Distance is a scalar representing the length of a traveled path. Displacement is the length of the straight line (a vector) connecting start and end points.
In a Euclidean plane, they appear to be described by the same number of units.
Light travels in a straight line, analogous to the straight line in a plane.
Is displacement measured using luminosity equal to the corresponding cosmological distance?
Are there experiments? Are there theoretical proofs? Are there articles about this? What are the cites?
The question implicitly raises the question whether space is Euclidean. If it is uncertain whether cosmological space is Euclidean, then it is uncertain whether what applies to Euclidean distance and displacement generalizes to cosmological space.
Distance is a scalar representing the length of a traveled path. Displacement is the length of the straight line (a vector) connecting In a Euclidean plane, they appear to be described by the same number of units.
Light travels in a straight line, analogous to the straight line in a plane.
Is displacement measured using luminosity equal to the corresponding cosmological distance?
Displacement in the context of cosmology, particularly when measured using luminosity, is generally referred to as the "luminosity
Luminosity Distance and Cosmological Distance:
Luminosity distance (D_L) is derived from the inverse-square law of light, which states that the observed flux of an object decreas
D_L = (L / (4πF))^1/2
where L is the intrinsic luminosity of the object and F is the observed flux. This measure accounts for the expansion of the universe.
Experiments and Observations
Several experiments and observational techniques have been employed to measure cosmological distances using luminosity. These include:
1. Type Ia Supernovae: These are standard candles used to measure distances across the universe.
The relationship between their intrinsic luminosity and observed brightness allows for precise distance measurements [oai_citation:3,[1511.07459] Calculating Luminosity Distance versus Redshift in FLRW Cosmology via Homotopy Perturbation Method](https://ar5iv.org/pdf/1511.07459v2).
2. Cepheid Variables:
These pulsating stars have a well-defined period-luminosity relationship, making them useful for determining distances to nearby galaxies [oai_citation:4,Cosmology Tutorial - Part 2](https://www.astro.ucla.edu/~wright/cosmo_02.htm).
3. Radio-loud Quasars:
Recent studies use the X-ray luminosity of radio-loud quasars to establish a correlation with their optical and UV luminosity, providing another method to measure cosmological distances [oai_citation:5,[2207.08390] A cosmological distance measure using radio-loud quasars](https://ar5iv.org/abs/2207.08390).
Key Articles and Proofs
Several key papers and articles discuss these concepts in detail. Notable works include those on the cosmological distance ladder, which outlines the methods for measuring distances in astronomy, and the use of radio-loud quasars for cosmological measurements.
Additionally, theoretical proofs and derivations of the relationships between different distance measures are well-documented in cosmological literature
- [oai_citation:7,[2112.11567] Hubble distancing: Focusing on distance measurements in cosmology](https://ar5iv.org/pdf/2112.11567) [oai_citation:8,[2207.08390] A cosmological distance measure using radio-loud quasars](https://ar5iv.org/abs/2207.08390) [oai_citation:9,Testing cosmological models with the brightness profile of distant galaxies | Astrophysics and Space Science](https://link.springer.com/article/10.1007/s10509-021-04016-3) [oai_citation:10,[1511.07459] Calculating Luminosity Distance versus Redshift in FLRW Cosmology via Homotopy Perturbation Method](https://ar5iv.org/pdf/1511.07459v2).
For further reading, you can refer to:
- "Hubble distancing: Focusing on distance measurements in cosmology" on arXiv
- "A cosmological distance measure using radio-loud quasars" on arXiv
- Cosmology tutorials from the University of California, Los Angeles (UCLA)
- Detailed articles on distance measures in cosmology from sources like SpringerLink and Astrophysics and Space Science
hope this helps
H
Dear Professor Shour,
This is a good question.
The answer is simply that "distance" is "distance" as normally understood.
There is no Special Relativity and no General Relativity, because there is no "spacetime". The Lorentz relations (light cone &c.) describe the offsets and corrections to the light rays -only-, such that space and time are left Absolute.
The reason why we know, for certain, that we have an Absolute character to space and time, is because the "Relativity of Simultaneity" has been demonstrated to be a logical impossibility. Confer above and below, tilting-mirror demonstration, and also the proof by Kılıç (2005) :
Preprint Precis of the proof we have an Absolute character to time an...
Article The incompatibility of Einstein's relativity of simultaneity...
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