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Could a space traveler accelerate at 1g forever?
I was reading this Reddit post and was curious about whether the passengers of this theoretical spaceship could experience 1g of acceleration forever assuming the ship has an infinite fuel source.
They shouldn’t be able to pass the speed of light relative to an outside observer, but is there some phenomenon where the passengers can feel like they are accelerating forever?
My answer is actually no: even assuming a magic fuel source, there is an important aspect to consider, which is that you are travelling though the universe and the universe is full of stuff, like hydrogen atoms. At this speed you would be basically forcing them to undergo nuclear fusion with the front of your spacecraft which is going to exert a backwards force. I think (not entirely sure) that at a really stupendous fraction of the speed of light even the radiation pressure from the (highly blueshifted) cosmic microwave background might be enough to overcome the forward force of your engine.
Look at xkcd's Relativistic Baseball - this is in Earth's atmosphere but infinite acceleration would probably be enough to make it relevant to the vacuum of space.
I'd agree with this.
And the particles and dust would get you before the CMB does. The radiation pressure of the CMB would be tiny until you are really going fantastically fast.
But the energy involved with anything slamming into the front of your spaceship would be absurd. Though I'd worry about damage and heating before drag.
So you'd need some magical way to get rid of this along with the infinite massless fuel that somehow still works.
Though it's worth noting if you solve propulsion these issues won't start hurting you until you already hit ridiculous speeds.
My idea with the CMB was along this line - if you were travelling through a truly empty cosmic void with literally no dust or gas at all just for the sake of the argument - eventually even just the light emitted from the CMB, some of the lowest energy stuff in existence, would be able to stop you from accelerating further.
In the book Tau Zero they 'solve' both issues (getting rid of the hydrogen in the path, and the fuel) by having a system that collects the hydrogen and uses this as fuel through fusion.
I put "solve" in quotes, because it obviously doesn't eliminate either problem completely, but I thought it was an interesting concept.
Don't know who thought it up first, or if both arrived to that idea independantly, but that's also the principle behind Alastair Reynolds's Atalanta.
Edit: apparently, both got the idea from an actual real life theoretical engine. The Bussart ramjet
Well, that's a coincidence. I'm literally working through Reynolds' Revelation Space series right now. Currently on Redemption Ark. So I might encounter it sooner than I'd expect.
Reynolds was actually an astronomer at the European Space Agency. Quite a lot (not all of course) of the ideas in his books have some kind of plausible theory behind them.
It's a very cool idea.
Though in the real world I can't imagine it helping. Admittedly I don't know the book.
But if you collect the hydrogen you still get momentum transfer from the hydrogen to the spaceship, only now you need it to stop moving in the spaceship's reference frame. This would make the problem only worse than if you'd just let it slam into the front. It would still be bombarding your spaceship, wrecking and cooking it as well as slowing it down. You end up paying the insanely large kinetic energy cost of the particles, to only gain a bit of energy from the fusion. Not worth it.
My guess is that if you make the spaceship even remotely "aerodynamic", you gain more than trying to use it as fuel.
Unless you can somehow make the particles keep its kinetic energy. But that would involve redirecting it from the front to the back in a way that is energetically efficient. So you'd need to teleport it into the engine without touching it or something like that. But that is possible, then you've already solved the problem. If you then still have the ambition to use it as fuel, you somehow have to make fusion happen between particles that are moving basically at light speed in the same direction. If that is not hard enough in and of itself, the time you have to make it happen will be a tiny fraction of a second because light speed.
This is so deep into the science fiction, I doubt such a technology could ever exist. No matter how long a civilization lasts. Or at least that is so far into the future that they may have some completely different way of solving this, beyond anything we'd think of today.
This isn't just a conceptual issue either; if you group cosmic rays in terms of energy and frequency you observe that they become much less frequent above a certain energy scale. This scale is consistent with the GZK limit, which comes about exactly because of this process.
That's really cool
en.wikipedia.org/wiki/Bussard_ramjet
In theory you might be able to generate a giant magnetic field that will scoop up anything in your way, and then process it into fuel for a fusion drive. Which provides thrust and powers the magnetic field.
Nothing we would be capable of making anytime soon though. And possibly there isn't enough interstellar medium for it to work. And a bunch of things could prove impossible to implement.
Yes, it’s called orbit. If you were on the ISS you would be at a constant acceleration. Technically we are also at a constant acceleration relative to the sun.
In a circle, sure? Rotational gravity has been experimented with, and if spun up to 1g, it should be able to maintain for a long period of time, fuel not withstanding.
I just want to add that you could only accelerate at 1G for approximately 3.68 years (ship time) to reach .9999 c.
Ignoring technical issues the idea would be to accelerate at 1G for 50% of the journey then flip around and decelerate at 1G for the second half of the journey. Also this would only be 41 ish lightyears of distance which is relatively (zing!) nothing on the cosmic scale.
The books/TV show The Expanse does a really good job of demonstrating this. The concept does rely on impossible fuel efficiency. But that's what makes it science fiction (or extrapolative fiction if you prefer.)
It should be noted that this number blows up a lot as you go on for longer. I ran the numbers once when General Relativity was still fresh 8n my mind and concluded that if you did constant forward acceleration of 1g for just a few years shiptime you can get to other galaxies, and you can actually get outside of what is the to us observable universe this way, within a human lifetime (but afaik you still hit a limit eventually as the expansion of the universe eventually out-accelerates you). Of course the drawback is that millions of years pass outside the ship...
Sadly at this point it's been a few years and I can't show my work anymore. But the takeaway is that constant acceleration is very strong compared to just going fast.
This contradicts the definition of observable universe. If you can get there without surpassing the speed of light, then light can get from there to us, so it's observable.
It doesn't. The observable universe is everywhere from where light could have gotten to us in the time between the beginning of the universe (ignoring the very very beginning) and now. I am talking about the observable universe centered on Earth, mind. The spaceship is of course always in its own observable universe.
Also, you argue that by the time we get there, light must have gotten back from there to earth, so the observable universe has grown to include that location in the meantime. However, unintuitively you can outrun light indefinitely while moving slower than c as long as you keep accelerating, so I believe even that's not necessarily true!
Also, perhaps more relevantly, once you're far enough away from earth, the expansion of the universe is going to make your distance to earth grow faster than light as well.
I definitely don't understand what you're saying. The first place you lost me was when you said "you can outrun light indefinitely while moving slower than c as long as you keep accelerating". I don't follow what you mean by that.
I tried doing some quick research to understand better, but I ran into this even more confounding thing: the speed of light is constant regardless of the observer. Meaning an object on a body that is moving 50% of c is going to measure the speed of a wave of light as the same speed of a "stationary" observer would. My understanding of that is that from our perspective and understanding of all things we measure, they are getting a different result for the speed of that thing. If the light was a baseball, and one person moving with it at 29 meters per second measures it moving 29 meters per second away from them, the person standing still would measure it moving 58 meters per second away from them. But with light, they both measure it as 29 meters per second. Suffice it to say, I have no reference frame of anything I have experienced in my life under which to comprehend this. How do we even know how fast we are moving? (I guess we probably don't?)
Hell, I really just want to take a deep breath, say something that sounds smart but is ultimately meaningless like "it sounds like C is actually the speed of time" and move on with my life.
Maybe I'll leave relativity to the physicists for today.
...light moves at C, but it's easier to conceptualise relativity as the speed of causality: if you're travelling close to C from a 'stationary' observer's perspective, time moves much more slowly for you, so that same light wave propagating ahead of you is still moving at C from your own perspective...at C, time dilation reaches infinity: i.e. time stops entirely and causality becomes undefined, photons arrive at the same moment they depart, etcet...
(it's a bit more complicated when you account for relativistic changes to distance and mass, but that's the gist of it)
I did not say anything about growing to include new locations, but even if you want to define it that way, that still doesn't let you reach a location outside of it.
I don't see how that squares with anything I know about relativity. You have some extraordinary explaining to do if you want to maintain this claim. If you're slower than c, then by definition you do not outrun light.
Yes but that is true of everything, including things that aren't moving, so actually, I don't think that's relevant at all.
I should be clear here that when I say outrun, I do not mean overtake (which is, I believe, indeed impossible) but manage to maintain an ever-shrinking but always positive lead. I cannot perform the math for you anymore, but I remember what the spacetime diagram looks like: Light forms its usual light cone, going up at a 45 degree angle. The world-line of the accelerating spaceship has the shape of a hyperbola with asymptote said 45 degree line. This hyperbola manages to always stay outside the light cone while never actually going faster than c (its tangents are never flatter than 45 degrees).
Edit: Also, I think I should try to be clearer on the original statement: What I had calculated back then, I'm pretty sure, was that if you kept accelerating, you could get to the edge of what is now the observable universe within a human lifetime. I then also found a larger number somewhere that took into account how far you can actually get (in today distance) when accounting for the accelerating expansion of the universe - I don't remember if I was able to verify that number myself though. I just remember that it's somewhat larger than the current radius of the observable universe. I hope this clarification makes it clear I'm not really trying to make all that extraordinary a claim.
I'm really not sure if you can ever truly leave the observable universe in the sense that eventually, no light from you will ever make it back to earth, but I feel like it should be possible?
It’s been a long time since I was looking at relativity and the expansion of the universe, but if the rate of expansion is increasing, wouldn’t you automatically cross the effective “observable universe boundary” (as defined by Earth’s perspective) just by being arbitrarily close to the boundary today with zero relative motion and waiting for the universe expansion to do its thing? I thought the definition of the “observable universe boundary” is the point where the space between Earth and that point expands faster than c and therefore light cannot reach us?
https://math.ucr.edu/home/baez/physics/Relativity/SR/Rocket/rocket.html
This does the math for travel time and also fuel requirements and some of the other strange relativistic effects.
Are you sure about that? I'm not a math major but I've followed along with the math before.
(Totally cheating on this math)
a = 1G =9.80665 m/e^2
1year = 365.25 * 25 * 3600s = 31,557,600 s
Distance = 1/2Acceleration Time^2
d= .05 * 9.80665 * (31,557,600)^2
d= 4.89 10^15m
d = .52 light years
Even this miniscule example has us accelerating past the speed of light. So with relativity in mind it's even less than .52 light years.
Can you elaborate on your calculations?
Edit: sorry I'm on mobile and my formatting is going wild.
Once you get to relativistic speeds, the phrase "constant acceleration" cannot be defined as a constant change in outside observer velocity anymore, since as you mention, that will eventually lead to going faster than c. The more accurate phrasing would be "constant force", with the relationship between force and change of velocity becoming increasingly less newtonian as you get closer to c.
I think I see 25 hours per day, and given how much of my week is eaten by my commute, I would like to vote in favour of 25 hours per day please! Just to give me a bit more time in the week to get stuff done!
{genie twinkle}
YOUR WISH IS MY COMMAND!
{Discordant noise}
YOU HAVE BEEN GRANTED ONE MORE HOUR OF TRAFFIC PER DAY
Traffic? Hah! Genie should have asked more questions before trying to curse my wish — my commute doesn’t involve traffic, we have great public transit! Traffic is a problem for those who have to drive to work, and that ain’t me!
This is the topic of Tau Zero by Poul Anderson. The novel follows a vehicle and its crew that set off on a mission to reach another planetary system, by accelerating at 1g for several years, but for reasons become unable to slow down and are forced to accelerate indefinitely. The novel solves the issue fraughtGYRE mentions of the thin interstellar gas becoming a significant obstacle at relativistic speeds by having the vehicle capture/reroute the hydrogen atoms to be used as reaction mass, thereby also addressing the issue of needing infinite fuel. It also discusses the effects of time dilation and CMB temperature shifting. I'm not qualified to say whether the mechanism is scientifically plausible, but it's an interesting (if pulpy) read.
I really love that book. Sitting on my shelf right now actually! I've read it three or four times, it's a great way to spend some time. I looked into the mechanism as described and from what I understand it doesn't really work because accelerating particles to move them out of the way causes them to emit radiation (I think this is called Bremsstrahlung) and this radiation will slow you down.
In principle you could. At least from a fundamental point of view.
For an outside observer it would look like you are asymptotically approaching c, but you never reach it. It would feel like earth gravity.
The caveat is that the energy required to keep this going grows without bounds, meaning unless your fuel source is truly infinite and massless this is not possible with regular linear acceleration from engine power.
You could instead consider rotation. In this case, you only need fuel to start spinning the spaceship. From the perspective of the people onboard, this will feel like you are experiencing a force (meaning acceleration) outward. This would be the centrifugal force. If the goal would be to engineer artificial gravity, this may be your best bet.
If the goal is just to get from A to B there's nothing really stopping you other than fuel. But you'd need to keep in mind that real fuel has mass. So the more fuel you carry the heavier your spaceship becomes and the harder it is to achieve 1g.
This in turn means two things:
If instead you wish to avoid the problem of carrying infinite mass, you could for instance considering not carrying fuel at all and go sailing instead. Solar sails powered by the sun probably won't get you very far since the radiation pressure is tiny, but with a laser you may get further. Though the laser power required for anything with a significant mass is brutal. And then the redshift starts hurting you as you speed up, so you need increasingly more power to maintain the same acceleration. And that's ignoring the fact that it becomes increasingly hard to focus the laser as the distance increases.
On top of that, doing this indefinitely is not possible due to the Rindler horizon. Basically, since you are accelerating in the opposite direction and light needs time to travel, you need to send the power increasingly earlier. At some point you hit a horizon here. This means you have a finite time to send all the laser power needed to accelerate forever. So that's another way in which the laser would need to be infinitely powerful if using sails.
Ignoring that, waste heat would be another consideration. The amount of energy required quickly becomes ridiculous and all that heat needs to go somewhere. Cooling is not easy in space since in vacuum you cannot rely on convection or conduction, so you are basically stuck with only radiative cooling. This probably becomes one of the main challenges at some point.
This is also a problem again when carrying the fuel on board unless you can make the efficiency of the propulsion perfect.
So carrying the fuel with you would make it impossible to accelerate, and beaming it towards you requires infinitely powerful lasers. Neither is possible. At this point we are already talking warp drive/wormhole/teleportation level of science fiction when it comes to propulsion.
Of course you also have the issues pointed out by /u/fraughtGYRE. So you'd have to solve that somehow. This would also come with the issue of heat again.
Then there's the issue of navigation. Unless you can perfectly aim your ship ahead of time, eventually you will need to correct you course. Eventually all the light gets squeezed into a tight cone in front of your spaceship and gets increasingly blue shifted. Somehow, your systems will have to be able to deal with that. And you can't just navigate from earth either, since then you'd end up running into the Rindler horizon again. Though perhaps you can do it from your destination.
And then on top of all of that, you'd probably want to slow down at some point as well if you actually aim to arrive somewhere. This means slowing down again.
TLDR fundamentally there is nothing stopping you. But in reality you will run into all sorts of issues that you'd need to solve beyond infinite fuel. Even with hypothetical scifi technology forever is one heck of a long time.
Infinite fuel is infinite mass in a finite volume. Tiny collisions with intergalactic protons are going to be the least of your worries as your ship collapses into the black hole caused by the infinite mass singularity, expanding outwards at the speed of light, consuming the universe in the reaches far beyond the Degenerate Era.
Instead using infinite matter, why not use merely exotic matter? All matter has positive mass and cannot take values of negative mass, according to the laws of physics (as we understand them). But if infinite masses are possible, then so might complex-valued Higgs fields. Suppose then that we had a large (but not infinite) amount of negative mass matter and enough normal matter to form a black hole.
Now we arrive at the Alcubierre Drive. It could probably be designed to accelerate at 1 g indefinitely, although you might still be floating inside it. Plenty of things could go wrong eventually, but if you have the power to make and concentrate exotic matter with negative mass, dealing with the occasional hydrogen atom collision should be no trouble at all.
As for all that pesky blue-shifted radiation: well, the universe is only going to be making visible light for the next 800 billion years, and that's in the rest frame. Once you are twenty eight 9s into your fraction of c, a trillion years will be just another Tuesday. In fact, you'll need the blue shift to make out what's happening out there in the dark. Hydrogen might not slow you down, but a giant, cold, starving black hole gliding through the void would definitely end the cosmic pleasure cruise in the unlikely event of a collision.