Journal of Theoretics

Transcription

1 Journal of Theoretics Box Normalization and The SCTE Land J Harri T Tiainen PO Box 5066 Chatswood West NSW 1515 Australia harri@healingearth.com.au The SCTE Land constant of 0 A constant of 1 constant of i t B <50 % 50 %> Abstract The role of the box in Schrödinger s Cat Thought Experiment SCTE is examined in some detail and it is shown that the box must have a series of properties in its course throughout all paths of all histories. This series of properties leads to three normalization constants for the box throughout its paths for all parts of all histories. The first normalization constant of the box is explored in detail. Keywords: Schrödinger s cat thought experiment, box normalization Introduction That box has a lot of blood in it. That bloody box is capable throughout all paths of all histories of forming 1) a perfectly hidden system to a general observer (Point A to the first closing) 2) a perfectly self-contained system (for t) and 3) a system that can interact with everything measurable (after the second opening)

2 In more detail the box acts as the imaginary i in the region from Point A until the box captures the cat the first time (i is the private time system excluded from the observer recall there are interactions of the parts of the SCTE which cannot interact after the second opening) a pure complex number from the first closing until the second opening by an arbitrary real-number observing system (or the purely complex number system is the hidden variables system timelessly excluded to the observer and the environment) a pure real number from the second opening operated by the excluded observer until the environment suffers heat death by the process of partitioning all matter (since the box can now work thermodynamically with anything else including an observer) That bloody box That box of Schrödinger s has a lot of blood in its history. Let us look in detail at the role of the box in the Schrödinger Cat Thought Experiment SCTE Land. 1) From point A until the box captures the cat: the cat and the box form their own private hidden system to a general observer. These quantum variables are never revealed. How can we construct a box that excludes all of Wigner s friends? 2) During t of the thought experiment the cat is perfectly hidden to the outside environment and to all observers that is strictly there is no mixing of the outside and the inside allowed. So does what happens for t inside the box contribute to the distribution of parts on the outside or is the interior of the box at absolute zero? Simply external work cannot penetrate the box yet it has parts of all histories? 3) After t to point B: the box, its contents, and a general observer can interact that is general events can now interact with the environment and the cat and the box. That is there are three box normalization constants for the SCTE land. 1) i from Point A to the first closing (this achieves an independent time system) 2) 0 during t (this achieves a self-contained system from the environment at 0K) 3) 1 from the cut to Point B (this achieves a working system with everything else) The SCTE Land Complex eigenvalues A totally hidden and private system to a general observer. constant of 0 A constant of 1 constant of i t B 50 %> <50 %

3 Region 1 From Point A until the box captures the cat we have a totally private system to a general observer (that is all of Wigner s friends), these hidden variables are never revealed. Putting it another way what mathematical region in quantum mechanical phase event space is perfectly hidden to a general observer? How can the box form a perfectly hidden region to a general observer yet somehow the box can miraculously interact with everything after the second opening of the box? What in QM is totally hidden and unchanging in relation to a real-eigenvalued state or operator? Or in other words what entity is always hidden yet can interact (mathematically) with real eigen-numbered states and operators (=the physical world we experience and can measure)? In other terms what is unchanging to the realeigenvalued world yet is timelessly (via a mathematical transformation) connected to the real-eigenvalued world? This hidden region cannot be altered (or be affected) by physical interactions that happen after the second opening that is simply this region must be absolute and unchanging. So what is absolute and enteral and hidden to the real-number world? What entity is totally hidden (that is cannot be measured) yet is needed mathematically in every measurement after the second opening? Recall [A,B]=iC is how we connect incompatible observables in QM. What variables are always hidden to a general observer? There is one variable that is always hidden that is the imaginary i, it is involved in all observations yet can never be measured itself. All QM logical structures are based on i, yet i can never be measured. [A,B] = ic Look at the perfectly hidden entity that cannot be measured yet is always hanging about. Get the point i is the ultimate hidden variable for Nature, What does i mean to us when we can never measure i and in fact nothing physical can interact with i? Really is i something that should be included in the inventory of the real physical world? That complex eigenvalue i; that cat; that box; and that cut everything in Greek (normal) QM relies on a constant that is by definition an entity outside space-time in fact any real-valued eigenstate, should we on rely on entities that cannot be experimentally observed?! Exactly what measurement can we do to establish the physical existence of i. Which happens to be involved in all Greek (normal) QM conceptions of what a measurement is in [A,B] = ic. Look at the entity that cannot be measured yet somehow is involved in everything physical. How does an entity by definition outside normal QM (Greek) observational limits interact with entities that are bound by its pure mathematical construct (a quantum equation eg Schrödinger s equation)? What is i? The eigenvalue i is the ultimate constant of Nature because every single observation is in commutator form and i holds the three counting systems together as one whole. That is the imaginary i is the ultimate constant of Nature, because it stands outside all real and natural measurements, or in other words all real-valued and natural-valued eigen-states and operators are timeless connected to i.

4 the imaginary i the complex numbers the real numbers the natural numbers Recall the imaginary i is -1 it completes algebraically the real number system, for without this entity basic arithmetic is found to be wanting. That is the imaginary i makes complete the truth of the natural number counting system, recall the distribution of parts in the SCTE Land must include a natural number counting system (the measurement itself) this system is the quantum system that consists of real-life objects for example the counting of one dead cat or one alive cat to get a measurement (by the thought experiment) of what an observation is (at any time) with the environment and any of its observers. The process of the paths of all history is fundamentally due to the affect of i, the imaginary entity completes the process of counting simple objects that are observable and can be instigated by Wigner s friends. Basically the imaginary i is needed by the logic of mathematics to make complete the process of simple counting. The imaginary i is the square root of one. The imaginary entity using mathematical logic makes complete the counting of real-life physical objects, which use physical logic. i completes the truth for counting of all parts and the counting of the parts of all paths of all histories by definition is entropy clearly i makes the counting of all things mathematical true, using non-physical processes. That is counting physical things always includes the imaginary entity yet we cannot measure or count this imaginary entity. That is i uses a different process then natural simple counting, which is the physical process we humans use to count real or natural number quantum states. The region from point A until it captures the cat the first time the box must be the imaginary entity residing in the complex number system. Loosely the box has a normalization constant of i, because the chances of a real-life object being the imaginary entity is i. Region Two In the thought experiment by definition for t, external heat is forbidden to enter and internal work is forbidden to exit the box, that is a work cycle is forbidden between the cat and the observer, or the box is a perfect insulator. Simply since the mixing of internal and external parts is forbidden, no measure of the entropy of the box can be established. In the region t we have the box being a pure complex number, with a normalization constant of 0. Loosely there is no physical chance of a real-life object being purely complex. Region Three After the second opening the box has a normalization constant of one that is the box does contain real-life objects that can be counted thermodynamically by any observer. Loosely there is every chance of the box containing a real-life counting event somewhere in all paths of all parts of all histories. From 10 The principles of quantum mechanics by P.A.M. Dirac, Fourth Ed Oxford Uni Press 1958, reprinted 1978 When we make an observation we measure some dynamical variable. It is obvious physically that the result of such a measurement must always

5 be a real number, so we should expect that any dynamical variable that we can measure must be a real dynamical variable. One might think one could measure a complex dynamical variable by measuring separately its real and pure imaginary parts. But this would involve two measurements or two observations, which would be all right in classical mechanics, but would not do in quantum mechanics, where two observations in general interfere with one another it is not in general permissible to consider that two observations can be made exactly simultaneously, and if they are made in quick succession the first will usually disturb the state of the system and introduce an indeterminacy that will affect the second. We therefore have to restrict the dynamical variables that we can measure to be real, Conclusion of Box Normalization and The SCTE Land That bloody box of the SCTE land must have three normalization constants throughout all paths of all parts of all histories. These normalization constants are an artefact of the logic of the mathematical processing of simple counting. That is going from the purely imaginary to the purely natural, and the converse going from the purely natural to the purely imaginary. The two chains below represent the artefact the imaginary i the complex numbers the real numbers the natural numbers natural counting real number counting complex number counting the imaginary i Complex Numbers Real numbers Natural Numbers The relationship of the three number systems Since we must rely on the truth of the existence of the imaginary entity to complete simple counting we must have non-physical processes for counting real-life objects which are hidden to a physical observer. Or in other words the existence of i outside the real and natural number systems guarantees the absolute truth of simple counting. The outside system to the natural numbers is the real number system and the outside system to both the real and natural number systems is the complex number system, with the existence of the imaginary i guaranteeing completeness of the three counting systems as a whole. That is in total there must be three normalization procedures represent by the chain the complex numbers the real numbers the natural numbers to completely detail the path of all histories of a counting object. These procedures are constructed from complex numbers going to the natural numbers, loosely speaking going from the complex outside to the natural inside forces us to normalise the box three ways. Conversely there must be three sets of processes that count all objects represented by the chain natural number counting real number counting complex number counting

6 to completely detail the part distribution of all histories. These processes are constructed from the natural numbers going to the complex number system, loosely speaking going from the natural inside to the complex outside forces us to have three ways of counting objects. Region One Two Three Number system Purely imaginary Purely complex Purely real Box Normalization Constant i the imaginary entity 0 the zero entity Result of normalization An independent time system A self-contained system at absolute zero 1 the unit entity A working thermodynamic system Explanation of chance There is i chance that the cat is the imaginary entity There is no chance that the cat is at absolute zero There is every chance that the cat is in the box and can interact Table One How the different regions of the SCTE Land act as the three number systems Journal Home Page