The Planck Length and the Constancy of the Speed of Light in Five Dimensional Spacetime Parametrized with Two Time Coordinates

In relativity and quantum field theory, the vacuum speed of light is assumed to be constant;the range of validity of general relativity is determined by the Planck length. However, there has been no convincing theory explaining the constancy of the light speed. In this paper, we assume a five dimensional spacetime with three spatial dimensions and two local time coordinates giving us a hint about the constancy of the speed of light. By decomposing the five dimensional spacetime vector into four-dimensional vectors for each time dimension and by minimizing the resulting action, for a certain class of additional time dimensions, we observe the existence of a minimal length scale, which we identify as the Planck scale. We derive an expression for the speed of light as a function of space and time and observe the constancy of the vacuum speed of light in the observable universe.

A Unified Newtonian-Relativistic Quantum Resolution of the Supposedly Missing Dark Energy of the Cosmos and the Constancy of the Speed of Light

Time dilation, space contraction and relativistic mass are combined in a novel fashion using Newtonian dynamics. In this way we can surprisingly retrieve an effective quantum gravity energy-mass equation which gives the accurate experimental value of vacuum density. Furthermore Einstein’s equation of special relativity E = mc2, where m is the mass and c is the velocity of light developed assuming smooth 4D space time is transferred to a rugged Calabi-Yau and K3 fuzzy Kahler manifolds and revised to become E=(mc2)/(22), where the division factor 22 maybe interpreted as the compactified bosonic dimensions of Veneziano-Nambu strings. The result is again an accurate effective quantum gravity energy-mass relation akin to the one found using Newtonian dynamics which correctly predicts that 95.4915028% of the energy in the cosmos is the hypothetical missing dark energy. The agreement with WMAP and supernova measurements is in that respect astounding. In addition different theories are used to check the calculations and all lead to the same quantitative result. Thus the theories of varying speed of light, scale relativity, E-infinity theory, M-theory, Heterotic super strings, quantum field in curved space time, Veneziano’s dual resonance model, Nash Euclidean embedding and super gravity all reinforce, without any reservation, the above mentioned theoretical result which in turn is in total agreement with the most sophisticated cosmological measurements which was deservingly awarded the 2011 Nobel Prize in Physics. Finally and more importantly from certain viewpoints, we reason that the speed of light is constant because it is a definite probabilistic expectation value of a variable velocity in a hierarchical fractal clopen, i.e. closed and open micro space time.

A Workable Solution for Reducing the Large Number of Vehicle and Pedestrian Accidents Occurring on a Yellow Light

Traffic intersections are incredibly dangerous for drivers and pedestrians. Statistics from both Canada and the U.S. show a high number of fatalities and serious injuries related to crashes at intersections. In Canada, during 2019, the National Collision Database shows that 28% of traffic fatalities and 42% of serious injuries occurred at intersections. Likewise, the U.S. National Highway Traffic Administration (NHTSA) found that about 40% of the estimated 5,811,000 accidents in the U.S. during the year studied were intersection-related crashes. In fact, a major survey by the car insurance industry found that nearly 85% of drivers could not identify the correct action to take when approaching a yellow traffic light at an intersection. One major reason for these accidents is the “yellow light dilemma,” the ambiguous situation where a driver should stop or proceed forward when unexpectedly faced with a yellow light. This situation is even further exacerbated by the tendency of aggressive drivers to inappropriately speed up on the yellow just to get through the traffic light. A survey of Canadian drivers conducted by the Traffic Injury Research Foundation found that 9% of drivers admitted to speeding up to get through a traffic light. Another reason for these accidents is the increased danger of making a left-hand turn on yellow. According to the National Highway Traffic Safety Association (NHTSA), left turns occur in approximately 22.2% of collisions—as opposed to just 1.2% for right turns. Moreover, a study by CNN found left turns are three times as likely to kill pedestrians than right turns. The reason left turns are so much more likely to cause an accident is because they take a driver against traffic and in the path of oncoming cars. Additionally, most of these left turns occur at the driver’s discretion—as opposed to the distressingly brief left-hand arrow at busy intersections. Drive Safe Now proposes a workable solution for reducing the number of accidents occurring during a yellow light at intersections. We believe this fairly simple solution will save lives, prevent injuries, reduce damage to public and private property, and decrease insurance costs.

Faster than the Speed of Light Is a Quantum Phenomena

Classical Mechanics using Einstein’s theories of relativity places a limit on speed as the speed of light. Quantum Mechanics has no such limitation. To understand space accelerating faster than the speed of light and information being exchanged instantaneously between two entangled electrons separated by huge distances, one uses Planck’s length, Planck’s time, and Planck’s mass to indicate that space and time are discrete and therefore along with masses smaller than Planck’s mass are Quantum Mechanical in nature. Faster than the speed of light c = 3 × 108 m/s is a classical effect only in dimensions of space lower than our 3-D Universe, but it is a Quantum effect in all dimensions of space. Because space can oscillate sending out ripples from the source, it is the medium used for transporting light waves and gravity waves.

The Speed of Light Is Not Constant in Basic Big Bang Theory

Starting from the basic assumptions and equations of Big Bang theory, we present a simple mathematical proof that this theory implies a varying (decreasing) speed of light, contrary to what is generally accepted. We consider General Relativity, the first Friedmann equation and the Friedmann-Lema?tre- Robertson-Walker (FLRW) metric for a Comoving Observer. It is shown explicitly that the Horizon and Flatness Problems are solved, taking away an important argument for the need of Cosmic Inflation. A decrease of 2.1 cm/s per year of the present-day speed of light is predicted. This is consistent with the observed acceleration of the expansion of the Universe, as determined from high-redshift supernova data. The calculation does not use any quantum processes, and no adjustable parameters or fine tuning are introduced. It is argued that more precise laboratory measurements of the present-day speed of light (and its evolution) should be carried out. Also it is argued that the combination of the FLRW metric and Einstein’s field equations of General Relativity is inconsistent, because the FLRW metric implies a variable speed of light, and Einstein’s field equations use a constant speed of light. If we accept standard Big Bang theory (and thus the combination of General Relativity and the FLRW metric), a variable speed of light must be allowed in the Friedmann equation, and therefore also, more generally, in Einstein’s field equations of General Relativity. The explicit form of this time dependence will then be determined by the specific problem.

A Topological Magueijo-Smolin Varying Speed of Light Theory, the Accelerated Cosmic Expansion and the Dark Energy of Pure Gravity

The paper presents a detailed analysis of ordinary and dark energy density of the cosmos based on two different but complimentary theories. First, and starting from the concept of the speed of light being an average over multi-fractals, we use Magueijo-Smolin’s ingenious revision of Einstein’s special relativity famous formula E = mc2 to a doubly special formula which includes the Planck energy as invariant to derive the ordinary energy density E(O) = mc2/22 and the dark energy density E(D) = mc2(21/22) wheremis the mass andcis the speed of light. Second we use the topological theory of pure gravity to reach the same result thus confirming the correctness of the theory of varying speed of light as well as the COBE, WMAP and Type 1a supernova cosmological measurements.

A New Discriminating Experiment on the Invariance Hypothesis of Light Speed

This thesis puts forward a conjecture that, owing to some unknown special character of light, it is impossible to determine whether the speed of light is variable by the interference method. To verify the hypothesis of the invariance of light speed, a new method must be found to take accurate measurement of the infinitesimal change in the travelling time of light. The thesis suggests the adoption of high frequency laser pulse technology to carry out the measurement. On the basis of this idea a new discriminating experiment is proposed to test the hypothesis of the invariance of light speed. The thesis also makes some forecast of the future prospects of this experiment and of the future development of the theory of special relativity.

A Probabilistic Method to Determine Whether the Speed of Light Is Constant

Although the formula of mass-energy equivalence was derived from the hypothesis that the speed of light in free space is constant, conversely, the purpose of this research is to show that a method of probabilistically determining whether the speed of light is constant is derived from this formula. By considering the formula of mass-energy equivalence to be a function of the energy of an object moving at speed V, the probability density function (PDF) of the energy can be obtained using the inverse function of this formula, if the speed of light obeys a probability distribution. The main result is that the PDF of the energy diverges to infinity at a certain energy value regardless of the PDF of the speed of light. Thus, when the speed calculated from this value enters a certain range of the speed of light as V increases stepwise from below 299,792,458 m/s, the PDF of the energy should increase abruptly. If not, then the speed of light is constant. This is the method of probabilistically determining whether the speed of light is constant. An experimental method is proposed to confirm this.

Extraction of the Speed of Gravity (Light) from Gravity Observations Only

We show how one can measure the speed of gravity only using gravitational phenomena. Our approach offers several ways to measure the speed of gravity (light) and checks existing assumptions about light (gravity) in new types of experiments. The speed of light is included in several well-known gravitational formulas. However, if we can measure this speed from gravitational phenomena alone, then is it the speed of light or the speed of gravity we are measuring? We think it is more than a mere coincidence that they are the same. In addition, even if it is not possible to draw strong conclusions now, our formulations support the view that there is a link between electromagnetism and gravity. This paper also shows that all major gravity phenomena can be predicted from only performing two to three light observations. There is no need for knowledge of Newton’s gravitational constant G or the mass size to complete a series of major gravity predictions.

The Effect Density Has on the Speed of Light, Time, and the Dimensions of the Multiverse

We show that as the dimensions of the Multiverse increase so does its density. This increase in density has the effect of decreasing the speed of light, slowing down time, and increasing the life span of each higher dimension and the life span of human beings occupying that higher dimension. We use the tenth dimension as the highest dimension as a special case but show that it is not possible to exactly determine its value because of varying factors that can end the Multiverse, sending all the Energy back into the original levels of the Quantum of the void that started the creation process.

On the Possibility of Variable Speed of Light in Vacuum

We previously revealed a quantitative relation by which the fine-structure constant α can be described by the temperature T of cosmic microwave background (CMB) with several other fundamental constants, including the elementary charge e, the Boltzmann constant k, the Planck constant h, and the light of speed in vacuum c. Given that the value of α is quite conserved but T is variable across CMBs, we propose that c changes with T and can be given by T, the present CMB temperature T0 and the present light speed c0. As T is continuously decreasing, c is thus predicted to decrease at a rate of ~2.15 centimeters/second (cm/s) per year. Moreover, we provide a lot of evidence to support this finding. In conclusion, this study suggests a possibility of variable speed of light in vacuum.

Star Mass Inertia Dictates the Speed of Light

This paper indicated that Newton’s law of gravitation is a statistical relation of two adjacent objects with a distance and Einstein’s general relativity shows the internal connection of material distribution through space-time warping in our universe so general relativity is referred as a gravity theory. Here the paper gives an extension of general relativity in the sense of the metric theory of gravity which is consistent with Einstein’s equivalence principle and generates a weak field approximation which extends Newtonian dynamics. Thus, the extended theory of gravity can infer that the light has a speed limit of photon escaping the mass inertia of a star.

Gravity Constraints on the Measurements of the Speed of Light

The speed of light in a vacuum is a constant of special relativity, electromagnetic wave theories, and astrophysical distances. However, several measurements of its speed (c) at locations on the Earth’s surface seem to vary at different times during the last century. Efforts have been made on instruments performance to achieve a unique viable value in any spacetime referential. The time-variability on c-values obtained is here addressed inside the gravity field (g) in which the measurements of c have been estimated. It appears a correlation of c and g both daily (tidal) and yearly (no-tidal) variations which suggest that the gravity acceleration control the c-variability everywhere in a spacetime referential. Implications of this model provide a sensitivity constant of c from g, and the estimates of c on planets of the solar system where g values are known. It is deduced an upper limit of gravity in black hole that can cancel the speed of light in the horizon.

On the Question of the Invariance of the Light Speed

This article is devoted to the key concept of modern electrodynamics—the invariance of the speed of light. The general principle of relativity is considered in detail. Some critical remarks to the relativistic invariance and to the Lorentz transformations are presented. The general invariance of Maxwell equations is discussed. Different theoretical expectations for possible results of Michelson-Morley experiment and some physical consequences are considered. Some critical remarks to the notion of the light speed and its constancy are given. The relativistic law for velocity addition, including strangeness of a noncollinear addition and a superluminal motion, is discussed. Critical analysis of two works which proof the need for existence of an invariant velocity is consequentially made.

Why the Speed of Light (c) Keeps Constant?

In this paper we demonstrate that the “pure” spacetime and electromagnetic spacetime are bound together. The “pure” spacetime and electromagnetic spacetime all behave as the wave in character and furthermore, both of them change at the same speed. Based on the understanding of the “pure” spacetime and electromagnetic spacetime, we give out the reasonable explanation why the speed of light keeps constant and how the gravity is created among the matters. In addition, some practical applications of the concepts developed in this work are proposed.

Experiments on the Speed of Light

Many experiments concerning the determination of the speed of light have been proposed and done. Here two important experiments, Michelson-Morley and Sagnac, will be discussed. A linear moving variation of Michelson-Morley and Sagnac devices will then be proposed for probing experimentally the invariance of the speed of light.

Reviewing Michelson Interferometer Experiment and Measuring the Speed of Starlight

The wave-aether model was proposed long time ago. We study Michelson interferometer experiment and find that its theoretical calculation erroneously neglected the aether drag effect. We take the drag effect into account and reanalyze the theoretical interference pattern shift. The result is null because the drag coefficient of aether is zero. Such that the wave-aether model fulfills all light propagation characteristics. We design and implement a system to measure the starlight speed by comparing to that from a local source. We observe that the arrival times are different. It implies the apparent speeds of starlights are not equal to c.

Why the Speed of Light Is Not a Constant

A variable Speed of Light is supported by the fact that all direct measurements of that speed are basically flawed, because the “meter per second” is proportional to the Speed of Light. Since it is impossible to measure the Speed of Light directly, any variations of it can only be obtained in an indirect way. It will be shown that the recent Supernovae data are in very good agreement with a universe that is slowly expanding exponentially with a Speed of Light that falls over time, inversely proportionally to the expansion of the universe. It will be shown that the definition of the angular and standard impulse momentum has to be modified to get a consistent expansion of the universe. And that all clocks run inversely proportionally to the red-shift z + 1. General Relativity remains valid even with a varying Speed of Light and also Quantum Mechanics is unaffected.

Calculating the Exact Experimental Density of the Dark Energy in the Cosmos Assuming a Fractal Speed of Light

Fractal speed of light theory is a variation of Magueijo-Smolin varying speed of light (VSL) theoretical modification of Einstein’s energy mass relation. We use this theory to derive an exact value for the missing dark energy which is found to be in astonishing agreement with the latest result of the WMAP measurement and the independent supernova analysis. Thus while Einstein’s formula predicts 95.5% more energy than found in highly precise astrophysical measurement, our VSL- based calculation indicates an exact theoretical value of only 4.508497% real energy. Consequently, the exact conjectured missing dark energy must be 95.491502%. By any standards, this is an astounding confirmation for both the cosmological measurement and the VSL theory.

A Supplement to the Invariance Principle of the Speed of Light and the Quantum Theory

Richard Feynman once said, “I think it is safe to say that no one understands Quantum Mechanics”. The well-known article on the Einstein-Podolsky-Rosen (EPR) paradox brought forth further doubts on the interpretation of quantum theory. Einstein’s doubt on quantum theory is a doubleedged sword: experimental verification of quantum theory would contradict the hypothesis that speed of light is finite. It has been almost a century since the creation of quantum theory and special relativity, and the relevant doubts brought forward remain unresolved. We posit that the existence of discontinuity points and quantum wormholes would imply superluminal phenomenon or infinite speed of light, which provides for an important supplement to the invariance principle of the speed of light and superluminal phenomena. This can potentially resolve the inconsistency between special relativity and quantum theory.