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I know where the relation comes from, but cannot see its physical meaning.

Thank you

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- Thread starter AlephClo
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- #1

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I know where the relation comes from, but cannot see its physical meaning.

Thank you

- #2

Chalnoth

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Just to make sure I get it right. For 2 photons (photon-1 z=1.59 and photon-2 z=1.61) with the same proper distance at emission time, but with small delta z (0.01) relative to the maximum (z= 1.6), the one with z=1.59 would have to travel more distance for the extra 0.01 due to faster Universe expansion at that time, than the extra distance due to the extra 0.01 for the photon with 1.61 because Universe expansion was not as sever at that later time.

Thank you AlphaClo

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Chalnoth

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First, for the distance a photon has traveled, you can trivially use the light travel time, which is by definition equal to the distance along the path the photon traveled. So a higher-redshift photon will always travel a larger distance, because light travel time does monotonically increase with redshift. So the z=1.61 photon is guaranteed to travel a longer distance.

Now, a caveat: I'm not certain that the fact that photons at high redshifts recede from us before moving toward us later changes over at exactly the same redshift that is also the maximum distance. This is a conceptual tool that can be used to understand what's going on, but it isn't necessarily exact. I would have to look into it in a bit more detail to be sure.

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I agree that the photon with 1.61 will travel more than the 1.59. Sorry I did not expressed myself clearly.

Using a matter-lambda-no curvature model where the time of emission = 13.5Gyears * (1+z) to the -3/2

the travel time only for z = 0.01 gives:

1) for the photon-1 z=1.59 a travel time of 0.196 Gyr

2) for the photon-1 z-1.61 a travel time of 0.177 Gyr

Obviously photon-2 has to travel an extra 0.02 (1.61 - 1.59) than photon-1.

Thank you AlephClo

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Chalnoth

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marcus

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I think the changeover between photon losing ground (proper distance increasing) and approaching (distance decreasing) happens the redshift (about 1.6) where you also get the...I'm not certain that the fact that photons at high redshifts recede from us before moving toward us later changes over at exactly the same redshift that is also the maximum distance. This is a conceptual tool that can be used to understand what's going on, but it isn't necessarily exact. I would have to look into it in a bit more detail to be sure.

You may have miscalculated, Chal. For an object we see at z = 1.6, the recession speed at the time of emission is c, . That's why the light emitted in our direction is stalled between losing and gaining ground. At the time it is emitted, it just barely manages to hold its ground.

[tex]{\scriptsize\begin{array}{|c|c|c|c|c|c|}\hline R_{0} (Gly) & R_{\infty} (Gly) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14.4&17.3&3400&67.9&0.693&0.307\\ \hline \end{array}}[/tex] [tex]{\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline a=1/S&S&T (Gy)&R (Gly)&D_{now} (Gly)&D_{then}(Gly)&D_{hor}(Gly)&V_{now} (c)&V_{then} (c) \\ \hline 0.385&2.600&4.0442&5.8333&15.177&5.837&12.179&1.05&1.00\\ \hline 0.423&2.363&4.6381&6.6088&13.706&5.800&12.777&0.95&0.88\\ \hline 0.466&2.148&5.3092&7.4492&12.195&5.678&13.355&0.85&0.76\\ \hline 0.512&1.952&6.0634&8.3444&10.652&5.457&13.903&0.74&0.65\\ \hline 0.564&1.774&6.9052&9.2789&9.086&5.121&14.414&0.63&0.55\\ \hline 0.620&1.612&7.8372&10.2316&7.510&4.658&14.882&0.52&0.46\\ \hline 0.682&1.466&8.8602&11.1774&5.938&4.052&15.302&0.41&0.36\\ \hline 0.751&1.332&9.9721&12.0895&4.385&3.292&15.670&0.30&0.27\\ \hline 0.826&1.211&11.1686&12.9430&2.866&2.367&15.986&0.20&0.18\\ \hline 0.909&1.100&12.4430&13.7175&1.395&1.268&16.253&0.10&0.09\\ \hline 1.000&1.000&13.7872&14.3999&0.000&0.000&16.472&0.00&0.00\\ \hline \end{array}}[/tex]

http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7/LightCone.html

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marcus

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AlephClo,

Lightcone calculator calls the proper distance at time of emission the "distance then" or D_{then}

The maximum proper distance at time of emission is about 5.8 Gly and the time of emission, you can see, is around year 4 billion. You can say the light travel time was therefore around 9.7 billion years.

A good way to picture the teardrop shape of the lightcone with its maximum bulge, its maximum girth, at z = 1.6 is to look at the TOP PANEL

of Lineweaver Figure 1. The widest point in the lightcone comes just exactly where the Hubble radius crosses it. Hubble radius is where recession speed equals c. You may need to enlarge the top panel to see that the "hubble sphere" line crosses the lightcone curve exactly where the latter is vertical---the light cone's widest point. The lightcone curve shows the career of a photon that is trying to reach us and finally does, at the present time. If it starts earlier (before year 4 billion) it is at first swept back by expanding distance, until it reaches proper distance 5.8 Gly and then it begins to make headway towards us.

Lightcone calculator calls the proper distance at time of emission the "distance then" or D

The maximum proper distance at time of emission is about 5.8 Gly and the time of emission, you can see, is around year 4 billion. You can say the light travel time was therefore around 9.7 billion years.

A good way to picture the teardrop shape of the lightcone with its maximum bulge, its maximum girth, at z = 1.6 is to look at the TOP PANEL

of Lineweaver Figure 1. The widest point in the lightcone comes just exactly where the Hubble radius crosses it. Hubble radius is where recession speed equals c. You may need to enlarge the top panel to see that the "hubble sphere" line crosses the lightcone curve exactly where the latter is vertical---the light cone's widest point. The lightcone curve shows the career of a photon that is trying to reach us and finally does, at the present time. If it starts earlier (before year 4 billion) it is at first swept back by expanding distance, until it reaches proper distance 5.8 Gly and then it begins to make headway towards us.

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Chalnoth

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You're right, I did miscalculate! This makes more sense now. I divided instead of multiplying.You may have miscalculated, Chal. For an object we see at z = 1.6, the recession speed at the time of emission is c, . That's why the light emitted in our direction is stalled between losing and gaining ground. At the time it is emitted, it just barely manages to hold its ground.

- #11

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Essentially, for photons at Dthen = 5,831, one was emitted at T=3.83 Gy and observed with S=2.7 while the other photon was emitted at T=4.28 Gy and observed with S= 2.5. The bottom line gives the difference between photon S=2.5 minus photon S=2.7. The middle line is about S=2.6 where a photon would receed at about the speed of light; that is what the plot shows with more details. Thank you again for your valuable inputs. AlephClo

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