Time is invariant but no clock is invariant under gravitational influence:

Is time Lorentz invariant? It is the same interval of proper time. It also follows from the relation between Δs and that c²Δτ that because Δs is Lorentz invariant, the proper time is also Lorentz invariant. 

Proper time Δτ, by definition, is the time measured by an observer in their own rest frame, we can say Δτ = Δt and therefore Δs² = c²Δt² = c²Δτ².

All observers in all inertial frames agree on the proper time intervals between the same two events.

So, how come time dilation t' possible when proper time t is Lorentz invariant? It cannot.

1. Considering t<t', where t' is not in the same scale of t, because of enlagement in t.  

Note: t' is not t+x or t-x, but it is t<t', where x is Δt. The Δt is infinitisimally small t.

2. The general rule is frequency represents time in inversed relationship f = 1/T = 1/λ, and wavelength equivalents period of time λ∝T.

So wavelength λ cannot be invariant but only T. 

Due to Relativistic effects, phase shift in frequencies distort wavelength. So wavelength is not invariant but we know time is invariant because Δs is Lorentz invariant too.

3. Time dilation equation t' = t/√(1 - v²/c²) 

The equation attempts to modify t through the influence of velocity v. This is illegal operation in mathematics, as none can modify invariant t with the effect of velocity v or speed..

4. Experiment made on piezoelectric oscillator show that speed or gravity influence wavelength λ, and wavelength corresponds to period of time, so error occurs in T, as in the relationship λ∝T.

Conclusion so called time dilation is relativistic error and not change in T, in order to get time dilation t'.

There is no dilation in time but in wavelength.

Time dilation is wrong and it's equation too.

Reference: https://doi.org/10.36227/techrxiv.22492066.v2

Proof of Invariant time even in relativity:

Abstract:

Due to the relative effects on the phase shift of the frequencies, it is concluded that the error in the clock mechanism distorts the wavelength of the clock oscillation. This made wavelength covariant in events, but time was invariant because time is invoked by events.

Introduction:

In mathematics time and space are mathematical parameters. Relativity represents space and time as relativistic covariants, but the relativistic effects on phase shift of frequencies invalidates time dilation; and, presents relativistic time (a component of relativistic spacetime) as invariant.

The event of existence invokes time. According to the definition of the SI unit of time, the frequency of the cesium 133 atom must be 9192631770 Hz. equals to s¯¹, subject to undisturbed ground condition. This means, continuous frequency represents time

The research paper titled, 'Relativistic effects on phaseshift in frequencies invalidate time dilation II.' It states, the relativistic time emerge from relativistic frequencies. It is the phase shift in relative frequencies due to the infinitisimal loss of wave energy and the corresponding increase in the wavelength of oscillation; which occurs at any clock between relative locations due to the relativistic effects or difference in gravitational potential; resulting error in clock time reading; which is improperly represented as time dilation. 

Relationship between time and wave oscillation:

Time is called 𝑇, the period of oscillation. The reciprocal of the period, or the frequency 𝑓, in oscillations per second, is given by the expression 𝑓 = 1/𝑇 = 𝜔/2𝜋 = 𝐸/ℎ = 𝑣/𝜆. Where h is Planck constant, 𝑓, 𝑣, 𝜆, 𝑇 and 𝐸 respectively represent frequency, velocity, wavelength, time period and Energy of the wave.

Whereas the time interval 𝑇(𝑑𝑒𝑔) for 1° of phase is inversely proportional to the frequency (𝑓). We get a wave corresponding to the time shift. For example, 1° phase shift on a 5 MHz wave corresponds to a time shift of 555 picoseconds (ps). 

Experimental Result:

We know, 1° phase shift = 𝑇/360. As 𝑇 = 1/𝑓, 1° phase shift = 𝑇/360 = (1/𝑓)/360. For a wave of frequency 𝑓 = 5 𝑀𝐻𝑧, we get the phase shift (in degree°) = (1/5000000)/360 = 5.55 𝑥 10ˉ¹º = 555 𝑝𝑠

Therefore, for 1° phase shift for a wave having a frequency 𝑓 = 5 𝑀𝐻𝑧, and so wavelength 𝜆 = 59.95 𝑚, the time shift (time delay) 𝛥𝑡 = 555 𝑝𝑠 (approx.)

Time shift of the caesium-133 atomic clock in the GPS satellite: The GPS satellites orbit at an altitude of about 20,000 km. with a time delay of about 38 microseconds per day. For 1455.5° phase shift (or, 4.04 cycles) of a 9192631770 Hz wave; time shifts (time delays) 𝛥𝑡 = 0.0000004398148148148148 𝑚s approx) or, 38 microsecond time is taken per day.

Decision:

Time is the indefinite continued progress of existence and events in the past, present, and future regarded as a whole, succeeding in irreversible and uniformed succession, referred to in the fourth dimension above three spatial dimensions.

The undisturbed ground condition of continuous frequency represents time. However, wavelength distortions, due to the phase shift in relative frequencies correspond to time error; through the relationship 𝜆 ∝ 𝑇. 

Conclusion:

Therefore, it is concluded that the error in clock mechanism distorts the wavelength of the clock oscillation due to the relative effects on the phase shift of the frequencies; This made wavelength (𝜆) covariant in events, but time (𝑇) was invariant, because events invoke time and time as stated above is the indefinite continuous progression of existence and events.

Reference: Relativistic effects on phaseshift in frequencies invalidate time dilation II.

#invarianttime #CovariantWavelength

Relativistic effects affects photons, and so, a hypothetical "Light clock" is not invariant:

A "single photon" can never bounce between two mirrors for the reasons mentioned below. A hypothetical 'light clock' is not demonstrable so such an undetectable clock is not accepted in physical science, because physical science is physical. Finally, the photon will be known as the bouncing event, and we know from the paper entitled, "Relativistic effects on phaseshift in frequencies invalidate time dilation II" that the event invokes time. Therefore, the so-called, light clock is not time itself, only events can invoke time. Events and time are completely different things. 

A photon exhibits an event of propagation wave. As every event has a consequence; so an incident photon will also have a similar consequence. A photon is subject to relativistic effects expending energy as it leaves the source of a gravitational well.

When a photon hits the mirror, the photon's energy is absorbed by an electron in the metal on the surface of the metallic backing mirror. As the incoming photon interacts with the free electrons of the metal and is absorbed. The electron then uses this extra energy to jump from a lower energy level to a higher one, moving further away from the atom's nucleus. A photon carries momentum, so each photon hitting the mirror causes an electron in the metal atom to absorb the original photon and emit a new photon with a different momentum, known as scattering. As the free electrons oscillate, a new photon is emitted and exits the mirror. So the photon is reflected and loses energy.

The lost photon energy: And we know from the paper entitled, "Relativistic effects on phaseshift in frequencies invalidate time dilation II" that, Relative time emerges from relative frequencies. It is the phase shift in relative frequencies due to infinitesimal loss in wave energy and corresponding enlargement in the wavelengths of oscillations; which occur in any clock between relative locations due to the relativistic effects or difference in gravitational potential; result error in the reading of clock time; which is wrongly presented as time dilation.

So called, a "Light clock" is not invariant, as relativistic effects affects photons.

Scientific interpretation of the above article:

Photon Interaction: When a photon collides with an atom on a mirror's surface, it can be absorbed by an electron, causing the electron to gain energy (hf) and move to a higher energy level. This process is similar to photoelectric absorption.

Mirror's Reflectivity: Mirrors are designed to optimize reflectivity by minimizing absorption (ΔE) to maintain high reflectivity. The reflected photon has energy hf−ΔE, where ΔE represents the energy lost within the mirror.

Angle of Incidence and Reflection: The angle of incidence (Θi) is equal to the angle of reflection (Θr). This relationship is also expressed in terms of angles in degrees (θi and θr), where θi+θr=180°.

Photon Energy Absorption: The difference in energy between the incident photon (γi) and the reflecting photon (γr) is ΔE, representing energy absorbed by the mirror. This energy difference is also equal to the time delay (Δt) between the incident and reflecting photons.

Infinite Time Delay: When a photon is reflected by a mirror, there is an infinite time delay (Δt) between the colliding photon (γi) and the diffusing photon (γr) to change the direction of travel. This phenomenon contributes to a time distortion in the behavior of light.

When a photon (hf) interacts with an atom on a mirror's surface, it can indeed be absorbed by an electron in the atom. This interaction results in the electron gaining energy (hf) from the absorbed photon. This increase in energy can cause the electron to move to a higher energy level within the atom, farther away from the nucleus. photoelectric absorption takes palce. Mirrors are made to minimize absorption (ΔE) in order to maintain high reflectivity.  optimize reflectivity (hf- ΔE) and minimize light absorption (ΔE). The reflected photon will have energy (hf- ΔE). The reflected photon will have an energy of (hf−ΔE).

The angle of incidence (Θi) is equal to the angle of reflection (Θr). Since, the angle of incidence (θi) is equal to the angle of reflection (θr), θi = θr; and, the sum of the angles of incidence (θi) and reflection (θr) always equals 180°, θi + θr = 180°. Therefore, if the angle of incidence (Θi) = 180°, so the, angle of reflection (Θr) = 180°. 

The reflected photon having energy (hf- ΔE) travels in the opposite direction of the interacting photon with energy (hf), the angle of incidence is equal to the angle of reflection. This means that the direction of the reflected photon is related to the direction of the incident photon but is not necessarily opposite to it.

In summary, incident photon energy (γi) = hf;  reflecting photon energy (γr) = (hf−ΔE); photon energy absorption (γi - γr) = (ΔE); 

So, when a photon of light at the speed of light strikes or collides with a mirror wall, initially, the photon is absorbed by electrons in the mirror's surface atoms. In effect, the collision causes another photon to detach from an electron in an atom on the mirror surface, and the detached photon travels at the speed of light but in the opposite direction to the colliding photon. As a result, some of the energy of the colliding photons is lost in the collision with the mirror surface. 

The reflected photon having energy (hf- ΔE) travels in the opposite direction of the interacting photon with energy (hf), at an 180° angle, when the angle of incidence was 180°. 

In summary, when a photon collides with a mirror surface, it is initially absorbed by electrons in the mirror's surface atoms. The collision causes another photon to detach from an electron in an atom on the mirror surface. The detached photon travels at the speed of light but in the opposite direction to the colliding photon. Some energy of the colliding photons is lost in the collision with the mirror surface. 

The energy of the incident photon is hf, where h is Planck's constant and f is the frequency of the photon. The energy of the reflecting photon is hf−ΔE, where ΔE represents energy loss due to interactions within the mirror. The difference in energy between the incident and reflecting photons is ΔE. This difference represents the energy absorbed by the mirror and not reflected.

The photon energy absorption = (γi - γr), the difference in energy between the incident and reflecting photons = ΔE.

Assuming, the incident photon frequency = f1; when, the incident photon energy = (γi); and, the reflecting photon frequency = f2; when, the reflecting photon energy = (γr); The change in energy between incident photon and reflecting photon = ΔE;

Given Equations:

γi−γr = ΔE (Infinitesimal loss in wave energy)

f1 = incident photon frequency

f2 = reflecting photon frequency

T(deg) = T/360 = (1/f)/360 = Δt

f = E/h = 1/360*T(deg)

T(deg) = 1/f*360 = Δt

So, the relationships are -

ΔE =γi−γr

Δt=f1−f2

Thereofre,

ΔE = Δt.

Since, ΔE = Δt;

The change in energy (ΔE) is equal to the time delay (Δt) between the incident photon and the reflecting photon . This suggests a relationship between the energy difference of the incident and reflecting photons and the difference in frequencies (f1 and f2) of those photons.

Therefore when, there is an infinite time delay (Δt) between the colliding photon (γi) and the diffusing photon (γr) to change direction of travel. Therefore, the constancy of motion of a photon of light is broken when it is reflected by a mirror.

Synchronization of atomic clocks:

As per SI unit of time, it's frequency that represents time. (The unit of time is defined by taking the fixed numerical value of the cesium frequency to be 9192631770 Hz.)

Atomic clocks are automatically synchronized to a radio signal that is continuously broadcast by the National Institute of Standards and Technology in the United States.

Atomic clocks are also subject to various external influences, including gravity.

Atomic clocks are used onboard GPS satellites orbiting the Earth, but must send updates twice daily to correct the clock's natural drift.

However, although the method is a simple correction of clock frequency depending on distance from Earth and other factors, the method is still inappropriate, as it is based on time distortion when it should be wavelength distortion.

It is the phase shift in the frequency due to the infinitisimal loss of wave energy under the relativistic effect on the clock mechanism, and other distortions.

#synchronization #atomicclock #waveenergy #phaseshift #timesynchronisation

Lorentz transformation cannot establish the geometry of space and time covariant, except in the covariable contents within the invariants space and time:

Lorentz transformation cannot establish the geometry (dimensions) of space and time covariant, except in the covariable contents (existential events) within the invariant dimension of space and time, or so called, spacetime. The geometry of frame of reference and its content are not the same. 

As for example, at Planck threshold, geometry of Euclidean space vibrates, reasoning limit in our perception. 

To falsify relativistic spacetime, if any, why should one has to encounter Lorentz's abstract mathematical presentation than encountering relativistic spacetime directly? 

So irrespective of what Lorentz transformation conveys, the author of relativity did not physically established Lorentz, before he robbed of the independence of time and married off space and time after making them illegally "natural" without providing a single experiment to support this. 

His paper, specifically relevant to the time dilation and spacetime should have been rejected by the reviewer of the paper then. As the author of relativity cannot simply present an illegal mathematical presentation and get his paper published for others to prove his paper through experiments. 

The author of relativity claimed full credit for his paper in Relativity and remained protected by others as he let others to face the questions arising out of his papers, to Lorentz and the experimenters who confirmed time dilation, biased. The author of relativity should not escape in facing the questions relevant and it's consequences.  

All of the experiments with time dilation were biased and invalid as they don't follow the mathematical or scientific norms to hold that the wavelength distortions corresponding error in clock oscillation resulting erroneous time being erroneously presented as time dilation by the author concerned, 

When it's obvious that none can get whatever time is, if there is erroneous clock oscillation, or no oscillation at all.

We know, as per SI unit of time, it's frequency that represents time. So before considering Relativistic effects on frequency, or it's wavelength, we canot directly jump on to the relativistic effects on time, because a clock time is always as per the order of time,  representation of frequency, resulting oscillations, and subjects to various distortions too.

I have my paper invalidating time dilation as referred below.

Lorents transformation or relativistic spacetime cannot establish covariant spacetime, ash they are invariants indeed.

Reference Relativistic effects on phase shift on frequencies invalidate time dilation II