Soumendra Nath Thakur
ORCiD: 0000-0003-1871-7803
26-10-2024
Abstract:
This section of the research explores the concept of time dilation within the framework of special relativity, where dilated time t′ exceeds proper time t, impacting conventional clock measurements. By examining clock mechanics, where time is traditionally divided into 12 segments of 30° each, we analyse how time dilation disrupts this design, leading to “errored” time readouts when applied to a clock designed for proper time. Through comparisons with wave phase shifts and frequency, this study introduces a model where each degree of phase shift corresponds to a measurable time distortion. It reveals that a clock built for standard intervals is incapable of accurately reflecting relativistic time dilation, underscoring the challenge of measuring dilated time with conventional systems. This analysis provides insights into the physical limitations of traditional time-keeping devices in representing relativistic effects.
Keywords: Time dilation, proper time, special relativity, phase shift, clock mechanics, relativistic time measurement, time distortion, frequency,
Relativistic Time Dilation and Clock Mechanics:
According to special relativity, time dilation (denoted as t′) exceeds proper time (denoted as t), expressed as t′ > t. Special relativity shifts the concept of time from an abstract, independent quantity to one defined operationally: “time is what a clock reads.” In this framework, a clock measures proper time.
Structurally, a standard clock face divides 360 degrees into 12 equal segments, assigning 30° to each hour (360°/12). When the minute hand completes a full rotation (360°), it marks one hour, correlating the clock’s full rotation to one period, T=360°. Similarly, in wave mechanics, a full cycle of a sine wave spans 360° of phase, establishing a period T = 360°. The frequency f of a wave is inversely related to its period T, given by T = 1/f. For each degree of phase in a sine wave, time shift per degree is expressed as T/360°, or
(1/f)/360°. Extending this, for x° of phase, the time shift T(deg) = Δt = (x°/f)/360.
In the case of proper time t, a full oscillation corresponds to T = 360, yielding Δt = 0 by design. However, with time dilation, Δt′ > Δt, making Δt′ > 0. Therefore, for a 1° phase shift in Δt, we get Δt′ = (1° /f)/360°, and for an x° phase shift, Δt′ =(x°/f)/360°.
Applying this to a clock, each hour segment designed for proper time t measures exactly 30° (360°/12). If time dilation Δt′ stretches the interval to 361°, each segment would measure 361°/12 ≈ 30.08°, thus exceeding the clock’s 30° marking for proper time t. Consequently, the clock, designed for proper time, cannot precisely reflect the dilation in t′, resulting in an “errored” time readout.
This demonstrates that time dilation t′ represents a distorted time measurement on a clock originally designed for proper time t, highlighting the misalignment introduced by relativistic time dilation.
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