Understanding Relativistic Effects in Acceleration Initiation:

Soumendra Nath Thakur

ORCiD: 0000-0003-1871-7803

Tagore’s Electronic Lab, W.B. India

16-05-2024

The Lorentz factor (γ = 1/√(1-v²/c²) serves as a pivotal metric for determining the significance of relativistic effects. Typically, these effects become noticeable when γ deviates notably from 1, with a common threshold set at a deviation exceeding 1%. At a velocity where γ reaches 1.01, relativistic effects start to become appreciable, which typically occurs around 14% of the speed of light, precisely 41,970,944.12 meters per second. At this velocity, γ is approximately 1.01, marking the onset of measurable impacts on phenomena such as time dilation, length contraction, and mass increase.

Velocities significantly below this threshold, such as 0.8174% of c (v = 2,449,437.338 m/s or 0.008174c), exhibit noticeable relativistic effects in line with the Lorentz factor. For instance, at γ = 1.00001, the corresponding velocity v is approximately 2,449,437.338 m/s, representing approximately 0.8174% of the speed of light or 0.008174c. Similarly, at γ = 1.00000, the corresponding velocity v is approximately 2,449,288.829 m/s, representing approximately 0.8173% of the speed of light or 0.008173c.

Mathematical Threshold of Relativistic Effects in the Lorentz Factor:

Relativistic effects start to become appreciable at a velocity where γ reaches 1.01, which typically occurs around 14% of the speed of light, or precisely 41,970,944.12 meters per second. At this velocity, γ is approximately 1.01, marking the onset of noticeable impacts on phenomena such as time dilation, length contraction, and mass increase.

Even at velocities significantly below this threshold, for example, at γ = 1.00001, the corresponding velocity is approximately 2,449,437.338 m/s, representing approximately 0.8174% of the speed of light or 0.008174c. Thus, these velocities fall within the mathematical threshold where relativistic effects, in line with the Lorentz factor, become significant.

When γ = 1.00000, the corresponding velocity is approximately 2,449,288.829 m/s, representing approximately 0.8173% of the speed of light (0.008173c). Relativistic effects are noticeable only when γ deviates from 1.