I How far into the Universe can we theoretically reach?

[Bandersnatch]

OP asked about furthest distance we can reach using speed of light fraction in a starship setting. This is asked due to the expansion of the universe having an effect on the question at hand.

Therefore maximum speed is c 299,792.458 km/sec
Expansion of universe factor is H0 = 67 km/sec/Mpc (Megaparsec)

Thus c/Ho = 4474.514 Mpc (or 14586.92 light years (ly) or 14.6 billion ly)

This is not the correct answer.
What you have calculated there is the Hubble radius, i.e. the distance at which recession velocity reaches the speed of light. This in and of itself is not a horizon. For example, such radius exists even in expansion models that are not accelerating. At the same time, in those models, it is possible for a signal to reach arbitrarily far, given enough time (cf. 'ant on a rubber rope' exercise, e.g. on Wikipedia).

The limit to the reach of a signal exists only in accelerating models, and is determined by the distance to the cosmic event horizon, which has already been discussed earlier in this thread. At present, this horizon is a good couple billion light years further out than the Hubble radius.

The Hubble radius and the event horizon can coincide, but this only happens in exponential expansion models, which are fully dominated by dark energy (i.e. have no matter or radiation in them). This happens during inflation. It's also what our universe appears to be evolving towards - but only asymptotically so.

 

[MathematicalPhysicist]

"To infinity and beyond" is the catchphrase of Buzz Lightyear from the Toy Story franchise. It's aimed at children under 12. I propose that there's little value in arguing about its scientific validity.

Well you know, in set theory there are quite bizarre notions of infinity.
I am waiting to find the time to read Jech's green book on Set Theory.

 

[phinds]

I am waiting to find the time to read Jech's green book on Set Theory.

I always wonder what people mean when they say that. Where are you going to look? Did you perhaps leave the time in your other pants? Under the bed?

Personally, I believe in making time in my schedule to do things, or not making the time if i decide it's just something I'm not ever really going to do.

 

[MathematicalPhysicist]

I always wonder what people mean when they say that. Where are you going to look? Did you perhaps leave the time in your other pants? Under the bed?

Personally, I believe in making time in my schedule to do things, or not making the time if i decide it's just something I'm not ever really going to do.

Well, I have this book on my shelf hard copy which I purchased back then, so I intend to read it sometime in the future.

Today, I am reading on off the handbook on QCD of Mueller's.
Anyway, if the problem of time in quantum cosmology is real, then time is an illusion anyways...
The book by Jech I started reading and finished reading chapter one, but never continued to read.

 

[PAllen]

Well, I have this book on my shelf hard copy which I purchased back then, so I intend to read it sometime in the future.

Today, I am reading on off the handbook on QCD of Mueller's.
Anyway, if the problem of time in quantum cosmology is real, then time is an illusion anyways...
The book by Jech I started reading and finished reading chapter one, but never continued to read.

The key is to draw a circle and write “tuit” inside. Cut it out, and you’ve got ”a round tuit”.