29 May 2023

Phase shift in relative frequencies due to relativistic effects invalidates relativistic covariant spacetime:

In relativity, time and space are relativistic covariant but phase shift in frequencies due to relativistic effects invalidate relativistic covariant spacetime.


Explanation

In physics and statistics, time and space are polymorphous, but in pure mathematics time and space have no physical properties. They are only mathematical parameters:

In classical physics, time and space are determinist and invariant; 

In statistical physics, time and space are probabilistic and invariant; 

In relativity, time and space are relativistic, covariant, and downgraded mere components of relativistic spacetime; 

In quantum physics, time and space are probabilistic and invariant.

However, in relativity, time and space are relativistic covariant but Phase shift in relative frequencies due to relativistic effects invalidates relativistic covariant spacetime.



My observation - "A moving particle of mass (m), spends half of its total energy in achieving electromagnetic speed":

  • A particle having no rest mass (m=0), and moving at the speed of light, spends half of its total energy (E/2), in becoming a particle at rest.  
  • And, a particle having mass (m=1), and at rest, spends half of its total energy (E/2), in achieving the speed of light. 
  • Where, total energy of any particle equivalents it's potential energy and kinetic energy E = (E.P+E.K) = mv²; E = (E.P+E.K) = mc²; (Note: p=mv but p=Ec).


Explanation:

A moving particle has total energy (E), mass (m), speed (v) but its mechanical speed is less than the speed of light (c). 

In this case, the moving particle will have total energy (E) = {kinetic energy (E.k) + potential energy (E.p)}.

E = (E.k + E.p)....... (1).

However, according to Newtonian mechanics, the kinetic energy of a moving particle,

(E.k) = 1/2mv²........(2).

When the mechanical speed (v) of the particle attains the speed of light (c) in vacuum, the total energy of the particle becomes,

E = m(c)²/2 ............(3).

According to mass-energy equivalence, the total energy (E) of mass (m),

E = mc² ................(4).

At full speed of light, the total kinetic energy of a particle should be only (E=mc²).

However, comparing all the above equations, especially equations three (...3) and four (...4), we get the total kinetic energy of the particle (E = m(c)²/2).

That is, half of the particle's total energy (E = mc²), expended from potential energy (E.p), so that the particle acquires mechanical to electromagnetic speeds.

Soumendra Nath Thakur. May 29, 2023.


28 May 2023

Error is not time dilation.

Relativistic effects cause the corresponding energy loss or gain on the time scale, it's not time dilation but error.


Any wave or oscillation carries energy, be it an electromagnetic wave or a mechanical wave. A wave or oscillating force is distorted under relativistic effects.

A change in electrical polarization is produced in materials when they are subjected to mechanical stress. This pressure-dependent change in polarization demonstrates as a measurable potential difference across the material. Piezoelectricity, known as the piezoelectric effect, is the presence of an electric potential voltage around a crystal when subjected to mechanical stress, including gravitational forces due to a gravitational potential difference. A piezoelectric sensor is governed by Newton's law of motion F = ma. The force sensed by the piezoelectric crystal is proportional to the seismic mass times the input acceleration. The greater the mass or acceleration, the greater the applied force and the greater the electrical output from the crystal.

(i). G-forces cause internal particles of matter to interact, resulting in stresses and deformation (strain).

(ii) The kinetic energy of a particle having a mass ‘m’ and travelling with velocity ‘v’ is given by the formula K.E = 1/2 mv². The velocity of the particle is directly related to the wavelength and the frequency of the wave of the particle. The frequency of the particle is given by the relation f = v/λ. Therefore, E = 1/2m.f²λ² or, f = 1/λ √(2E/mλ).

(iii) The total energy of the particle is proportional to the square of the frequency (f) = ω/2π, hence E ∝ f², where (ω) is the angular frequency. Angular frequency (ω), also known as circular frequency, measures angular displacement per unit time, in degrees (t°). 𝑓 = 1/𝑇 = 𝜔/2𝜋 => ω = 2π/T = 2𝜋f.

(iv). The energy of electromagnetic radiation (E) is directly proportional to its frequency (f). E = hf.

(v) Time interval T(deg) for 1° of phase is inversely proportional to frequency. We get a wave corresponding to the time shift. 1° phase shift = 𝑇/360 = (1/𝑓)/360. The time delay for a 1° phase shift with a frequency of 5 MHz and a wavelength of 59.95 m, 𝛥𝑡 = 555 𝑝𝑠.


Summary of "Relativistic effects on phase shift in frequencies invalidate time dilation II"

 Authors: 

Thakur, Soumendra Nath (Corresponding); Samal, Priyanka; Bhattacharjee, Deep (Co-authors) (Year 2023):

Preprint Repository: 

TechRxiv. Preprint https://doi.org/10.36227/techrxiv.22492066.v2

Abstract:

Relative time is caused by a phase shift in relative frequencies due to infinitesimal loss in wave energy and enlargement in wavelengths of oscillations, resulting in error in the reading of clock time.

1. Introduction:

The Theory of Relativity adopts Minkowski spacetime, which combines three-dimensional Euclidean space and fourth dimensional time into a four-dimensional manifold. The proper time is dependent on relativistic effects and expressed as 𝑡 < 𝑡′. The equation of time dilation is 𝑡՚ = 𝑡/√(1− 𝑣²/𝑐²).

Proper time is an emerging concept, space is a three-dimensional extent, and spacetime is a four-dimensional extent as a mathematical concept. It is not natural, inevitable, or dependent on relativistic effects. Time is not distorted due to relativistic effects, it does not have time, rather error in the clock oscillation.

Counterexamples show that wave distortions are caused by relativistic effects, invalidating the conjectural equation of time dilation.

The conjectural equation of time dilation was based on Doppler's formula, which failed to identify any cause. The wave equation and Planck equation have been able to identify distorted frequencies due to the relativistic effect, yielding a relative value of time for wavelength dilation.

Time is defined as the indefinite progression of events in the past, present and future existences. Stephen Hawking upheld the concept of imaginary time in his book "The Universe in a Nutshell".  

2. A scientific misconception in time dilation:

The equation 𝑡՚ = 𝑡/√(1− 𝑣²/𝑐²) is flawed because relativistic effects cannot interact with the proper time (t) in the fourth dimension. Piezoelectric crystal oscillators show that the error in the wave corresponds to time shift due to relativistic effects.

Dark energy does not affect time in any way, except enlarging the wavelength due to expansion of space, so enlargement in scale of time is unauthorized and disprovable.

G-forces cause internal particles of matter to interact, resulting in stresses and deformation (strain).

Wavelength distortions due to phase shifts in relative frequencies correspond to time distortion; through the relationship 𝜆 ∝ 𝑇, due to relativistic effects such as speed or gravitational potential differences. This result in errors in reading of the clock time, but incorrectly perceived as time dilation.

Real events in space cannot reach the fourth direction of time due to interactions or relativistic effects such as motion or gravity. As a result, any effects on proper time beyond its ideal succession will not cause time dilation. The dimension of time is considered abstract, rather conceptual.

Proper time should never be stripped of its independence and retained as 'natural' even in the four-dimensional continuum of spacetime. There is no time dilation anywhere, but the dilation of the wavelength of the clock oscillation causes errors in the clock time. Wavelength distortions mathematically correspond to time distortions, as in 𝜆 ∝ 𝑇.

3. General Foundations:

Time is called T, and the reciprocal of the period, or frequency, is given by the expression  𝑓 = 1/𝑇 = 𝜔/2𝜋 = 𝐸/ℎ = 𝑣/𝜆, where h is the Planck constant.

Doppler shift is the change in frequency of a wave relative to an observer moving.

Time distortion arises from wavelength distortion, but special relativity's time dilation is not influenced by it.

Special relativity cannot escape the fundamental equivalence between wavelengths and time, which is much more general than special relativity.

Distortions of wavelengths exactly correspond to time distortions λ∝T.

Time is the indefinite progress of existence and events in the past, present, and future, referred to as the fourth dimension above three spatial dimensions. It is not time dilation, but error in the in wave.

Time is an imperceptible fourth dimensional concept, not subject to real interference or influence from cosmic events.

Cosmic time is the relationship between time since the Big Bang and events in the Universe. Proper time is subject to synchronization with ideal time, as done with atomic clocks, due to wavelength distortion.

4. Experimental results:

Waves of piezoelectric crystal oscillators show a time shift due to relativistic effects.

Wavelength is directly proportional to time period, that is 𝜆 ∝ 𝑇, derived from the wave equation 𝑓 = 𝑣/𝜆 = 1/𝑇 = 𝐸/ℎ, where h is Planck constant and 𝑓, 𝑣, 𝜆, 𝑇 and 𝐸 represent frequency, velocity, wavelength, time period and energy.

Time interval T(deg) for 1° of phase is inversely proportional to frequency. We get a wave corresponding to the time shift. For 1° phase shift on a 5 MHz wave equivalent time shift to 555 ps.

1° phase shift = 𝑇/360. 𝑇 = 1/𝑓.

1° phase shift = 𝑇/360 = (1/𝑓)/360.

Wave frequency 𝑓 = 5 𝑀𝐻𝑧,

we get the phase shift "in degree (°)"

= (1/5000000)/360 = 5.55 𝑥 10ˉ¹º = 555 𝑝𝑠.

The time delay for a 1° phase shift with a frequency of 5 MHz and a wavelength of 59.95 m, 𝛥𝑡 = 555 𝑝𝑠.

The time delay for a 360° phase shift with a frequency of 9192631770 Hz,

𝛥𝑡 = 0.0000001087827757077666 m𝑠.

The caesium-133 atomic clock of GPS satellites orbit at an altitude of 20,000 km with a time delay of 38 microseconds per day.

The time delay for a 1455.5° phase shift or 4.04 cycles (4.04 Hz.) with a frequency of 9192631770 Hz,

𝛥𝑡 = 0.00000010878 m𝑠. Hence 38 microsecond per day.

5. Conclusion:

Time dilation is actually wavelength dilation, caused by gravitational potential differences or relativistic effects, which causes errors in the clock reading. Time dilation is actually wavelength dilation.

26 May 2023

Expressions of Lorentz transformations and contradictory summation:

Lorentz transformations express concepts of relativity involving space, time, length, mass, motion relative to an observer, and the speed of light.

The aforementioned concept holds, 

“(1) Space and time are not absolute but natural.

(2) Variation of length, time and mass with respect to the relative motion of the observer.

(3) The speed of light is constant and independent.

(4) The effect of gravitational potential difference on said transformation is questionable."

Therefore, I submit the following,

1. (i) Whether, Relativity/SR is also based on the above concept.

(ii) Whether Lorentz transformation or time distortion originate from wavelength distortion but they are not understood from wavelength distortion and so it does not follow the general rules.

(iii) Whether in the above concept it is not scientifically clear why space and time are not absolute.

(iv) Whether, in the above concept it is not scientifically clear why space and time are natural.

2. (i) Whether the change in said length is more of a relative error in the length of the physical object than the change.

(ii) Whether not only the relative motion but also the gravitational potential difference corresponds to the same error/change in length of the object.

(iii) Whether length conversion is possible only in physical objects, but not in conceptual extensions of moving reference frames.

(iv) Whether the said time conversion is more of a relative error in the corresponding time than the physical change in time.

(v) Whether not only the relative motion but also the gravitational potential difference corresponds to the same error/variation in relative time.

(vi) Whether transformation in time is possible only in physical objects, but not in conceptual extensions of relative frames of reference.

3. Whether the speed of light is constant but not independent but dependent on relativistic/gravitational effects.

(4) Whether changes in length, time and mass also be considered in gravitational aspect too, in the said concept of transformation?

Reference: https://www.techrxiv.org/authors/Soumendra_Nath_Thakur/15208633

#LorentzTransformation #Relativity