viXra: 1906.0139 The Redshift Effect is Caused by the Decreasing Speed of Light Due to the Curvature of Space – a Proposed Experiment Krzysztof Sudlitz, PhD Former Researcher at the University of Warsaw, Warsaw, Poland E-mail: [email protected] Abstract In the following work, a hypothesis is proposed in which the curvature of space modifies the basic equations of electrodynamics. This is done based on the assumption that the universe is a three-dimensional sphere in four-dimensional space. The modification of the equations results in the slowing of the speed of light over very large distances, which results in the observed redshift of distant galaxies. An experiment is proposed that would ultimately validate or refute the hypothesis: the experiment would require a direct comparison of the angles of incidence and reflection of light from very distant galaxies, and would need to be performed in outer space to avoid atmospheric blur. Keywords: Big Bang, Redshift, Stationary Universe 1. Preface In this work, I decided to put all my hypotheses and assumptions into readable form for those with a scientific I am a former researcher at the University of Warsaw. My background, as well as those with popular science interests. activity can be described as a combination of atomic physics Therefore, I have decided not to include detailed mathematical and plasma physics. In the distant past, I also worked on derivations or references in my work; but for those interested, isotope production, and for a while at a nuclear reactor. the details of certain derivations and assumptions can be found Theories concerning the construct of the universe have in common mathematics and physics textbooks. always existed. Academically, astrophysics and cosmology The first chapter of this document is an introduction to the deal with these topics, but from my experience, an employee problem at hand and an overview of the concept of space with working in the "mainstream" focuses on very minor problems, non-zero curvature. In the following chapters I assume that the whilst additionally burdened by plans, deadlines, and grants. basic equations of electrodynamics are affected by the Very few tackle these problems fully, and usually only do it curvature of space, and I present the reasoning behind my part-time. In terms of the origins of the universe, there exists hypothesis. This assumption eventually leads to the a group of individuals who are not entirely convinced by the conclusion that the speed of light decreases due to the Big Bang theory. Personally, I never liked the theory, or the curvature of space, and as such, light is affected by the path it explanation of the redshift of distant galaxies using the travels. This leads to the widely observed phenomenon of the Doppler Effect. First of all, what exactly exploded? Why 14 redshift of distant galaxies. Finally, I propose an experiment billion years ago and not 4? The cosmological principle is that would ultimately validate or refute my hypothesis. accepted in relation to space, but why not time? The microwave background radiation is assumed to be a remnant 2. Introduction of the explosion, but it's easy to calculate (as outlined in Section 5) that it is just as likely a result of summing the At the end of the twentieth century there was a dispute radiation of galaxies after taking their redshift into account. regarding the geometry of the universe. In the end, it was These combined observations lead to the conclusion that the assumed that the most likely geometry is Euclidean - also Big Bang theory is quite far-fetched. referred to as 'flat'. Of course, this concerned areas of cosmic 1 viXra.org viXra: 1906.0139 Krzysztof Sudlitz dimensions, because in the "everyday" world, Euclid's analytically unsolvable - one can only try to solve them geometry works with great accuracy. It also works well for numerically. inter-galactic distances - the problem concerns vastly larger The following work also proposes an experiment that distances. would determine whether the model presented here is For now, the so-called Big Bang theory is widely accepted, reasonable. The experiment would require a direct comparison but the question remains - what exploded? There are still of the angles of incidence and reflection of light emitted at several phenomena that are difficult to explain, including the very large distances - cosmic distances. The difference in the absurd brightness of the so-called quasar, or the synchronous speed of incident and reflected waves would also potentially emission of radiation from structures whose size would explain the problems observed with telescopes outside of exclude the possibility of such synchronicity. Earth's atmosphere - including Hubble's Mirror Flaw. The main evidence supporting the theory of an expanding universe is the redshift of distant galaxies (the increased 3. Electrodynamics in Non-Euclidean Space wavelength of electromagnetic radiation from these galaxies), which is attributed to the Doppler effect. This model predicts In Euclidean space (also referred to as flat, or “everyday”), that the universe expands by reducing its density. Assuming the distance 푑푆 between any two points in a reference system an expanding universe, the fulfilment of the cosmological is described by: principle (the lack of a specific centre of the "world" - that is, each place is the same) requires the adoption of an infinite 푑푆2 = 푑푟2 + 푟2푑ѳ2 + 푟2푠푖푛2휃푑휑2 (1) universe. An infinite universe can hardly expand, since it is difficult to be ever more infinite. Therefore, the model of a where 푟 is the radius (distance from the origin), 푑휃 is the three-dimensional spherical universe - in four-dimensional vertical angle difference and 푑휑 is the azimuth angle space - must remain. This assumption automatically imposes difference (see Figure 1). For positively curved space, the a curvature of space - the surface of a sphere has non-zero formula becomes more complex: curvature. This is contrary to the commonly assumed Euclidean geometry, and requires a different view on the 푟 푟 푑푆2 = 푑푟2 + 푅2푠푖푛2 ( ) 푑ѳ2 + 푅2푠푖푛2 ( ) 푠푖푛2휃푑휑2 (2) mechanisms of light propagation - since the Laplace operator 푅 푅 of the wave equation takes a different form. The laws of electrodynamics in non-Euclidean space would also act where 푅 is the radius of curvature - a measure of the deviation differently. from Euclidean space (i.e. the magnitude of space curvature). The following work attempts to explain the observed In each geometry, the shortest line between any two points is phenomenon of the redshift of distant galaxies by adopting the referred to as the geodesic line. In Euclidean space, geodesic following hypothesis: the speed of electromagnetic waves lines are straight. In space with non-zero curvature, light also decreases with distance travelled, due to the curvature of travels along geodesic lines, but they are no longer straight. In space. It is commonly assumed that in every possible frame of reference, the speed of light is constant - c. However, in the presented hypothesis, it is assumed that the speed of light in non-Euclidean space is dependent on the path travelled. Therefore, the path of light must be considered relative to the point of emission, reflection, or the point at which the light enters a particular medium. Failure to comply with this rule often leads to absurd conclusions (e.g. the interpretation of the Michelson's - Morley experiment). Based on the aforementioned hypothesis, an attempt is made to create a model of a stationary universe with a non- Euclidean geometry and a constant positive curvature. Because it is difficult (impossible) to predict how "physics" will behave in curved space, conclusions are drawn based on heuristic considerations. The wave equation for positively curved space includes trigonometric functions which, even after significant Figure 1: The figure shows a convenient way of determining the simplifications (adopting a spherical symmetry and the distance between two points on a sphere, e.g between stars in the 푠푖푛(푟⁄푅) function as a slow-changing one), seem to be proposed non-Euclidean space. 2 viXra.org viXra: 1906.0139 Krzysztof Sudlitz 푟 휋 reference to equation (2), it can be seen that when = , It is worth noting that in the case of positively curved space 푅 2 푟 휋 (and for an identical telescope aperture), the observed solid 푠푖푛2 ( ) = 1, i.e. 푑푆 reaches a maximum and 푟 = 푅 푅 2 angle of a distant galaxy would be much larger than that becomes the so-called horizon. For small distances, 푟 ≪ 푅, observed in Euclidean space (see Figure 3). This could explain 푟 푟 푠푖푛 ( ) = , and equation (2) simplifies into equation (1), i.e. the observed absurd brightness of certain distant objects (e.g. 푅 푅 certain quasars). for small distances, space is (almost) flat. It can be seen that initially, as 푟 increases, 푑푆 grows just as 3.1 Magnetic Fields of Electric Current in Curved Space quickly in both geometries, but for values of 푟 ~ 푅, the geodesic lines diverge slower for geometries with positive 휋 The laws of electrodynamics require that the product of the curvature; and for 푟 = 푅 , they become parallel (see Figure 2 length of the circle surrounding an electric current flow line 2). So in the case of curved space, light moves as if it enters and the magnetic field induction intensity remain constant an increasingly dense medium: light rays converge towards regardless of the radius of the circle. More generally, the linear each other and – according to the wave description – light integral of the magnetic induction intensity, 퐵, on the contour slows down. So if light slows down after traveling a long surrounding the conductor must be equal to the current distance (푟 ~ 푅 after a very long flight time), the measured multiplied by the constant 휇0 (see Figure 4): wavelength of light from distant objects will be larger, relative to the point at the which the light was emitted - i.e.