A 360° clock cannot display time dilation due to varying time scales:

The time scale for proper time (t) and the time scale for time dilation (t') are different. The time scale for proper time (t) is 360°, as represented by the 𝑇(𝑑𝑒𝑔) = 𝑇/360 equation. The time scale for time dilation (t') is greater than 360°, Since, Time scale for Time dilation > 360°. Since the two time scales are not the same, the clock that measures proper time (t) cannot display or measure time dilation (t') in the same units.

As per the Special Theory of Relaitivity, time dilation results from relativistic effects that cause time to run differently for the moving object compared to an observer at rest. Due to this difference, the time dilation cannot be directly measured using the same time scale (clock) used to measure proper time.

Conclusion: proper time (t) and time dilation (t') are associated with different time scales, and a clock that measures proper time cannot directly display or measure time dilation in the same units. The relativistic effects of time dilation cause time to be dilated or stretched for the moving object compared to an observer at rest, leading to different time scales for proper time and time dilation.

Mathematical Representation:

The equation of time dilation is 𝑡՚ = 𝑡/√(1 − 𝑣²/𝑐²) where 𝑡′ is dilated time, 𝑡 is proper time, v is relative speed, and c is the speed of light in free space.

1. 𝑇(𝑑𝑒𝑔) = 𝑇/360 = (1/𝑓)/360 = ∆t; Time scale = 360 (𝑇/360); t < t';  
2. Time scale for Proper time = 360°; Proper time = t; 
3. Time scale for Time dilation > 360°; Time dilation = t';  
4. Since, [Time scale for Proper time]  ≠  [Time scale for Time dilation];
5. Therefore, Time scale (clock) for Proper time cannot display Time dilation.

Time distortions in clocks or oscillators having mass:

Time distortion is possible for clocks, or oscillators, with rest mass m, and applied speed v<c, or gravitational potential difference h>0, where, v and h denote velocity in m/s and height above ground in m, respectively.

However, when clocks undergo time distortion, electromagnetic waves do not undergo the same distortion, but such waves maintain a time delay of 3.335641 µs/km; propagating at speed c, where, c represents the speed of light in free space. As such, redshift corresponds to time delay.

Mathematical Presentations for time distortions in clocks or oscillators:

1. If time distortion (𝛥𝑡) is possible for clocks or oscillators with the given rest mass (m), applied speed (v) < c, and gravitational potential difference (h) > 0. Where, rest mass (m) = 9.1093837 × 10^-31 kg;  height above ground (h) = 1 Km; v = 1 km/s.

To determine if time distortion (𝛥𝑡) is possible for clocks or oscillators with the given conditions, we need to check the two conditions:

v < c (object's speed is less than the speed of light).

h > 0 (there is a gravitational potential difference).

Given:

m = 9.1093837 × 10^-31 kg (rest mass)

v = 1 km/s = 1000 m/s (applied speed)

h = 1 km = 1000 m (height above ground)

g = 9.8067 m/s^2 (acceleration due to gravity)

v < c:

1000 m/s < 299792458 m/s (True)

The object's speed (v) is less than the speed of light (c), so condition 1 is satisfied.

h > 0:

1000 m > 0 (True)

The gravitational potential difference (h) is greater than 0, so condition 2 is satisfied.

Both conditions are satisfied, so time distortion (𝛥𝑡) is possible for clocks or oscillators with the given conditions. Time distortion occurs when an object's speed is less than the speed of light (v < c), and there is a gravitational potential difference (h > 0). In this case, both conditions are met, so time distortion is possible.  

2. If time distortion (𝛥𝑡) is possible for clocks or oscillators with the given rest mass (m), applied speed (v) < c, and gravitational potential difference (h) > 0. Where, rest mass (m) = 9.1093837 × 10^-31 kg;  height above ground (h) > 299792458 m; v = 299792458 m/s = c.    

To determine if time distortion (𝛥𝑡) is possible for clocks or oscillators with the given conditions, we need to check the two conditions:

v < c (object's speed is less than the speed of light).

h > 0 (there is a gravitational potential difference).

Given:

m = 9.1093837 × 10^-31 kg (rest mass)

v = 299792458 m/s (applied speed, equal to the speed of light c)

c = v (equal to the speed of light c)

h > 299792458 m (height above ground, greater than the speed of light c)

g = 9.8067 m/s^2 (acceleration due to gravity)

v < c:

299792458 m/s < 299792458 m/s (False)

The object's speed (v) is equal to the speed of light (c), not less than it, so condition 1 is not satisfied.

h > 0:

The given height above ground (h) is greater than the speed of light (c), h > c, which means there is a gravitational potential difference.

Both conditions are not satisfied, so time distortion (𝛥𝑡) is not possible for clocks or oscillators with the given conditions. 

Time distortion occurs when an object's speed is less than the speed of light (v < c), and there is a gravitational potential difference (h > 0). In this case, neither condition is met, so time distortion is not 

3. z is proportional to the time delay (𝛥𝑡):

To determine if there is a proportional relationship between redshift (z) and time delay (𝛥𝑡), we can compare the expressions for z and 𝛥𝑡:

z = k (𝜆/360)

𝛥𝑡 = (𝜆/360)

From the above expressions, we can see that both z and 𝛥𝑡 have the same term (𝜆/360) on the right-hand side. This indicates that z and 𝛥𝑡 are proportional to each other, and the constant of proportionality (k) is equal to 1.

There is a proportional relationship between redshift (z) and time delay (𝛥𝑡) for the given expressions, and the proportionality constant is 1. 

This means that as the redshift (z) increases or decreases, the time delay (𝛥𝑡) will also increase or decrease in direct proportion.

Conclusions:

Time distortion (𝛥𝑡) is possible for clocks or oscillators with the given rest mass (m), applied speed (v) < c, and gravitational potential difference (h) > 0. When the rest mass (m) is 9.1093837 × 10^-31 kg, the height above ground (h) is 1 km, and the applied speed (v) is 1 km/s, both conditions are satisfied, and time distortion is possible.

Time distortion (𝛥𝑡) is not possible for clocks or oscillators with the given rest mass (m), applied speed (v) < c, and gravitational potential difference (h) > 0. When the rest mass (m) is 9.1093837 × 10^-31 kg, the height above ground (h) is greater than 299792458 m, and the applied speed (v) is equal to the speed of light (c), the first condition is not satisfied, and time distortion is not possible.

There is a proportional relationship between redshift (z) and time delay (𝛥𝑡). The expressions for redshift (z) and time delay (𝛥𝑡) both involve the same term (𝜆/360), indicating a direct proportionality between the two. The proportionality constant (k) is equal to 1.

#TimeDistortion

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.