|Insincere nature of Symmetry- II
|29th September 2017
"Weyl gave a good definition, the substance of which is that a thing is symmetrical if there is something we can do to it so that after we have done it, it looks the same as it did before."
- R. P. Feynman
"Einsteinís great advance in 1905 was to put symmetry first, to regard the symmetry principle as the primary feature of nature that constrains the allowable dynamical laws.....This is a profound change of attitude."
- David J. Gross
We had earlier discussed the concept of "circuit" in context of determining
"form or arrangement". If the circuit is complete then the
surface of the form or arrangement, can be measured accurately. Subsequently a structure will be formed and a symmetry would exist.
However if due to whatever reason
the information needs to be measured, is more than that contained
the existing form or arrangement, the circuit can not completed. The
corresponding surface which is a macroscopic structure, will be
disrupted and the symmetry will be broken.
In the context of the diagram above as symmetries are broken, we are moving from right to the left. Similarly as the symmetries are added we are moving from left to the right. The time-axis will exist, only for the observer ObsM measuring the macroscopic structures on the right. True discrete measurement space or j-space, does not allow any symmetry. At the same time a circuit can not be completed, unless a symmetry is assumed. Hence ObsM can only measure structures burdened with numerous symmetries, in the lower level information space.
Most of the symmetries observed in physics such as translational symmetry in space and time, reflection, rotation in space, and uniform velocity in straight line are observed by the macroscopic observer. Next group of symmetries corresponding to higher information space are time reversal, phase conservation in wave-function, exchange symmetry, particle-antiparticle symmetry etc. These are the symmetries influencing the measurements made by ObsM. Another was of stating it is that these are the symmetries which exist in all-inclusive Humpty Dumpty.
The observer Obsc (v/c ~ 1) has the capacity to measure more information than that contained in the structures measured by ObsM. Nevertheless, there are phenomena which even Obsc can not measure accurately. The consequence is the phenomenon such as Gravity. The spherical symmetry, once the gravity's influence must be accounted for in the measurements, is not conserved.
There are symmetries which are broken when the "form or arrangement" (spherical symmetry), encounters phenomenon obeyed by the "point" as defined in j-space by Obsc, itself. Such breaking of symmetry is known as explicitly broken symmetry. It is known that light waves or photons which represent Obsc, are influenced by gravity. In the case of explicit symmetry the circuit can not be completed, in a manner similar to spontaneous symmetry. Hence no forms or arrangements can be precisely measured by the macroscopic observer ObsM.
Symmetries lead to conservation laws. Conservation laws require that the action is conserved. The action is the minimum amount of resources required to travel the path AB between two points. A path will be measured uniquely in true j-space. However ObsM or Obsc may measure path AB as a difficult path, a path with very high information content, inaccurately and come up with multiple results while measuring the path AB, within their measurement capabilities. These results are linked to each other by appropriate transformations. We can then make a statement that action is invariant under a transformation for internal symmetries.
We do not change the space-time continuum while discussing such transformations. Which is equivalent to stating that path AB remains unchanged during these transformations. It is just the amount of the information contained with this path which is being measured by different macroscopic observers differently. None of these macroscopic observers will be able to measure the path AB completely. The time-axis of these measurements may be long enough for the measurements to be considered representing stable structures by ObsM. But for i-Space daemon Obsi, these measurements are fleeting and resulting structures no more stable than soap bubbles.
Explicit symmetries occur when the observers can measure only an infinitesimal portion of the path AB. Most of the explicit symmetries are likely to be not even measurable. It will make it very difficult to predict true nature of creation.
Observer from either q=2 or q=1 state will measure the Higgs Boson, as just another particle in a much more complex picture. In this case the Higgs Boson along with particles of similar level of information, will constitute a higher information state much more refined than the universe as we know it. This higher information state can be measured or observed only but infinitesimally, by any measurement apparatus we can design in the q=3 information state which is based on electron-photon interaction.
In true j-space there will be an infinite number of Higgs bosons, each completely unique with no shared properties with others. The information contained within our universe is no more than a mite in this description.
The information landscape represented by j-space, is neither static nor inert. It is a vibrant and dynamic landscape of which life as we understand it, is also a part of. The symmetries define different interactions taking place at different levels within this landscape.
Symmetries are the consequence of the limitation of the measurement apparatus used by the observer. More precise the apparatus, less number of symmetries it must measure. In context of humans the measurement apparatus, is the human body which is the result of our genetic makeup. Symmetries are ingrained in observers. Different observers different set of symmetries. Symmetries should not be attributed to the creation, which is much too sophisticated to repeat itself.
We will be discussing Quantum Computing next.
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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