Curvature versus Expansion: Both Relativistic Observations of Space

[Maartenn100]

Curvature versus Expansion: Both Relativistic Observations of Space

We observe the deflection of light around massive objects.

Light bends due to the curvature of spacetime around those masses according to the General Theory of Relativity (Einstein's General Relativity);
From its own perspective, this photon follows the straightest path from A to B.
From our perspective, spacetime there is curved, and the Light follows a curved path.

To itself, there are no curved paths in time and space for objects over there. Just as the photon thinks of itself. From its own perspective, the paths are straight through time and space for every object within that spacetime sphere of that massive object.

We, external observers, however, have a relatively faster ticking clock than the clock within that spacetime curved by those heavier masses for us.

The spacetime there is curved, relative to our spacetime within our weaker gravitational field.

So, when we see a gravitational field heavier than ours from here, we see a more curved spacetime there, relative to our less curved and, according to us, 'uncurved spacetime', which we take as a reference frame for curved spacetime: objects there follow a curved path, relative to our path.

What happens then when we see a gravitational field lighter than ours from within our gravitational field?

Then straight paths should become straighter than ours, but 'straighter than straight' is not possible.

What is the reverse equivalent of following a curved path in a more curved spacetime?

One will see space expanding between objects in a less curved spacetime than that of the observer.
The expansion of space in the cosmos is the reverse equivalent of curvature.


The reverse of a curved spacetime is an expanding spacetime when we observe a gravitational field weaker than ours.

Both are relativistic observations of space.

Edited March 22 by Maartenn100

[KJW]

It is commonly assumed that straightness in curved spacetime is a modified form of straightness and not a true form of straightness. And the Christoffel symbol in the formulae for straightness doesn't help to dispel that view. But along any spacetime trajectory in an arbitrary spacetime, a Minkowskian coordinate system can be applied, and in that local coordinate system, a straight line is truly straight in the ordinary sense.

A spacetime trajectory that is straight in spacetime may appear curved to us because we are assuming a flat spacetime. In other words, we have made an error in our assumptions about the spacetime, the apparently curved trajectory being the manifestation of this error. If one considers the orbit of a planet around the sun to be a trajectory in spacetime, where the distances in the time direction are very large compared to the distances in space, then the trajectory of the planet in spacetime doesn't appear to be very curved at all. Also, if the trajectory of the planet in spacetime is projected onto a three-dimensional space, then the trajectory in the three-dimensional space will be curved. But that curvature is because all consideration of the time dimension has been removed.

 

 

Edited March 22 by KJW

[Mordred]

This is oft something poorly understood. Geodesic paths are never truly straight nor smoothly curved. You learn to understand this via the Principle of least action which further applies calculus of variations. 

 Take for example a thrown ball. At each infinitesimal of its flight, there will be variations in its direction. Those variations will result from the principle of least action. The geodesic path is the extremum of those variations. A common misunderstanding also includes trying to think in terms of 3d space which under graph vs a 4d spacetime graph can have rather surprising results. For example that thrown ball  lets say you throw it a height of 20 meters and a distance of 10 meters on a 3d graph it would be a curved arced path. However lets say it took 1 second to travel there and 1 second back. Under a Minkowskii spacetime diagram using the interval (ct) you will find  that the path is incredibly straight.  Now further apply Interval (ct) to your different observers under the Minkowskii spacetime diagrams

Edited March 23 by Mordred

[Maartenn100]

But isn't it logical that when there is no universal clock, (no universal reference frame for time) there is also no universal reference frame for space?

There is no universal ruler.

And from that principle of relativity of space, can we logically infer that everything concerning space, absolutely everything, is also relative? Any theory that contradicts this must be flawed somewhere.

That everything we see happening with space is a relativistic observation?

(like the expansion of space far away (redshift of emitted light of distant galaxies.) 

 

There are referenceframes where the age of the universe is zero. And there is no prefered referenceframe for time in the universe.

So, there are referenceframes where 'space' = zero too. And there are no preferred referenceframes for space in the universe.

 

So, why scientists keep talking about an absolute universe with an absolute age and an absolute amount of expanded space at every moment?

Edited March 23 by Maartenn100

[Mordred]

33 minutes ago, Maartenn100 said:

But isn't it logical that when there is no universal clock, (no universal reference frame for time) there is also no universal reference frame for space?

There is no universal ruler.

And from that principle of relativity of space, can we logically infer that everything concerning space, absolutely everything, is also relative? Any theory that contradicts this must be flawed somewhere.

That everything we see happening with space is a relativistic observation?

(like the expansion of space far away (redshift of emitted light of distant galaxies.) 

 

Under GR every observer and event is inertial. There is no at rest frame. All frames of reference are also equally correct, there is no preferred frame of reference. Yes everything we see or measure is relative to the observer. However that was even true prior to GR/SR under Galilean relativity. That in and of itself is nothing new and has been understood for centuries. They key difference is time is absolute Under Galilean relativity. 

Edited March 23 by Mordred

[Maartenn100]

27 minutes ago, Mordred said:

Under GR every observer and event is inertial. There is no at rest frame. All frames of reference are also equally correct, there is no preferred frame of reference. Yes everything we see or measure is relative to the observer. However that was even true prior to GR/SR under Galilean relativity. That in and of itself is nothing new and has been understood for centuries. They key difference is time is absolute Under Galilean relativity. 

So, why are scientists still talking as if we live in an absolute universe with an absolute age (time) and an absolute amount of expanded space at any moment? 

Quote

 Yes everything we see or measure is relative to the observer. However that was even true prior to GR/SR under Galilean relativity. That in and of itself is nothing new and has been understood for centuries. 

So, why is this topic under 'speculations'? Or it is speculation or it is nothing new. It can't be both true.

Edited March 23 by Maartenn100

[Maartenn100]

I have the following question:

Imagine you are in a spaceship that is approaching the speed of light very closely. Normally, according to the theory of special relativity, you would see the space between you and the next planet you are traveling to shrink (length contraction). And then see it expand again as you decelerate.

Suppose you are traveling very close to the speed of light towards a galaxy that is moving away from us due to the so-called expansion of the universe. What happens then to the space in between? Does it shrink or does it actually expand? Is the observer in the spaceship correct in saying that the universe is contracting in one direction (lengthcontraction due to high speed near the speed of light)? Or are we right from Earth, claiming that the entire space in the entire universe is expanding as a whole?

You too easily ignore that the absoluteness of space expansion according to the Big Bang theory was refuted by the very precise measurements of the James Webb Telescope and the very precise measurements of the ESA satellite, which differed from each other. The only explanation is that different observers perceive this space expansion differently. Relativity of space-observations.

[swansont]

3 hours ago, Maartenn100 said:

So, why is this topic under 'speculations'?

Because you are presenting a pet theory of yours.

[Bufofrog]

1 hour ago, Maartenn100 said:

Is the observer in the spaceship correct in saying that the universe is contracting in one direction (lengthcontraction due to high speed near the speed of light)? Or are we right from Earth, claiming that the entire space in the entire universe is expanding as a whole?

They are both correct.

[Maartenn100]

35 minutes ago, Bufofrog said:

They are both correct.

I agree. And that's why, in my opinion, you can not make absolute statements about the state of the universe in itself. Different observers will disagree on the expansion.

Like James Web Telescope and ESA Planck Satelite disagree on the speed of expansion, even if they are both very accurate observers.

 

Edited March 23 by Maartenn100

[Mordred]

5 hours ago, Maartenn100 said:

I have the following question:

Imagine you are in a spaceship that is approaching the speed of light very closely. Normally, according to the theory of special relativity, you would see the space between you and the next planet you are traveling to shrink (length contraction). And then see it expand again as you decelerate.

Suppose you are traveling very close to the speed of light towards a galaxy that is moving away from us due to the so-called expansion of the universe. What happens then to the space in between? Does it shrink or does it actually expand? Is the observer in the spaceship correct in saying that the universe is contracting in one direction (lengthcontraction due to high speed near the speed of light)? Or are we right from Earth, claiming that the entire space in the entire universe is expanding as a whole?

You too easily ignore that the absoluteness of space expansion according to the Big Bang theory was refuted by the very precise measurements of the James Webb Telescope and the very precise measurements of the ESA satellite, which differed from each other. The only explanation is that different observers perceive this space expansion differently. Relativity of space-observations.

Don't pay to much attention to the pop media coverage of findings from the James Webb telescope for starters. No result from the James Webb telescope tells us that the universe isn't expanding.  

lets look at your scenario for a second, Expansion is roughly 70 km/Mpc/sec. That is extremely slow relative to the speed of light, especially considering that a single Mpc has roughly \[ 3.262*10^6\] light years.  It is only at extreme distance that expansion becomes measurable, also it only occurs in regions that is not gravitationally bound.

The evidence of an expanding universe occurs in a great deal of observational evidence. For example the CMB wouldn't even exist if expansion didn't occur. The temperature history which shows the universe cooling down as a direct result of expansion and how it applies to the ideal gas laws is another key piece of evidence. Cosmological redshift is another but certainly not the only piece of evidence

Edited March 23 by Mordred

[Maartenn100]

1 hour ago, Mordred said:

Don't pay to much attention to the pop media coverage of findings from the James Webb telescope for starters. No result from the James Webb telescope tells us that the universe isn't expanding.  

lets look at your scenario for a second, Expansion is roughly 70 km/Mpc/sec. That is extremely slow relative to the speed of light, especially considering that a single Mpc has roughly

3.262∗106

light years.  It is only at extreme distance that expansion becomes measurable, also it only occurs in regions that is not gravitationally bound.

 

The evidence of an expanding universe occurs in a great deal of observational evidence. For example the CMB wouldn't even exist if expansion didn't occur. The temperature history which shows the universe cooling down as a direct result of expansion and how it applies to the ideal gas laws is another key piece of evidence. Cosmological redshift is another but certainly not the only piece of evidence

yes, I agree with the expansion. Only, I think, it's a relativistic observation of space, not an expansion of the universe in itself.

I think we should take a foton as a standard observer. It has absolute properties: for every observer a foton travels the same speed. 

A foton in vacuum can tell us something about the propereties of the universe in itself, without observers. It can give us absolute values (= not relative) about the universe in itself without having to avarage it out.

Edited March 23 by Maartenn100

[Mordred]

All observations are calibrated to include any relativistic effects. The evidence of expansion goes well beyond simply relativistic effects. They also go beyond those involved in cosmological redshift. These methods include those such as interstellar parallax, the various methods are collectively called the cosmological distance ladder.

https://en.wikipedia.org/wiki/Cosmic_distance_ladder

 

Physicist can never rely on any single methodology in any given observation or experiment. In order to become Robust any theory must match any number of experimental and observational evidence.

As far as the Hubble contention, there is ongoing evidence supporting that our local region is under-dense which has ramifications with regards to the near and far Hubble rates. This is something not mentioned in pop medial coverage of the JW telescope findings

here is the related paper

https://arxiv.org/abs/1907.12402

here is a later counter paper

https://arxiv.org/abs/2110.04226

I post these to show other ongoing research beyond what you see in pop media. As shown there are other possibilities for the contention that go beyond claims of LCDM being incorrect or the BB itself. One thing most people also are not aware of is that the Hubble constant evolves over time. We call it a constant strictly in the historical sense. It isn't constant over time but merely constant everywhere at a given time. It should really be treated as simply a parameter. 

The Hubble parameter itself is in actuality decreasing in time in our Universe  evolution history.

the formula as a function of redshift is given by

\[H_z=H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}}\]

this formula accounts for how matter density, radiation density and the Cosmological constant evolves overtime and its subsequent effects on our universe expansion rates. To understand how this formula is derived you would also require the equations of state for each which are a direct result of thermodynamics under the ideal gas laws. 

https://en.wikipedia.org/wiki/Equation_of_state_(cosmology)

these equations of state are further applied to the FLRW deceleration oft call acceleration equation.

https://en.wikipedia.org/wiki/Friedmann_equations

included in last link. That link also ties into the first link.

You will note that relativity is inclusive the GR EFE equation used is in the Newtonian limit. Here is the route to the equation.

FLRW Metric equations

\[d{s^2}=-{c^2}d{t^2}+a({t^2})[d{r^2}+{S,k}{(r)^2}d\Omega^2]\]

\[S\kappa(r)= \begin{cases} R sin(r/R &(k=+1)\\ r &(k=0)\\ R sin(r/R) &(k=-1) \end {cases}\]

\[\rho_{crit} = \frac{3c^2H^2}{8\pi G}\]

\[H^2=(\frac{\dot{a}}{a})^2=\frac{8 \pi G}{3}\rho+\frac{\Lambda}{3}-\frac{k}{a^2}\]

setting \[T^{\mu\nu}_\nu=0\] gives the energy stress mometum tensor as 

\[T^{\mu\nu}=pg^{\mu\nu}+(p=\rho)U^\mu U^\nu)\]

\[T^{\mu\nu}_\nu\sim\frac{d}{dt}(\rho a^3)+p(\frac{d}{dt}(a^3)=0\]

which describes the conservation of energy of a perfect fluid in commoving coordinates describes by the scale factor a with curvature term K=0.

the related GR solution the the above will be the Newton approximation.

\[G_{\mu\nu}=\eta_{\mu\nu}+H_{\mu\nu}=\eta_{\mu\nu}dx^{\mu}dx^{\nu}\]

Thermodynamics

Tds=DU+pDV Adiabatic and isentropic fluid (closed system)

equation of state

\[w=\frac{\rho}{p}\sim p=\omega\rho\]

\[\frac{d}{d}(\rho a^3)=-p\frac{d}{dt}(a^3)=-3H\omega(\rho a^3)\]

as radiation equation of state is

\[p_R=\rho_R/3\equiv \omega=1/3 \]

radiation density in thermal equilibrium is therefore

\[\rho_R=\frac{\pi^2}{30}{g_{*S}=\sum_{i=bosons}gi(\frac{T_i}{T})^3+\frac{7}{8}\sum_{i=fermions}gi(\frac{T_i}{T})}^3 \]

\[S=\frac{2\pi^2}{45}g_{*s}(at)^3=constant\]

temperature scales inversely to the scale factor giving

\[T=T_O(1+z)\]

with the density evolution of radiation, matter and Lambda given as a function of z

\[H_z=H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}}\]

 

This I already had posted on this site under a thread I currently have underway regarding nucleosynthesis in our expanding universe and an examination of the various processes as a result.

https://www.scienceforums.net/topic/128332-early-universe-nucleosynthesis/

The only reason I posted this thread in Speculations is that I wish to maintain the Privilege of toy modelling. However every single formula in that thread are commonly used and are main concordance formulas. 

 

Edited March 24 by Mordred

[Maartenn100]

ok, thank you very much. I appreciate your effort. I don't know enough about these formula to understand it properly. My idea is wrong then.

[Mordred]

Your idea of considering the effects of relativity in regards to expansion related measurements is something that has already been examined so take heart in that. 

edit 

I should add that one of the biggest pieces of evidence of our expanding history is its metallicity history. Factors such as the density of hydrogen, lithium etc in our evolution history. The Saha equations in the nucleosynthesis link apply there. As well as the Bose_Einstein and Fermi-Dirac statistics.

 

Edited March 23 by Mordred

[Maartenn100]

1 hour ago, Mordred said:

Your idea of considering the effects of relativity in regards to expansion related measurements is something that has already been examined so take heart in that. 

edit 

I should add that one of the biggest pieces of evidence of our expanding history is its metallicity history. Factors such as the density of hydrogen, lithium etc in our evolution history. The Saha equations in the nucleosynthesis link apply there. As well as the Bose_Einstein and Fermi-Dirac statistics.

 

ok, thanks. Finally someone who explains this with patience without offending people. Thank you.

[Maartenn100]

15 hours ago, Mordred said:

Your idea of considering the effects of relativity in regards to expansion related measurements is something that has already been examined so take heart in that. 

 

Do you know who examined the concept of the relativity of 'expansion', the reasoning behind their ideas, and why they were ultimately disproven? I'd like to understand why these ideas were considered incorrect. Thanks. Additionally, out of curiosity, I'm interested in learning more about the individual who first explored this idea and their rationale. 

Edited March 24 by Maartenn100

[Maartenn100]

I will explain my idea and where it's coming from, even when it is wrong, so you understand the reasoning behind it:

 

If we throw a ball in the air, and it falls down further away, it follows a bell curve in the air. 

According to GRT, it's a straight line in curved space. (and time).

According to the ball's perspective, it's a straight line.

But we, observers of space and time, we have a particular idea of a straight line, even in curved spacetime here.

To us, the path of the ball is a bell curve, and our idea of straight uncuved and unstretched ruler is different from this bell curve of the ball, following it's trajectory through curved space.

 

Well, it's this particular ruler of ours, this particular idea of a straight uncurved and unexpanded path, within a curved spacetime environment like the vicinity of Earth, the Sun, the Milkyway and clusters of galaxies that we see 'expanded', when we observe the redshift of the light of galaxies moving away from us, far way, according to Hubble's Law.

 

Our particular idea of a straight line, as observers, is observed as stretched or expanded in spaces that are less curved then our space(time).

 

That's a matter of perception. Even if the metric of the universe in itself is expanding, our particular idea of a straight line is observed as being stretched in less curved spaces than ours, because we have a particular idea of a straight ruler, an idea of a straight uncurved and unstretched ruler in our curved spacetime environment(s).

 

Compare it with a clock. To us, time flows 'normal'. But in reality, time is dilated by the curvature of spacetime due to the mass of Earth, the mass of the Sun and the mass of the Milkeyway, the mass of the clusters of galaxies etc.

But we 'observe' time normal. And it is this particular idea of time and this particular idea of a straight line in our curved spacetime environment that makes us see expanded straight lines somewhere else, as observers.

So, in my opinion,

this expansion of space, we observe, is a matter of perception or perspective from the point of view of an observer in a curved spacetime environment, watching objects in a less curved spacetime environment following a straight line.

Even if the universe is expanding in itself.   Personally, I believe that the universe in itself, without observers has properties of time and space that you can deduce based on an object that is absolute, like a photon in vacuum. For every observer it has the same values. So it can tell us something about the absolute (non-relative) nature of the universe in itself.

 

  

 

Edited March 24 by Maartenn100

[Maartenn100]

 I don't want to change the science of ART. I'm not capable of doing that!

Only the interpretation to explain that science is different. The observed expansion is, for me, an observed expansion of our private ruler and not of the metric of the universe itself.

Because when you want to know properties of the universe by itself, you have to look at an object that has the same properties for all observers: a photon in vacuum. Well, take that as a reference frame to posit things about the universe itself, without observers.

You want to know something about space and time about the universe itself, independent of observers. Ask a photon in vacuum. A photon has absolute properties (not relative) for all observers. It can tell us something about the universe that is the same for all observers. The mathematics and science for it already exist.

So, this is just a different interpretation of the existing scientific truths. Nothing changes about the science, but something changes about the interpretation of expanding space and what the universe without observers means by looking at a photon in vacuum.

This is a matter of interpretation, not of science, because the science and math are the same:

 

If you want to find something that all observers agree on, it's the properties of a photon in a vacuum. And as strange as it may sound: according to a photon, the actual age of the universe, and thus the real time in the universe, is ZERO.

t' = (t - vx/c^2) / sqrt(1 - v^2/c^2) = 0

Time, just like space, is a property of observation. Not a property of the universe itself.

Edited March 24 by Maartenn100

[Mordred]

7 hours ago, Maartenn100 said:

Do you know who examined the concept of the relativity of 'expansion', the reasoning behind their ideas, and why they were ultimately disproven? I'd like to understand why these ideas were considered incorrect. Thanks. Additionally, out of curiosity, I'm interested in learning more about the individual who first explored this idea and their rationale. 

It isn't any one individual but rather the scientific community. Lets do a bit of history.  The FLRW metric allows for positive, negative and flat spacetimes.

\[d{s^2}=-{c^2}d{t^2}+a({t^2})[d{r^2}+{S,k}{(r)^2}d\Omega^2]\]

\[S\kappa(r)= \begin{cases} R sin(r/R &(k=+1)\\ r &(k=0)\\ R sin(r/R) &(k=-1) \end {cases}\]

in the above equation k is the curvature term. Historically even after Hubble discovered the universe was expanding we still could not confirm whether or universe had curved or flat spacetime on the global mass distribution. This was a point of contention all the way up to the early 90's. We did not know the universe geometry in this aspect. However we knew that curved spacetime  causes visual distortions.   

 To understand this lets examine how those distortions would occur. If you take two parallel laser beams as the beams travel through spacetime you can have 3 results. If the beams remain parallel then the spacetime the beams travelled through is flat and have a Euclidean geometry with no overall time dilation effect. In this case you would have no distortions. However If the beams converge then you have a positive curvature and you would get distortions. The same would occur if you have negative curvature. To easily understand how this curvature affects images all one has to do is look through a convex or concave lens. 

 Clear examples are gravitational lensing and the Einstein Ring around massive objects.

How does this knowledge help up. Well we have a very handy stellar region we can use. The CMB (Cosmic microwave background). This was one of the primary goals of the COBE satellite was to use the CMB background to search for those distortions and help determine the geometry of the universe. Unfortunately the COBE images were too blurred due to not being sensitive enough to make a conclusive determination. However the WMAP images that came later were much clearer and showed no distortions caused by curved spacetime. Later on Planck also confirmed these findings.

 We still make use of how spacetime curvature affects images, redshift, luminosity etc to this very day. A great deal of the furthest distance that Hubble viewed was through usage of intervening gravitational lenses. In point of detail Hubble couldn't get many of its images without using gravitational lenses. We also use spacetime curvature to look for under dense and over dense regions using the Sache Wolfe effect. (this is an application of redshift).

 

Now I want to consider one further detail. You cannot have curvature if the mass distribution is uniform. You can only get curvature by having regions with higher or lower mass densities. The reason I mention this is this is another examination. There is a relation between the luminosity and mass

https://en.wikipedia.org/wiki/Mass–luminosity_relation

with this tool we can further look for the mass distribution as a further confirmation.

further details of universe geometry can be found here

http://cosmology101.wikidot.com/universe-geometry

page two further details on what effect curvature has on angles Pythagorus theorem is only accurate in flat spacetime and requires corrections in curved spacetime.

http://cosmology101.wikidot.com/geometry-flrw-metric/

that is one of the effects of length contraction you mentioned above. So once again we can look for this effect.

 

Edited March 24 by Mordred

[Maartenn100]

Thank you.

 

But do you agree with the following statement:

we can disagree on the measured distances (space)

But we always agree on the calculated spacetimedistances.

 

Spacetimedistances are calculated or deduced. Distances in space can be measured with lasers for example.

The measured spaces are always relative, but the deduced (not observable) spacetimedistances are absoluut.

 

So: every observed expansion of space is a relativistic observation of space.

We cannot observe spacetime. (the universe in itself) We can only deduce it.

 

Is that true?

Edited March 24 by Maartenn100

[swansont]

12 minutes ago, Maartenn100 said:

Distances in space can be measured with lasers for example

I don’t think lasers are used to measure anything outside of our solar system. Certainly nothing where relativity is a factor. We get distances from the light that comes from the entity being measured, and those aren’t lasers.

[Mordred]

1 hour ago, Maartenn100 said:

Thank you.

 

But do you agree with the following statement:

we can disagree on the measured distances (space)

But we always agree on the calculated spacetimedistances.

 

Spacetimedistances are calculated or deduced. Distances in space can be measured with lasers for example.

The measured spaces are always relative, but the deduced (not observable) spacetimedistances are absoluut.

 

So: every observed expansion of space is a relativistic observation of space.

We cannot observe spacetime. (the universe in itself) We can only deduce it.

 

Is that true?

Your sort of on the right track. In cosmology we have to make certain adjustments due to expansion as well as relativity. So we have a couple of different distances. We have the commoving distance as well as the proper distance. The proper distance is the invariant distance (same for all observers).

 

The wiki coverage isn't bad, not nearly as good as a textbook but it will do in this case.

https://en.wikipedia.org/wiki/Comoving_and_proper_distances

The Lineweaver and Davies article in the link below has a handy graph of both commoving distance and proper distance.

page 8

https://arxiv.org/pdf/astro-ph/0402278v1.pdf

 

below is a copy from the calculator in my signature. All calculations are in Proper distance. The row 0.000 is time now rows after that are in the future while rows previous to that is in our past up till the CMB. I can set the calculator to examine prior to that but for this purpose its unnecessary. Included is the distance to the particle horizon aka the Cosmological event horizon 

 

\[{\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline z&Scale (a)&S&T (Gy)&R (Gly)&D_{now} (Gly)&D_{then}(Gly)&D_{hor}(Gly)&D_{par}(Gly)&H(t) \\ \hline 1.09e+3&9.17e-4&1.09e+3&3.72e-4&6.27e-4&4.53e+1&4.16e-2&5.67e-2&8.52e-4&1.55e+6\\ \hline 7.39e+2&1.35e-3&7.40e+2&7.10e-4&1.17e-3&4.50e+1&6.09e-2&8.33e-2&1.66e-3&8.32e+5\\ \hline 5.01e+2&1.99e-3&5.02e+2&1.34e-3&2.16e-3&4.47e+1&8.91e-2&1.22e-1&3.20e-3&4.51e+5\\ \hline 3.39e+2&2.94e-3&3.40e+2&2.49e-3&3.95e-3&4.42e+1&1.30e-1&1.79e-1&6.11e-3&2.46e+5\\ \hline 2.30e+2&4.34e-3&2.31e+2&4.59e-3&7.18e-3&4.36e+1&1.89e-1&2.61e-1&1.15e-2&1.36e+5\\ \hline 1.55e+2&6.40e-3&1.56e+2&8.40e-3&1.30e-2&4.29e+1&2.74e-1&3.80e-1&2.16e-2&7.49e+4\\ \hline 1.05e+2&9.44e-3&1.06e+2&1.53e-2&2.34e-2&4.20e+1&3.97e-1&5.53e-1&4.01e-2&4.15e+4\\ \hline 7.09e+1&1.39e-2&7.19e+1&2.77e-2&4.22e-2&4.10e+1&5.70e-1&8.00e-1&7.40e-2&2.31e+4\\ \hline 4.77e+1&2.05e-2&4.87e+1&5.00e-2&7.58e-2&3.97e+1&8.14e-1&1.15e+0&1.36e-1&1.28e+4\\ \hline 3.20e+1&3.03e-2&3.30e+1&9.01e-2&1.36e-1&3.81e+1&1.15e+0&1.65e+0&2.48e-1&7.15e+3\\ \hline 2.14e+1&4.47e-2&2.24e+1&1.62e-1&2.44e-1&3.61e+1&1.61e+0&2.35e+0&4.53e-1&3.98e+3\\ \hline 1.42e+1&6.59e-2&1.52e+1&2.91e-1&4.38e-1&3.38e+1&2.23e+0&3.31e+0&8.22e-1&2.22e+3\\ \hline 9.29e+0&9.71e-2&1.03e+1&5.22e-1&7.84e-1&3.09e+1&3.00e+0&4.61e+0&1.49e+0&1.24e+3\\ \hline 5.98e+0&1.43e-1&6.98e+0&9.35e-1&1.40e+0&2.75e+1&3.94e+0&6.31e+0&2.69e+0&6.94e+2\\ \hline 3.73e+0&2.11e-1&4.73e+0&1.67e+0&2.50e+0&2.33e+1&4.92e+0&8.42e+0&4.86e+0&3.90e+2\\ \hline 2.21e+0&3.12e-1&3.21e+0&2.98e+0&4.37e+0&1.83e+1&5.69e+0&1.09e+1&8.73e+0&2.23e+2\\ \hline 1.18e+0&4.60e-1&2.18e+0&5.21e+0&7.34e+0&1.24e+1&5.71e+0&1.33e+1&1.56e+1&1.33e+2\\ \hline 4.75e-1&6.78e-1&1.47e+0&8.79e+0&1.11e+1&6.06e+0&4.11e+0&1.53e+1&2.73e+1&8.74e+1\\ \hline 0.00e+0&1.00e+0&1.00e+0&1.38e+1&1.44e+1&0.00e+0&0.00e+0&1.65e+1&4.63e+1&6.74e+1\\ \hline -3.19e-1&1.47e+0&6.81e-1&1.97e+1&1.63e+1&4.93e+0&7.23e+0&1.71e+1&7.51e+1&5.99e+1\\ \hline -5.36e-1&2.15e+0&4.64e-1&2.61e+1&1.70e+1&8.54e+0&1.84e+1&1.72e+1&1.18e+2&5.73e+1\\ \hline -6.84e-1&3.16e+0&3.16e-1&3.27e+1&1.72e+1&1.11e+1&3.50e+1&1.73e+1&1.81e+2&5.64e+1\\ \hline -7.85e-1&4.64e+0&2.15e-1&3.94e+1&1.73e+1&1.28e+1&5.95e+1&1.73e+1&2.74e+2&5.62e+1\\ \hline -8.53e-1&6.81e+0&1.47e-1&4.60e+1&1.74e+1&1.40e+1&9.55e+1&1.74e+1&4.11e+2&5.61e+1\\ \hline -9.00e-1&1.00e+1&1.00e-1&5.27e+1&1.74e+1&1.48e+1&1.48e+2&1.74e+1&6.11e+2&5.60e+1\\ \hline -9.32e-1&1.47e+1&6.81e-2&5.93e+1&1.74e+1&1.54e+1&2.26e+2&1.74e+1&9.05e+2&5.60e+1\\ \hline -9.54e-1&2.15e+1&4.64e-2&6.60e+1&1.74e+1&1.58e+1&3.39e+2&1.74e+1&1.34e+3&5.60e+1\\ \hline -9.68e-1&3.16e+1&3.16e-2&7.27e+1&1.74e+1&1.60e+1&5.06e+2&1.74e+1&1.97e+3&5.60e+1\\ \hline -9.78e-1&4.64e+1&2.15e-2&7.93e+1&1.74e+1&1.62e+1&7.51e+2&1.74e+1&2.90e+3&5.60e+1\\ \hline -9.85e-1&6.81e+1&1.47e-2&8.60e+1&1.74e+1&1.63e+1&1.11e+3&1.74e+1&4.26e+3&5.60e+1\\ \hline -9.90e-1&1.00e+2&1.00e-2&9.27e+1&1.74e+1&1.64e+1&1.64e+3&1.74e+1&6.27e+3&5.60e+1\\ \hline \end{array}}\]

 

if your reading the correct line you will see at time now. The distance to the cosmological even horizon from our location is 46.3 Gly.

 

Edited March 24 by Mordred

[Mordred]

There is a particular section in the Lineweaver and Davies paper that is related to this discussion

"These velocities are with respect to the comoving observer who observes the receding object to have redshift, z. The GR description is written explicitly as a function of time because when we observe an object with redshift, z, we must specify the epoch at which we wish to calculate its recession velocity. For example, setting t = t0 yields the recession velocity today of the object that emitted the observed photons at tem. Setting t = tem yields the recession velocity at the time the photons were emitted (see Eqs. A.3 & A.10). The changing recession velocity of a comoving object is reflected in the changing slope of its worldline in the top panel of Fig. 1.1. There is no such time dependence in the SR relation. Despite the fact that special relativity incorrectly describes cosmological redshifts it has been used for decades to convert cosmological redshifts into velocity because the special relativistic Doppler shift formula (Eq. 2.2), shares the same low redshift approximation, v = cz, as Hubble’s Law (Fig. 2.1). It has only been in the last decade that routine observations have been deep enough that the distinction has become significant."

The First equation I posted on this thread has the terms for the corrected and currently used equation from the originally used cosmological redshift equation given below. The equation below that you see in everyday links, textbooks etc for cosmological redshift quickly becomes increasingly inaccurate at greater distances. 

\[1+Z=\frac{\lambda}{\lambda_o} or 1+Z=\frac{\lambda-\lambda_o}{\lambda_o}\] 

further details can be found here

https://arxiv.org/pdf/astro-ph/9905116.pdf

Edited March 24 by Mordred

[KJW]

3 hours ago, Maartenn100 said:

Thank you.

 

But do you agree with the following statement:

we can disagree on the measured distances (space)

But we always agree on the calculated spacetimedistances.

 

Spacetimedistances are calculated or deduced. Distances in space can be measured with lasers for example.

The measured spaces are always relative, but the deduced (not observable) spacetimedistances are absoluut.

 

So: every observed expansion of space is a relativistic observation of space.

We cannot observe spacetime. (the universe in itself) We can only deduce it.

 

Is that true?

There seems to be confusion about the nature of general relativity, conflating it with special relativity. In special relativity, one speaks of measurements by different observers, leading to such notions as time dilation, length contraction, relativistic mass, etc. General relativity isn't like that. In general relativity, one may consider different coordinate systems. Coordinate systems are not necessarily the perspective of any observer. Therefore, there isn't the question of whether different observers agree about some notion in general relativity. For example, one often specifies a spacetime using a metric. Everyone agrees on the metric, but no one regards the metric as THE metric, because one can coordinate-transform the metric to some other equally valid metric. All coordinate systems are equally valid in general relativity. One can construct a metric based on a particular observer, but this is no more valid than any other metric obtainable via a coordinate transformation, even if such a metric is not based on any observer. Some metrics may be preferable to other metrics for practical reasons, such as manifesting inherent symmetries of the spacetime, but even in such cases, all the possible metrics obtainable by a coordinate transformation are equally valid.

In general relativity, one may determine the distance between two points in spacetime along some curve between them. Although the specification of the two points and the curve between them may vary according to the coordinate system, in all coordinate systems the distance will be the same. This is also true in a proper treatment of special relativity. But unfortunately, much of the confusion regarding special relativity occurs because one is not dealing with points in spacetime, but is trying to deal with space and time separately. It is my impression that many people think that motion distorts space and time. The formulae that usually introduce people to special relativity give that impression, but seeing special relativity in terms of four-dimensional Minkowskian spacetime provides clarity to the nature of relativity.

 

 

Edited March 24 by KJW