Light travel distance, proper distance, comoving distance and luminosity distance:

Light travel distance is the distance light travels in free space in a given time, influenced by redshift, and is calculated as ‘light travel time’.

The proper distance refers to the distance between an observer and a source at a specific time t, which can change over time due to the expansion of the universe. It represents the distance between two galaxies at that time (t), which can also change due to the universe's expansion.

Comoving distance, a measure of the constant distance between the universe's expansion and its proper distance, remains constant despite changes in proper distance due to the expansion of space.

The Luminosity Distance depends on cosmology and it is defined as the distance at which the observed flux f is from an object. The Photon Energy gets red shifted. Where λ(obs), λ(emit) are observed and emitted wave lengths and a0,ae are corresponding scale factors.

#LightTravelDistance #ProperDistance #ComovingDistance #LuminosityDistance

Summary: Cosmic Speed Beyond Light:

Gravitational and Cosmic Redshift

Cosmic Speed Beyond Light: Gravitational and Cosmic Redshift explores the complex relationship between gravitational and cosmic redshift phenomena, shedding light on how light behaves as it traverses the cosmos. This groundbreaking research unveils profound insights into the perceived speed of light across the universe.

Abstract:

The study commences by examining gravitational redshift, a well-established concept rooted in Albert Einstein's theory of general relativity. Gravitational redshift occurs as photons move away from massive gravitational sources, such as stars within galaxies. Gravitational redshift, expressed as (λ/λ0), operates within the gravitational influence and extends to the boundary of the "zero-gravity sphere" enveloping galaxies.

Within this intriguing zero-gravity sphere, gravitational effects persist, while the antigravity influence of dark energy remains negligible. Consequently, gravitational redshift dominates, and cosmic redshift is absent. Photons within this sphere maintain their constant speed 'c' and undergo gravitational redshift exclusively.

However, as photons exit the zero-gravity sphere at a distance 'r' equivalent to the source star's radius, they encounter the onset of cosmic redshift, quantified as {(λobserved - λemitted)/ λemitted}. Cosmic redshift combines with gravitational redshift, forming the effective redshift of the photon. Notably, the effective cosmic redshift surpasses gravitational redshift, revealing that photons traverse a greater "light-traveled distance" than their proper distance from the source.

In essence, cosmic redshift signifies that photons move across their intended distances at their intrinsic speed ('c'), while the expanding universe introduces relative distance expansion, influenced by antigravity. This research delves into the intricate dance between gravitational and cosmic redshift, illuminating their implications for our comprehension of the expanding universe.

Introduction:

The cosmos is a tapestry woven with space, time, and light, captivating astronomers and physicists throughout history. Gravitational and cosmic redshift phenomena are central to our understanding of the universe. Gravitational redshift, based on general relativity, occurs near massive objects, while cosmic redshift arises from the universe's expansion. This research explores their interplay and consequences for the speed of light perception.

Method:

A combination of theoretical foundations, astrophysical observations, and mathematical modeling forms the research methodology. General relativity serves as the theoretical cornerstone, with a focus on the "zero-gravity sphere," where gravitational effects persist. Astrophysical observations provide empirical data, and mathematical models quantify redshift phenomena.

Discussion:

Gravitational redshift occurs when photons escape strong gravitational fields, stretching their wavelengths. Cosmic redshift results from the universe's expansion, impacting all cosmic regions. The zero-gravity sphere marks a transition zone, where gravitational redshift dominates but yields to cosmic redshift beyond. The effective cosmic redshift suggests that light traverses greater distances than expected due to cosmic expansion.

Implications and Future Research:

This research opens avenues for exploring dark energy, the universe's structure, and cosmological principles. Precise measurements, simulations, and deeper investigations into cosmic speed promise to advance our understanding of the cosmos.

Conclusion:

Cosmic Speed Beyond Light: Gravitational and Cosmic Redshift provides profound insights into the interplay of gravitational and cosmic redshift, challenging our notions of light speed and cosmic dynamics. It invites us to rethink our cosmic paradigms and offers fresh perspectives on the fabric of the universe.

References:

Antigravity - Dark energy: zero-gravity sphere enveloping galaxies:

Chernin, A. D., Бисноватый-коган, Teerikorpi, P., Valtonen, M. J., Byrd, G. G., & Merafina, M. (2013, May 1). Dark energy and the structure of the Coma cluster of galaxies. Astronomy and Astrophysics; EDP Sciences. https://doi.org/10.1051/0004-6361/201220781

Gravitational Redshift:

Einstein, A. (1911). "On the Influence of Gravitation on the Propagation of Light." Annalen der Physik, 35(10), 898-908.

Pound, R. V., & Rebka, G. A. (1959). "Gravitational Red-Shift in Nuclear Resonance." Physical Review Letters, 3(9), 439-441.

Peebles, P. J. E., & Ratra, B. (2003). "The cosmological constant and dark energy." Reviews of Modern Physics, 75(2), 559-606.

Cosmic Redshift:

Hubble, E. P. (1929). "A relation between distance and radial velocity among extra-galactic nebulae." Proceedings of the National Academy of Sciences, 15(3), 168-173.

Riess, A. G., et al. (1998). "Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant." The Astronomical Journal, 116(3), 1009-1038.

Planck Collaboration, et al. (2018). "Planck 2018 results. VI. Cosmological parameters." Astronomy & Astrophysics, 641, A6.

Do a hot object have low energy or high energy?

When the temperature of an object increases, the average kinetic energy of its particles increases. When the average kinetic energy of its particles increases, the object's thermal energy increases. Therefore, the thermal energy of an object increases as its temperature increases.

The temperature of an object increases, means that the average kinetic energy of its particles has increased. This increase in kinetic energy corresponds to an increase in thermal energy. Thermal energy is the energy associated with the motion of particles within a substance.

The formula Q = m * c * ΔT, is used to calculate the thermal energy (heat) transferred to or from an object when its temperature changes. Here's a breakdown of the variables in the formula:

Q represents the amount of heat energy transferred (measured in joules).

m is the mass of the substance (measured in kilograms).

c is the specific heat capacity of the substance (measured in joules per kilogram per degree Celsius or joules per gram per degree Celsius, depending on the units used).

ΔT is the change in temperature (measured in degrees Celsius or Kelvin).

By using this formula, one can calculate how much heat energy is gained or lost by an object when its temperature changes. It's a fundamental concept in thermodynamics and is widely used in various fields of science and engineering to understand and control heat transfer processes.

Is there any particle moving more than the velocity c (speed of light ) in the universe?

Replied that -

There are basically two types of known effects in which the macro-existence of the universe is observed.

1. Gravitationally bound objects, such as a galaxy, cluster of galaxies, mega or super cluster of galaxies.
2. Dark energy influenced objects, such as a galaxy, cluster of galaxies, mega or super cluster of galaxies, where antigravity rules.

Beyond such gravitationally bound objects are their respective zero-gravity spheres, where dark energy rules.

Planck ratio which expresses the ratio of Planck length and Planck time determines speed limit: ℓP/tP = c;

However, outside the zero-gravity sphere, the speed limit does not apply, as there can be accommodated by speeds greater than ℓP/tP = c.

There an entire galaxy can travel much faster than light, even at multiples of c.

Question: mass-energy equality and photon energy?

Your mathematical representation of mass m0 in the equation {m = m0/√(1 − v2/c2)}, when v = c, is an incorrect approach in mathematics and also in special relativity.

The reason is that the equation, which you mentioned in your paper, does not apply when you consider a speed v = c.

Also, at a speed (c), m0 is no longer mass.

When the momentum of such a massless photon needs to be evaluated by the equation

• p = h/λ,

where λ is the photon wavelength, p (roh) is the photon momentum and h is Planck's constant.

Such a massless photon would have energy 

• E = hf,
• since, f = c/λ; E = hc/λ, p = h/λ
• Therefore, E = pc

The equation you chose to calculate the mass m0 at speed v = c is an incorrect application.

Please note, the time dilation equation (due to motion) is also an incorrect application, because the speed v and c used in the time dilation equation, should not modify the proper time (t), unless intentionally inviting error in the calculation.

The part of the equation √(1 - v²/c²) in {t' = t/√(1 − v2/c2)} should not modify the proper time (t), to get the dilated time (t'), because the proper time t should not be interfered by some external effect, such as speed (v), unless one invites intentional error in calculations.

Regarding the last comment above, this paper is noteworthy

Preprint Relativistic effects on phaseshift in frequencies invalidate...

Relative mass is the mass assigned to a body in motion:

Relativistic mass is also invariant mass, just as the relativistic energy of a single particle is equal to its rest energy as seen from its rest frame.

Relative velocity is the motion of an object relative to an observer, as described by the theory of relativity. Basically, special relativity explains the relationship between space, time, mass and energy in speed or velocity but does not include gravity. Therefore, relative speed or velocity is relevant in special relativity.

Relative speed:

Refers to the speed at which relativistic effects become significant for the desired accuracy of measurement of the observed phenomenon. Time dilation, in special relativity, is the difference in elapsed time measured by two clocks due to a relative velocity between them.

Note that Time distortion occurs only in clocks with mass under relativistic effects, not in electromagnetic waves, where electromagnetic waves move at the speed (c). Therefore, at the speed (c) there will be no clock to measure the time for massless photon. Refer here -

Chapter Time distortion occurs only in clocks with mass under relativistic ... 

Necessarily such relative velocities, in special relativity, are less than the speed of light (c). However, at the speed of light (c), there will be no time dilation, because electromagnetic waves traveling at the speed of (c) do not have time dilation, but there is a propagation delay in (c).

Also, in (c) motion there will be no clock to measure relative time.

From the relativistic mass equation, it can be seen that as the object accelerates faster and faster, its mass becomes larger and larger. However, consider that such mass must be between and less than the speed of light (c), because at speed (c) there would be no clock to measure relative time. But (c) has propagation delay.

Therefore, your mathematical representation of the mass m0 in the equation {m = m0/√(1 − v2/c2)}, when v = c, is an incorrect approach in mathematics and also in special relativity.

The reason is that the equation, which you mentioned in your paper, does not apply when you consider a speed v = c.

Also, at a speed (c), m0 is no longer mass, but energy.