Well...
On the distance issue:
Proper distance when the light was emitted was 4 billion LY away.
The light traveled for 13 Billion years and gives us the image of an object when it was 4 billion LY away.
The current proper distance to the object is 28 Billion years.
I don’t know why you’re repeating yourself. Apparently you didn’t understand my response.
When astronomers mean “proper distance” or “comoving distance,” they say “proper distance” or “comoving distance.” Otherwise, they mean “light-travel distance,” aka “lookback time” – the distance that the light has traveled as the scale factor of the universe has changed. When a popular science article says “a FRB from a dwarf galaxy 3 billion light-years away,” they mean that the light has traveled across 3 billion light-years of distance as the universe has been expanding, so we’re seeing the source object as it was 3 billion years ago.
This is a perfectly reasonable measure of distance in the context of an expanding universe. It’s not as rigorous a definition of distance as proper distance or comoving distance. But it’s appealing because it draws a clear picture of how far the light has traveled, which corresponds to how far back in the past we’re seeing the object in question. That's why it's the preferred measure of distance in the popular science press.
For example, let’s look at one prominent example in the press, FRB 121102, a source of multiple fast-radio bursts located in a distant dwarf galaxy. The popular press has provided these estimates of the distance to that host dwarf galaxy:
“Astronomers announced today at the 229th meeting of the American Astronomical Society that, for the first time, they’d pinpointed the origins of one of these FRBs: a small dwarf galaxy about 2.5 billion light-years away.”
Fast radio bursts now a bit less mysterious
“Astronomers aren’t sure what causes them, and none of these bursts have ever repeated — except one, FRB 121102, which made headlines with the identification of its host galaxy, sitting nearly 3 billion light-years away.”
The single strange repeating fast radio burst is at it again
“Fast radio bursts are brief, bright pulses of radio emission from distant but largely unknown sources, and FRB 121102 is the only one known to repeat: more than 150 high-energy bursts have been observed coming from the object, which was identified last year as a dwarf galaxy about 3 billion light years from Earth.”
https://phys.org/news/2017-08-distant-galaxy-high-energy-radio.html
“The localization and characterization of the one known repeating source, FRB 121102, has revolutionized the understanding of the source class. FRB 121102 is identified with a galaxy at a distance of approximately 3 billion light years, well outside the Milky Way Galaxy, and embedded in an extreme environment.”
Fast radio burst - Wikipedia
“What causes the fast radio bursts, and why do they repeat? Astronomers don’t know but are trying to find out, aided by the information about FRB 121102 that’s only now accumulating. In 2016, astronomers pinpointed the location of the bursts on our sky’s dome, associating them with a dwarf galaxy about 3 billion light-years from Earth.”
Alien seekers report 15 more fast radio bursts from FRB 121102 | EarthSky.org
So what do they mean by “a distance of about 2.5 to 3 billion light-years?” Do they mean proper distance, comoving distance, or light-travel distance? The only way to know for sure is to know the redshift, and to use the Hubble law equation to find out.
It turns out that FRB 121102 has a redshift of .193:
“Tendulkar et al. (2017) obtained spectroscopic observations of the FRB host galaxy, measuring a redshift z = 0.193 and thus decisively confirming the extragalactic origin of FRB 121102.”
Focus on the Repeating Fast Radio Burst FRB 121102 - The Astrophysical Journal Letters - IOPscience
So we plug that redshift into a handy cosmology calculator programmed with our current ΛCDM cosmology equation that accounts for matter density, dark energy density, and the Hubble expansion of the universe:
Cosmology calculator | kempner.net
And we get:
lookback time to z = 2.45576 Gyr
And at that distance the cosmological expansion of the universe isn’t very significant anyway – that cosmology calculator also gives us the comoving radial distance to FRB 121102:
comoving radial distance dc = 822.231 Mpc (which is about 2.682Gly)
So lookback time and comoving distance are pretty close in this example, so it doesn’t make much difference which measure of distance they use in this case.
Now let’s look at your original statement:
The signals come from 3 billion light years away and would have taken about 6 billion years to get here.
In this statement, you’re assuming that when astronomer’s say “3 billion light-years away” they mean “the source of the signal was 3 billion light-years away when the signal was emitted.”
That’s
never what astronomers mean when they say “3 billion light-years away.” When they say “a signal was received from a source 3 billion light-years away,” they mean light-travel distance, aka, the lookback time. Sometimes they mean “the comoving distance to the source of the signal [its present proper distance relative to us] is now 3 billion light-years away,” but they usually say “comoving distance” when they mean that, to avoid confusion, especially when dealing with high-redshift sources near the cosmic horizon.
And note that you have it backwards anyway: because the light is
approaching us during its flight-time, while the source of the signal is
moving away from us with the Hubble flow, it takes less time for the light signal to arrive, than the comoving distance to the source. Not more.
So let’s say that the source of the signal is at a proper distance of 3 billion light-years (919.804Mpc) away. That corresponds to a redshift of about z = 0.21729. Plugging that into our ΛCDM cosmology calculator we find:
lookback time to z = 2.71989 Gyr
So it only took 2.71989 billion years for the light to travel through the expanding spacetime between Earth and the source of the signal, which is now 3Gly away.
Anyway, like I said before, light-travel time distances are what we see in press articles about astronomy, for better or worse (and the consensus is "for worse" because the redshift is a much better unit to use). If you don’t want to believe me, here it is from Dr. Edward L. Wright, a Harvard PhD astrophysicist who worked on the WMAP project and a professor at MIT and UCLA:
“Since public information offices in the US never want to mention the redshift of an object, distances are usually given as light travel time distances. “
Light Travel Time Distance
The problem with fusion is that your fusion generator would have to fuse about 571 Gigatons of hydrogen a second under pressures and temperatures at about 100 times those of the sun.
Would actually be easier to capture energy from a star.
I never said that a civilization would
create a star rather than building a Dyson sphere – obviously you’d just create a large number of small fusion reactors and put them wherever you needed them – in your home, on a starship, to power a skyscraper or a city, whatever. Assuming of course that you couldn’t come up with a better source of energy; something we haven’t even dreamed up yet. I think that by the time you have the capability to harvest entire planets to build a ring or a shell around a star, you’d probably have made some significant advancements in physics and found some new methods of energy production.
