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my favorite astrophysics question.

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#1 adamphillips

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Posted 21 October 2018 - 09:54 PM

my question is simple. let me lay it out. the furthest galaxies we have imaged are say 13.2 million light years away. this is evidence that galaxies were forming just half a billion years after the big bang. therefore we are seeing them in the past just 500 million years after the big bang.

 

but, how did they get 13.2 billion light years away in just 500 million years?

 

I do finally know the answer to this question, but what i would really like is an astrophysicist to show me some numbers to back it up.



#2 Nicole Sharp

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Posted 21 October 2018 - 10:17 PM

The standard explanation is via cosmological inflation.  Space itself expands nonlinearly over time.  So two points in spacetime not gravitationally bound will eventually be too far apart to see at lightspeed.  E.g. as space continues to expand, we will eventually not be able to see anything outside of our gravitationally bound Virgo Local Supercluster, due to objects being too far away for their light to reach us.  For now, gravitational binding energy (e.g. of our Local Supercluster) is greater than dark energy, so you cannot usually see the expansion of space other than at extremely large distances.  But some theories postulate a second inflation or Big Rip, whereby all points in spacetime eventually become isolated within their own lightcones (the region of spacetime where signals can be received at lightspeed).


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#3 Nicole Sharp

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Posted 21 October 2018 - 10:25 PM

Fun fact, but if you have a really good equatorial mount for long exposures, at least 8 inches of aperture, and a spectroscopic filter, you can actually measure the cosmological redshift of distant galaxies using amateur equipment to prove for yourself the Hubble expansion of the universe.


Edited by Nicole Sharp, 21 October 2018 - 10:25 PM.

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#4 adamphillips

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Posted 21 October 2018 - 10:41 PM

Fun fact, but if you have a really good equatorial mount for long exposures, at least 8 inches of aperture, and a spectroscopic filter, you can actually measure the cosmological redshift of distant galaxies using amateur equipment to prove for yourself the Hubble expansion of the universe.

i have all those things except a spectroscopic filter. that sounds pretty cool i would like to know more about that, ill have to look it up



#5 TOMDEY

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Posted 21 October 2018 - 10:57 PM

I'll say this now, and then look to see what others are saying. Anyway, the SHORT answer is that there are actually several "times" associated with looking OUT into the universe, and seeing stuff whose information had to travel... quite slowly, actually (?!), even at "the speed of light."

 

When you (properly) take that into account... it ALL makes perfect sense!  Tom



#6 MikeTahtib

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Posted 21 October 2018 - 11:11 PM

I always wondered about this myself. although in a different way.  I thought, if we all start from the saem point and start expanding, then the light from the beginning would have shot past us immediately, never to be seen again.  And we shouldn't be able to see anything any older than what it takes us to move the same number of light eyars from where it was at the time.  (I'm not sure that last sentence makes complete sense, but I hope you understand).  So if we're seeing something 13 billion light years away, and we're not travelling close to the speed of light, we would have had to start from the same point much earlier than 13 billion years ago so we could get 13 billion light years apart.  I once asked someone at a party who claimed to be a real astronomer about this, as he was talking about looking back ot the beginning of the universe, and he couldn't answer it.  He said something about light bending around the universe.  I nodded politely, but thought, Oh ya, as if we could unwind the path of light through 13 and a half billion years as it flew by stuff that we really don't know where it was or how massive it was.

But my understanding of current thinking now is that we didn't travel through space at some sub-light speed.  During the Big Bang, the universe sorta popped into existence, stretching across many light years, all in a fraction of a second, in a process called inflation (as Nicole points out above).  It seems like stuff moved much much faster than the speed of light, although physicists will say the primordial material wasn't moving through space, but space itself was expanding and carrying matter with it, and the stuff that was carried 13+ billion light years away are the things that formed galaxies that we are trying to look at now.

It's pretty crazy stuff, but it gives me hope that someday, if we can figure out how to harness inflation, we could get to far-away places quickly.  I don't know if anyone knows anything about inflation, or under what circumstances it can occur.  I would like to hear from any real astrophysicists about this.



#7 Nicole Sharp

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Posted 22 October 2018 - 01:30 AM

i have all those things except a spectroscopic filter. that sounds pretty cool i would like to know more about that, ill have to look it up

 

To measure the cosmological redshift of distant quasars, the recommendation is at least 8 inches of aperture and the ability to obtain at least 15 minutes of integration time:

 

https://www.rspec-as...ample-projects/

 

2 billion lightyears is a redshift of about 0.2 which can be detected with amateur equipment.


Edited by Nicole Sharp, 22 October 2018 - 01:30 AM.


#8 Mister T

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Posted 22 October 2018 - 07:04 AM

my question is simple. let me lay it out. the furthest galaxies we have imaged are say 13.2 million light years away. this is evidence that galaxies were forming just half a billion years after the big bang. therefore we are seeing them in the past just 500 million years after the big bang.

 

but, how did they get 13.2 billion light years away in just 500 million years?

 

I do finally know the answer to this question, but what i would really like is an astrophysicist to show me some numbers to back it up.

Because they didn't get 13.2 BLY away in 500 M years, it took them(or us) 13.2 B years to separate this far



#9 adamphillips

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Posted 22 October 2018 - 07:12 AM

Because they didn't get 13.2 BLY away in 500 M years, it took them(or us) 13.2 B years to separate this far

that isn't true, when they are saying we are seeing them as they were 500 million years after the big bang. the light left them 13.2 billion years ago.

 

according to what ive read about the redshift calculations if the light travelled that long, then they are now approximately 27 billiob light years away now



#10 MikeTahtib

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Posted 22 October 2018 - 08:23 AM

that isn't true, when they are saying we are seeing them as they were 500 million years after the big bang. the light left them 13.2 billion years ago.

 

according to what ive read about the redshift calculations if the light travelled that long, then they are now approximately 27 billiob light years away now

That isn't quite right either.  That would require everything to be moving away from each other at the speed of light.  I haven't seen anything that says exactly how fast everything is moving away, or how much the universe has grown since the big bang, but I'm sure it's nowhere near the speed of light.



#11 EJN

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Posted 22 October 2018 - 10:31 AM

That isn't quite right either.  That would require everything to be moving away from each other at the speed of light.  I haven't seen anything that says exactly how fast everything is moving away, or how much the universe has grown since the big bang, but I'm sure it's nowhere near the speed of light.

 

Yes it is right. Lookup comoving and proper distance.

 

https://en.wikipedia...roper_distances

 

When we look at distant galaxies, we are seeing them where they were then, not now.

If the speed of light were infinite, we would see them where they are now. They are

further away than the lookback time because the universe has expanded between then

and now.

 

Because the speed of light is finite, the concept of distance becomes ambiguous at cosmological

distances, and depends on knowing the proper cosmological model to determine how much the

universe expanded in the intervening interval.

 

https://en.wikipedia...res_(cosmology)


Edited by EJN, 22 October 2018 - 10:47 AM.

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#12 tchandler

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Posted 22 October 2018 - 11:01 AM

This explains it quite well, too. 


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#13 EJN

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Posted 22 October 2018 - 11:31 AM

I do finally know the answer to this question, but what i would really like is an astrophysicist to show me some numbers to back it up.

 

In the coordinate system for a FLRW universe, the metric takes the form
ds2 = − c22 = − c2dt2 + a(t)2(dr2/1 − κr2 + r2(dθ2 + sin2θdϕ2))

 

In this case the comoving coordinate distance r is related to χ by

χ = |κ|−1/2 sinh−1 sqrt(|κ| r) , if  κ < 0   (a negatively curved ‘hyperbolic’ universe)
χ = r , if  κ = 0                           (a spatially flat universe)
χ = |κ|−1/2 sin−1 sqrt(|κ| r) , if  κ > 0    (a positively curved ‘spherical’ universe)

 

(from the link above)


Edited by EJN, 22 October 2018 - 11:37 AM.


#14 RaulTheRat

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Posted 22 October 2018 - 11:46 AM

That isn't quite right either. That would require everything to be moving away from each other at the speed of light. I haven't seen anything that says exactly how fast everything is moving away, or how much the universe has grown since the big bang, but I'm sure it's nowhere near the speed of light.


In fact a lot of it is moving away from us faster than the speed of light and is forever causally disconnected from our part of the universe.

#15 gvk

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Posted 22 October 2018 - 07:30 PM

my question is simple. let me lay it out. the furthest galaxies we have imaged are say 13.2 million light years away. this is evidence that galaxies were forming just half a billion years after the big bang. therefore we are seeing them in the past just 500 million years after the big bang.

 

but, how did they get 13.2 billion light years away in just 500 million years?

 

I do finally know the answer to this question, but what i would really like is an astrophysicist to show me some numbers to back it up.

No, we were much closer together than 13 Gly (billion light years) when the universe was only a few hundred million years old. The universe has been expanding as the light we are seeing now was travelling, and we are much farther away now.

 

The following results for galaxy GV-z11 were obtained by numerically solving for time and distance versus redshift using the Einstein and Friedmann equations of the Lambda-CDM model with FLRW metric (see EJN's post above), following David W. Hogg, "Distance Measures in Cosmology," 2000.

(https://arxiv.org/ab...ro-ph/9905116v4)

 

Inputs for the calculations are the following.

 

z = 11.09 (redshift of galaxy GN-z11)
Planck 2015 Parameters (normalized to critical density, 3 Ho^2 / 8 Pi G)
Ho = 67.74 km/s-Mpc  (Hubble parameter now)
OmegaM = 0.3089 (total matter density, baryon + dark matter)
OmegaR = 0 (radiation density is now negligible)
OmegaK = 0 (curvature, assuming flat universe)
OmegaL = 0.6911 (dark energy density, or cosmological constant)

 

Results of the model using above parameters are as follows.

 

Age of universe now (Gyr):        13.80
Age of universe then (Gyr):         0.410
Horizon of universe now (Gly):  46.26
Horizon of universe then (Gly):   3.83
Distance of source now (Gly):   32.19
Distance of source then (Gly):    2.66
Light travel time (Gyr):               13.39

 

Note that distances above are the line-of-sight or longitudinal comoving distance. They are equivalent to the proper distance or space-like separation at the given time.

 

A google search on "cosmological calculator" should lead to several web pages that will produce similar results using these same inputs. Slightly different numbers will result from other Hubble parameter values, densities, etc. that are often used.

 

Note that I'm a retired phycisist, but only an "armchair astrophysicist," and you did ask for numbers. smile.gif

 

Gerry


Edited by gvk, 22 October 2018 - 07:37 PM.

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#16 MikeTahtib

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Posted 22 October 2018 - 08:29 PM

Wow, this is mind-bending.  So we moved 29.5 billion ight years apart in 13.4 billion years, or more than twice teh speed of light.  Does this mean that inflation is still occurring?  Or occurred for more than a few hundred million years after the big bang?



#17 MikeTahtib

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Posted 22 October 2018 - 09:15 PM

While I have an audience of really smart people, I want to ask what it really means that space expands, vs. stuff moving through space.  If the space in my kitchen expanded, what would I see, and how would it differ from all the stuff in my kitchen just moving away from each other?



#18 gvk

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Posted 22 October 2018 - 10:16 PM

Wow, this is mind-bending.  So we moved 29.5 billion ight years apart in 13.4 billion years, or more than twice teh speed of light.  Does this mean that inflation is still occurring?  Or occurred for more than a few hundred million years after the big bang?

Not surprising, since the universe expanded from small (say ~15 Mly at around z=3000, or 60k yrs old) to over 46 Gly in 13.8 Gy.

 

Inflation ocurred much earlier. The inflation hypothesis says that very rapid expansion occurred before about 10^-32 sec. This very rapid expansion is needed to understand how large scale structure of the universe formed.

 

The Lambda-CDM model shows that expansion in the early universe was much faster than today. The universe was matter dominated, and expansion slowed till somewhere around ~10 Gyr, when the cosmological constant (dark energy) began to accelerate expansion again.

 

The Hubble parameter is not constant with time, but varies with the scale factor of the universe, a(t), and thus redshift. I believe that H(t) is roughly proportional to (1+z)^3/2 in a matter dominated universe, so expansion rate was maybe ~40X today's value when light we see today was emitted from galaxy GV-z11.

 

Update:  I should not do "back of the envelope" physics late at night! A more careful calculation of the Hubble parameter at redshift z=11, gives ~23X the current value, mostly because dark energy has increased today's Ho over what it would have been in a matter dominated universe.

 

Gerry


Edited by gvk, 23 October 2018 - 11:51 AM.


#19 EJN

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Posted 22 October 2018 - 10:42 PM

While I have an audience of really smart people, I want to ask what it really means that space expands, vs. stuff moving through space.  If the space in my kitchen expanded, what would I see, and how would it differ from all the stuff in my kitchen just moving away from each other?

 
Using the term "space" is expanding is misleading, it's spacetime which is expanding. Absolute space
and absolute time are obsolete concepts from Newtonian mechanics.
 
In 3D Euclidian space the metric would be
 
ds2 = dx2 + dy2 + dz2
 
In the simplest form of spacetime, the Minkowski metric (flat spacetime without gravity) is
 
ds2 = -c2dt2 + dx2 + dy2 + dz2

 

(These are expressed in Cartesian coordinates, the FLRW metric in the previous post is in polar

coordinates) 

 

There is a term for time in the Minkowski metric, thus spacetime.

 

If galaxies were just moving through fixed space, we would have to be at the center of movement

to see uniform expansion in all directions.

 

In 4D spacetime, any location is equivalent and sees uniform expansion.

 

 

Also - stars, galaxies, planets, people, kitchens do not expand. The local gravitational field

overcomes it, as well as the nuclear forces binding together atoms, which are orders of magnitude

stronger.


Edited by EJN, 23 October 2018 - 12:10 AM.

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#20 MikeTahtib

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Posted 23 October 2018 - 03:38 AM

So if the space-time in my kitchen were expanding, time would slow down relative to the world around me?



#21 Mister T

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Posted 23 October 2018 - 06:29 AM

So if the space-time in my kitchen were expanding, time would slow down relative to the world around me?

That's why you burn dinner some times.

Your kitchen timer needs to be calibrated to the expansion of the universe



#22 EJN

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Posted 23 October 2018 - 01:17 PM

So if the space-time in my kitchen were expanding, time would slow down relative to the world around me?

 

It depends on whether the kitchen has a blender or not, and if so what direction it spins.

 

Rotating Cylinders and the Possibility of Global Causality Violation

 

 


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