04 July 2023
01 July 2023
How do relativistic effects such as motion and gravity distort time?
Abstract:
The concepts I discussed here demonstrate an understanding of the principles and equations related to time distortion due to momentum and gravitational potential differences.
I have covered various concepts related to time distortion including Doppler Effects, phase shift, wavelength, frequency and their relationship to wave propagation. I also mentioned the application of these principles to piezoelectric crystal oscillators and how the wave distortion due to relativistic effects corresponds to the time distortion
In my explanation, I correctly stated that there is an inverse relationship between the period (T) and frequency (f) of a wave, expressed as T = 1/f. and also correctly pointed out that the wavelength (λ) of a wave is directly proportional to its period, λ ∝ T. Additionally, I have included relevant equations such as f = v/λ = 1/T = E/h, where v is the wave velocity, E is the wave energy, and h is Planck's constant.
Moreover, I discussed the concept of phase shift and the measurement of degrees (°). The total phase shift (Φ) accumulated over a period of time (Δt) can be represented as the area under a frequency versus time curve and the equation ΔΦ = Δω × Δt relates the differential phase shift (ΔΦ) to the frequency shift (Δω) and Time interval (Δt).
I have also given an example calculation for a wave frequency of 5 MHz, where a 1° phase shift corresponds to a time shift of 555 picoseconds (ps). Furthermore, I noted that a 1455.50° phase shift (equivalent to 4.04 cycles of a 9192631770 Hz wave) results in a time shift of approximately 0.0000004398148148148148 ms. or, 38 microseconds per day
Overall, my explanation incorporates various scientific principles and equations related to time distortion due to speed and gravitational potential differences. It demonstrates an understanding of wave propagation and time measurement concepts and their applications
Keywords: Doppler Effects, phase shift, gravity, piezoelectric crystal oscillators, atomic clock.
Description:
The SI time unit of the International System of Units is defined as the time interval equal to 9192631770 vibrations of the ground state cesium-133 atom, represented as s or seconds. This means time is defined as vibrations or frequency (specifically) cesium-133 atom. Therefore, frequency represents time.
Time distortion due to speed follows the Doppler Effect, it is the change in frequency of a wave as the source moves relative to an observer. So when frequency changes, energy of frequency too changes.
Doppler shift considers the frequency change of a wave in propagation but gravitational potential difference considers the frequency change of the oscillating body.
It may be referred that if the path between a source S and an observer O is changed by an amount Δx, the phase of the wave received by O is shifted by Δn = −Δx/λ = −fΔx/c, where λ and f are, respectively, the wavelength and frequency of the disturbance and c is the speed of propagation, all measured by an observer fixed in the medium. The resulting change in observed frequency is Δf = Δn/Δt, where Δt is the time taken for the observation of the phase change. It is shown that these two statements are sufficient for the derivation of the acoustic Doppler Effect equations in all cases. The extension to the relativistic optical Doppler Effect also follows this.
This is the acoustic distortion in frequency due to speed. The wave equation shows that the energy of a wave is proportional to the square of its amplitude and its frequency. A change in the frequency of the sound wave can cause a corresponding change in the energy carried by the wave.
The Planck's equation helps us to calculate the energy when their frequency is known, as such wavelength is known, so one can calculate the energy by using the wave equation to calculate the frequency and then apply Planck's equation to find the energy. Incase of electromagnetic waves, Planck's equation shows us how frequency of the wave is proportional to energy of the wave.
However, in case of gravitational effects, gravity exerts a mechanical force on any object that deforms the object and pushes on the surrounding atoms. Using gravity, energy is obtained by the so-called piezo method, which converts mechanical stress into electrical energy.
When mechanical stress is applied to a piezoelectric crystal, the structure of the crystal is deformed, the atoms push around and the crystal conducts an electric current. It occurs when motion or mechanical energy is converted into electrical energy due to crystal deformation. Piezoelectric materials are materials that can generate electricity due to mechanical stress. The mechanical stress of a piezoelectric crystal is greatest in the ground state.
In the case of a gravitational potential difference, there is less gravitational stress on a piezoelectric crystal, which correspondingly reverses the deformation of the structure, thereby pushing the atoms around, causing the crystal to conduct less electric current than in the ground state.
Oscillatory systems with relative velocity or gravitational potential difference experience phase shifts, causing wave energy loss and errors in clock time readings.
Therefore, both acoustic distortion and electromagnetic distortion at their respective frequencies due to motion correspond to distortions of the corresponding wave energy.
However, Doppler shift considers the frequency change of a wave in propagation but gravitational potential difference considers the frequency change of the oscillating body.
Experiments made on piezoelectric crystal oscillators show that wave distortions correspond to time distortions due to relativistic effects such as speed or gravitational potential difference, besides, relative time between clock frequencies relativistic effects causes clock error, so time distortion is misrepresented as time dilation.
Relative time emerge from relative frequencies. A phase shift in relative frequency results in an infinitesimal loss of wave energy, and a corresponding enlargement in the wavelength of oscillation can lead to errors in clock time readings between relative locations due to differences in velocity or gravitational potential.
The phase shift in relative frequencies refers to a change in the timing or synchronization of oscillations between two clocks in different relative locations. This can occur due to factors such as differences in velocity or gravitational potential. As a result, there can be a discrepancy or error in the measurement of time between the clocks.
The wavelength, as a spatial property, can be affected by these factors and undergo distortion or enlargement. However, it's important to note that the wavelength itself does not directly represent clock time. Rather, it is the timing or synchronization of the oscillations that is relevant for measuring time.
The time-related distortion, which represents the temporal aspects of the phenomenon, can be influenced by the phase shift and changes in wavelength. This can lead to errors in the reading of clock time between relative locations.
A phase shift refers to the displacement of a wave form in time. A complete wave cycle, also known as a period (T), corresponds to a phase shift of 360 degrees or 2π radians.
When representing a complete wave cycle in degrees (°), it can be denoted as T(deg). In this notation, T(deg) represents the angular measure of one complete cycle of the waveform in degrees.
In terms of frequency (f), which represents the number of wave cycles per unit of time, there is an inverse relationship between the period and the frequency. The period (T) is the reciprocal of the frequency (f), and the relationship can be expressed as:
• T = 1 / f
If we express the period in degrees, T(deg), the relationship still holds:
• T(deg) = 360° / f
In this case, T(deg) represents the angular measure of one complete cycle of the waveform in degrees, and it is inversely proportional to the frequency (f).
Phase shifts can occur under the effects of relative velocities of observers and gravitational potential differences. These effects can introduce changes in the perception of time and the behavior of clocks, which may manifest as phase shifts in oscillatory systems and cause errors in time between relative clock oscillations under the effects of both relative velocities and gravitational potential differences.
Experiments made in electronic laboratories on piezoelectric crystal oscillators show that the wave corresponds to time shift due to relativistic effects. We get the wavelength λ of a wave is directly proportional to the time period T of the wave, 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 of the wave respectively.
The frequency and wavelength are indirectly proportional to each other, f = 1/λ.
The frequency of a wave multiplied by its wavelength gives the speed of the wave, fλ = v or, f = v/λ.
The frequency is inversely proportional to the time period of the wave, f = 1/T.
The frequency of a wave is directly proportional to the energy of the wave, f = E/h, where h is Planck constant.
• Combined Equation given by f = v/λ = 1/T = E/h.
Where f, v, λ, T and E represent frequency, velocity, wavelength, time period and Energy of the wave respectively,
• The wavelength of a wave is directly proportional to the period of the wave, λ ∞ T.
The instantaneous phase (ϕ) represents an angular shift between two relative sine waves and is measured in degrees. After a time Δt, the two relative sine waves are initially synchronized in phase but differ in frequency by Δω degrees per second, developing a differential total phase shift (ΔΦ). Where Φ is the total phase shift accumulated over a period of time (Δt) and ω(t) is the frequency shift that may vary as a function of time. The total accumulated phase shift (Φ) can be thought of as the area under a frequency vs time curve.
• Equation given by: ΔΦ = Δω × Δt.
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.
• 1° phase shift = T/360; T = 1/f.
• 1° phase shift = T/360 = (1/f)/360.
• A wave frequency = 5 Mhz. we get the phase shift (in degree°) corresponding time shift.
• 1° phase shift on a 5 MHz wave = (1/5000000)/360 = 5.55 x 10ˉ¹º = 555 ps. Corresponds to a time shift of 555 picoseconds
Therefore, for 1° phase shift for a wave having a frequency 5 MHz., and so wavelength 59.95 m, the time shift Δt is 555 ps.
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 1455.50° phase shift or, 4.04 cycles of a 9192631770 Hz wave; time shifts Δt = 0.0000004398148148148148 ms. or, 38 microsecond time is taken per day.
Concluding that the equation for time dilation, t' = t / √ (1 - v²/c²) is incorrect and fails to explain the cause of time distortion, whereas, the phase shifts can occur and cause errors in time between relative clock oscillations under the effects of both relative velocities and gravitational potential differences; it is actually error in clock time due to relativistic effects, misrepresented as time dilation.
Reference Paper : Relativistic effects on phaseshift in frequencies invalidate time dilation II
Planck Units. - The Planck units are a set of natural units derived from fundamental constants:
· Name Dimension Value (SI units)
· Planck length(ℓᴘ) length (L) 1.616255(18) ×10⁻³⁵ m.
· Planck mass
mass
(M) 2.176434(24) ×10⁻⁸ kg.
· Planck time
time
(T) 5.391247(60) ×10⁻⁴⁴ s.
· Planck temperature temperature (Θ)1.416784(16) ×10³² K.
· Planck angular frequency (ωᴘ)rad/s 1.885 ×
10⁴³ s⁻¹
· Planck’s frequency (fᴘ): Hz
2.952 ×10⁴² Hz
· Planck Constant (h)
6.62607015 × 10⁻³⁴ J·s
· The energy of Planck Frequency
is E ≈ 1.232×10⁹ J
The Planck frequency, a repeating event that occurs once every Planck period (Fp) with a frequency of about 2.952 ×10⁴² Hz. This frequency is called the upper limit of frequency of electromagnetic waves or cosmic rays.
The Planck units are a set of natural units derived from fundamental constants, such as the speed of light, Planck's constant, and the gravitational constant. These units represent the scale at which quantum effects become significant and are used in theoretical physics to explore phenomena at the smallest scales or in extreme conditions.
The Planck frequency is not directly obtained as the inverse of the Planck time (5.391247×10^-44 s). Instead, it's derived from fundamental physical constants such as Planck's constant (h), the speed of light (c), and the gravitational constant (G), utilizing these values in the formula for frequency.
The precise value for the Planck frequency is approximately 2.952 ×10⁴² Hz, calculated from these constants and their relationships, and it's considered a fundamental limit in physics, just like other Planck units. This frequency is not directly the inverse of the Planck time but is a distinct value derived from different fundamental constants and their interrelations.
The Planck frequency (Fp) is a frequency that corresponds to the inverse of the Planck time. It is approximately 2.952 ×10⁴² Hz. This frequency represents an upper limit for the frequency of electromagnetic waves or cosmic rays.
The Planck length (L) (ℓP) is approximately 1.616255(18)×10^−35 meters. It is considered the smallest meaningful length scale in the universe.
The Planck mass (M) is approximately 2.176434(24)×10^−8 kilograms. It represents the mass at which quantum gravitational effects become important.
The Planck time (T) (tP) is approximately 5.391247(60)×10^−44 seconds. It is the smallest meaningful unit of time and represents the time it takes for light to travel the Planck length.
The Planck temperature (Θ) is approximately 1.416784(16)×10^32 Kelvin. It is the highest temperature that can be meaningfully defined in physics.
It's worth noting that there may be slight variations in the reported values of Planck units due to ongoing research and refinement of measurement techniques.
These Planck units provide a theoretical framework for understanding the fundamental scales of the universe, but their extreme values make them inaccessible to current experimental observations. They are primarily used in the context of theoretical physics and as a basis for exploring quantum gravity and the nature of spacetime at the Planck scale."
Additional:
Planck units are a set of units of measurement defined exclusively in terms of four universal physical constants. Originally proposed by the German physicist Max Planck in 1899, these units are a system of natural units because their definition is based on properties of nature. It may be mentioned here that Einstein first published his special theory of relativity in 1905, which describes his revolutionary ideas about light, time and energy.
The four universal constants, by definition, have a numerical value of 1 when expressed in these units:
1. Speed of light in vacuum, c,
2. Gravitational constant, G,
3. Reduced Planck constant, ħ, and
4. Boltzmann constant, kB.
• Planck length = ℓP = L ≈ 1.61626 × 10^−35 m;
• Planck time = tP = T ≈ 5.391247 × 10^−44 s;
• ℓP/tP is the ratio of the Planck length to the Planck time;
Since, ℓP/tP = (1.61626 × 10^−35 m) / (5.391247 × 10^−44 s);
1. To divide two numbers in scientific notation, we subtract the exponents of the 10 and divide the coefficients:
2. Coefficient: (1.61626) / (5.391247) ≈ 0.299792458
3. Exponent: (10^(-35)) / (10^(-44)) = 10^(-35 - (-44)) = 10^9
4. So the simplified value is approximately:
5. 0.299792458 × 10^9 m/s
6. Now, we recognize that this is the speed of light in a vacuum, which is denoted by 'c':
7. c ≈ 2.99792458 × 10^8 m/s
8. So, the simplified expression is:
9. (1.61626 × 10^−35 m) / (5.391247 × 10^−44 s) ≈ 2.99792458 × 10^8 m/s;
The ratio of the Planck length to the Planck time (ℓP/tP) yields a value to the speed of light in a vacuum, c;
This is a fundamental constant in physics and is denoted by 'c'.
#planckunits #plancklength #planckmass #plancktime #plancktemperature #planckfrequency #PlanckConstant
The anti-gravitational effect observed in galaxies...
The anti-gravitational effect observed in galaxies and their drift leads to the concept of a mysterious energy called dark energy. Dark energy is usually described by w ≡ P/ρ, where P and ρ denote its pressure and energy density. Dark Energy is un-massive, roughly 10¯²⁷ kg/m³. Dark energy causes repulsive gravity through negative internal pressure. (10¯²⁷ = 0.000000000000000000000000001).
Dark energy is often described by its equation of state parameter, denoted as "w," which is the ratio of its pressure (P) to its energy density (ρ). Dark energy is characterized by a negative pressure, which results in a repulsive gravitational effect, driving the observed accelerated expansion of the universe.
The equation of state parameter w for dark energy is typically close to -1, indicating that the pressure is negative and its magnitude is equal to the energy density. This negative pressure counteracts the attractive gravitational force of matter, leading to the expansion of the universe becoming accelerated.
The energy density of dark energy is estimated to be around 10¯²⁷ kg/m³. It is an extremely low density compared to other forms of energy in the universe, such as matter and radiation. Despite its low density, dark energy is thought to dominate the total energy content of the universe at present, comprising about 70% of the total energy density.
The exact nature and origin of dark energy are still not well understood, and it remains an active area of research in cosmology and theoretical physics. The term "dark energy" is a placeholder for the unknown source of the observed accelerated expansion, and its precise composition and underlying physical mechanism are subjects of ongoing investigation.
__________________________________________
Dark energy is often described by the parameter w, which represents the ratio of its pressure (P) to its energy density (ρ). Mathematically, it is defined as w ≡ P/ρ. Dark energy is characterized by a negative pressure, meaning that it behaves in a repulsive manner, counteracting the attractive gravitational force due to matter and causing the accelerated expansion of the universe.
The exact nature of dark energy is still a mystery, and its physical origin is not well understood. One of the leading candidates for dark energy is the cosmological constant, represented by the Greek letter lambda (Λ), which is often associated with vacuum energy. The cosmological constant is a constant energy density that permeates space, leading to a negative pressure and driving the accelerated expansion of the universe.
The energy density of dark energy is roughly 10⁻²⁷ kg/m³, making it extremely diffuse compared to other forms of energy and matter in the universe. Despite its low density, dark energy is believed to dominate the energy budget of the universe at present, accounting for about 68% of the total energy content, while dark matter makes up about 27%, and ordinary matter (baryonic matter) constitutes only about 5%.
The existence of dark energy and its role in the accelerated expansion of the universe were discovered through observations of distant supernovae and other cosmological probes, such as the cosmic microwave background radiation. The discovery of dark energy has been one of the most significant and intriguing findings in modern cosmology, and understanding its nature remains a fundamental challenge for theoretical physics.
Acknowledgement:
The author of this Bolg expresses his sincere gratitude for significant help in the creation of this article, and so gives most credit to ChatGPT that significantly contributed to the content of this article.
29 June 2023
Why there is accelerated expansion in the distance among galaxies?
Abstract:
The accelerated expansion of the universe is explained by the Friedmann equation, derived from Einstein's field equations in general relativity. This equation relates the rate of expansion (Hubble parameter), energy density of universe components (such as matter, radiation, and dark energy), and the geometry of space. The simplified Lambda-CDM model incorporates dark energy effects, resulting in a more accurate understanding of the universe's expansion.
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