Energy - frequency Relation. - What is frequency in terms of energy?

Abstract:

Frequency is the rate at which energy vibrates, and it is a fundamental property of waves, whether mechanical waves (e.g., sound waves) or electromagnetic waves (e.g., light waves).

For mechanical waves:

The kinetic energy (Eₖ) of a mechanical wave is given by Eₖ = 1/4(μA²ω²λ), where μ is the linear mass density of the wave medium, A is the amplitude of the wave, ω is the angular frequency of the wave oscillator, and λ is the wavelength of the wave.

The frequency (f) of the kinetic energy (Eₖ) of a mechanical wave is given by f = √ {Eₖ / (π²μA²λ)}.

The period in degrees {T(deg)} of the kinetic energy (Eₖ) of a mechanical wave is given by T(deg) = 1/[360√{Eₖ/(π²μA²λ)}].

For electromagnetic waves:

The energy (E) of an electromagnetic wave is related to its frequency (f) through Planck's equation, E = hf, where h is Planck's constant.

The energy of electromagnetic waves is directly proportional to their frequency. As the frequency increases, the energy of the wave also increases.

Kinetic energy | Radians and degrees | Radian-degree relation | Angular frequency relation | Kinetic energy frequency | Period kinetic energy | Wave potential energy | Energy mechanical wave | Energy EM wave | Maximum wave speed | Phase shift-frequency | Relationships | Time reading error | Photon momentum | An electron | Electron rest mass |  Electron energy | A photon | Photon energy | Electron energy | Energy in mass

Frequency is the rate at which energy vibrates.

Frequency, in terms of energy, refers to the rate at which energy oscillates or vibrates. It is a fundamental property of waves, whether they are mechanical waves, such as sound waves, or electromagnetic waves, such as light waves.

1.0. For mechanical waves, e.g., sound waves, the frequency is related to the kinetic energy of the wave. The kinetic energy (Eₖ) of a mechanical wave is given by the formula:

Eₖ = 1/4(μA²ω²λ);

Where:

Eₖ = Kinetic energy of the mechanical wave

μ = Linear mass density of the wave medium (in kg/m)

A = Amplitude of the wave (in meters)

ω = Angular frequency of the wave oscillator (in radians per second)

λ = Wavelength of the wave (in meters)

1.1. The radians and degrees:

Degree (°):

A degree is a unit of angular measurement. A full circle is divided into 360 degrees, with each degree representing 1/360th of the complete rotation. The symbol for degrees is "°." For example, a right angle measures 90 degrees (90°), and a straight line measures 180 degrees (180°).

Radian (rad):

A radian is another unit of angular measurement and is defined as the angle subtended at the center of a circle by an arc equal in length to the radius of the circle. In other words, if the length of the arc is equal to the radius of the circle, then the angle formed is one radian. The symbol for radians is "rad."

1.2. Relationship between Radian and Degree:

The relationship between radians and degrees is based on the fact that a full circle (360 degrees) is equal to 2π radians. More precisely:

1 full circle = 360 degrees = 2π radians

Degrees = Radians * (180/π)

Where: π (pi) is approximately 3.14159.

To convert from radians to degrees: Multiply by (180/π).

To convert from degrees to radians: Multiply by (π/180).

1.3. The angular frequency (ω) is related to the frequency (f) by the equation:

ω = 2πf;

1.4. Angular Frequency (ω) of Eₖ:

We have: ω = 2πf;

ω = 2π√ {Eₖ / (π²μA²λ)};

1.5. The equation for the frequency (f) of the kinetic energy (Eₖ)

We have: Eₖ = 1/4(μA²ω²λ); ω = 2πf;

By substitution:

Eₖ = 1/4(μA² (2πf) ²λ);

f² = Eₖ / (π²μA²λ);

So, the equation for the frequency (f) of the kinetic energy (Eₖ) of a mechanical wave is:

f = √ {Eₖ/ (π²μA²λ)};

Relationship of the variables:

• Wavelength (λ): λ = 2π / k;
• Speed of the Wave (v): v = fλ = ω / k;
• Frequency Times Wavelength (fλ): fλ = ω / k;
• Angular Frequency (ω): ω = 2πf;
• Wavenumber (k): k = 1 / λ;
• Kinetic Energy (Eₖ): Eₖ = 1/4 * μ * A² * ω² * λ

Example: In the equation for kinetic energy of a mechanical wave (Eₖ = 1/4 * μ * A² * ω² * λ), we can determine the values of the variables wavelength (λ), speed of the wave (v), frequency times wavelength (fλ), angular frequency (ω), wavenumber (k), and kinetic energy (Eₖ) by providing the values of amplitude (A), frequency (f), mass (m), and length (x) of the vibrating string.

Given,

Eₖ = 1/4(μA²ω²λ); 

where, the frequency of the oscillation is f = ω /2π;

linear mass density µ = mass/length = m/x kg/m; 

At a given time the distance between successive points, y = A, called the wavelength (λ), λ = 2π /k . 

The speed of the wave, v = fλ = ω /k; 

Given values of, 

Amplitude, A = 1m; 

Frequency, f = 60Hz = ω/2π = 1/λ; 

Mass of the string, m = 0.06 kg; 

Length of the string, x = 2 m;

Degrees = radians * (180/π);

To find, λ, fλ, ω/k, y, v, ω (in Degree); of the kinetic energy (Eₖ) of the mechanical wave?

Solution:

We have,

Amplitude (A): A = 1 m;

Frequency (f): f = 60 Hz;

Mass of the string (m): m = 0.06 kg;

Length of the string (x): x = 2 m;

Degrees = radians * (180/π);

Derived:

Linear mass density (µ): µ = m / x = 0.06 kg / 2 m = 0.03 kg/m;

Solution:

Wavelength (λ): The relationship f = 1/λ, so λ = 1 / f = 1 / 60 Hz ≈ 0.01667 meters;

Angular Frequency (ω): We have f = ω / 2π, so ω = 2π * f = 2π * 60 Hz ≈ 376.99 rad/s;

Wavenumber (k): We have λ = 2π / k, so k = 2π / λ ≈ 376.99 rad/m;

Speed of the Wave (v): v = fλ = ω / k = f / k = (2π * 60 Hz) / (2π / λ) ≈ 60 * 0.01667 m/s = 1 m/s;

Frequency Times Wavelength (fλ): fλ = ω / k = f / k = 1 m/s;

Angular Frequency (ω) in Degrees: Given that Degrees = radians * (180/π), 

we convert ω from radians to degrees: ω_deg = ω * (180/π) ≈ 21599.16 degrees

Kinetic Energy (Eₖ): Using the given formula for kinetic energy, Eₖ = 1/4 * μ * A² * ω² * λ, substituting the known values: Eₖ = 1/4 * (0.03 kg/m) * (1 m)² * (376.99 rad/s)² * (0.01667 m) ≈ 1.424 J

 1.6. The T(deg) (period in degrees) of the kinetic energy (Eₖ) equation is:

T(deg) = T/360; where T is the period in seconds, the reciprocal of the frequency (T = 1/f).

T(deg) = (1/f)/360 = [1/√{Eₖ/(π²μA²λ)}]/360;

So, the equation for T(deg) (period in degrees) of the kinetic energy (Eₖ) of a mechanical wave is:

T(deg) = 1/[360√{Eₖ/(π²μA²λ)}];

1.7. The potential energy (Eₚ) of the mechanical wave, the equation is:

Eₚ = 1/4(μA²ω²λ);

1.8. The total energy (Eₜ) of the mechanical wave is:

Eₜ = Eₖ + Eₚ;

Eₜ = 1/4(μA²ω²λ) + 1/4(μA²ω²λ) = 1/2(μA²ω²λ);

2.0 The Energy of electromagnetic waves:

For electromagnetic waves (e.g., light waves), the energy is related to frequency through Planck's equation:

E = hf;

Where:

E represents energy (in joules),

h is Planck's constant (approximately 6.626 x 10^-34 J · s), and

f is the frequency of the electromagnetic wave (in hertz).

The energy of an electromagnetic wave is directly proportional to its frequency. As the frequency increases, the energy of the wave also increases.

2.1 Maximum speed of any wave:

It's worth noting that the maximum speed of any wave, including electromagnetic waves, is determined by the ratio of the Planck length to the Planck time (ℓP/tP), which yields the speed of light in a vacuum (c), approximately 299,792,458 meters per second (approximately 3.00 x 10^8 m/s).

This is a fundamental constant in physics and serves as a speed limit for the propagation of any energy or information in the universe.

2.2. Relationships - phase shift, frequency, wavelength, period, T(deg)

i. Phase shift is a small difference between two waves; in math and electronics, it is a delay between two waves that have the same period or frequency. The phase shift is expressed in terms of angle, which can be measured in degrees or radians, and the angle can be positive or negative. For a shift to the right, the phase shift is positive, or negative for a shift to the left.

ii. Frequency (f) is a measure of how many cycles or oscillations of a wave occur in one second.

iii. Wavelength (λ) refers to the distance between two consecutive points on a wave that are in phase.

iv. The period of the wave is represented by T, and the period in degrees is represented by T(deg).

v. The period of the wave (T) is the time taken for one complete cycle of the wave, measured in seconds.

vi. The period in degrees T(deg) represents the time taken for one complete cycle of the wave to cover 360 degrees.

vii. The relationship between frequency (f) and wavelength (λ) is: f = 1/λ.

viii. The period is inversely proportional to the frequency and the relationship between them is: 

T = 1/f;

ix. The relationship between the period in degrees T(deg) and period (T) is: T(deg) = T/360;

x. The period in degrees T(deg) is inversely proportional to the frequency (f), and the relationship between them is:

T(deg) = (1/f) * 360.

xi. The angular frequency (ω) is directly proportional to the frequency (f), and the relationship between them is:

ω = 2πf.

xii. The relationship between wavelength (λ) and period (T) for a wave is directly proportional, it can be expressed as:

λ ∝ T.

xiii. To be more precise, the relationship between wavelength and period is given by:

λ = v * T.

xiv. The wave equation describes the relationship between the speed of a wave (v), its frequency (f), and its wavelength (λ). The equation is given as:

v = f * λ.

xv. The phase shift in degrees T(deg) is directly proportional to the product of the time shift (Δt), the frequency (f), and 360. The relationship between them is given by the equation:

T(deg) = (360 * Δt * f);

xvi. The phase shift in radians (ϕ) is directly proportional to the time shift (Δt) in seconds. The relationship between them is given by the equation:

ϕ = ω * Δt;

Where ω is the angular frequency of the oscillation (in radians per second)

xvii. The conversion formulas between phase shifts in radians (ϕ) and degrees T(deg) are:

T(deg) = (ϕ * 180)/π;

ϕ = (T(deg) * π)/180;

2.3. The time interval T(deg) for 1° of phase is inversely proportional to the frequency. If the frequency of a signal is given by f, then the time T(deg) (in seconds) corresponding to 1° of phase is T(deg) = 1/(360f) = T/360. Therefore, a one-degree (1°) phase shift on a 5 MHz signal shows a time shift of 555 picoseconds.

2.4. A change in the frequency (f) of clock oscillation due to a phase shift T(deg) in degrees will cause an error in time (Δt) reading in a clock designed for a 360-degree time scale.

2.5. The symbol 'ρ' (rho) is commonly used to represent the momentum of a photon, and it is related to the photon's wavelength (λ) through the equation:

ρ = h/λ

Where:

ρ is the momentum of the photon, measured in kilogram meters per second (kg·m/s).

h is Planck's constant, approximately equal to 6.62606868 × 10^-34 joules per second (J·s).

λ is the wavelength of the associated electromagnetic wave, measured in meters (m).

This equation shows that the momentum of a photon is inversely proportional to its wavelength. Photons with shorter wavelengths have higher momentum, while photons with longer wavelengths have lower momentum. The concept of photon momentum is important in various areas of physics, especially in the context of particle interactions and the study of electromagnetic radiation.

2.6. An electron is a subatomic particle and one of the fundamental constituents of matter. It carries a negative electrical charge and is an elementary particle, meaning it is not composed of smaller sub particles. Electrons are classified as leptons, which are one of the six types of elementary particles in the Standard Model of particle physics.

Properties of electrons include:

Charge: An electron carries a negative elementary charge of approximately -1.602176634 × 10^-19 coulombs (C).

Mass: The rest mass of an electron (when it is not moving) is approximately 9.1093837 × 10^-31 kilograms (kg).

Location: Electrons are found outside the nucleus of atoms. They orbit around the nucleus in specific energy levels, forming the electron cloud of the atom.

Behavior: Electrons exhibit both particle-like and wave-like behavior, known as wave-particle duality. This behavior is fundamental in quantum mechanics.

Interaction: Electrons interact with other particles through electromagnetic forces, which are mediated by photons, the particles of light.

Energy Levels: Electrons occupy discrete energy levels in an atom, and they can move between these levels by absorbing or emitting energy in the form of photons.

Conductivity: The mobility of electrons allows them to carry electric current in conductive materials like metals.

Electrons play a vital role in various physical phenomena, including electricity, magnetism, chemical bonding, and the behavior of matter at the atomic and subatomic scales. Understanding electrons and their interactions with other particles is fundamental to many areas of physics, chemistry, and engineering.

2.7 The electron rest mass (mₑ) is a fundamental constant in physics and represents the mass of an electron when it is at rest or not moving with respect to an observer. Its value is approximately:

Electron rest mass (mₑ) ≈ 9.1093837 × 10^-31 kilograms (kg).

The electron is one of the elementary particles, and its rest mass is an important parameter in various physical calculations and theories. It is used to describe the mass of an electron in its rest frame and is often used as a reference point to compare the masses of other particles.

2.8. The electron rest energy is the energy equivalent of the electron's rest mass (mₑ) given by Einstein's famous mass-energy equivalence equation:

For an electron, its rest mass (mₑ) is approximately 9.1093837 × 10^-31 kg, we can calculate its rest energy (Eₑ):

Eₑ = mₑc²;

Eₑ ≈ (9.1093837 × 10^-31 kg) × (2.99792458 × 10^8 m/s)²

Eₑ ≈ 8.187105776 × 10^-14 J

≈ 8.19 × 10^-14 J (approximately)

2.9 The electron rest energy in terms of electron volts (eV):

1 electron volt (eV) ≈ 1.602176634 × 10^-19 J

Eₑ ≈ 8.19 × 10^-14 J ÷ (1.602176634 × 10^-19 J/eV) ≈ 0.511 MeV

So, the electron rest energy is approximately 0.511 MeV or 8.19 × 10^-14 J, depending on the preferred unit of measurement.

3.0. A photon is a fundamental particle in physics that is associated with electromagnetic radiation, including visible light, radio waves, microwaves, X-rays, and gamma rays. Photons are elementary particles and are considered the force carriers of the electromagnetic force. They play a crucial role in the interaction between charged particles and are responsible for transmitting electromagnetic waves.

Key properties of photons include:

No Rest Mass: Photons are massless particles, meaning they have zero rest mass. Unlike other particles such as electrons and protons, which have rest masses, photons travel at the speed of light and do not experience time or aging.

Energy and Frequency: Photons have energy (E) and are characterized by their frequency (f) or wavelength (λ) of the associated electromagnetic wave. The energy of a photon is related to its frequency by the equation E = hf, where 'h' is Planck's constant.

Wave-Particle Duality: Photons exhibit both wave-like and particle-like behavior, known as wave-particle duality. In some experiments, photons behave like waves, and in others, they behave like discrete particles.

Quantum of Electromagnetic Energy: Photons carry quantized packets or quanta of electromagnetic energy. The energy of a photon is directly proportional to its frequency. Higher frequency (shorter wavelength) photons have higher energies, and vice versa.

Propagation at the Speed of Light: Photons always travel at the speed of light in a vacuum, which is approximately 2.99792458 × 10^8 meters per second (m/s). This constant speed of light is a fundamental constant in physics and plays a key role in the theory of special relativity.

Interaction: Photons can interact with charged particles, such as electrons, by transferring their energy and momentum. This interaction is the basis for various phenomena, including the photoelectric effect, which led to significant developments in quantum theory.

Photons are central to the study of quantum mechanics and are essential in understanding the behavior of light and other electromagnetic waves. Their wave-particle nature makes them a fascinating and essential aspect of modern physics and is foundational to many areas, including quantum mechanics, atomic and molecular physics, and quantum electrodynamics.

3.1. Photons are massless particles, which mean they do not have rest mass (m). As massless particles, they travel at the speed of light in a vacuum (approximately 2.99792458 × 10^8 meters per second) and always move at this constant speed.

Given the energy-frequency equivalence for photons, which is E = hf, where 'E' is the photon's energy and 'f' is the wave frequency; we can calculate the kinetic energy of a photon using this relationship.

Since photons have no rest mass, their energy (E) is entirely kinetic energy, which is the energy associated with their motion. Thus, the kinetic energy (Eₖ) of a photon can be represented by E = hf:

Eₖ = hf

Where:

Eₖ is the kinetic energy of the photon, measured in joules (J).

h is Planck's constant, approximately 6.62606868 × 10^-34 J s.

f is the wave frequency of the photon, measured in hertz (Hz).

The kinetic energy of a photon is directly proportional to its frequency. Photons with higher frequencies (shorter wavelengths) have higher kinetic energies, while photons with lower frequencies (longer wavelengths) have lower kinetic energies.

3.2. The change in potential energy (Δmₑ) of an electron after absorbing a photon:

When an electron absorbs a photon, the energy of the photon increases as the energy of the photon is transferred to the electron. This change in energy is known as the change in potential energy (Δmₑ) of the electron. However, it's important to note that electrons do not have "rest" potential energy in the same sense as in classical mechanics, where potential energy is associated with the position of an object in a gravitational field. In the context of quantum mechanics, the potential energy of an electron typically refers to the interaction potential energy in an atomic or molecular system.

In the case of an electron absorbing a photon, we can calculate the change in energy (Δmₑ) by considering the change in the electron's total energy before and after the absorption process.

Before absorption, the electron's total energy (Eᵢ) is its rest energy (mₑc²) since electrons at rest have no kinetic energy:

Eᵢ = mₑc²

After absorption, the electron's total energy (E_f) will be its rest energy plus the energy of the absorbed photon (E_photon):

E_f = mₑc² + E_photon

The change in energy (Δmₑ) is then the difference between the final and initial total energies:

Δmₑ = E_f - Eᵢ

Δmₑ = (mₑc² + E_photon) - mₑc²

Δmₑ = E_photon

So, the change in potential energy (Δmₑ) of an electron after absorbing a photon is simply equal to the energy of the absorbed photon. The absorbed energy increases the electron's total energy, and depending on the context, it can lead to various phenomena such as excitation of the electron to higher energy levels in an atom or electron ejection in the case of the photoelectric effect.

3.3. Invariant mass (mₑ) of an electron after absorbing photon:

When an electron absorbs photon energy (hf), its total energy increases by that amount. The absorbed energy can cause the electron to transition to a higher energy level in an atom or molecule, leading to an excited state. This phenomenon is fundamental in various physical processes, including the interaction of light with matter.

In terms of the electron's mass, the absorption of a photon (hf) does not directly impact its rest mass (mₑ). The rest mass of an electron remains the same before and after absorbing the photon, as the rest mass is an intrinsic property of the electron and is not affected by the energy it possesses.

The energy absorbed by the electron increases its total energy, but it does not change its rest mass. The kinetic energy of the electron can increase if it absorbs a photon, but the rest mass energy remains constant.

After absorbing the photon, the electron will have an increased total energy given by:

Total Energy after absorption (E_f) = E₀ + Eᵏ + hf

Where:

E₀ is the rest mass energy of the electron, which is approximately 8.19 × 10^−14 J (corresponding to the rest energy of 0.511 MeV).

Eᵏ is the kinetic energy of the electron before absorbing the photon.

hf is the energy of the absorbed photon.

The electron's mass (mₑ) is still represented by its rest mass, and any increase in energy due to the absorbed photon will manifest as additional kinetic energy or potential energy, depending on the specific context and the electron's environment.

The consequences of electron-photon interactions can be varied, absorption of a photon can lead to electronic excitation, while in the photoelectric effect, and an absorbed photon can eject an electron from a material. The behavior of electrons when interacting with photons is crucial.

#frequency #energy #wave

Events invoke time. (v1):

The paper, titled 'Events Invoke Time' provides a comprehensive overview of the concept of time, its role in events and its relationship to the dimensions of space. It emphasizes the inextricable connection between events and time and how time serves as the fundamental framework for understanding the unfolding of events in our reality.

Description of SI unit of time, the second (s): [1]

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: [2] (Existential events invoke conceptual 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: [3]

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: [4] [5]

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. 

References: 

[1] National Institute of Standards and Technology. (2022, December 6). SI Units – Time. National Institute of Standards and Technology - SI Units – Time. Retrieved August 5, 2023, from https://www.nist.gov/pml/owm/si-units-time

[2] Relativistic effects on phaseshift in frequencies invalidate time dilation II DOI https://doi.org/10.36227/techrxiv.22492066.v2 Accessed 5 August 2023.

[3] Oxford University Press. Archived Retrieved October 28, 2022 Definition for time - Oxford Dictionaries Online (World English). (n.d.).  https://web.archive.org/web/20120704084938/http://oxforddictionaries.com/definition/time

[4] Britannica, The Editors of Encyclopaedia. "Euclidean space". Encyclopedia Britannica, 8 Jun. 2023, https://www.britannica.com/science/Euclidean-space. Accessed 5 August 2023.

[5] Osserman, Robert. "dimension". Encyclopedia Britannica, 13 Jul. 2023, https://www.britannica.com/science/dimension-geometry. Accessed 5 August 2023.

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.

#time #events #dimensions #space

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.