GM Jackson

Quantum entanglement can be explained using decks of cards. This paper shows how these decks of cards violate Bell's inequality, and that "hidden operators" determine a quantum measurement outcome. If these hidden operators could be known prior to measurement, one could predict the outcomes of quantum events. The herein thought experiment demonstrates that no faster-than-light communication takes place between entangled pairs. Further, when teleportation is scrutinized, there is no evidence that information passes through a wormhole.

According to R.P. Kerr, a black hole need not contain a singularity.  Such an assertion prompted this author to explore alternate black-hole models where a singularity is unnecessary.  The models presented here show that a sufficiently large black hole could contain a universe; that an average black hole could contain a neutron star.  This paper also shows why micro-black holes are untenable and why a typical black hole has a mass of at least approximately three solar masses. As an additional bonus, the models presented conserve quantum information inside the black holes, and, are consistent with black-hole entropy and temperature.

Hawking radiation has not been directly observed.  Maybe it exists, maybe it doesn't.  Even it it exists, some very fundamental physical laws prevent black hole evaporation.  At the quantum level, Hawking radiation can be turned on its head.  It could just as easily add mass to a black hole.

According to Einstein's theories of relativity, nothing is faster than light; yet, observations made by Newton, Laplace and Van Flandern led them to believe gravitational information is much much faster than light, virtually instantaneous. To thicken the plot further, LIGO observed gravitational waves propagating within the light-speed limit. Then there's the vacuum energy problem where the vacuum seems to have up to infinite energy! By making use of quantum physics and changing an initial assumption about the vacuum energy, it is possible to connect the dots between quantum physics and General Relativity. By exposing a fundamental flaw in the rubber-sheet model for curved spacetime, it is possible to create a superior model that reconciles the speed of gravitational waves with the illusion of faster-than-light gravitational information.

This paper shows mathematically and experimentally why it is highly unlikely that the speed of gravity was successfully measured. Consider the rubber-sheet analogy. If you place an iron ball on a rubber sheet, you will see the ball depress and curve the rubber sheet. If you roll the ball accross the sheet, you will see the sheet flatten out at the ball's previous position and the sheet will begin to curve at the ball's current position. Over a given distance, it takes time for the curve to flatten and reform. We can calculate the speed of this process by dividing the distance by the time. One might assume we can calculate the speed of gravity in an analogous manner. In fact, I had an email exchange with Sergei Kopeikin who claimed that during the Jovian Deflection Experiment he observed Jupiter's gravity fading and reforming as Jupiter moved through space. The speed of this process turned out to be the speed of light or close to it. He also informed me that the gravity was stronger at Jupiter's previous (retarded) position and weaker at Jupiter's current position due to the light-time delay.

According to Relativity Theory, everything propagates through spacetime at light speed. However, a mass at rest propagates solely through time and experiences zero velocity. A massless photon propagates solely through space and experiences no time. Other objects propagate through time and space, and, experience both time and subluminal velocities. This paper demonstrates that both gravity (the fundamental interaction) and gravitational waves propagate at light speed through spacetime, but with varying degrees through time and space, i.e., they each have different velocities through space.

According to Relativity Theory, everything propagates through spacetime at light speed.  However, a mass at rest propagates solely through time and experiences zero velocity.  A massless photon propagates solely through space and experiences no time.  Other objects propagate through time and space, and, experience both time and subluminal velocities. This paper demonstrates that both gravity (the fundamental interaction) and gravitational waves propagate at light speed through spacetime, but with varying degrees through time and space, i.e., they each have different velocities through space.

Many P vs. NP discussions leave out what is perhaps the most important question any problem solver could ask: "Are there any clues?" This paper shows how clues can lead to solving the most complex problem, and, how the lack of clues prevents one from solving a seemingly simple problem. Sudodu is deemed NP-complete, but the player is provided clues, and these clues cut the complexity of Sudoku down to size, a size that can be managed by a typical personal computer or a player that employs three deduction strategies. According to Arto Inkala, the Sudoku puzzle below is the hardest ever. It took him three months to design it, but I was able to solve it … ... in less than 10 seconds ... with the help of a python app I created. Here

Re: the Continuum Hypothesis: Is there any set which has more members than the set of natural numbers (N), but fewer members than the set of real numbers (R)?  The short answer is no. The long answer, that includes mathematical proof, shall be set forth in this paper.

This paper reveals why Cantor's diagonalization argument fails to prove what it purportedly proves and the logical absurdity of "uncountable sets" that are deemed larger than the set of natural numbers. Cantor's diagonalization proof (CDP) is used to prove various things like Gödel's Incompleteness theorem (GIT) and the uncountability of real numbers (URN). In the case of GIT, it is assumed that you can have a complete list of provable statements. You use CDP to prove a statement that is not on the list, then conclude the statement is not a provable statement; otherwise, it would be part of the list of all provable statements. However, if your complete list is not really complete, then it makes sense that you can prove a new provable statement not on the list. In the case of proving the URN, you use proof by contradiction: assume the real numbers are countable and assume a complete list of them between, say, .000 ... and .111 ... The list is believed to be complete because an infinite number of counting numbers (1 to n) each allegedly have a oneto-one correspondence to each real number on the list. CDP is then used to show there is a real number that is not on the list (a contradiction). Therefore, according to the proof, there is no bijection between the real numbers and the counting numbers. Below, we will work through an example proof using CDP and demonstrate why it comes up short. Let's begin with an nXn matrix of real numbers in base 2. We go along the diagonal and flip each bit from 0 to 1 or 1 to 0 to create a new number not on the list. If we think the number is on the list, say, at row r, we can check it and see that its bit at column r doesn't match. We can repeat this exercise for all rows and see that we truly have a new real number not on the list.

This paper shows how Gödel failed to prove his first incompleteness theorem and shows a standard of proof that completes a system containing genuine, not contrived, undecidable statements. Gödel's First Incompleteness Theorem is often stated as follows: "Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e., there are disproved in F."

This paper shows what happens when Gödel's theorem is turned on itself, and the logical inconsistency that occurs when selfreferencing statements are converted to Gödel numbers. Gödel's First Incompleteness Theorem (GFIT) is often stated as follows: "Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e., there are statements of the language of F which can neither be proved nor disproved in F." Here's another way GFIT is stated: "In any reasonable mathematical system there's always true statements that can't be proved."

The four color map theorem states that no more than four colors are needed to color the regions of any map so that no two adjacent regions have the same color. More specifically, the theorem states that no more than four colors are required to color the vertices of any planar graph where any two adjacent vertices don't have the same color. This paper shows how the theorem arises from a broken correlation between the number of colors and the number of vertices (dots), and, how repairing this broken correlation leads to maps requiring more than four colors. However, if three dimensions are not invoked on a on planer graph, it can be shown that no more than four colors are needed to color it. Premise: All maps, regardless of their shapes and sizes, can be represented by planer dot-and-line diagrams. Such drawings make analysis easier and more universal. Each dot (vertex) represents a country and each line represents a border. The rules are any two dots connected by a line cannot be the same color and lines cannot intersect.

Supersymmetry or ad hoc methods such as renormalization are often used to tame infinities that result from divergent functions in quantum physics. Although SUSY particles have yet to be discovered and may be too massive to fulfill their purpose, and, renormalization seems to lack mathematical rigor. Here we offer an alternative method that employs the least-action and Heisenberg uncertainty principles.

This paper shows a new mathematical algorithm that allows weak-force bosons to have mass and leaves photons massless while giving mass to neutrinos and other leptons. The right side of equation 1 below is the Higgs vector used to ensure that photons don't have mass and that the weak-force gauge bosons have mass. This same vector also ensures that leptons will have mass except for neutrinos.

Re: the information paradox. When a theory contains a paradox, it is a clue that one or more premises the theory relies on are faulty. In this paper, we examine the premises, arguments and assumptions that are the foundation of blackhole physics. All roads lead to Rome. Somewhere in Rome there is a particle trapped in a rotating potential well. Which road (or path) did the particle take to get to Rome? The Heisenberg Uncertainty Principle prevents us from simultaneously knowing the particle's position and momentum. That information could help us determine from whence the particle came.

If a black-hole singularity is treated as a quantum particle, and, if the Heisenberg Uncertainty Principle is strictly enforced, the black-hole information paradox is resolved. The information thought to be lost is encoded in Hawking radiation. Imagine your favorite book. It is filled with letters, words, sentences paragraphs, pages and chapters-all of great importance! Information you never want to lose. But alas, just when you thought it was safely tucked away on a shelf, it falls into a black hole, past the event horizon where not even light can escape. You wish your book was burned instead. No doubt a forensic team could

In his paper titled "Aberration and the Speed of Gravity," S. Carlip argues that gravity propagates at light speed, and, its "action at a distance" and the lack of observed aberration is canceled by velocity dependent interactions. However, the underlying assumption of his thesis is that gravity is caused by gravitational radiation propagating at light speed. Another assumption held by much of the physics community is the quantization of gravitational waves will lead to a spin-2 massless particle known as the graviton. In this paper, I show why gravitational waves and gravitons are not the root cause of gravity. Gravity emerges from an entangled relationship between spacetime and matter. Modern physics has two conflicting ideas: 1. gravity propagates at light speed, and 2. the equivalence principle. Why are these two ideas in conflict? The first proposes that gravity works in the following manner: a person holds a pen in his hand and drops it. Before it hits the floor, however, the floor must emit gravitons that propagate at c to create a field of gravity, so the pen can receive the gravitational information; otherwise, the pen won't fall. The second idea is often set forth using a thought experiment where the person holding the pen is in a spaceship. The thrust of the engines cause the floor to accelerate toward the pen when the pen is dropped; otherwise, the pen would float freely in space and never make contact with the floor. In this scenario, no gravitons or gravitational field are needed. The floor is on a collision course with the pen and does not need to send a signal to the pen to let it know it's coming. According to Einstein, this is indistinguishable from gravity. Therefore, this great idea and the one that precedes it create a paradox: the first idea implies a force is causing the pen to fall, so a force-carrying particle is necessary. The second idea implies there is no force. 1.

It is commonly postulated by string theorists that gravity is weak due to gravitons existing and propagating in dimensions beyond our well-understood 3D space. By contrast, the other forces are much stronger than gravity, since their strings stay attached to a 3-brane that is representative of our observable universe. However, a recent paper by Pardo, Fishbach, Holz and Spergel entitled "Limits on the Number of Spacetime Dimensions from GW170817" showed that gravitational waves failed to behave as though they were subject to an inverse-cube law. Rather, they behaved as though they were subject to an inverse-square law. The implication being that the extra spacetime dimension, known as "the bulk," does not exist. Further, if gravitons propagate through dimensions beyond 3D space, and, assuming they are massless and move at light speed, gravitational waves should appear to arrive later than electromagnetic waves, since they must cover extra-dimensional distance consistent with the Pythagorean theorem:

By using two fair coins, a cylinder, and something resembling a skateboard ramp, it is possible to simulate and demonstrate quantum entanglement in a real physical experiment or a thought experiment. This paper will use the thought experiment approach. Imagine Alice and Bob each simultaneously tossing a fair coin. As the coins spin in the air, it is as if they are in a superimposed state. Since the coins are not entangled, they are separable. Equation 1 below represents the state of superposition, i.e., the coins spinning in the air: The different possible states are HH, TT, HT or TH. Equation two shows the probability of each state, which is .25: 1.

By borrowing some concepts from quantum physics such as propagating particle waves and harmonic oscillators it is possible to discover the essence of time, time dilation, length contraction and relativistic mass. Why does mass seem to increase when a particle is moving at a substantial subluminal velocity v? If we begin with the relativistic mass equation (equation 1), we can derive equation 4 below:

Cosmic rapid expansion resolves the horizon problem, the magnetic-monopole problem, and flatness problem. More than one hypothesis has been proffered to describe the mechanics of cosmic rapid expansion, including the inflaton hypothesis. Einstein's theory of relativity can also explain the phenomenon of cosmic rapid expansion-even though such expansion appears to exceed the light-speed barrier. The mu-meson experiment conducted in 1962 by David H. Frisch and James H. Smith demonstrated the mu-meson decay rate slowed when mu-mesons moved at high subluminal speeds. In other words, the mu-meson's proper time ran slower. This result was consistent with the following Lorentz equation: 1.

By unifying the concept of gravity with the concept of dark energy we can explain the following: 1) why galaxies are moving apart; 2) how space-time actually curves; 3) why objects fall down instead of up (and the elliptical orbits of satellites); 4) why gravity is weak compared to the other fundamental interactions.