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SubstantialFrivolity I'm not even supposed to be here today
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Friday Fun Thread for October 14, 2022
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I've been waiting for the Fun Thread to post this, since it is manifestly not CW. I had a conversation about physics, namely about the expansion of space and the feasibility of intergalactic travel, in the CW thread a few days back. I came back to it, and some things I wrote have been bugging me enough that I want to issue a clarification.
Here's the relevant thread.
https://www.themotte.org/post/120/culture-war-roundup-for-the-week/15941?context=8#context
Basically I said that the expansion of the universe renders galaxies that are beyond a certain distance unreachable absent some form of FTL travel, since the universe's expansion isn't set at any constant rate of speed - any two points in space recede at a rate proportional to their distance from each other, and that distance is increasing, therefore the rate of recession of the two points is increasing. This means there will be some galaxies far enough away from us that they recede faster than the speed of light.
I got this question in response: "Is it not the case that, once we start moving towards those distant objects (in say a colony ship), the expansion behind us compensates for a growing portion of that total expansion? It's my understanding that there IS an inflection point as you describe, but we haven't reached it yet."
And this was my reply: "The case for an inflection point is pretty strong. It’s my understanding that for objects that have already crossed the boundary of the event horizon, no reduction of the distance between us and that object will occur. Think about it this way: There are objects far enough away from you that they are moving away at a rate that exceeds the speed of light, meaning without FTL travel they will be receding from you faster than you can travel to them. The space between you and any object beyond that horizon will only increase and the further they go, the faster they recede. If you try to reach it in a relativistic colony ship, all that happens is that you’ll be stranded from your original galaxy group and will never reach the new one as your galaxy of origin passes out of your event horizon. Sure, you are closer to the object and further away from your point of origin than you would've counterfactually been, but that does not equate to closing the distance."
The issue here is that there are additional real-life complexities absent in the model I was outlining which I neglected to address when I wrote this (note: do not write when you're tired unless you want to omit things you should've mentioned). Now, I don't have too much of a problem with what I wrote here - I stand behind my point that ceteris paribus, anything in a superluminally receding region of space in which expansion is driving the objects away from you faster than light would simply be completely unreachable, and you wouldn't be able to magically "close the distance" and catch up. The area where things are receding from us slower than light is called our Hubble volume, and is a sphere approx 14 billion light years in radius (everything outside of it is moving away faster than light). However, I want to clear something up: We can sometimes receive light from galaxies outside our Hubble sphere at the time the light was emitted, meaning light-speed information in a region of space which is receding from us faster than light can in fact travel to us. So how can this be possible?
The reason is because the Hubble constant (the unit that describes how fast the universe is expanding at different distances from a particular point in space) is decreasing, causing our Hubble volume to expand. This means that photons emitted by galaxies in a superluminal region can eventually enter inside of our Hubble volume and be able to reach us, and this is not because light is magically "catching up" - it is receding, but its recession doesn't outpace the growth of our Hubble volume. Similarly, the recession speed between light we emit and an object farther than the Hubble distance is initially positive, but can become negative as the Hubble distance increases. Here's a Veritasium video with a visual representation of how this can happen.
Of course, there's a limit to this too - there's a point beyond which light emitted from objects are receding from us so fast that they will never fall inside of our Hubble volume, and this boundary is delineated by the "cosmological event horizon" which is currently about 16 billion light years in radius.
There is another bigger issue that I want to correct here, and that's my statement that we might not make it outside our Local Group (and that this has something to do with expansion). I knew previously that our reachable universe was much larger than that, but of course practically speaking that's very optimistic and assumes we leave now and at the speed of light. What I was thinking was that 1: if relativistic speeds are hard to accomplish, our closest galaxies might be expanding away from us faster than we can travel, and 2: even if relativistic speeds are possible expansion might set a limit on how much we can progress before our closest galaxies are eventually isolated from us. Again, I wrote this bit while not thinking too deeply about it, and have since reasoned myself out of this position.
With regards to the first point, one of our closest galaxy clusters (the M81 Group) is currently 11.4 million light years away from us, and the Hubble constant (according to some estimates) is 68 km/s/Mpc. 11.4 million light years is equivalent to 3.5 megaparsecs, and that means the M81 Group is expanding away from us at 238 km/s. That is a very small fraction of the speed of light, and probably isn't impossible for us to exceed given that the Parker Solar Probe has already been able to reach speeds of 163 km/s. The rate of recession only becomes prohibitive for objects much further from us.
Note, this doesn't mean that I think travel to another galaxy cluster is actually that feasible, it just means expansion wouldn't pose too large an obstacle for us. The reason why it would be difficult in a practical sense is not just because of the difficulty of finding a reasonable propulsion method, it's also because of the time involved to travel the entire distance. Even in a colony ship travelling at 99% of the speed of light, the trip to the M81 Group would take an unrealistically long time, even accounting for relativistic effects from the perspective of the traveller. As viewed from the spaceship, an 11.4 million light-year trip would be 1,624,412 years long, which is far longer than the entirety of human history (here's a neat website that helps you calculate these things, for the lazy). This is assuming that we travel constantly at 99% the speed of light the entire way, it's not taking into account acceleration and deceleration to the destination, so this is a minimum estimate. There's simply no way to design for missions of that length, nor will there be for a very long time, if indeed ever.
Accelerating to 99.99999999...% of the speed of light would create enough dilation to get us there in an acceptably short time, but there's something else stopping us from doing that (even assuming we manage to find a method of propulsion which will allow us to go that fast, which is a big assumption). And that's space dust. At 99% of the speed of light, hitting a 4 milligram grain of dust in space gets you 2,188,941 megajoules of kinetic energy (here's the calculator I used, I use them because I want to mess with the variables without having to do the calculation again and again). A ton of TNT contains 4,184 megajoules of energy, so that 4 milligram grain of dust at 0.99c is going to be equivalent to 523 tons of TNT exploding. Even hitting a dust grain of 0.1 mg at that speed is going to yield you 54,724 megajoules of kinetic energy, equivalent to 13 tons of TNT.
Get closer and closer to the speed of light so that the travel duration becomes more reasonable, and eventually these grains of dust are going to start looking more and more like Hiroshima.
So it's not that I think that travelling to another galaxy cluster is feasible, it's rather that at this point, expansion is a red herring. If we can't travel faster than 238 km/s in the first place, the travel time would be far too long for us to even think about starting a mission even assuming that the M81 Group isn't receding from us. Even non-lethal relativistic speeds won't take us there in any reasonable time. Travelling to other galaxy clusters is probably FTL or nothing (we're talking Alcubierre drives and wormholes here and not actual travel faster than light, because of the constraints relativity poses, and there are still many problems with those methods which means there is plenty of reason to suspect FTL is not possible).
As to the second point about the time limit expansion imposes, it turns out the timeframe we have before our closest neighbours have receded into superluminally receding regions of space which we will never be able to reach (without FTL, that is) is hundreds of billions of years, so this timeframe probably doesn't pose too much of an obstacle. Whether exiting our Local Group is actually feasible or not in the first place is almost certainly the main factor. And the reasons why it might not be feasible are huge.
Oh dang, I just now saw this, in the October Quality Contributions thread! As the interrogator in the initial conversation, thank you for posting this. That's one hell of a follow-up, hah! This kinda stuff interests me quite a bit, but I know very little, so I very much appreciate your patience and thoroughness with this reply! Would you mind horribly if I impose on your grey matter some more? Having read this response, I think my original question was poorly put. It was based on something vaguely remembered from a throwaway conversation somewhen that made sense to me but I didn't fully grok, regarding the interplay of reference frames.
The Hubble constant indicates that the rate of recession increases as distance between the observer and the object in question increases, right? In practice thus far, all observations/measurements are made from Earth (or at least Earth-local) frames, so it seems everything outside our local frame is expanding away from us, with M81 expanding away at 238 km/s from Earth given its current distance of ~12 megaparsecs. So if we travel in that direction at 239 km/s, the rate of expansion between it and us begins to slow down, because we're a bit closer, yah? And that property scales all the way up to lightspeed: as long as we go a little faster than current expansion, we can get there. Which means we have a few thousand years to develop 99.7/c travel without unrecoverably losing much, if any, of the observable universe. (of course those atom lives matter too, but we may simply not be able to save them all)
It's possible I was thinking the Hubble constant was non-linear, which would seem to create some weirdness with multiple observers, but I'm honestly not sure. Either way, thanks again for this comment--I've been reading cosmophysics all day, lol.
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