The effective mass of electrons (mₑ*):

In the 80s, in our electronics classes in semiconductor or solid state physics, such as semiconductor diodes, LEDs, transistors, integrated circuits, BJTs, thyristors, triacs, fets, mosfets and many more, we learned the effective mass of electrons, a very interesting topic, which I'm sharing now.

Electron effective mass (mₑ*) is a concept in solid-state and semiconductor physics that describes the behavior of electrons in a crystal lattice or semiconductor material. In these materials, electrons experience periodic potentials, causing them to behave differently based on their momentum and the crystal's band structure. Effective mass is the modified mass of electrons, which can vary in different crystal directions. It is determined experimentally or theoretically from the element's electronic band structure. In some cases, the effective mass of electrons in a semiconductor can be negative, causing unusual phenomena like negative differential resistance.

It is important to note that the electron rest mass (mₑ) is a fundamental constant and is always the same for electrons, regardless of the material in which they reside. On the other hand, electron effective mass (mₑ*) is a material-dependent property that describes how electrons behave in certain materials under certain conditions.

Question: Lorentz transformation involves mass change but mass cannot be transformed into another form?

Answered by Others: The Lorentz transformation is a mathematical tool that helps understand how physical quantities change under relativistic conditions. It does not involve the direct conversion of mass into another form, such as energy or frequency. The Lorentz transformation deals with the relativistic effects of high velocities.

In the context of the Lorentz transformation, the mass of an object does not change. The concept of "relativistic mass" was introduced in the early days of special relativity to describe how an object's mass appears to change with its velocity. However, this concept has fallen out of favor in modern physics, and the more accepted view is that an object's mass is an invariant quantity, meaning it remains the same regardless of its velocity or the reference frame from which it is observed.

The Lorentz transformation does not involve any change in an object's rest mass. It is a mathematical tool used to understand how physical quantities vary between different inertial reference frames and is consistent with the principles of special relativity. Mass (m) remains an invariant quantity in all inertial reference frames, meaning its value remains the same for all observers, regardless of their relative velocities.

Massless discrete energy (hf) is stored in matter mass (m) without considering wave speed:

Author: Soumendra Nath Thakur ORCID iD: 0000-0003-1871-7803 

Dated 30-July-2023, Country: India.

Summary: Mass and energy are interconnected, but not always. Energy exists without being converted into mass, such as photons. Mass is converted into energy through nuclear reactions, fission, fusion, or radioactive decay. Energy is stored in mass without considering wave speed. Energy conversion units include Joules and electron volts. Small amounts of mass can be converted into energy through fission, fusion, or spontaneous radioactive decay.

Description: Energy exists in massless subatomic particles like photons, but not always vice versa. Electrons absorb photons without mass change. Mass converts into energy through nuclear reactions or radioactive decay. Discrete energy is stored in the mass without nuclear reactions, without considering wave speed. 1 kg m^2/s^2 energy is the derived unit of 1 joule in SI units for mass-energy conversion. The electron volt (eV) is a unit of energy. 1 eV = 1.6 * 10^-19 J. Incredible amounts of energy are converted from small amounts of mass through fission, fusion, and spontaneous radioactive decay. The mass of matter (m) contains discrete energy, similar to the atomic nucleus, electron, and electron energy. 

Conclusion: Therefore, when mass represented by (m), it is equal to (m + Em) or (m + hf) or (m + Ep), representing the cold mass of matter, the discrete energy of the mass, the discrete energy of the photon at its frequency, or the discrete energy corresponding to Planck's constant, respectively.

Lorentz transformation, but mass cannot be transformed into another form:

It's nice to say that where there's mass, there's energy, but not always it's actually the opposite.

Because some forms of energy exist without being converted into mass. such as massless energetic subatomic particles, such as photons.

A photon absorbed by an electron is not converted into mass but remains there as electron energy, without changing the electron's mass.

Mass is converted into energy by nuclear reactions of atoms, especially through fission and fusion, or spontaneous radioactive decay in unstable atoms.

Otherwise, mass is not converted to pure energy without nuclear reactions but instead energy is stored in the mass without consideration of the wave speed.

In mass-energy conversion, 1 kg m^2/sec^2 mass of energy is called 1 Joule. Thus, the Joule is a derived unit of energy in SI units.

The electron volt (eV) is a unit of energy.

1 eV = 1.6 * 10^-19 J.

In particular, small amounts of mass are turned into energy from the breaking up through fission, or by combination through fusion of the nuclei of atoms. 

Even spontaneous radioactive decay converts some mass into incredible amounts of energy.

In conclusion, Lorentz's transformation of mass into another form is physically false.

Experiment made with piezoelectric film sensors:

When a mechanical force is applied to the piezoelectric film sensor, the seismic mass loads the piezoelectric element according to Newton's second law of motion F=ma. The force applied to the piezoelectric material is observed in the change in electrostatic force or voltage generated by the piezoelectric material.

#piezoelectric #PiezoelectricFilmSensor #PiezoelectricCrystalOscillator

Planck Equation and Wave motion:

Planck's equation doesn't define electromagnetic wave motion, but Planck units do, and the energy description invokes wave motion.

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'.

Planck equation conveys mass (m) invariant:

Planck equation E = hf conveys h constant but f variant, therefore mass (m) invariant.

            E          =          energy

h          =          Planck's constant
f           =          frequency

m         =          mass 

where m>0 in particle oscillation. 

Update: Here mass means where the atomic nucleus of matter is intact nuclear reaction, decay is not occurring.

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'.

Relativistic physics is unrelated to classical, and quantum physics, applied mathematics:

In applied mathematics, classical physics, and quantum mechanics, the domains of space and time are indeed considered fundamental aspects of the physical universe. Although they are represented mathematically, their existence and role in shaping physical phenomena is well established and supported by experimental evidence and experimental observations. 

In terms of applied mathematics, space and time are indeed abstract and conceptual constructs or imaginary. They are represented mathematically using coordinates and metrics to describe the location and relationship between objects and events.

Between classical physics and quantum mechanics, space and time are considered fundamental aspects of our physical universe. They provide the framework in which all physical events occur and are essential for describing the behavior of matter and energy.

While space and time do not interact in the same way as particles or energy do, they are interconnected in classical physics and quantum mechanics. The behavior of particles and matter described by classical mechanics, quantum mechanics depend on the geometry of space and time.

Space and time play an important role in shaping the behavior of the universe in both classical physics and quantum mechanics. They are used to formulate equations of motion, determine energy and momentum, and understand the evolution of physical systems over time.

In classical physics and in many aspects of quantum mechanics, space and time are treated as invariant. This means that the laws of physics remain consistent regardless of the observer's position or orientation.

The concept of spacetime, as described specifically in the context of relativistic physics, is not necessarily relevant to this domain. Instead, classical and quantum theories address the behavior of matter in space and time without the need for a unified spacetime structure.

#relativity #ClassicalPhysics, #quantumphysics #AppliedMathematics

The reasons behind emphasising Max Planck:

There is a deeper reason behind why I emphasized Max Planck.

The first thing I want to mention is the equation E= hf. It is a great equation to represent the whole universe and the universe is very clearly understood. It was a very pure and fundamental kind of discovery by Max Planck. Max Planck was a pioneering physicist who made significant advancements in our understanding of the universe, particularly in the realm of quantum mechanics.

In my opinion, Planck's energy-frequency equivalence provides a better understanding of the entire universe than the energy-mass equivalence E=mc^2 presented by Einstein. The equation E=hf, where E represents energy, h is Planck's constant, and f is frequency, is a fundamental equation in quantum mechanics. It relates the energy of a photon or any quantum particle to its frequency. This equation was a groundbreaking discovery and laid the foundation for quantum theory, which is crucial in understanding the behavior of particles at the smallest scales.

I have a very strong feeling that the main concept of energy-mass equivalence was developed from Max Planck's concept of energy-frequency equivalence. My argument that Planck's energy-frequency equivalence provides a better understanding of the entire universe than Einstein's energy-mass equivalence (E=mc^2). It’s important to clarify that they are not competing concepts but rather complementary. E=mc^2 is a special case of the more general energy-momentum relation in relativistic physics. It shows the equivalence between energy (E) and mass (m) and is crucial in understanding the energy released in nuclear reactions and the concept of mass-energy conversion

Frequency is a more fundamental representation of the universe than mass, so to understand the universe as a whole, and to understand it in an intelligent way, express the universe in terms of energy and frequency rather than energy and mass. Planck's energy-frequency equivalence is essential for understanding the quantum behavior of particles, particularly in the context of photons and the quantization of energy levels in quantum systems.

However, energy-mass equivalence is more necessary for the benefit of local human society, whereas Max Planck's energy-frequency equivalence is more useful for understanding the universe as a whole in a novel way. Though energy-frequency equivalence is a more fundamental representation of the universe compared to energy-mass equivalence, but it's worth noting that both concepts are fundamental in their own right, and they emerge from different physical theories.

The fact is, everything in the universe can be represented by energy-frequency, and its energy level determines the amount of entropy. I think that if energy-frequency equalization is considered a treatment for intelligent human species, and then energy-mass might be a good alternative for treating monkeys, chimpanzees, or even more primitive species. Entropy is a concept from thermodynamics/statistical mechanics that describes the level of disorder or randomness in a system. It is related to the number of ways in which the microscopic constituents of a system can be arranged, given its macroscopic properties (e.g., temperature, pressure, volume). Entropy is a measure of the system's uncertainty or the distribution of energy among its various degrees of freedom.

A comparison between the energy-frequency and energy-mass relations, as it seems to me, the former is much better than the latter, but, for some unscientific reason, the energy-mass equivalence is unreasonably more popular in society, instead of the energy-frequency equivalence. Energy-frequency equivalence is more specific to the realm of quantum mechanics and finds applications in understanding the behavior of photons, electrons, and other elementary particles. While quantum mechanics has been incredibly successful in describing the microscopic world, its concepts and principles are often counterintuitive and can be more challenging to grasp for the general public.

I think it is more a social acceptance than a scientific one, between the two principles, and obvious to the average mind.

Planck units are another aspect of Max Planck as described in my post, where the Planck length, Planck time, and Planck frequency represent our limit in understanding of the universe, where beyond the Planck frequency the source of Euclidean geometry begins to vibrate, and some frequency beyond that threshold are forever imperceptible to us. Planck units are 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 and gravitational interactions become significant. The Planck length, Planck time, and Planck frequency are the respective scales at which our current understanding of physics breaks down, and the effects of gravity and quantum mechanics cannot be neglected.

So the Planck time or frequency plays an important role in determining the limits of our perception. Both energy-mass equivalence and energy-frequency equivalence are valuable concepts in physics, applicable in different domains and with different levels of generality. They are not mutually exclusive but rather complementary in our quest to understand the universe at both macroscopic and microscopic scales.

Space itself does not expand but the distance between physical bodies increase due to dark energy:

Space itself is not a physical entity in the same sense as matter or objects. Space is a mathematical and conceptual framework used to describe the relationships and distances between physical bodies. 

When we talk about the expansion of the universe, we are referring to the observed phenomenon where the distances between galaxies and clusters of galaxies increase over time. This expansion is described mathematically using various parameters and metrics.

While the term "stretching" is often used in the context of describing the expansion of the universe, it is important to understand that it is not a literal stretching of physical space, as space itself is not a physical substance. Rather, it is an expansion of the distances between physical objects within the conceptual framework of space.

The driving force behind the expansion of the universe is thought to be dark energy, which is a hypothetical form of energy that is thought to permeate the universe and contribute to its accelerated expansion. Dark energy is postulated to exert a repulsive gravitational effect, causing galaxies and clusters of galaxies to move apart from each other.

Observational evidence, such as the redshift of distant galaxies, supports the notion of the expanding universe, but is not a literal stretching of physical space, as space itself is not a physical substance. This redshift is interpreted as a result of the expansion of space, causing the light from distant objects to be stretched to longer wavelengths. 

• The expansion of the universe refers to the increase in distances between physical objects within the conceptual framework of space.

• The term "stretching" is indeed used as a metaphorical description of the expansion of the universe. It helps to convey the idea that the distances between galaxies and clusters of galaxies increase over time, resulting in the observed redshift of light from distant objects.

• The driving force behind the accelerated expansion of the universe is commonly attributed to dark energy, a theoretical form of energy that is postulated to permeate space. Dark energy is hypothesized to exert a repulsive gravitational effect, causing the expansion of the universe to accelerate and leading to the increased separation between galaxies.

• Observational evidence, including the redshift of light from distant galaxies, supports the concept of an expanding universe. The redshift is a result of the stretching of the wavelength of light as space expands, and it provides valuable insights into the dynamics of the universe.

Why is there so much dispute over phenomenons explained by special theory of relativity like time dilation and length contraction?

The disputes over the phenomena of time dilation and length contraction are obvious and therefore need to be verified according to the interpretation of the general laws of physical science and applied mathematics, but certainly do not accept what relativity or the Lorentz transformation promotes.

In time dilation, the obvious flaw is between the concepts of time and space. The theory of special relativity assumes Minkowski spacetime that combines three-dimensional Euclidean space and fourth-dimensional time into a four-dimensional manifold, where time is stripped of its independence, rather considered 'natural

The hypothetical equation of time dilation was based on the Lorentz transformation and Doppler's formula, which failed to identify the cause of time distortion. Doppler shift is the change in frequency of a wave relative to an observer moving relative to the source of the wave. Whereas, the Lorentz transformation is a mathematical representation of the relationship between two different coordinate frames moving at a constant velocity and relative to each other.

This concept of special relativity is wrong, imposed and unrealistic, because events invoke the concept of time and never the other way around. Time is a purely mathematical parameter and cannot occupy space dimensionally, therefore, physical events cannot interact with time because we cannot perceive time physically but time is a consideration of the mind. So time has no physical existence and therefore cannot be dilated through physical relativistic effects. A lower, three-dimensional space can never influence or interact with a higher fourth-dimensional time.

Time distortion always arises from wavelength distortion but in special relativity time dilation cannot be understood from wavelength distortion and therefore does not follow the general rules. Time dilation is rather wavelength dilation. 

The wave equation in combination with the Planck equation has been able to successfully identify the distorted frequencies due to the relativistic effect, which has an effect factor. Relative time is derived from relative frequency. It is the phase change in relative frequency due to the infinite loss of wave energy and the corresponding increase in the wavelength of oscillation; which occurs at any clock between relative positions due to the relativistic effect or difference in gravitational potential; Clock time reading result error; which is incorrectly represented as time dilation

Reasons & extperiments: 

Planck's equation shows us that the frequency of a wave is proportional to the energy of the wave. Gravity exerts a mechanical force on any object that deform objects and pushes on surrounding atoms. In the case of a gravitational potential difference, there is less gravitational stress on a piezoelectric crystal, which reverses the deformation of the structure, thereby pushing the atoms around, causing the crystal to conduct less electric current than in the ground state.

Experiments on piezoelectric crystal oscillators show that wave distortions correspond to time distortions due to relativistic effects. A phase shift in relative frequency refers to a change in the timing or synchronization of oscillations between two clocks at different relative positions. This can occur due to factors such as differences in velocity or gravitational potential.

We get that the wavelength 𝜆 of a wave is directly proportional to the wave period T, i.e. 𝜆 ∝ 𝑇, obtained from the wave equation 𝑓 = 𝑣/𝜆 = 1/𝑇 = 𝐸/ℎ where h is Planck's constant and 𝑓, 𝑣, 𝜆, 𝑇 and 𝐸 represents the frequency, velocity, wavelength, period and power of the wave respectively.

Where the time interval 𝑇(𝑑𝑒𝑔) is inversely proportional to the frequency (𝑓) for 1° phase. We get a wave of similar shit at times. For example, a 1° phase shift in a 5 MHz wave corresponds to a time change of 555 picoseconds (ps)

• 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 phase shift (degrees °) = (1/5000000)/360 = 555 𝑝𝑠.

Time variation of Cesium-133 atomic clock in GPS satellite: GPS satellite orbits at an altitude of about 20,000 km. with a time delay of about 38 microseconds per day.

• For a 1455.50003025° phase shift or, 4.043055639583333 cycles of the 9192631770 Hz wave; Time variation (time delay) 𝛥𝑡 = 0.0000004398148148148148 𝑚𝑠 (approx) or, 38 microseconds per day.

Concluding that the time dilation equation is incorrect and fails to explain the cause of time distortions, where, under the influence of both relative velocities and gravitational potential differences, phase shifts in relative clock oscillations can occur and cause errors in timing; This is actually the clock timing error due to relativistic effects.

Therefore,the disputes over the phenomena of time dilation and length contraction are obvious and valid.

A good clock cannot show dilated time:

The clocks are required to tell time, and that clocks oscillate so such oscillations follow the wave equation.

In addition, the flow of time requires a 360 degree dial or scale so that the oscillating part of the clock can represent the correct time at a specific frequency, so that the oscillating state of a certain fixed frequency is maintained.

But if time dilates due to motion or gravitational effect then the dilated time within the dial of a 360 degree watch will not be able to accurately display the time dilated, so the watch cannot display the dilated time on its specific 360 degree dial. Can't be seen at all. So how can you measure time dilation on the clock? No one can do that.

Relativistic events and frames of reference are universal, follow universal applicability:

The Special Theory of Relativity introduces the relativistic frames of reference by introducing an additional frame of reference, mathematically, for presenting relativistic events within the universal frame of reference. 

A co-ordinate geometrical digram of relativistic frames of reference can be presented within the universal frame of reference under the influence of gravity.

As for example, when we present the digit 1, it's magnitude is considered as the difference between 1 and 0 so that  (1-0) = 1, necessarily we do not mention 0 or the difference between them to present the magnitude of 1. 

Similarly, when introducing an additional frame of reference, that would physically mean a mathematical or geometrical introduction of another frame of reference, within the universal frame of reference even when not defined. 

Therefore, relativistic events are relative universal events, and they occur within universal frame of reference, and therefore follow universal applicability. 

The Lorentz transformation is no exception in terms of universal applicability.

Author: Soumendra Nath Thakur, ORCID: 0000-0003-1871-7803

A photon passes near a massive object simultaniously gains and loses momentum:

The momentum of a photon is given by the equation p = E/c, where p represents momentum, E represents energy, and c represents the speed of light. Since the energy of a photon is directly related to its frequency or inversely related to its wavelength, any change in the photon's energy will result in a corresponding change in its momentum.

When a photon passes near a massive object, it simultaniously gains and loses energy (and thus momentum) due to gravitational interactions. This exchange of momentum causes the photon's path to be curved or deflected in the presence of a gravitational field.

Despite the exchange of momentum, a photon continues to travel at the speed of light (c) and covers the same distance (d) relative to its constant speed. The curvature of the photon's path is a result of the gravitational interaction and exchange of momentum.

Redshift due to motion, when phase shift T(deg) of the observed frequency and the source frequency f(rest) are know.:

Redshift due to motion - an alternative formula. 

A 1° phase shift in the wave oscillation is due to motion, we can calculate the redshift using the formula.

z = {1 - 360 * f(rest)} / {360 * f(rest)}.

Where, T(deg) represents the phase shift in degrees and f(rest) represents the source frequency

Frequency and phase in sin:

The equation y(x) = sin(f * x + p). What does f represent and what does p represent?

In the equation y(x) = sin(f * x + p), the variables f and p represent parameters that affect the behavior of the sine function.

f: The variable f represents the frequency of the sine wave. It determines how many oscillations occur over a given interval of x values. The frequency f controls the rate at which the sine function completes a full period, which is 2π radians or 360 degrees. Higher values of f result in more oscillations within the same interval, while lower values lead to fewer oscillations.

p: The variable p represents the phase shift of the sine wave. It indicates the horizontal displacement or translation of the wave along the x-axis. Specifically, it determines the initial position of the wave at x = 0. The phase shift p is measured in radians or degrees and can move the wave to the left or right. Positive values of p shift the wave to the left, while negative values shift it to the right.

By adjusting the values of f and p, you can modify the frequency and position of the sine wave, respectively, in the y(x) equation.

Equations of f frequency; T time period; v velocity; λ wavelength; λ₀ source wavelength; Δλ changed wavelength; T(deg) phase shift in degree; z gravitational or cosmic redshift:

Author ORCID: 0000-0003-1871-7803

Given below are the simplified expressions based on the equation and the relationship between the variables. Where, f is the frequency; T time period; v velocity; λ is the wavelength; λ₀ is the source wavelength; Δλ observed change in wavelength; T(deg) phase shift in degree; z gravitational/cosmic redshift. When,  f = 1/T = v/λ = v/λ₀; T(360) => T(deg) = z * 360; For 1° phase shift, T(deg)  = T/360 = (1/f)/360 = z * 360; z = Δλ/λ₀. 

• f is the frequency.

• We are given f = 1/T = v/λ = v/λ₀.
  

• Therefore, frequency f is equal to the reciprocal of the time period T, the velocity v divided by the wavelength λ, and also v divided by the source wavelength λ₀

• The specific velocities of the waves involved (343 m/s) for acoustic waves or (299,792,458 m/s) for electromagnetic waves.

• T time period.

• We are given a complete time period T in 360°, T(360) => T(deg) = z * 360.

• This equation represents the phase shift in degrees T(deg) being equal to the gravitational or cosmic redshift z multiplied by 360.

• For a complete time period T, the phase shift in degrees T(deg) is equal to z * 360, where z represents the gravitational or cosmic redshift.

• v velocity

• We are given v/λ = f = 1/T = v/λ₀.
  

• From these equations, we can see that v is equal to the product of the frequency f and the wavelength λ, and it is also equal to the product of the frequency f and the source wavelength λ₀.

• The specific velocities for acoustic waves (343 m/s) and electromagnetic waves (299,792,458 m/s) indicate the speed at which the waves propagate.

• λ is the wavelength

• We are given v/λ = f = 1/T =  v/λ₀.

• This equation indicates that the wavelength λ is equal to the velocity v divided by the frequency f, and it is also equal to the source wavelength λ₀.

• The wavelength (λ) is related to the velocity (v) and frequency (f) through the equation λ = v/f. Using the specific velocities provided, the wavelength can be calculated by λ = v/f.

• λ₀ is the source wavelength

• We are given v/λ₀ = v/λ = f = 1/T.

• Therefore, the source wavelength λ₀ is equal to the velocity v divided by the frequency f, and it is also equal to the wavelength λ.

• The source wavelength (λ₀) can be obtained by dividing the velocity (v) by the frequency (f), using the specific velocities given. Thus, λ₀ = v/f.

• Δλ observed change in wavelength

• We are given z = Δλ/λ₀.
  

• This equation represents the gravitational or cosmic redshift z being equal to the change in wavelength Δλ divided by the source wavelength λ₀

• T(deg) phase shift in degree

• We are given T(deg) = T/360 = (1/f)/360 = z * 360.

• This equation states that the phase shift in degrees T(deg) is equal to the time period T divided by 360, which is also equal to the reciprocal of the frequency f divided by 360, and it is equal to the gravitational or cosmic redshift z multiplied by 360. For a complete time period T, the phase shift in degrees T(deg) is equal to z * 360, where z represents the gravitational or cosmic redshift

• z gravitational/cosmic redshift.

• We are given z = Δλ/λ₀.

• This equation indicates that the gravitational or cosmic redshift z is equal to the change in wavelength Δλ divided by the source wavelength λ₀.

These are the simplified expressions based on the given equations and the relationships among the variables.

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

#frequency #timperiod #velocity #wavelength #sourcewavelength #restewavelength #observedwavelength #changedwavelength #Tdeg #phaseshift #degree #gravitationalredshift #cosmicredshift

There is a direct relationship between Phase shift T(deg) and Gravitational/Cosmic Redshift (z):

Authored by Soumendra Nath Thakur. 

 Author ORCID: 0000-0003-1871-7803

Author's Conclusion: T(deg) = z * 360.

The phase shift T(deg) is a measure of the change in phase of a wave, often caused by factors such as motion or gravitational effects. It is typically measured in degrees.

The gravitational/cosmic redshift (z) represents the change in wavelength or frequency of a wave due to gravitational or cosmological effects. It is a dimensionless quantity.

The relationship T(deg) = z * 360 indicates that the phase shift in degrees T(deg) is directly proportional to the gravitational/cosmic redshift (z) multiplied by 360. 

This means that for a given redshift value, the corresponding phase shift will be proportional to that value multiplied by 360.

Phase shift: Phase shift represents the displacement or shift in the phase of a wave. It occurs when a wave encounters a change in its medium or when the observer or source is in motion. Phase shift is related to the relative frequencies of the waves involved.

Redshift: Redshift refers to the phenomenon where the observed wavelength of light or any other wave is larger (shifted towards the red end of the spectrum) compared to the rest wavelength of the source. It indicates the stretching of the wavelength due to various factors such as relative motion or gravitational effects.

Example: T(deg)

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. 

In gravitational and cosmological redshifts, the observed wavelength (λ(obs) is compared to the source wavelength (λ₀). The ratio of the change in wavelength, Δλ, to the source wavelength, λ₀, gives the redshift (Z). This redshift implies both a wavelength enlargement and a time distortion. The equation for gravitational redshift and cosmic redshift is Z = Δλ/λ₀.

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

#PhaseShift #RedShift #GravitationalRedshift #CosmicRedshift

Time dilation (t') is an error and falls outside the time scale:

Authored by Soumendra Nath Thakur. 

  Author ORCID: 0000-0003-1871-7803

The redshifts correspond to distortion in time: - The effects of redshift on wavelength, frequency, and time.

Authored by Soumendra Nath Thakur. 

  Author ORCID: 0000-0003-1871-7803

Redshift is the wavelength enlargement that causes the error in time as wavelength dilation.

Authored by Soumendra Nath Thakur. 

Author ORCID: 0000-0003-1871-7803

Summary:

In various forms of redshift, including Doppler redshift and gravitational and cosmic redshifts, the observed wavelength λ(obs) and Δλ is enlarged compared to the rest wavelength λ(rest) or λ₀ of the source. This wavelength enlargement corresponds to a distortion in time, as wavelength (λ) and period (T) of a wave are inversely related. The enlargement in wavelength λ(rest) and Δλ corresponds to a change in time period (ΔT) of the wave.

In the case of time dilation, relativistic effects such as speed or gravitational potential difference can cause phase shifts in the frequency of a wave, resulting in infinitesimal loss of wave energy and corresponding enlargement in the wavelength of the wave. This wavelength dilation then leads to errors in the reading of clock time.

The relationship between wavelength and time distortion is expressed as Δλ ∝ ΔT. This means that changes in wavelength correspond to changes in time. For example, a phase shift of 1455.50° in the wave of an atomic clock oscillation with a frequency of 9192631770 Hz can result in a time delay (ΔT) of 38 microseconds per day.

Based on this relationship, it can be concluded that redshift, which is the enlargement of wavelength, is also associated with the error in time due to wavelength dilation.

Description:

For electromagnetic waves or light, there is an inverse relationship between the period (T) and frequency (f) of a wave, expressed as T = 1/f. and the wavelength (λ) of a wave is directly proportional to its period, λ ∝ T. The distortions of wavelengths exactly correspond to time distortions; through the relationship is λ ∝ T., where λ denotes wavelength and T denotes period of oscillation of the wave.

The relativistic effects, such as speed or gravitational potential difference, cause phase shift in the frequency due to infinitesimal loss of wave energy, corresponding to the enlargement in the wavelength of the wave or light.

Enlargement of wavelength in various redshifts:

Whereas all forms of redshifts are the wavelength enlargement. Whereas, observed wavelength of light in Doppler redshift, or in Gravitational and Cosmic Redshifts enlarged as λ(obs) or Δλ compared to their respective sources λ(rest) or λ₀. The corresponding formulas for these redshift are –

• Z = {λ(obs)-λ(rest)}/λ(rest); for Doppler redshift.
• Z = Δλ/λ₀ and also
• Z = Δλ/λ₀, for Gravitational and Cosmic redshifts respectively.

Since, the enlargement of wavelength exactly corresponds to time distortions; through the relationship Δλ ∝ ΔT. 

Therefore, for Doppler redshift wavelength of observed light is λ(obs) that corresponds to time period T(obs) of the light and for Gravitational and Cosmic redshifts the wavelengths of observed light is Δλ, those correspond to its time period ΔT..

Enlargement of wavelength in time dilation:

The relativistic effects, such as speed or gravitational potential difference, affects the clock mechanism, and causes phase shift in the frequency due to infinitesimal loss in the wave energy, and corresponding enlargement in the wavelength of the clock oscillation, correspondingly results error in the reading of the clock time through the relationship λ ∝ T.

Since distortions of wavelengths exactly correspond to time distortions as in the expression Δλ ∝ ΔT.

Whereas, for 1455.50° phase shift of the wave of atomic clock oscillation having a frequency 9192631770 Hz., the time shifts (time delay) ΔT = 38 microsecond/day.

The relationship is Δλ ∝ ΔT in all causes of electromagnetic waves, either in redshift or in time distortion. 

Therefore, the scientific conclusion is that the redshift is the wavelength enlargement that also causes the error in time as is wavelength dilation. 

#PhaseShift #RedShift #GravitationalRedShift #CosmicRedshift #DopplerRedshift #relativisticeffects #wavelengthdilation #eventtime #TimeDilation