Relativistic effects cause error in time reading (v2):

RG DOI : https://doi.org/10.32388/3YQQBO.2 

Abstract

The paper, titled 'Relativistic effects cause errors in time reading', highlights how the concept of time dilation, a consequence of the theory of relativity, creates different time scales for proper time and time dilation. This difference in time scale introduces errors in clock readings when attempting to measure time dilation using the same units as proper time.

The theory of relativity adopts Minkowski spacetime which 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 theory of relativity also implies that proper time (t) is dependent on relativistic effects and is expressed as 𝑡 < 𝑡′, where t' is the time dilation. The equation for 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.

Experiments carried out in the electronics laboratory on piezoelectric crystal oscillators show that the waves correspond to changes in time due to relativistic effects. where the time interval 𝑇(𝑑𝑒𝑔) is inversely proportional to the frequency (𝑓), for 1° phase. We get a wave associated with time change. For example, a 1° phase shift in a 5 MHz wave corresponds to a time change of 555 picoseconds (ps). Phase shifts in relative frequency, due to motion or gravitational potential differences, correspond to wavelength enlargement of clock oscillations in the clock mechanism, resulting in errors in clock readings. [1]

As per the Special Theory of Relaitivity, time dilation results from relativistic effects, such as speed or gravitational potential difference, that cause time to run differently for the moving object compared to an observer at rest.[2] Due to this difference, the time dilation (𝑡՚) cannot be directly measured using the same time scale (clock) used to measure proper time (𝑡).

Mathematical Representation:

We know, the equation of time dilation due to speed is 𝑡՚ = 𝑡/√(1 − 𝑣²/𝑐²); where, 𝑡՚> 𝑡;  

The instantaneous phase (ϕ) represents an angular shift between two relative sine waves and is measured in degrees. After a time Δt, the two relative sine waves are initially synchronized in phase but differ in frequency by Δω degrees per second, developing a differential total phase shift (ΔΦ). Eq. Given by: ΔΦ = Δω × Δt.

The time interval 𝑇(𝑑𝑒𝑔) is inversely proportional to the frequency (𝑓);

Where the time shift ∆t, due to the speed or gravitational potential difference, represents the error in the exact time (t) and consequently t < t'; For mathematical and geometric reasons as described below.

𝑇(𝑑𝑒𝑔) = 𝑇/360 = (1/𝑓)/360 = ∆t; Time scale = 360 (𝑇/360); t < t';

Time scale for Proper time = 360°; Proper time = t; 

Time scale for Time dilation > 360°; Time dilation = t';  

Since, [Time scale for Proper time]  ≠  [Time scale for Time dilation];

Therefore, Time scale (clock) for Proper time cannot display Time dilation.

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°, and 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.

Conclusion: 

Propoer 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 unit. The relativistic effect of time dilation causes time to dilate or stretched for a moving object or object in gravitational potential difference relative to an observer at rest, which creates different time scales for proper time and time dilation, where, due to motion or gravitational potential, the phase changes in relative frequency corresponds to an increase in the wavelength of the clock's oscillation, which results in an error in the clock's reading.

In short, proper time and time dilation have different time scales, causing errors in clock time reading.

Reference:

[1]  Thakur, Soumendra Nath. Effect of Wavelength Dilation in Time.-About Time and Wavelength Dilation. No. 9182. EasyChair, 2022. Retrieved August 05, 2023, from https://easychair.org/publications/preprint/M7Zt 

[2]  Relativity : the Special and General Theory by Albert Einstein. (n.d.). Project Gutenberg. Retrieved October 28, 2022, from https://www.gutenberg.org/ebooks/5001

Events invoke time. - Dimensions of space and time:

Description of the unit of time, the second (s):

The second (s) is the SI unit of time. It is defined based on the fixed numerical value of the cesium frequency ΔνCs. The second is the duration of 9192631770 cycles of the radiation corresponding to the transition between two hyperfine levels of the cesium 133 atom. 

In other words, the second is defined as the time taken for a specific number of oscillations of the cesium atom, making it a reliable and precise unit for time measurement. The value of ΔνCs is 9192631770 Hz, which is equivalent to s^-1.

Events Invoke Time: 

Existential events by their very nature invoke time. In our reality, event or events are fundamentally tied to the concept of time. Whenever something happens or comes into existence, it does so within a temporal framework. Time is the dimension that provides the context in which events occur, and through the progression of time events unfold, develop and eventually cease to exist.

Here is a description of how existential events invoke time:

Temporal Sequence: Time enables the sequencing of events. Each event occurs one after the other or at a specific time. The concept of "before" and "after" is possible only because of time. For example, we can say that the force of gravity over time causes an object to fall to the ground before bouncing back up.

Duration and Persistence: Duration provides the duration for which the event exists. Whether it is a fleeting moment or a prolonged process, events have a temporal span The duration of an event can be infinitely short or extend over an extended period of time, and this duration is defined by time.

Cause and Effect: Timing is crucial for establishing causal relationships between events. Cause and effect are closely tied to the temporal order of events. A cause precedes its effect, and this temporal relationship is essential to understanding how events are interconnected in the fabric of reality.

Change and Transformation: Time is the canvas on which change and transformation take place. Events can evolve, change and change their status as time progresses. For example, plant growth from a seed to a mature plant is a process that unfolds over time.

Birth and Death: Time defines the beginning and end of events, including the birth and death of entities. Whether it is the birth of a star in the universe or the passing of a living organism, both events are characterized by their occurrence over time.

Perception and Experience: Our perception and experience of reality is intertwined with time. As conscious humans, we experience events in a temporal flux. Our memory, awareness and ability to recall past events or anticipate the future depends on our sense of time.

In short, existential events invoke time because time provides the framework within which events occur, persist, and change. Time is the invisible thread that weaves together the tapestry of existence, enabling us to understand the relationship between events and their unfolding within perceptible space.

Time: 

Time is a concept that defines the indefinite and continuous progression of past, present and future existence and events. It is a fundamental dimension that exists alongside the three spatial dimensions (x, y, and z). Time is regarded as an irreversible and unidirectional flow, meaning that events occur in a sequence that moves forward without the possibility of going back to a previous state.

The nature of time can be described as follows:

Indefinite progression: Time has no definite beginning or end; It extends infinitely in both directions. We can trace the events of history and look into the future, but there is no finite point that marks the origin or conclusion of time.

Including past, present and future: Time contains past, present and future as a unified whole. Events that occurred in the past led to the present moment, and current actions and decisions will shape what will unfold in the future.

Irreversible Flow: Time moves forward in an irreversible manner. Once an event occurs, it becomes part of the past and cannot be undone. There is no mechanism in our macroscopic reality that allows us to go back in time.

Uniform succession: Time progresses uniformly, meaning it moves at a constant speed without changing speed or direction. In our macroscopic reality, time is considered consistent and operates at a constant speed across all events and experiences.

Fourth Dimension: Time is considered the fourth dimension when added to the three perceptible spatial dimensions (x, y, and z). Together, these four dimensions provide a framework within which objects, events, and phenomena exist and interact in our observable reality.

Perceptible space is inextricably linked: time and the three spatial dimensions are intertwined. The unfolding of events within perceptible space invokes the concept of time. Events occur at specific points in space and are characterized by their temporal order. 

In short, time is an abstract dimension that encompasses the ongoing progression of existence and phenomena in our macroscopic reality. It is distinct from the three spatial dimensions and is considered an irreversible and unidirectional flow, which is integral to our understanding of the manifested universe. 

Dimensions of Space and Time: 

Perceptible space: This refers to the three spatial dimensions (x, y, and z) in which objects can be observed and experienced in our macroscopic reality.

Invisible dimensions: These are non-local dimensions beyond the three perceptible dimensions (x, y, and z) that are not directly observable or experienced in our macroscopic reality. One such invisible dimension is time (t).

Invisible Dimension (t): It specifically refers to time (t) as a separate and distinct dimension from the three spatial dimensions. Time (t) is one of the four fundamental dimensions that we experience, and although not directly observable to a spatial extent, the progression and sequence of events in perceptible space is called time (t).

Based on the given (x, y, z, t) coordinate system, the definitions are as follows:

x, y, z: Three spatial dimensions representing the length, width and depth of an object or event in perceptible space.

t: The time dimension represents the progression of events and the order in which they occur and is considered an invisible dimension.

With these definitions, we can further clarify:

Time (t) is considered an invisible dimension because we cannot directly perceive or experience time as a spatial dimension, but it is fundamental to describing the sequence and duration of events in our perceptible space.

Perceptible events are conceptual (time) = t: This means that in our perceptible space (x, y, z), events occur and invoke the concept of time (t) to describe their occurrence and duration.

In short, in the (x, y, z, t) coordinate system:

Realizable dimensions: x, y, z (local dimensions)
Invisible dimension: t (time dimension)

Time (t) is crucial to understanding the sequence and progression of events in our perceptible space. It is considered an invisible dimension because we cannot feel or experience it directly like the spatial dimension.

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