> "In fact, so long as you kept adhering to this plan, you could choose any destination at all that’s presently within 18 billion light-years of us, and reach it after merely 45 years, max, had passed. That ~18 billion light-year figure is the limit of the reachable Universe, set by the expansion of the Universe and the effects of dark energy. Everything beyond that point is currently unreachable with our present understanding of physics"
There is a misconception that expanding space prevents us from ever reaching a destination. It's counter-intuitive (https://en.wikipedia.org/wiki/Ant_on_a_rubber_rope) but falls out of the math. If space expands at a constant rate, you could eventually reach any destination at any velocity.
But if the expansion of space is accelerating (which we believe currently), this is not true. There really would be destinations that are unreachable.
You would continue to travel further from your origin, but also witness your destination accelerate away.
Let's say the universe is turn-based, and consists of a single dimension. At the end of each turn the distance between two points in this universe doubles (because new empty space is created between them). Let the maximum speed in this universe be 300.000.000 distance-units per turn. When two points are, say, 5 units apart, we can easily travel between them (for a couple of turns, at least). But when two points are more than 600.000.000 distance-units apart, we can never again travel between them. Let's try.
We're at turn 0, at point A. Point B is 600.000.000 distance-units apart. We have infinite! acceleration and accelerate to 300.000.000 units/turn, and start our travel to point B. We move 300.000.000 units. Distances double.
We're at turn 1. Point A is now 600.000.000 units behind us, and point B is still 600.000.000 units ahead of us. We travel 300.000.000 units! Distances double.
We're at turn 2. Point A is now 1.800.000.000 units behind us, and point B is still 600.000.000 ahead of us. We're starting to wonder if we should have stayed at point A... hopefully there is a point C that was between point A and point B that we can still get to, because we don't seem to be making much progress.
The universe is a bit like that, except that it looks more continuous, it has some more dimensions, and it's not doubling quite so quickly.
Hmm, I see, thank you. So it's space itself that expands, not just the objects in it that accelerate apart from one another. But then doesn't that mean that some of that space is expanding inside the objects? Do we know what happens there? How do objects just get more space inside them?
(Assuming space expands evenly) we don't notice the expansion of space inside objects because the electromagnetism and gravity are vastly more powerful on the scales we care about and nullifies the effect. That's why atoms and galaxies in the Local Group stay together, but everything farther away is flying further away.
If expansion never stops accelerating, one day in the far future it will overcome all the other fundamental forces and everything will be torn apart in a Big Rip.
wait - does this mean that some super capable civilisation could link the various galaxies in their inter-galactic empire with a space-railway (i.e. using actual physical tracks between them in space) assuming they have the staggeringly vast amount of matter and/or energy needed, then this would gravitationally bind them together and space between them could not expand?
No, "gravitationally binding" is not a thing that you can do by connecting things via railways. Over the long distances, the railways would be torn apart by expansion.
If you could drastically increase the mass of the local group, then you could increase the range at which gravitational attraction to it was dominating, but it would require seriously increasing the mass of the local group.
> over the long distances, the railways would be torn apart by expansion
i'm not sure i get it. as i understood it, it was the fact that forces over a small scale dominate the effects of space expanding that prevents e.g. atoms getting bigger. so why would my space-railway tracks (made of continuous welded steel space-rails) not stay the same size (2m wide by thousands of light years long) as well?
Imagine a rope, and an infinite crowd of people wanting to play tug of war. If the rope is only 4 meters long, only a few people can tug, and the rope stays together. Now imagine the rope is 1 light year long. Say each person needs about 1 meter of rope, and 1 light year is about 9,5e+15 meters. So we can make two teams of almost 5 quadrillion people each, and they can start tugging. The rope is probably going to snap.
The space expansion effect is very weak at small scales, so it's easily overcome by small objects, such as a short rope (or a railway). But this small force acts on the entire object, so when the object is twice as long, it pulls twice as hard. When distances become extreme, it always wins. Imagine a railway where the the far ends are moving apart from one another faster than the speed of light. It's either an infinitely stretchy railway, or it's breaking (probably long before we got to this point).
so, how does this square with the statement claiming "[...] galaxies in the Local Group stay together" despite space-time expansion, since a galaxy seems rather larger than my proposed space-railway...
edit: also, thanks for the explanations - i think i need to learn more and/or head to physicsoverflow ;)
Galaxies in the Local Group stay together because they are already gravitationally large enough and close enough to outweigh spacetime expansion. So, adding railways between them wouldn’t help or hurt. If you tried to add railways between galaxies that were not already gravitationally bound, they would keep moving apart and just tear the railway.
At the risk of adding yet another analogy. Imagine we have built an enormous balloon the size of a small moon. You and I are put on the balloon with our two vehicle and a steel winch. If they continue to blow up the balloon, things will get farther apart, but it isn’t going to tear the front times from the ear tires, and if we put the cars 1 meter apart, and connected the steel winch cable, it wouldn’t be an issue. At 1 meter, the balloon is expanding by a centimeter an hour. But if you drove 150 kilometers away from me, with the cable connected, and we tried to hold them together at the same distance, the balloon is moving at 25 meters per minute. To each of us, things would look and feel normal, but the pressure on the cable would snap it immediately. If you then decided to keep driving, there would be a point where you could never drive back to me because the distance between us as the balloon was expanding, would be more than the top speed of your car.
Thinking of spacetime as some sort of expanding fabric permeating every-day objects is not a good analogy in my opinion.
First, like any other gravitational effect, locally, spatial expansion would manifest as pseudo-forces that can be counter-acted by all the other forces that are far more relevant at human scale.
Second, the local effect of spatial expansion should be an indirect one: Friedmann cosmology - which is how we describe an isotropic, expanding universe - is a large-scale approximation. More realistic would be 'swiss-cheese' models, where spacetime in our neighbourhood can look vastly different from the Friedmann one, except that the spacetime patches need to properly fit together to yield the correct large-scale behaviour.
Point is, illustrative models and analogies are limited. Ideas like 'space itself expanding' or 'space flowing like a river and falling into a black hole like a waterfall' might help visualize some things, but can also lead to wrong ideas if taken too seriously.
No matter how fast you accelerate, you'll chew up distances at a local(!) rate of less than c, so it's enough to consider the limiting case of light and skip the complications introduced by acceleration. The analogous classical problem is the "ant on a rubber rope". If the endpoint of the rope moves at a constant speed, the ant will be able to reach it, no matter the rope's length. If the endpoint accelerates, the ant might not, and only be able to asymptotically approach some point somewhere on the rope.
Hmm, but if we treat the end of the rope as an object which accelerates at x m/s^2, and I accelerate at 2x m/s^2, wouldn't I eventually reach that object? I don't know what I'm not getting...
Your top speed is bounded by the speed of light. The thing you’re trying to reach is not, since that acceleration is mostly actually space expanding between you and it. It’s going faster that you can ever go, and as the distance between you and it increases it accelerates even more.
I don’t quite understand this. I think I’d maybe understand if space dilated to the point where you couldn’t quite hit that edge. Though now that I say it that “solution” seems to come with a whole bunch of problematic consequences.
But “not getting to anything past the furthest thing we can see from earth today” seems fundamentally incompatible with the idea of reaching those farthest points in a reasonably bounded timeframe. There is stuff beyond the limits we can see, it’s just further than light has had a chance to travel so far (and may ever travel).
My intuition is that as you approached those far objects, you’d observe them rapidly evolving forward in time until they reached their “present day” situation, able to see billions in light years in all directions with Earth right at the edge.
But then what happens when you look at Earth? Surely you don’t see it’s billions of years old past. You’d have to see it at least as old as it was when you left. But something doesn’t seem quite right about that to me. Surely I’m missing something.
If you go far enough, stuff moves fast enough away from us than the speed of light. Thus, some places can't be reached from someone starting at our present location, ever, even though we might still see their light. That light is closer to us than the object that sent it out.
So, when you reach the "edge" you were going for, you arrive at the point when everything has already moved past your horizon (including Earth), there isn't a single hydrogen atom around, so you're stuck in the darkness forever?
Yeah from current understanding that's your fate. Everyone's fate actually, if you see gravitationally bound structures as one unit. You'd be alone waiting for the heat death. Therefore, I recommend decelerating to somewhere interesting during the time window which allows intergalactic travel.
Ah, I think I understand! Something 18bnly away from us today has a light bubble that includes objects outside our light cone.
If you can get there in 45y, that doesn’t mean 45y has passed at that location. In fact if it’s 18bnly away, that means you’d arrive in 18bn years from their perspective. And not 18bn years from what you saw when you left, but 18bn years from when they saw you leave. By that time, space will have expanded enough that it’s no longer possible to see past.
Not with our current understand of physics. Even reaching the speed of light takes infinite amount of energy for things with mass. This is because the faster you go the more massive you become. Furthermore, even before reaching the speed of light you will become a black hole as more energy is added.
Things without mass, instead, can only travel at the speed of light (photons for instance).
Finally, there is a quirk in the math that would allow for the appearance of faster than light travel. If you compress the spacetime in front of you and expand it behind you you could can move faster than light without turning into a black hole or needing infinite energy (Google Alcubierre drive for more information). It is only an appearance than faster than light travel because you would still move at sub-luminal speed in your bubble of "normal" space time, but the compression/expansion effect would drag you through space-time at faster than light speed. This, however, require so called "exotic matter", ie matter with negative energy density (this is not anti-matter, but matter that has a repulsive gravitational field) and it is probably only a quirk of the math and nothing more.
No, the "speed of light", c, is actually the speed of energy and matter. Everything is always moving at this speed in 4-dimensional space-time. If you are not moving in space, you are moving through "time" at this speed. Since this is just the speed things move at, it makes no sense to discuss moving faster or slower than this speed.
Nothing can outpace photons (in vacuum, that is - in a medium, cf Cherenkov radiation). However, velocity is a surprisingly tricky concept. While the relative velocity of two objects passing each other by is well-defined, velocity at a distance tends to require a clock synchronization convention, which is to some degree arbitrary. In consequence, in special relativity, the speed of light is only isotropic by convention (cf various discussions about the one-way speed of light, which became a topic of online conversations due to Veritasium posting a video about it), and in general relativity, recession velocities (ie change in proper distance at constant cosmological time) of far away, but still observable galaxy can in fact formally be greater than c.
Well, if you take a really strong laser pointer and point it at the moon, than a flick of the wrist can make that point race faster along the moon's surface than the speed of light.
If I installed a really bright light source on two opposite ends of the observable universe and timed everything correctly, I could make it seems like the point traveled across the universe in a fraction of a second. Same idea, same flawed logic. Nothing actually moved.
But its not really a point thats traveling faster than speed of light.
The individual photons that makes the point travel always at the speed of light from your laser pointer to the moon. Its not point on the moon thats traveling, the travel is just ilusion because it looks like the point that was there a split second ago.
I am not sure how to define the point, but my way of thinking is that its not the same point. The point never moves, instead it continuously vanishes and a new point is being continuously made next to it.
That way, there really isnt a point that is traveling or moving, its just our perception mistaking it for a point because it looks and move like one.
The thing is that lots of our 'concrete' real world objects have more in common with the later pointer point than with physical reality. Concreteness is a bit of an illusion, it's all wave functions at the bottom.
(Of course, real world objects still can't go faster than light.)
Yeah, exactly this. If you think of it like waving a garden hose back and forth it's very clear why this is flawed logic. Also because of quantization the further away you put the target surface, to try to raise the "speed" of the not actually existing point, the more discontinuous it becomes.
Expansion of the (visible) Universe is hypothesis, not a fact. Nobody pointed to an incredibly powerful energy source required to expand the whole visible Universe. A non-zero curvature of space is not confirmed also.
We are able to see gravitational waves at this point. Where is a gravitational turbulence, created by the massive expansion?
Well, an accelerating mass emits gravitational waves; and your spaceship is asymptotically infinite-mass; so at some point you destroy the universe. (Or at least the parts that are causally connected to you -- I guess cosmic expansion would save parts of it?)
The way I understand it is that it's not impossible to cover the distance, but that by the time you do, the distance between your starting point and your destination will have (at least) doubled due to the expansion of space.
So you're still as far away from your destination as in the beginning (or even further), but now you're the same distance from your starting position as well and are effectively stranded.
I'm afraid not, the accelerating expansion of the universe will stretch out space ahead of you faster than you can traverse it. From your perspective the galaxies will become sparser and sparser over time until you're in an ever colder eternal black void.
So you witness the heat death of the universe at ~50 years. Yet you and your spaceship are still intact then, and at times exponentially beyond it. Weird.
Though perhaps the amount of energy it would take to accelerate that much exceeds the available energy in the universe? So maybe that's what balances it.
What happens if I just keep going?