Simple Explanation of Monotonically Increasing Redshifts

[jbahr]

I was a physics major 35 years ago (they didn't even know what quasars were and black holes were exotic theories). I've recently been reading my tail off here and 100 other Google hits on cosmology. I've completed a couple of relativity tutorials, and done the math on Hubble's Parameter and topics relating to it. And still ...

 

I must be missing something fundamental. I can't figure out why increasingly distant objects should have increasing redshift (assuming that this is the appearance of receding velocity). In Newtonian terms, this would mean that distant objects have had more time to accelerate, but I'm cool with an isotropic universe, so there are no "distant objects" (or perhaps, better said, I'm just as distant to somebody out there, with identical redshift).

 

I think I'll stop here and ask more dumb questions after a response

 

J

[jbahr]

Well, I'm impatient, so let me wander around my question a bit longer.

 

Suppose there are two objects (galaxies will do), one 10 ly from us and one 20 ly from us. In the absence of non-expansion velocity relative to us, all one would have a redshift and an apparent velocity twice the other. Two things are evident:

 

1. The apparent velocity of one is twice the other.

2. Light has traveled in the presence of expansion twice as long for the one more distant.

 

So does the redshift have a component that is attributable to the velocity of the galaxy relative to us at the point of light emission PLUS some redshift attributable to universe expansion while it was traveling? Or is the galaxy at rest relative to us, and the reason that the more distant galaxy has twice the redshift is that it's simply traveled in the presence of expansion twice as long?

 

J

[Martin]

I was a physics major 35 years ago (they didn't even know what quasars were and black holes were exotic theories). I've recently been reading my tail off here and 100 other Google hits on cosmology. I've completed a couple of relativity tutorials, and done the math on Hubble's Parameter and topics relating to it. And still ...

 

I must be missing something fundamental. I can't figure out why increasingly distant objects should have increasing redshift (assuming that this is the appearance of receding velocity). In Newtonian terms, this would mean that distant objects have had more time to accelerate, but I'm cool with an isotropic universe, so there are no "distant objects" (or perhaps, better said, I'm just as distant to somebody out there, with identical redshift).

 

I think I'll stop here and ask more dumb questions after a response

 

J

 

J Bahr, we have to have a division of labor here. What I hope is that Spyman, who knows this stuff, will reply even though not officially designated "SFN-physiker"

or somebody else .

 

Just to get you started, I will say that the Hubble law deals with distances at the present moment and recession speeds at the present moment

 

and it says that ALL DISTANCES ARE CURRENTLY INCREASING AT A RATE OF ONE PERCENT EVERY 138 million years.

 

that is the mathematically the content of the Hubble law, just put in terms of percentage which most of us understand (instead of Megaparsecs and kilometers per second)

 

another way to say that is that the Hubble time (the inverse of the hubble parameter) is 13.8 billion years but don't bother with that.

 

================================

 

the punchline of all that is simple: since all distances increase at the same percentagewise rate, the longer distances are increasing

faster in absolute terms

 

 

that all there is to it. the law says that the absolute km/s rate of increase of a distance is proportional to its length.

 

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its not good to try to understand the redshift as a doppler effect depending on some speed----what speed? the speed the galaxy had when it sent the light or the speed it has now long afterwards as we are receiving the light?

 

the redshift is governed by a simple formula they give you on day one in cosmology class----the redshift of some light is the percentage that distances expanded during the time the light was traveling

 

so it depends on the whole history of expansion that happened (maybe slowing at times and accelerating at other times) during the travel time.

 

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Like I say we need division of labor here, so if you like someone else's explanation, fine, or if you want to talk it over with whoever, fine. I've said my piece

 

(but eventually you should learn to use the cosmology calculators put online by Ned Wright and by S. Morgan---they convert redshift to other useful info)

[Martin]

...

 

1. The apparent velocity of one is twice the other.

2. Light has traveled in the presence of expansion twice as long for the one more distant.

 

So does the redshift have a component that is attributable to the velocity of the galaxy relative to us at the point of light emission PLUS some redshift attributable to universe expansion while it was traveling? Or is the galaxy at rest relative to us, and the reason that the more distant galaxy has twice the redshift is that it's simply traveled in the presence of expansion twice as long?

 

J

 

YES YOU UNDERSTAND

the "cosmological" redshift is the part that doesnt depend on the random peculiar individual velocity of the galaxy---and that puts a doppler term into the mix.

but the little individual doppler contribution is mostly NEGLIGIBLE so we forget to mention it.

 

btw the velocity of the solar system relativity to the CMB----or equivalently relative to the expansion process---is 370 km/second in the direction of the constellation Leo

 

that means that all observations have to be corrected to compensate for our own motion

 

otherwise the CMB would look artificially "hot" in the Leo direction

and galaxies wouldnt be receding as fast if you look in the Leo direction

 

thats an example of a small individual motion that has to be adjusted for

 

OK, I see now you understand whats happening. I didnt have to respond at such length. Maybe you can start helping with the greenhorns some.

[jbahr]

I just had to think about homologous expansion (meanwhile, I'm reading Wright's tutorials: http://www.astro.ucla.edu/~wright/cosmolog.htm). For an expansion to be homologous, the expansion must "not alter the shape of patterns in the Universe". This leads to a kind of proportionality constraint (see Wright's face stretch in different ways with alternative expansions here: http://www.astro.ucla.edu/~wright/distort.html). So in a simple example, an object A may at some point in time be 1 LY away, and another object B be 2 LY away. After some time, to maintain proportionality we note that object A is now 2 LY away. Every other object (except us) is also twice as far away as it was before, including B. But means that B expanded away from us 2 LY (4 - 2) in the same time that object A expanded away from us 1 LY (2 - 1). Hence, B has to have appeared to always have, during this interval of time, twice the velocity of A.

 

One thing that sort of puzzles me is that you seldom see this expressed in the usual physics units. We have recession velocity as a function of distance, thanks to the Hubbard Parameter. But the first thing a physics guys would ask (I would think) is what are the velocity and acceleration in terms of time. Ignoring gravitational effects and other niggles, if two bodies at time t(0) are relatively close, then we could view the expansion as the acceleration of body B from body A. Knowing the function for velocity, we could integrate from 0 to some arbitrary time t®. That would give us the distance R between the bodies. We also know that V(t®) = R*H. In any event, I don't think I've seen any kind of estimate for the velocity or acceleration in terms of t, unless it related to the 3ct that Wright alludes to here: http://www.astro.ucla.edu/~wright/cosmology_faq.html#DN.

 

Most of the explanations along these lines seem to involved arguments involving successive distances, as if everyone is avoiding calculus.