How far into the Universe can we theoretically reach?

[plin092]

TL;DR Summary

What is the farthest distance you can get from Earth before the expansion of the universe stops you?

We know that the large majority of galaxies we see can never be reached. We know in 100 billion years we will lose sight of any galaxy outside out local group (which will itself merge into one big galaxy). But what is the maximum distance you could theoretically go if you made it your #1 mission?

Say tomorrow, a ship leaves Earth going at 99.9999999% the speed of light. It carries on in one straight line, and continues to do so forever without slowing down. It is not concerned about getting back, and it can plow through anything it runs into. It is just concerned about getting as far away from Earth as possible.

How far would the ship go? I know it will definitely surpass a billion light years, since I’ve heard it speculated that 1 billion is the farthest away a stellar system could theoretically be artificially ”rescued” by humanity into our local group. Presumably someone not collecting resources, but just exploring, could go a few billion further and still make it back in time to not be “locked out”.

But how far could someone only concerned about maximum distance go? What is the maximum distance humanity could ever theoretically reach?

 

[anorlunda]

No matter what the speed, if it continues forever and never collides with anything, the distance it can travel in unlimited time is unlimited distance. Even walking speed for unlimited time gives unlimited distance.

I suggest you may want to state your question differently. Perhaps put a time limit on it. But then the question is trivial. If you know the speed, and you know the time, the distance is the product of the two.

 

[PAllen]

Maybe what you mean to ask is more like the following:

Are there distant galaxies we can see now (as they were long, long ago), such that a light signal we send now would never reach them? The answer is that it depends on the cosmological parameters, but for anything close to what we believe about our universe, the answer is yes. Then you could ask what is the minimum redshift for which this would be true (asking about redshift is much more meaningful than asking about distance, in cosmology).

 

[Bandersnatch]

If your spaceship were behaving like a light signal - i.e. if it were constantly accelerating in such a way so as to maintain the initial velocity w/r to the local space - then we can use the reasoning outlined above to name the maximum redshift (about 0.7) and the corresponding distance to the galaxy as it is now (about 8 billion ly). I.e. it's half the distance to the current extent of the event horizon. Half, since we have to be able to make a round trip.
A note here - it's specifically the acceleration of the expansion that causes this maximum distance to exist. If it were just expansion (neither accelerating nor decelerating), or decelerated expansion, such light-like explorer could go as far as he pleases, given enough time.

If your ship were just sent out with some initial velocity, then it becomes more complicated, as for massive objects expansion leads to losing their momentum w/r to the local space. I.e. the ship would find itself slowing down to match the local notion of being stationary. This should limit the maximum range at which it could turn around. I don't know how to put a number on this case.

 

[JimJCW]

Summary:: What is the farthest distance you can get from Earth before the expansion of the universe stops you?

If we send out a spaceship along a straight line at a speed c’ (very close to c), it will pass many objects on its way. At the beginning, the passing speed is c’, but its value continues to decrease. Close to the destination, the passing speed will approach zero. This means that it will take the spaceship infinite time to catch up with the destination object.

The current distance to the destination object can be estimated from the event horizon to be 16.5 Gly.

 

[plin092]

If your spaceship were behaving like a light signal - i.e. if it were constantly accelerating in such a way so as to maintain the initial velocity w/r to the local space - then we can use the reasoning outlined above to name the maximum redshift (about 0.7) and the corresponding distance to the galaxy as it is now (about 8 billion ly). I.e. it's half the distance to the current extent of the event horizon. Half, since we have to be able to make a round trip.
A note here - it's specifically the acceleration of the expansion that causes this maximum distance to exist. If it were just expansion (neither accelerating nor decelerating), or decelerated expansion, such light-like explorer could go as far as he pleases, given enough time.

If your ship were just sent out with some initial velocity, then it becomes more complicated, as for massive objects expansion leads to losing their momentum w/r to the local space. I.e. the ship would find itself slowing down to match the local notion of being stationary. This should limit the maximum range at which it could turn around. I don't know how to put a number on this case.

Thank you for introducing me to the particle event horizon. It essentially answers what I wanted to know.

I knew the observable universe was 93 billion light years across, and I knew a signal sent now could never reach the majority of what we see. But I wanted to know just how far something sent from Earth today could reach. I knew professionals would be curious about this too, so there absolutely must be a term for it - but I couldn’t find it. (I apologize for asking my question in such a “sci-fi” way too lol. In hindsight asking it about a light signal instead of a light-like explorer would have communicated what I wanted to ask better. But thankfully people here saved the day anyways)

So it seems the answer is: “Someone sent from Earth not concerned about getting back could reach just under 16.5 billion light years. An explorer from Earth who *wants* to come back could reach somewhere under 8 billion light years” (please anyone reading feel totally correct this if anything is inaccurate)

 

[Drakkith]

So it seems the answer is: “Someone sent from Earth not concerned about getting back could reach just under 16.5 billion light years.

No, there is no limit on how far you can go. In fact, as long as the universe keeps expanding at the same rate or faster, the separation velocity between you and Earth will increase without bound as the separation distance increases.

 

[plin092]

No, there is no limit on how far you can go. In fact, as long as the universe keeps expanding at the same rate or faster, the separation velocity between you and Earth will increase without bound as the separation distance increases.

What I mean is "how far away in current terms are the things you will never reach?". Obviously you can keep moving forever. But eventually, because of the accelerating expansion of the universe, there are targets so far away you will never reach them. If your target is currently 18 billion light years away from us, you can keep going forever, and you will never ever reach it. If your target is currently 15 billion light years, you *will* reach if eventually (though it will take you a lot longer than 15 billion years, even going at the speed of light, because of the expansion making you have to travel further). 16.5 billion light years is the limit of that. It's the furthest point from Earth in current terms that anything from Earth could actually reach.

 

[PeroK]

What I mean is "how far away in current terms are the things you will never reach?". Obviously you can keep moving forever. But eventually, because of the accelerating expansion of the universe, there are targets so far away you will never reach them. If your target is currently 18 billion light years away from us, you can keep going forever, and you will never ever reach it. If your target is currently 15 billion light years, you *will* reach if eventually (though it will take you a lot longer than 15 billion years, even going at the speed of light, because of the expansion making you have to travel further). 16.5 billion light years is the limit of that. It's the furthest point from Earth in current terms that anything from Earth could actually reach.

There's a great Insight here about this. Note that a light signal from Earth reaching a distant galaxy is the same problem as a light signal from that distant galaxy eventually reaching Earth - which I think is covered in the Insight:

https://www.physicsforums.com/insights/inflationary-misconceptions-basics-cosmological-horizons/

 

[Bandersnatch]

Thank you for introducing me to the particle event horizon.

Just a quick clarification - the ~16.5 Gly limit is properly called the 'event horizon'. There's also something called the 'particle horizon', which is essentially the size of the observable universe (the 93-ish Gly point). Saying 'particle event horizon' to describe either would likely just cause confusion.

 

[PAllen]

If your spaceship were behaving like a light signal - i.e. if it were constantly accelerating in such a way so as to maintain the initial velocity w/r to the local space ...

If your ship were just sent out with some initial velocity, then it becomes more complicated, as for massive objects expansion leads to losing their momentum w/r to the local space. I.e. the ship would find itself slowing down to match the local notion of being stationary. This should limit the maximum range at which it could turn around. I don't know how to put a number on this case.

There is no need to posit accelerated motion by a material body to track arbitrarily close to a light like trajectory. The tendency you describe in your second paragraph can be viewed as a temporal asymmetry (homogeneity and isotropy apply apply to spatial slices as I know you are very well aware). That is, for any timelike geodesic, the local speed relative to comoving bodies decreases with time (for an expanding universe). However, at any event, all speeds less than c are possible relative to a comoving body. They simply get even closer to c when followed back in time along a timelike geodesic path.

As a result, if you consider a galaxy with epsilon red shift less than than the maximum that can be reached by a light signal sent now, then an inertial (geodesic) timelike path can reach it. Just consider following backwards the timelike geodesic with speed epsilon less than c relative to a comoving body, starting from epsilon' after the event of a light like path reaching it from us, now.

 

[PAllen]

I'd like to pose a related question of interest, that further demonstrates the (to me) sometimes counterintuitive features of accelerated expansion.

Are there two galaxies such that if each sends a light signal towards the other at the same standard cosmological time, that the light signals will never meet? The answer is yes, and the challenge is, using concepts already explained in this thread, it should be straightforward to describe what galaxy we can see now would have this property with respect to a light signal we emit now.

Note how bizarre this is: we can see some galaxy now (of course, as it was long, long ago). We emit light towards it, it does the same 'now' (standard cosmological definition of now), yet the two signals will never meet even in the infinite future of the universe.

Per the well known Davis and Lineweaver paper's data, a galaxy with redshift greater than about 3.6 would have this property relative to us.

 

[JimJCW]

Are there two galaxies such that if each sends a light signal towards the other at the same standard cosmological time, that the light signals will never meet? The answer is yes, and the challenge is, using concepts already explained in this thread, it should be straightforward to describe what galaxy we can see now would have this property with respect to a light signal we emit now.

Will the proper distance 16.5 * 2 = 33.0 Gly be of any interest? We can use Earth as the photon meeting place.

 

[PAllen]

Will the proper distance 16.5 * 2 = 33.0 Gly be of any interest? We can use Earth as the photon meeting place.

Yes.

 

[JimJCW]

Note how bizarre this is: we can see some galaxy now (of course, as it was long, long ago). We emit light towards it, it does the same 'now' (standard cosmological definition of now), yet the two signals will never meet even in the infinite future of the universe.

Per the well known Davis and Lineweaver paper's data, a galaxy with redshift greater than about 3.6 would have this property relative to us.

I am confused about this. Let me use an example to illustrate it:

GN-z11 is a galaxy observed at z = 11.09 (greater than 3.6). Its current proper distance to Earth is 32.2 Gly. Let’s name a galaxy half way from Earth to GN-z11 ’O’. The current proper distance from O to Earth or to GN-z11 is 16.1 Gly. Since this proper distance is smaller than the event horizon at O (16.5 Gly), it seems lights emitted by GN-z11 and Earth now will meet at O.

 

[Bandersnatch]

While in that quoted bit @PAllen is simply stating that the particle horizon at the current epoch is significantly further out than the event horizon, I think the z=3.6 is a mistake (and well spotted). Twice the comoving distance does not mean twice the redshift. This is best seen on the conformal diagram from the referenced paper:

The signals from galaxies A and B eventually meet at the half way point, which they both currently see as having z=1.8. But both galaxies see each other as being at z>10.

 

[JimJCW]

The signals from galaxies A and B eventually meet at the half way point, which they both currently see as having z=1.8. But both galaxies see each other as being at z>10.

We can expect that lights sent now from Earth and a nearby galaxy will meet. This is also true for the case of GN-z11, which is 32.2 Gly away, as discussed in Post #15. However, we may want to know the boundary beyond which the corresponding lights will never meet. The following figure, obtained from the calculator developed by @Jorrie, shows the relation between the distance to the galaxy and its observed redshift:

As can be seen from the figure if a galaxy has a redshift greater than z = 12.5, its current proper distance is greater than 33.0 Gly. Based on the argument given in Post #13, lights emitted by it and Earth now will never meet (according the ΛCDM model).

 

[PAllen]

I am confused about this. Let me use an example to illustrate it:

GN-z11 is a galaxy observed at z = 11.09 (greater than 3.6). Its current proper distance to Earth is 32.2 Gly. Let’s name a galaxy half way from Earth to GN-z11 ’O’. The current proper distance from O to Earth or to GN-z11 is 16.1 Gly. Since this proper distance is smaller than the event horizon at O (16.5 Gly), it seems lights emitted by GN-z11 and Earth now will meet at O.

Yes, I mistakenly doubled red shift instead of proper distance.

 

[JimJCW]

The signals from galaxies A and B eventually meet at the half way point, which they both currently see as having z=1.8. But both galaxies see each other as being at z>10.

The quantity z = 1.8 is mentioned here and z = 1.8 * 2 = 3.6 in Post #12 by @PAllen. I assume these numbers are related to the writing in Section 2 of the paper by Davis and Lineweaver:

. . . in the ΛCDM model of Fig. 1, galaxies with redshift z ∼ 1.8 are currently crossing our event horizon. These are the most distant objects from which we will ever be able to receive information about the present day.​

Please allow me to add a graphic explanation of this. The following figure, obtained from the calculator developed by @Jorrie, shows the relation between the current distance to a galaxy and its observed redshift:

As can be seen from the figure if a galaxy has a redshift greater than z = 1.84, its current proper distance is greater than the event horizon, 16.5 Gly. Based on the discussions in this thread, light emitted by it from now on will never reach our location (according the ΛCDM model).

Note that the situation discussed above is similar to but different from that discussed in Post #17. There we are talking about whether lights emitted by a galaxy and Earth now will ever meet.

 

[JimJCW]

We can expect that lights sent now from Earth and a nearby galaxy will meet. This is also true for the case of GN-z11, which is 32.2 Gly away, as discussed in Post #15. However, we may want to know the boundary beyond which the corresponding lights will never meet. The following figure, obtained from the calculator developed by @Jorrie, shows the relation between the distance to the galaxy and its observed redshift:

View attachment 299638

As can be seen from the figure if a galaxy has a redshift greater than z = 12.5, its current proper distance is greater than 33.0 Gly. Based on the argument given in Post #13, lights emitted by it and Earth now will never meet (according the ΛCDM model).

The newly observed galaxy HD1 has a redshift z = 13.27. See Scientists Have Spotted the Farthest Galaxy Ever and HD1 (galaxy). This means lights emitted by HD1 and the Earth now will never meet.

 

[MathematicalPhysicist]

Summary:: What is the farthest distance you can get from Earth before the expansion of the universe stops you?

We know that the large majority of galaxies we see can never be reached. We know in 100 billion years we will lose sight of any galaxy outside out local group (which will itself merge into one big galaxy). But what is the maximum distance you could theoretically go if you made it your #1 mission?

Say tomorrow, a ship leaves Earth going at 99.9999999% the speed of light. It carries on in one straight line, and continues to do so forever without slowing down. It is not concerned about getting back, and it can plow through anything it runs into. It is just concerned about getting as far away from Earth as possible.

How far would the ship go? I know it will definitely surpass a billion light years, since I’ve heard it speculated that 1 billion is the farthest away a stellar system could theoretically be artificially ”rescued” by humanity into our local group. Presumably someone not collecting resources, but just exploring, could go a few billion further and still make it back in time to not be “locked out”.

But how far could someone only concerned about maximum distance go? What is the maximum distance humanity could ever theoretically reach?

To infinity and beyond////

 

[JimJCW]

To infinity and beyond////

What do you think about the following statement made by @plin092?

“We know that the large majority of galaxies we see can never be reached.”​

 

[MathematicalPhysicist]

What do you think about the following statement made by @plin092?

“We know that the large majority of galaxies we see can never be reached.”​

Never say "never"...

 

[JimJCW]

Never say "never"...

Does that mean you think the statement made by @plin092,

“We know that the large majority of galaxies we see can never be reached.”​

is not meaningful?

 

[Vick]

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)

 

[MathematicalPhysicist]

Does that mean you think the statement made by @plin092,

“We know that the large majority of galaxies we see can never be reached.”​

is not meaningful?

His statements are based on our current knowledge and understanding of the universe. Who says these won't change in the future?

 

[JimJCW]

His statements are based on our current knowledge and understanding of the universe. Who says these won't change in the future?

You are right; his statements are based on the Big Bang model. In that case, they are meaningful, right? When you say, “To infinity and beyond////”, you might want to add some explanations. The answer does not match the Big Bang model, but it might be true for a model of the universe that is infinite and non-expanding.

When you say, ‘Never say "never"...’, you are being playful, right? You are saying it yourself.

 

[MathematicalPhysicist]

You are right; his statements are based on the Big Bang model. In that case, they are meaningful, right? When you say, “To infinity and beyond////”, you might want to add some explanations. The answer does not match the Big Bang model, but it might be true for a model of the universe that is infinite and non-expanding.

When you say, ‘Never say "never"...’, you are being playful, right? You are saying it yourself.

I'll quote Arthur C. Clarke:

1. When a distinguished but elderly scientist states that something is possible, they are almost certainly right. When they state that something is impossible, they are very probably wrong.
2. The only way of discovering the limits of the possible is to venture a little way past them into the impossible.
3. Any sufficiently advanced technology is indistinguishable from magic.

https://en.wikipedia.org/wiki/Clarke's_three_laws
Also, technological advances may change the impossibility of reaching further through the universes.

 

[Ibix]

"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.

 

[berkeman]

"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.

Agreed. Let's all try to stay on-topic for this thread folks. Thanks.

 

[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”.