
The Frog in Well
Visual Complex Analysis
The Einstein Theory of Relativity
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