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