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Why can’t we derive velocity directly from it’s doppler factor?


TakenItSeriously

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Since we can measure the doppler shift, relativistic or otherwise, of a receding galaxy why can’t we use the equation for calculating the Relativistic Doppler Factor (fs/fo) which I will call r for ratio, to derive the galaxies recessional velocity?
 
fs/fo = √[(1+β)/(1-β)]
r = fs/fo
r = √[(1+β)/(1-β)]
(1+β)/(1-β) = r²
β+1 = r²(1-β)
β = r²-r²β-1
r²β+β = r²-1
β(r²+1) = r²-1
β = (r²-1)/(r²+1)
 
where:
fo is the frequency that an observer sees
fs is the source frequency that we can find from its spectrographic footprint
β = v/c
r = fs/fo
 
If the galaxy is in redshift then r > 1 
⇒ 0 < β < 1
 
If the galaxy is in blueshift then r < 1 
⇒ 0 > β > -1
 
The negative velocity only means that the objects are moving closer together instead of further apart so we can see that the absolute speed should never exceed c according to Special Relativity.
Edited by TakenItSeriously
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Recessional velocity is an apparent velocity that is not a true velocity that involves inertia. It is simply seperation distances from expansion/contraction and not inertia based upon Newtons laws of inertia ie f=ma.

 The seperation distance in excess of the Hubble horizon will give greater than c recessive velocities however this does not violate SR for the above reasons.

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Let's put it this way: the Relativistic Doppler shift only depend on the relative velocity difference between the source at the time of emission and the receiver at the time of reception.

For example, if the source is moving at 0.5 c relative to you at the time of emission, but you accelerate up to 0.5 in that same direction just before the light reaches you, you will measure no Doppler shift because  relative velocity difference between you at reception and the source at transmission is 0.

However, with cosmological red-shift we are dealing with the geometric expansion of space between the time of emission and reception.  This stretches the light waves.   So lets; say there was zero expansion of the universe at the moment of emission, then during some period between emission and reception there is some expansion. the light wave will share this expansion. Now the expansion stops before reception so that it is zero again. However, this does not mean that the light wave reverts to it original length. For that to happen, there would have to been a contraction of the universe.   This means that you the observer will measure the red-shift caused by this period of expansion even though it no longer exists a the time of reception.

So to put it simply, Relativistic Doppler shift only depends on the relative velocity difference between emission and reception ( You could change your velocity to many times while the light it traveling towards you, but the only thing that counts is your velocity at the moment of reception.)

Cosmological red-shift  is dependent on what occurs during the entire period that the light is traveling and not just the conditions at the "end points".

 

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On 5/5/2018 at 2:23 PM, Janus said:

Let's put it this way: the Relativistic Doppler shift only depend on the relative velocity difference between the source at the time of emission and the receiver at the time of reception.

For example, if the source is moving at 0.5 c relative to you at the time of emission, but you accelerate up to 0.5 in that same direction just before the light reaches you, you will measure no Doppler shift because  relative velocity difference between you at reception and the source at transmission is 0.

However, with cosmological red-shift we are dealing with the geometric expansion of space between the time of emission and reception.  This stretches the light waves.   So lets; say there was zero expansion of the universe at the moment of emission, then during some period between emission and reception there is some expansion. the light wave will share this expansion. Now the expansion stops before reception so that it is zero again. However, this does not mean that the light wave reverts to it original length. For that to happen, there would have to been a contraction of the universe.   This means that you the observer will measure the red-shift caused by this period of expansion even though it no longer exists a the time of reception.

So to put it simply, Relativistic Doppler shift only depends on the relative velocity difference between emission and reception ( You could change your velocity to many times while the light it traveling towards you, but the only thing that counts is your velocity at the moment of reception.)

Cosmological red-shift  is dependent on what occurs during the entire period that the light is traveling and not just the conditions at the "end points".

 

I’m not following the basis of your argument.

Luminosity which is used to determine distance is essentially the same source and time that relativic redshift came from. So how could light be an invalid source of information in the case of redshift, but be a valid source for distance?

In fact light is essentially the only source of information used in this case.

It seems as though you are just trying to make the claim that Special Relativity is wrong.

Edited by TakenItSeriously
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42 minutes ago, TakenItSeriously said:

I’m not following the basis of your argument.

Luminosity which is used to determine distance is essentially the same source and time that relativic redshift came from. So how could light be an invalid source of information in the case of redshift, but be a valid source for distance?

In fact light is essentially the only source of information used in this case.

It seems as though you are just trying to make the claim that Special Relativity is wrong.

Where did I say anywhere that light was an invalid source?  Both the examples I gave, for the Relativistic Red shift and Cosmological red shift, used light.  Nor did I ever imply that SR is wrong.

There is more than one mechanism that causes red shift.  They  each have  a different formalization, and you can't use the formulation for one to calculate the effect of the other.  You cannot use the Relativistic Doppler shift formula to calculate cosmological recession because they are different effects. 

 

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8 minutes ago, Janus said:

Where did I say anywhere that light was an invalid source?  Both the examples I gave, for the Relativistic Red shift and Cosmological red shift, used light.  Nor did I ever imply that SR is wrong.

There is more than one mechanism that causes red shift.  They  each have  a different formalization, and you can't use the formulation for one to calculate the effect of the other.  You cannot use the Relativistic Doppler shift formula to calculate cosmological recession because they are different effects. 

 

Ah, I see.

So your suggesting that if you use relativistic redshift then the numbers don’t agree with the Cosmological data is that correct?

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9 hours ago, Janus said:

You cannot use the Relativistic Doppler shift formula to calculate cosmological recession because they are different effects. 

Hi Janus,

If you only examined face on galaxies, where the light from all parts depart at roughly the same time, would the shift component of the light reflect the direction the galaxy was travelling in at the time of emission plus any cosmological recession shift of the emitted photons during transit? Surely a selection of face on galaxies of all types could be expected to be just as representative a sample as a mix of all types of galaxies with different planes of rotation and extra shift components.

Has anybody studied face on galaxies alone to analyse their various shift components and the respective limits of their directional/recessional velocities?

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 One has to apply each type of redshift for each dynamic involved.  While light crosses a gravity well, we need to apply gravitational redshift. For a galaxies actual motion relative to the observer, Doppler shift. For an expanding universe during transit times between emitter and reciever cosmological redshift.

 All three can be involved on the same signal.

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1 hour ago, Mordred said:

 One has to apply each type of redshift for each dynamic involved.  While light crosses a gravity well, we need to apply gravitational redshift. For a galaxies actual motion relative to the observer, Doppler shift. For an expanding universe during transit times between emitter and reciever cosmological redshift.

 All three can be involved on the same signal.

Yet Relativistic Redshift isn’t accounted for, for galaxies that are receding at speeds appraching the speed of light?

That suggests that time dilation isn’t accounted for at those speeds either. 

Time dilation will cause luminosity to dim which could have easily been overlooked just as length contraction was overlooked for the cause of time deviation in the Twin Paradox.

What may seem obvious in hind-site is not obvious in fore-site. Please trust me on this. It has been the lifelong bane of my existance.

 

 

Edited by TakenItSeriously
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3 hours ago, TakenItSeriously said:

Yet Relativistic Redshift isn’t accounted for, for galaxies that are receding at speeds appraching the speed of light?

There is minimal proper motion so any Doppler shift is insignificant compared to the cosmological red-shift.

3 hours ago, TakenItSeriously said:

That suggests that time dilation isn’t accounted for at those speeds either. 

The time dilation of distant galaxies exactly matches the red shift. (Note that this is cosmological time dilation, not that due to relative motion. In other words it is due to the change in scale factor.)

Note that SR is a subset of GR so any effect that is calculated using GR (eg. cosmological red shift) already includes any effects that would be described by SR.

 

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