The cosmological redshift is not the result of a Lorentz transformation

In summary, there is a misconception about the relationship between cosmological redshift and recession velocity in PF. While the SR formula can be used to calculate redshift in a Doppler scenario, different formulas are used in cosmology due to the modeling of the universe's expansion. These formulas, such as v = c ln(1+z) for an empty universe and v = 2c[1-(1+z)^-0.5] for a critical density universe, do not result from a Lorentz change of coordinates. The cosmological redshift is caused by space stretching out and lengthening wavelengths. However, it is still common for high redshift quasars to be reported as having recession velocities in terms of the speed
  • #1
marcus
Science Advisor
Gold Member
Dearly Missed
24,775
792
We have a theoretical issue here.
There is a misconception floating around PF about the relation of the cosmological redshift to present and past recession velocity.

If a redshift is Doppler in origin then in the context of Special Relativity one has Einstein's correction of the Doppler formula
1+z = sqrt[(1+beta)/(1-beta)] where beta=v/c

But the relation of redshift to speed is different in cosmology and depends on how the expansion of the universe is modeled. One gets comparably simple formulas, but different ones, in some simple cases, but none of the usual models give the SR formula. Here are two formulas which Ned Wright mentions:

v = c ln(1+z) ------empty universe case

v = 2c[1-(1+z)-0.5] --------critical density, zero cosmological constant

These are obviously not the result of a Lorentz change of coordinates as in Special Relativity! They simply result from space stretching out and in the process lengthening wavelength, the usual explanation of cosmological, as opposed to Doppler, redshift. But for a side-by-side comparison with the Doppler formula we can do a little algebra on the Doppler formula and solve for v.

beta = [(1+z)2 - 1]/[(1+z)2 +1]

v = c [(1+z)2 - 1]/[(1+z)2 +1]

Ned Wright discusses the cosmological redshift in

http://www.astro.ucla.edu/~wright/cosmology_faq.html#FTL

Since it's a short passage containing the two formulas I first mentioned, I will quote the whole thing:

Can objects move away from us faster than the speed of light?

Again, this is a question that depends on which of the many distance definitions one uses. However, if we assume that the distance of an object at time t is the distance from our position at time t to the object's position at time t measured by a set of observers moving with the expansion of the Universe, and all making their observations when they see the Universe as having age t, then the velocity (change in D per change in t) can definitely be larger than the speed of light. This is not a contradiction of special relativity because this distance is not the same as the spatial distance used in SR, and the age of the Universe is not the same as the time used in SR. In the special case of the empty Universe, where one can show the model in both special relativistic and cosmological coordinates, the velocity defined by change in cosmological distance per unit cosmic time is given by v = c ln(1+z) which clearly goes to infinity as the redshift goes to infinity, and is larger than c for z > 1.718. For the critical density Universe, this velocity is given by v = 2c[1-(1+z)^-0.5] which is larger than c for z > 3 .

http://www.astro.ucla.edu/~wright/cosmology_faq.html#FTL
 
Physics news on Phys.org
  • #2
Ned's handling of the topic is not entirely correct because he failed to point out that gravitational fields also cause redshifting. Thus his empty universe formula is valid because there are no gravitating masses, but in all other cases such formulae are misleading because we don't know exactly how much of the redshifting is being caused gravitationally. If we did, we could factor it out and obtain a more precise recessional velocity. Unfortunately, it's still very common to hear about some high redshift quasar receeding at some percentage of the speed of light.
 
  • #3
Originally posted by steinitz
...Unfortunately, it's still very common to hear about some high redshift quasar receeding at some percentage of the speed of light.

Dont know if its unfortunate tho its common enough. If the speed of light is one's measuring stick for speed one hasnt much choice.
For example a recent quasar had redshift 6.4 corresponding to comoving distance (observed at rest w/rt Hubble flow) 28 billion LY and therefore Hubble law recession speed currently 2c.

Would you prefer if this were expressed as 6E8 meters per second? Or 6E5 km/s? Dont see point of "unfortunately"
It is a good yardstick.
 
  • #4
Originally posted by marcus
Dont know if its unfortunate tho its common enough. If the speed of light is one's measuring stick for speed one hasnt much choice.
For example a recent quasar had redshift 6.4 corresponding to comoving distance (observed at rest w/rt Hubble flow) 28 billion LY and therefore Hubble law recession speed currently 2c.

Would you prefer if this were expressed as 6E8 meters per second? Or 6E5 km/s? Dont see point of "unfortunately"
It is a good yardstick.

By unfortunate, I'm referring to the way people like you who are just learning about cosmological redshifts are mislead by the way that professionals - even though they know better - report without qualification redshifts in terms of recessional velocities. It's better just to report the redshift itself and leave it at that.
 
  • #5
Originally posted by steinitz
By unfortunate, I'm referring to the way people like you who are just learning about cosmological redshifts are mislead by the way that professionals - even though they know better - report without qualification redshifts in terms of recessional velocities. It's better just to report the redshift itself and leave it at that.

I am embarrassed for you---by you I mean steinitz

I do not know to whom you are referring in saying
"you who are just learning about cosmological redshifts"
"you who are misled by ...professionals"

When astronomers report their findings in journals or
at conferences they often do simply give redshift--but
not always---sometimes km/s speeds of recession are
given.

What you-steinitz-may be reading in the popular press, which
I gather must be a great source of information for you, does
not concern me. If you disapprove of what astronomers say to
newspaper reporters, OK. That is your business.
Please do not bother me with your criticisms of the media.

In a professional journal, which is what I am talking about, if someone uses natural units c=G=hbar=1 and converts
velocity results into fractions of the speed of light that is
fine with me, and may actually be helpful to the people reading
the results.

I don't have time for this. Sorry. Bye
 
  • #6
Originally posted by marcus
I am embarrassed for you---by you I mean steinitz

I do not know to whom you are referring in saying
"you who are just learning about cosmological redshifts"
"you who are misled by ...professionals"

When astronomers report their findings in journals or
at conferences they often do simply give redshift--but
not always---sometimes km/s speeds of recession are
given.

What you-steinitz-may be reading in the popular press, which
I gather must be a great source of information for you, does
not concern me. If you disapprove of what astronomers say to
newspaper reporters, OK. That is your business.
Please do not bother me with your criticisms of the media.

In a professional journal, which is what I am talking about, if someone uses natural units c=G=hbar=1 and converts
velocity results into fractions of the speed of light that is
fine with me, and may actually be helpful to the people reading
the results.

I don't have time for this. Sorry. Bye

I post on sci.physics.research which is the newsgroup for professional researchers, but you can post there to. What you'll find is that smolin's book has been widely read by other high energy theorists. In fact it's quite common for scientists to read popular treatments by other scientists, not so much to learn anything that will fundamentally change their views, but to see how cleverly or elegantly the author was able to explain (or finesse where necessary) the difficult issues. In fact there are a number of sizeable threads on smolin's book because of it's controversiality, being scorned as it is by string theorists who regard it as excessively biased and self-serving. Go see for yourself.

As for you're extreme reaction to my honest responses to your posts, well that's really got nothing to do with me, now has it marcus? If you think I didn't realize immediately why you were so careful to claim that you'd never heard of one of the most well known recent works in popular science writing, you, my tempestuous friend, are mistaken. I answered you straightforwardly about the book out of politeness because I didn't want to embarrass you.

So, why am I here? Like most young researchers, I find it helpful to teach. But sci.phys is so heavily and inefficiently moderated that it takes days for posts to appear. So I'm giving this forum a spin. If you want to learn, I'm happy to help. You'll also find that when I discover I'm wrong - even when helping someone who I think knows less than I do - I have few qualms about admitting it. So don't take things so personally because you're really not doing yourself any favours.

Anyway, I'm not going anywhere and will continue to respond to you're posts.
 
Last edited:
  • #7
Originally posted by steinitz
I post on sci.physics.research which is the newsgroup for professional researchers, but you can post there to. What you'll find is that smolin's book has been widely read by other high energy theorists. In fact it's quite common for scientists to read popular treatments by other scientists, not so much to learn anything that will fundamentally change their views, but to see how cleverly or elegantly the author was able to explain (or finesse where necessary) the difficult issues. In fact there are a number of sizeable threads on smolin's book because of it's controversiality, being scorned as it is by string theorists who regard it as excessively biased and self-serving. Go see for yourself.

As for you're extreme reaction to my honest responses to your posts, well that's really got nothing to do with me, now has it marcus? If you think I didn't realize immediately why you were so careful to claim that you'd never heard of one of the most well known recent works in popular science writing, you, my tempestuous friend, are mistaken. I answered you straightforwardly about the book out of politeness because I didn't want to embarrass you.

So, why am I here? Like most young researchers, I find it helpful to teach. But sci.phys is so heavily and inefficiently moderated that it takes days for posts to appear. So I'm giving this forum a spin. If you want to learn, I'm happy to help. You'll also find that when I discover I'm wrong - even when helping someone who I think knows less than I do - I have few qualms about admitting it. So don't take things so personally because you're really not doing yourself any favours.

Anyway, I'm not going anywhere and will continue to respond to you're posts.
 
  • #8
Jeff ("steinitz" the name of a world chess champion) says he is a young researcher who has come to PF because he finds it helpful to teach.

The field mentioned here is "high energy theory"

Jeff says he posts at a newsgroup for professional researchers---suggesting that he is a professional researcher----tho not quite saying so outright.

In another thread he asked me "have you read Smolin's book?"
and I honestly did not know what book he was referring to.
It turns out that he was referring to a book called " 3 roads to
q. gravity". Anyway Jeff seems to be accusing me of lying when I said I didnt know what book of Smolin's he meant.

I'm reserving comment but feel there is more here than meets the eye.
 

1. What is the cosmological redshift?

The cosmological redshift is a phenomenon observed in astronomy where the light from distant galaxies or celestial objects appears to be shifted towards the red end of the light spectrum. This is due to the expansion of the universe, causing the wavelengths of light to stretch as they travel through space.

2. How is the cosmological redshift different from the Doppler redshift?

The cosmological redshift is often confused with the Doppler redshift, which is caused by the relative motion between a source and an observer. However, the cosmological redshift is not caused by the motion of objects, but rather the expansion of the universe itself. This means that the cosmological redshift is not affected by the relative motion of objects, and can be used to measure the distance and age of the universe.

3. Is the cosmological redshift the result of a Lorentz transformation?

No, the cosmological redshift is not the result of a Lorentz transformation. The Lorentz transformation is a mathematical equation used to describe the effects of relative motion on measurements of time and space. However, the cosmological redshift is caused by the expansion of space itself, which is not affected by relative motion.

4. What evidence supports the idea that the cosmological redshift is not caused by a Lorentz transformation?

One of the key pieces of evidence for the cosmological redshift being caused by the expansion of the universe is the observation of the redshift in all directions of the sky. If the redshift was caused by a Lorentz transformation due to the motion of objects, we would expect to see variations in the amount of redshift depending on the direction of observation. However, the redshift is observed to be uniform in all directions, supporting the idea that it is a result of the expansion of the universe.

5. How does the cosmological redshift impact our understanding of the universe?

The cosmological redshift is a crucial piece of evidence in support of the theory of the Big Bang and the expanding universe. It has also allowed scientists to measure the rate of expansion of the universe and estimate its age. Additionally, the cosmological redshift has been used to discover and study distant galaxies and has contributed to our understanding of the evolution of the universe.

Similar threads

  • Special and General Relativity
Replies
5
Views
929
  • Special and General Relativity
Replies
5
Views
736
Replies
2
Views
1K
Replies
1
Views
1K
  • Astronomy and Astrophysics
Replies
5
Views
2K
  • Astronomy and Astrophysics
Replies
13
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
743
  • Special and General Relativity
2
Replies
54
Views
1K
  • Advanced Physics Homework Help
Replies
8
Views
621
Back
Top