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25^{th} March 2019 |
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"Lightning has struck the rails on our railway embankment at two places A and B far distant from each other. I make the additional assertion that these two lightning flashes occurred simultaneously. If I ask you whether there is sense in this statement, you will answer my question with a decided “Yes.” But if I now approach you with the request to explain to me the sense of the statement more precisely, you find after some consideration that the answer to this question is not so easy as it appears at first sight." - Albert Einstein, On the idea of time in Physics, Relativity, The special and general theory. "Expression and shape mean almost more to me than knowledge itself."
-Hermann Weyl "Despite all the ink that has been spilled and all the noise generated by discussions about the nature of time, I would argue that it’s been discussed too little, rather than too much. But people seem to be catching on. The intertwined subjects of time, entropy, information, and complexity bring together an astonishing variety of intellectual disciplines: physics, mathematics, biology, psychology, computer science, the arts. It’s about time that we took time seriously, and faced its challenges head-on."
- Sean Carroll, From Eternity To Here: The Quest for the Ultimate Theory of Time.
- Leonard Susskind, Why is Time a One-Way Street?, Santa Fe Institute, 2013. |
Imagine that a colony of amoebae is commuting between Ottawa and Montreal, in a self-driving car named Bubble, which has no windows, no brakes, no accelerator, no steering-wheel and a fuel tank with an unlimited capacity. Furthermore in Bubble there is no odometer, no clock, nor any GPS, to indicate the exact location or time in a conventional sense. Only information available to the passengers or observers, is an instrument similar to the fuel-gauge, called action-gauge, which tells amoebae how efficiently the fuel or the resources have been consumed during their journey. The catch is that the observers have to design the action-gauge themselves. Now let us assume that among the observers is an enlightened amoeba named Aku, who is aware of its own mortality. With help from his fellow observers If we think about it, Aku has not been given any information about Bubble whatsoever except for what Aku can measure. Aku is not aware of the increasing entropy S, resulting in increasing resource consumption for the same destination, due to the lack of precision in measurements. An assumption can be made that entropy S does not affect a sub-system inside the vehicle, and the conditions such as Inertial Frames, Unitarity and Locality etc. can be used to describe the results measured by Aku inside Bubble. The important thing to note, is that the observers have no awareness of "outside" Bubble. The states: "inside" and "outside", are Aku's perceptions localized within Bubble. As it happens, the amoebae traveling to greater distances begin to notice something very odd going on. The precision observers An inevitable conclusion based on the measurements with continuously deteriorating precision, can be drawn that the blue marble is expanding like a gas balloon, which actually is a thermodynamic picture. This required precision is impossible as the observers Every measurement Aku can make, will have to derive from the readings the action-gauge is providing. It is equivalent to saying that the actual action-gauge providing the precise state of the available resources, is the topological space, Bubble is the manifold and the measurements made by the Aku, We can take the argument further, and assume that there are different types of amoebae and each of them riding their Bubbles of similar nature, albeit with similar inefficient action-gauges. This situation is like different observers using different manifolds and measurement metrics, while the underlying topological space remains unchanged. These observers can be anything or anyone, from an atom to an amoeba, each with their own unique characteristics and hence unique action-gauges. The bottom line remains that for each observer, the action-gauge and hence the underlying topology, does not change and the second law of thermodynamics, ΔS ≥ 0, is always applicable. Each Bubble will be affected by the same entropy, resulting in continuously increasing resource consumption during the same quantum of journey. Inside Bubble, Aku must complete a circuit before it can start counting. The sequence of events to accomplish this, is as follows: (i) Assume a VT-Symmetry, i.e. define the origin based on precision measurements of (ii) Complete a circuit based on VT-Symmetry. The circuit will be the curve of least energy or the curve of least disorder for Aku. (iii) Apply Stokes' theorem and Gauss' theorem to form the Surface of Least Disorder (SLD). (iv) Aku can start counting using SLD inside Bubble. We note that Aku is merely counting, not measuring either length or time. So how does the concept of time comes in to the picture inside Bubble? Let us assume the simplest case that the circuit to be completed inside Bubble, is a circle. And the observers measuring the circle are: Aku, Therefore in essence, the infinite time axis for Aku is nothing more than an instant for Obs
We will discuss this example later on, with respect to measurements in j-space. Also now that we are able to count, we should figure out how to build our LEGO blocks. ___________________ 1. The term "comparing notes by Akus" here, requires adhering to Lorentz Invariance and Möbius Transformations. Similarly fuel signifies the resource utilization in j-space of Akus. In essence we are discussing impossible-problem-1, which is the resource optimization in a closed system represented by Bubble. 2. A thermodynamic description implies that the internal mechanism and symmetries of the System, for e.g. spin, can not be precisely determined. This is how Aku approximates the interior of Bubble. The interior of the System and the interior of the Bubble are two different descriptions. Bubble must follow the topology which is set by the System. Bubble is at the far edge of the System, yet the interior of Bubble is all Aku has for measurements. Entropy represents the internal state of Bubble, thus the value of entropy would remain the same for any reference frame Aku is in, inertial or non-inertial. The values of dW, dQ, and T would change inside Bubble for relativistic coordinate frames. 3. Planck domain measurements are not possible. 4. Invariance of space-time interval in General Theory of Relativity. Entropy ensures that the information gathered during each successive space-time interval will be continuously diminishing. 5. Aku would have to assume action to be time independent inside Bubble. We will discuss the criterion behind this important assumption. 6. With grateful thanks from the notes of Dr. S. of Nikhef. || |
Previous Blogs:
Nutshell-2018
Curve of Least Disorder Möbius & Lorentz Transformation - II Möbius & Lorentz Transformation - I Knots, DNA & Enzymes Quantum Comp - III Nutshell-2017 Quantum Comp - II Quantum Comp - I Insincere Symm - II Insincere Symm - I Existence in 3-D Infinite Source Nutshell-2016 Quanta-II Quanta-I EPR Paradox-II Chiral Symmetry
Sigma-z and I Spin Matrices Rationale behind Irrational Numbers The Ubiquitous z-Axis Majorana ZFC Axioms Set Theory Nutshell-2014 Knots in j-Space Supercolliders Force Riemann Hypothesis Andromeda Nebula Infinite Fulcrum Cauchy and Gaussian Distributions Discrete Space, b-Field & Lower Mass Bound Incompleteness II The Supersymmetry The Cat in Box The Initial State and Symmetries Incompleteness I Discrete Measurement Space The Frog in Well Visual Complex Analysis The Einstein Theory of Relativity |

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