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Luminosity distance 
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#1
Aug2513, 03:56 PM

P: 98

Explain the difference between distances.
Red lines indicating light travel path. Green lines indicating distance. Why there is length difference between green lines? In this diagram object moves at 0.8c away from the observer in t FOR. How far away observer in t' FOR sees an object (t FOR) when t'=3? Which green line indicates luminosity distance? I know that luminosity distance should be measured by the bottom green line. But... If the object moves away from us and we emit light for example when t=1 (in this diagram), the number of photons hitting the moving observer (t') should be proportional to the green line above by R^2 law, because it takes time for light to catch moving observer (t'). Also, luminosity distance should not depend on 3+1 rotation (velocity) at the moment when light hits it (ignoring redshift), moving observer can change his rotation just before light hits him (at t=2.9999), for example making relative velocity v=0. Here's a similar diagram where t' makes a rotation just before light hits him: speed is 0.6c in this case, and rotation just before t'=2. At t'=2, t' observer sees t 1.5 away and t=1 :) FTL, none the less. If we take that luminosity distance is not a green line below, but a green line above we get following formulas: Which is really close to what we see with the universe expansion. No configurable parameters, except time which is unavoidable. Static universe, relativistic motion. Also it explains few phenomenas how some objects (like quasars) become so big so fast. t_observed is always equal to t/(z+1) in relativistic motion. Strangely enough, the ratio between two green lines is the change of scale factor or = (z+1)=√((1+β)/(1β)) 


#2
Aug2513, 05:32 PM

PF Gold
P: 4,087

Are you talking about this
Luminosity distance  Wikipedia, the free encyclopedia or radar distance ? 


#3
Aug2513, 05:41 PM

P: 98

Yes, not radar distance. Radar distance measurements include light coming back. There is no problem with that. All according to standard relativistic understanding. For example, in first diagram, if we send a beam of light at t=1, we will receive a signal back at somewhere around t=9 and we will see a distance of around 4 and t1's time of 3, All good.



#4
Aug2513, 06:52 PM

PF Gold
P: 4,087

Luminosity distance



#5
Aug2513, 07:31 PM

P: 98

I'm arguing about, that you need doppler^2 for luminosity distances which is not standard understanding. Because there is an paradox there, simply by looking from different frame of references.



#6
Aug2513, 08:35 PM

P: 3,967

Have you taken relativistic beaming into account? This is also known as the headlamp effect. If a bright object is moving in a given direction, the light is focused towards the front due to relativistic aberration. In our case the bright objects are moving away from us and the relativistic aberration makes the photons spread out and more dilute/dimmer than a simple 1/r^2 and relativistic Doppler effect would suggest.



#7
Aug2613, 12:31 PM

P: 98

This one explains quite good:
This one looks closer, but still, i have no idea how they calculated 24.2 for z=1: My calculations show that it should be 24.775 which is way closer. Giving a 56 Glyr luminosity distance difference from the results provided here. 


#8
Aug2613, 03:32 PM

PF Gold
P: 4,087

This post belongs in the Astronomy subforum. Why don't you ask a mentor to move it ?



#9
Aug2613, 08:29 PM

P: 3,967

In the t FOR the light left the blue source at approx t=1.6 (and t'=1) and arrived at t=3 having travelled a distance of approx Δx=1.3 (The length of the lower green line.) t can estimate if the source continued at a constant speed that the source is at a distance of 2.4 units away 'now' even thought it cannot directly see it now. In the t' FOR, the light left the black source at approx t'=1.6(and t=1) and arrived at t'=3 having travelled a distance of Δx'=1.3 (This is not the length f the upper green line.) t' can estimate if the source continued at a constant speed that the source is at a distance of 2.4 units away 'now' even thought it cannot directly see it now. Δx' is obtained by drawing a line parallel to the tilted d' axis and through t=1,x=0, or by transforming the whole diagram to the t' FOR. The upper green line is the distance to the blue object when t=5 in the t FOR and not the distance as measured by the t' FOR at t'=3. If you look at the measurements I have quoted above for the t and t' FORs, you will see they are identical except for swapping the primed and unprimed variables and swapping black for blue. There is no sense of one observer being the one that is actually moving away or being the one that is actually stationary. 


#10
Aug2713, 04:05 AM

P: 98

That's exactly what i read, when i read distances. But I'm interested in luminosity distances.
Suppose t emits light when t=1, in t FOR light catches up moving object at t=5 and d=4. In t' FOR it's t'=3, d'=1.33. Let's say the number of photons hitting an object at d=1 is 1 photon per second. In t FOR the number of photons hitting the moving object is (1/16)/s due to the distance, and (1/9) due to Doppler effect, resulting in a total of (1/144). Luminosity distance is 12. t' should observe that luminosity distance. Light travel path in t' FOR is equal to the bottom green line in t FOR. In this case, light travels a distance of 1.33, Doppler effect 3, resulting in luminosity distance of 4. Also if we take additional Doppler effect because of this aberration effect, we get a symmetry here, and t' sees luminosity distance of 12 too. LumD=D*(z+1)^2, both observers at t=3 sees each other D=1.33 away, and both measure luminosity distance LumD=12 


#11
Aug2713, 05:13 AM

P: 3,967




#12
Aug2713, 05:33 AM

P: 98

yuiop, I've asked to move this thread to Astronomy subforum.
Yes, i mean d'=1.33, I've made a fix just before you posted your answer. And you are right about D, i have added one Doppler to it. D, in this case, means light travel distance from emitter's FOR to the moving observer. Less confusing and more convenient formula would be by dividing that D by the Doppler effect. 


#13
Aug2713, 05:53 AM

P: 3,967




#14
Aug2713, 09:06 AM

PF Gold
P: 4,087

But you're right to say that luminosity distance is model dependent. 


#15
Aug2713, 11:58 AM

P: 3,967




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