Recession Relativity

Abstract

 Galileo made relativity between objects a principle. On the other hand, Einstein proposed the principle of invariance between a viewpoint and an object by light. Classical mechanics remains ambiguous as to what the observer is relativing. 

± Relative motion velocity = Object velocity - Observer velocity.

Absolute time ➔ Relative time.

± Relative motion velocity² = Relative wave speed² - c² .

 In absolute time, relative motion is derived from the motion between objects, but in relative time it is derived from the speed of light and relative waves. This article proposes a Easy and Exact relativity in Everything that removes the "strange contradictions" that Einstein says have lurked in theoretical physics from the beginning.

Introduction

 Einstein uses spherical waves to explain the principle of invariant speed of light.

 The equations of the Lorentz transformation may be more simply deduced directly from the condition that in virtue of those equations the relation x²+y²+z²=c²t² shall have as its consequence the second relation .

 This is the Einstein synchronization of the ratio of the speed of light invariance to the relative velocity. However, in the apparent relative motion, there is only the observation result of the asymmetrical progress of the clock.

 The implications of the two relativistic postulates are analyzed in terms of their reciprocity and symmetry aspects. Whereas the first postulate entails a perfect equivalence of all frames, the second postulate, as reflected by the Einstein-Lorentz equations, implies an asymmetry of values (not of forms) that clashes not only with the first postulate equivalence but with the possibility of experimental, all verifications of which are "asymmetric" in each concrete case. A double index notation is proposed at the end, in order to show more clearly these asymmetries, and to interpret in a realistic way, the referential (physical) meanings of the four space/time variables. Lorentzian versus Einsteinian relativities are contrasted. The former seems to cope better with the asymmetric experimental realities. The latter only does so by subreptitiously changing the meaning of the physical variables.

  And in the educational setting,

 Special Relativity (SR) is often necessarily taught at a superficial level and limited to certain foundational aspects such as the Lorentz transformations and the interpretation of seminal experiments. Some of the deeper foundational issues are typically either not presented or discussed only briefly, for instance, the difficulties involved in the measurement of the one-way speed of light and the conventionality of clock synchronization in SR.

 What was Einstein thinking about such problems?

Einstein in 1947

Here is a problem that is extended from that "Note" he wrote at the age of 26, "(...) the inaccuracy in the concept of simultaneity, which likewise must be resolved by abstraction", to which he may be speaking. The fact that a physical theory introduces, at the beginning, a "clock" and a "measure" at the same time as a "mass point" and an "electromagnetic field" is, indeed, a contradiction, and one that can only "give rise to a sense of strangeness". However, if, in order to resolve this contradiction, we erase the "clock and ruler" and "give up the physical interpretation of the coordinates", then the physical theory itself becomes impossible. If so, then this "contradiction" is a "contradiction" that exists at the point where physics itself is established. So says Einstein. And he says that this "contradiction" "needs to be removed". What we can see now is that this paradox of "clocks" and "simultaneity" was a question that pervaded Einstein's life, together with, and in a different way from, the unified field theory.

1, Synchronization by Relative time 

 First, rewrite the synchronization method by the apparent relative time from the observation reference system whose speed of light is the defined value c, without using the invariance of absolute time and speed of light.

According to Newton, absolute time exists independently of any perceiver and progresses at a consistent pace throughout the universe. Unlike relative time, Newton believed absolute time was imperceptible and could only be understood mathematically. According to Newton, humans are only capable of perceiving relative time, which is a measurement of perceivable objects in motion (like the Moon or Sun). From these movements, we infer the passage of time.

Wave speed in K' observed from K:　w₋ = √ (c² - v₋²).

Motion speed of K' observed from K:　v₋.

Time in K' observed from K:　t₋ ＝ t (w₋ / c),　w₋ / t₋ = c / t.

Wave speed of K observed from K':　w₊ ＝ c (c / w₋).
Spherical wave of K observed from K':

x'² + y'² + z'² = (w₊ t₋)² = x² + y² + z² = (c t)². 

Since the speed of light of the observer is also a wave, its relativity lies in the observed wave. But special relativity makes it immutable and tries to match it with the result using Lorentz transformations.

x'² + y'² + z'² = (c t₋)² ≠ x² + y² + z² = (c t)².

 Initially, this was interpreted as "Maxwell's equations hold only in the absolute static coordinate system [1]", and in inertial systems other than the absolute static coordinate system, Maxwell's equations transformed by Galilean hold. However, even if experiments with sufficient accuracy to find an absolute stationary coordinate system (Michelson-Morley experiment, etc.) were performed, the effect of Galilean transformation due to the difference in inertial system was not observed.

 However, the speed of light is isotropically constant in a free space without boundaries, regardless of the presence or absence of an absolute stationary coordinate system. Therefore, when abolishing absolute time and selecting relative time (Newton distinguishes), Lorentz transformation, speed of light invariance, and ad hoc hypothesis (Space-time dilation from absolute space) of world interval are not necessary. This time dilation based on the apparent relative time of the observer and the object is valid. Now let's look at this apparent relative time for the three types of frequency shifts.

2,  Asymmetry Doppler shift of light

1) When the light source (S) motion more than the observer (O). Secondary Doppler red-shifts, the wave speed of the light source is,

γ₊ = 1 / γ₋ = c / w₊,

　w₋ = γ₊ c = √(c² - v₋²),

　v₋ = c√(1 - γ₊²) = √(c² - w₋²)　(1).

γ±: Scale factor,　c: Light speed,　w±: Wave speed,　v±: Motion speed.

 The secondary Doppler frequency at which oscillates of (S) is,

γ₋ = 1 / γ₊ = c / w₋,

　f₋ = f₀ / γ₋　(2).

f±: Secondary Doppler frequency,　f₀: Reference frequency.

 When light is emitted from the boundary (S) of the inertial frame, the secondary Doppler wavelength (λ₋) becomes,

λ₋ = γ₋ λ₀　(3).

λ±: Secondary Doppler wavelength,　λ₀: Reference wavelength.

 When the light source (S) is motion at a speed (v₋) to the direction of the angle (θ) viewed from the observer (O), the observation frequency (f) and the observation wavelength (λ) is,

f  = f₋ / (1 - v₋ cos θ / c),

　λ = c / f　(4).

θ: moving angle of the light source seen by the observer.

2) When the observer (O) motion more than the light source (S). Secondary Doppler blue-shifts, the wave speed of light source and the speed of light propagation is,

w₊ = γ₋ c = √(c² + v₊²),

　v₊ = c√(γ₋² - 1) = √(w₊² - c²)　(5).

 The secondary Doppler frequency at which oscillates of (S) is,

f₊ = f₀ / γ₊　(6).

 When incident on the boundary (O) of the inertial frame, the secondary Doppler wavelength (λ₊) becomes,

 λ₊ = γ₊ λ₀　(7).

 When the light source (S) is motion at a speed (v₊) to the direction of the angle (θ) viewed from the observer (O), the observation frequency (f) and the observation wavelength (λ) is,

f = f₊ / (1 - v₊ cos θ / w₊),

　λ = c / f　(8).

3, Symmetry Cosmological red-shifts

 This is cosmological scale-downs (Deceleration in the time direction), as opposed to local scale-downs (Move in the direction of space).

 From Hubble's law: The recession velocity (v₊) and the scale factor (γ₊) are,

v₊ = H₀ d = c z,

　γ₊ = c / w₊ = c / √(c² + v₊²)　(9).

Here, the proportionality constant (H₀) is called Hubble constant, which determines the current expansion rate of the universe. The Hubble constant has the dimension of the reciprocal of time (T⁻¹), and the unit is usually kilo-meters per second per mega-parsec (symbol: km/s/Mpc).

 The relationship between energy and scale factor is as follows.

E = h f₊ = h(γ₊ f₀) = (γ₊ m₀)c²　(10).

h: Planck's constant, m₀: Rest mass.

 The relationship between wavelength (λ₊) and amount of red-shift (z) is

λ₊ = c / f₊ ,

　z = ⊿λ / λ₀ = (λ₊ - λ₀) / λ₀　(11).

 Light from distant galaxies appears to be red-shifted. On the contrary, it shifts to the red when viewed from a distant galaxy. This is a symmetrical time dilation. 

4, Asymmetric gravity red (blue) shift

 The local motion of the light source or the observer causes the clock drift of (Equation 3 and 5). In that case, the wave speed (w±) and the observation frequency (f±) can be calculated from the angle (θ), Reference frequency (f₀), and light source's motion velocity (v±) (Equations 2-5). Conversely, v± and w± can also be calculated from θ, f₀, and f±.

 For example, the reference frequency (f₀) of an atomic clock according to the definition of seconds is

 The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the caesium frequency ∆νCs , the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be 9192631770 when expressed in the unit Hz, which is equal to s−1.

 The ratio of the progress of the atomic clock mounted on the GPS satellite and the atomic clock on the ground surface is,

Ground surface speed of light (c): 299,792,458 m/s.
Geocentric gravity constant (GM): 3.986e⁺¹⁴ m³/s².
Earth radius (r): 6,378,000 m.
GPS satellite altitude (h): 20,200,000 m.
Orbital velocity of GPS satellites (v): 3,874 m/s.
Hyperbolic infinite wave speed: w∞ = √[c² + 2GM/r].
Wave speed of GPS satellites: wG = √[w∞² - 2GM/(r + h) - v²].
Difference in how the clock progresses: wG / c＝1 + 4.45e⁻¹⁰.

 Gravitational blueshift occurs because the observer reduces the resting energy by falling, but the energy of the light source and photons does not change.

Discussion

 Clock synchronization becomes possible by the clock recovery of the difference in how the clocks advance from each other. Clock synchronization exactly express the boundaries of Newton's apparent relative speed than the better translation recommended by Einstein. 

 In Newtonian mechanics, since there is no absolute stationary coordinate system in the universe, all velocities are always relative velocities seen by the observer at that time.

 And, Scale down of Newton's apparent relative time occurs always isotropic because there is no preferred frame like the absolute frame. In comparison, the Lorentz transformation is a mathematical deduction that causes a absolute time and a contraction to one direction of absolute space. This does not make the asymmetric phenomenon symmetrical. 

Asymmetric phenomenon ＊ Lorentz transformation = Asymmetric phenomenon.

 However, the self-consistency of the reciprocity of time dilation had already been demonstrated long before in an illustrative way by Lorentz (in his lectures from 1910, published 1931[A 21]) and many others—they alluded to the fact that it is only necessary to carefully consider the relevant measurement rules and the relativity of simultaneity. 

 One-way contraction of special relativity is a dead end because it impedes isotropic scale-down due to changes in apparent relative time. Furthermore, the relationship with general relativity is limited to the local inertial system.

 Added the related problems and solutions in the appendix.

Conclusion.

 Observer are not just mathematical coordinate points. There are a mistake to treat observers who also have features other than the coordinate points with only the coordinate points and perform a Lorentz transformation. The isotropically scale down by change of apparent relative time ensures that the velocity of light in a vacuum of the same inertial frame as the observer is remained constant. As a result, the speed of light between different inertial systems changes, however in Maxwell's equation, the speed of light does not change (c ± v) due to the movement of the light source. This implies a vacuum property where the speed of light in one inertial frame is isotropically constant, but the speed of light does not have to be a defined value (299,792,458 m/s) when there is anisotropy, as between different frames. In the first place, without such anisotropy, it was not necessary to introduce the invariance of the speed of light.

 Easy and Exact relativity in Everything does not use the principle of light velocity invariance because it must distinguish isotropic or anisotropic. So even in electromagnetism, since there is no absolute stationary coordinate system in the universe, also wave speed are always relative velocities seen by the observer at that time. The square of the object's wave and the square of the relative motion's progress or recession velocity (c² = w² ± v²) keep the speed of light in the observer's frame at an isotropically defined value c. There is no stationary universe that Einstein believed, only a local stationary system occurs at (c² = w₊² ₋ v₊²).

Acknowledgment.

 Thanks to Mr. Roger for teaching a better translation on the GSJ Physics Forum, and thank you to the parasite people for refuting on the 5ch site.

Appendix

 Scope of major unresolved problems by frequency shift type and solution presented by this paper (※).

1, From "Asymmetry Doppler shift of light".

 a) The SR clock hypothesis requires a double index notation ad hoc hypothesis for asymmetric phenomena.

　※ Suggested in this article.

 b) Earth fly-by anomaly.

What causes the small, inconsistent velocity changes found in some solar system probes approaching Earth in hyperbolic orbits?

   ※ Fly-by anomaly by light of superluminal

2, From "Symmetry Cosmological redshifts".

 c) The Lorentz transformation, which Einstein said is better than clock synchronization, contracts only in the direction of travel, violating the isotropic of the cosmological red-shift.

　※ Suggested in this article.

 d) Increased eccentricity of the moon.

Laser observations reveal that the moon is slowly motion away due to tidal friction, but at the same time the orbit is gradually descent. What causes this slight increase in eccentricity that is inconsistent with the mechanical model?

   ※ Increasing lunar eccentricity due to cosmological acceleration 

   ※ Increasing Moon-Earth Distance Due to Cosmological Acceleration

 e) Permanent increase in astronomical units.

In the astronomical unit system, the movement of the planet follows the laws of dynamics, but radar observations show that the planet is motion away, and it seems that the astronomical unit is increasing with respect to the meter. How to explain this phenomenon?

　※ Permanent increase in astronomical units due to cosmological acceleration

 f) Universe that accelerates and expands.

Why is the expansion of the universe accelerating, as observed? What is the nature of the dark energy that is responsible for this acceleration? If it is due to the cosmological constant, why is it not zero, even though it is so small? Why is it not huge, as predicted by many field quantum theories? And why isn't it 0 due to unknown symmetry? What exactly is the end of the universe?

　※ Suggested in this article.

3,  From "Asymmetric gravity red (blue) shift".

 g) On the other hand, gravity does not work because it does not become invariant to Lorentz transformation even when trying to vectorize in the range of special relativity [32]. General relativity is needed to deal with gravity.　

　※ Equivalent principle of momentum of light

 h) Delta function problem approximating an object as a point mass.

They pointed out that most treatments of the problem used “delta functions” as a way to approximate the bodies in the system as point masses. As a consequence, the “self-field,” the gravitational field of the body evaluated at its own location, becomes infinite.

　※ Exact solution of the perihelion motion of Mercury from Newtonian mechanics

 i) Quantum gravity.

How can quantum mechanics be integrated with general relativity to build a theory called "the theory of all things"? Is string theory on the way to quantum gravity, or is it a dead-end theory? Is there a way to derive experimentally consistent results for physical phenomena on the Planck scale?

　※ New relativity principle for quantum theory