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A spaceship of several kilometers length is accelerating to a very high fraction of $c$ (basically as close as they can possibly get).

Which problems can the machinery and the crew encounter?

And as follow-up question resulting from this:

Is a multiple kilometer long ship traveling at near light-speed feasible?

To clarify, I'm interested on how travelling at near-light-speed is different to travelling at "normal" speed. Dodging obstacles is not in the scope of this question and has already been addressed.

I expect the following things to be problematic, but don't know if they are actually. It would be nice if you could address them, as well as adding other problems you see.

  • Moving fuel to the engine. It has to be decelerated to move from the tank to the drive at the back of the ship. What happens with that energy?
  • Moving inside the ship. If it is possible for a human to actually accelerate enough to move, I expect moving down the same corridor in two directions can already be quite an adventure.
  • Communicating. If a sensor picks up a problem at the drive, the signal has to travel to a mechanics/computer console, be evaluated (maybe in slow human brains) and then be reacted on.
  • Turning the ship to brake. During the turning, different parts of the ship move at slightly different speeds.
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    $\begingroup$ When a vehicle accelerates to a high speed we feel the acceleration and the maneuvers, not the "speed". Wouldn't the crew's experience be relative to the ship, and thus not noticeable as long as the ship doesn't attempt any maneuvers? $\endgroup$
    – AndreiROM
    Commented May 9, 2016 at 20:29
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    $\begingroup$ @AndreiROM so can the crew, fuel and cargo be handled for all purposes as if in rest? That would change the question to How can I notice if I'm travelling near $c$? $\endgroup$
    – JFBM
    Commented May 9, 2016 at 20:45
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    $\begingroup$ I'm not a physics expert, so don't take my word for it as it were, however consider that when you're travelling in a very comfortable car at a relatively high speed (or a very smooth train) you don't even realize how fast you're moving. Your water bottle isn't shaking, and the water isn't being pushed into the side of the container, correct? However, if the car were to break sharply, boy do you feel it. Same thing with your ship, unless physics starts behaving differently at close to light speed. $\endgroup$
    – AndreiROM
    Commented May 9, 2016 at 20:49
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    $\begingroup$ I have a degree in physics and I can guarantee AndreiROM is one hundred percent correct. $\endgroup$
    – Akshat Mahajan
    Commented May 9, 2016 at 20:50
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    $\begingroup$ @AkshatMahajan - my only concern was that things might start behaving a little differently as you approach light speed. Glad to hear I'm not hopeless :-P $\endgroup$
    – AndreiROM
    Commented May 9, 2016 at 20:51

4 Answers 4

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Travelling at near-light speed is indistinguishable from being at rest.

This is the principle of Galilean relativity, and is preserved under special relativity: there is no feasible experiment to determine whether you are stationary or moving at a constant velocity. So there are no practical problems that would occur simply from moving at near-light speed that wouldn't occur at rest, and vice-versa.

Since everything inside the ship is moving with the ship at the same speed (this is why you aren't flung backwards when you jump while on a moving train), neither the crew nor the fuel nor the communications will be affected: for them, the world will be exactly as it would be it were not moving at all. It's the world outside the ship that would appear to experience the odd effects of Lorentz contraction, time dilation, redshifting, and what-not: everything inside the ship is its own protected bubble. (Of course, someone outside the ship would claim it was really the ship itself experiencing these odd effects, and that's perfectly fine).

The only time engineering is required is to handle the following cases:

  • Acceleration: This is the only time when frame invariance is relaxed. Deceleration will cause massive stresses on your ship building materials, depending on how quickly you want to come to an abrupt halt. You should anticipate long deceleration times, something your crew will have to take into account. Conversely, accelerating to light speed will also take a long time if you want to avoid enormous compression stress. This includes rotation. A full treatment of what the world looks like for such rotating frames can be explored by examining the Kerr metric.

  • Navigation: Your starboard computers will register large amounts of redshifting from nearby stars, which can skew your metrics of where you are or what you are dealing with if you're using Hubble's law. A correction factor must be applied to all of your sensors to account for this - this can be easily calculated by knowledge of the ship's velocity.

  • Synchronisation with off-ship clocks: For the crew inside the ship, it will appear as if life outside the ship is moving at a much slower rate. As a consequence, significant discrepancies between clocks at the ship's port of arrival and the ship's internal clocks will occur. This affects messages sent to the ship and any attempt to synchronise with the world outside. Again, a correction factor can be calculated and employed but must be known in advance.

  • Knowledge of ship velocity: While this is on the surface not hard to solve - just measure the velocity of things moving relative to the ship - the devil lies in the details. Objects moving relative to the ship have their own velocity prior to the ship's acceleration, which skews measurements. One way out is to use standard candles, which we already currently use to estimate distances - simply compare the luminous intensity from a standard candle at one second and the luminous intensity at another, and use it to work out the distance that has been travelled. From this you can work out velocity.

You may also want to consider general relativistic effects: a ship moving at that speed has an incredible amount of kinetic energy, and will thus exert a significant gravitational influence in its wake (assuming its mass is already sizable to begin with). You'd have to figure out a decent flight plan that doesn't leave too much damage behind.

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  • $\begingroup$ Actually if you put someone at one side of the ship, someone else at the other side. Let assume that the ship is 3km long, traveling at 99.9999% of c (=~300000km/s), a message from the rear to the front traveling at light speed (laser + morse code, easy) will seem to travel at 300m/s, slower than the speed of sound in air (=~ 350m/s). Am I right? $\endgroup$
    – Nyashes
    Commented May 9, 2016 at 23:02
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    $\begingroup$ No. Relativity requires that all observers, regardless of the speed they're moving at, measure the speed of light to be exactly c. In relativity, the traditional velocity addition rule is no longer valid - you have to use a modified version $\endgroup$
    – Akshat Mahajan
    Commented May 9, 2016 at 23:07
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    $\begingroup$ Note that the total distance covered by the message is exactly the same as if it were at rest: both person A and B are being displaced by the same amount at the same pace. The message will be transmitted at exactly c by fiat, and A and B will notice no difference than if they were 3 km apart on stationary ground. $\endgroup$
    – Akshat Mahajan
    Commented May 9, 2016 at 23:11
  • $\begingroup$ @AlexandreTHOUVENIN Time and Space get weird at relativistic speeds. "There is no feasible experiment to determine whether you are stationary or moving at a constant velocity" was already stated as fact (and proved). Your hypothetical example would imply that you could determine that you were moving at a relativistic velocity, ergo either there is a test or your example is wrong. $\endgroup$
    – Draco18s no longer trusts SE
    Commented May 15, 2016 at 5:00
  • $\begingroup$ Redshifting is just one issue - blueshifting is another. Since cosmic background radiation comes from all sides, part of that should be blueshifted to very short wavelenghts. Depending on your speed, the microwaves that "hit" the front of your ship are shifted to visible light, x-ray, gamma or beyond. $\endgroup$
    – Thomas
    Commented Apr 19, 2017 at 11:35
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One of the nice things about relativity is that it doesn't matter how fast you are traveling, only how fast you are traveling relative to something else. So what does that mean?

  • Moving fuel to the engine - as easy as if the ship was stopped
  • Moving inside the ship - this could be hard while you're accelerating or decelerating, and there would be a lot of that if you're getting close to light speed. However, the ship's speed doesn't matter - if you're accelerating at 1G, it will be as hard to move around whether the ship's just leaving orbit or already at 0.9c.
  • Communicating - from the perspective of anyone/anything on the ship, everything is as if the ship is moving slowly. So signals from the drive can make it to the bridge of the ship just as fast as if the ship was stopped.
  • Turning - it's as complicated as if you were turning while in orbit around a planet.

So what is a problem with near-light-speed travel? Reacting to outside stimuli, and getting to and from your desired travel velocity.

Reacting to outside stimuli is dodging, which is not the focus of your question, and navigating. Navigating shouldn't be a significant problem though - if you have the tech to get anywhere near light speed, you should be able to plot your trajectory well enough to make navigating fairly simple.

So getting to and from your desired travel velocity is the only real problem you have to worry about. What's so hard about this? At relativistic speeds, your kinetic energy is described by the following formula:

$$K=mc^2\Big(\frac{1}{\sqrt{1-v^2/c^2}}-1\Big)$$

If $v=\frac{\sqrt{3}}{4}c\approx 0.866c$, which you might not count as a "very high fraction of $c$", we get $K=mc^2=E$. In other words, the ship has as much kinetic energy as energy you could get from converting the entire mass of the ship into energy. So one way to get going that fast would be to have a fuel tank carrying as much mass as the entire rest of the ship, and have a way to convert every atom of fuel into pure energy with 100% efficiency.

With a nuclear reactor, we can currently use about 0.1% of uranium's mass worth of energy. So with a nuclear reactor that could run in space and convert the energy it produces into velocity with 100% efficiency, you could get your kinetic energy up to $K=0.001mc^2$. That gets you up to about $0.045c$. Again, this is if your fuel tank carries as much mass as the entire rest of the ship.

Oh, and don't forget that you have to decelerate once you get to your destination. So "your ship" that you have to accelerate consists of your actual ship and the fuel tank carrying enough fuel to decelerate.

In summary, to get a 10000 metric ton spaceship to $0.045c$, you need 10000 metric tons of uranium to decelerate, and 20000 metric tons of uranium to accelerate. Oh, and a 100% efficient reactor and engine, neither of which can actually exist due to entropy always taking a share. Also you may have realized that if you have 10000 metric tons of spaceship and 10000 metric tons of uranium, you're got to accelerate all the unused uranium.

So getting to a "very high fraction of $c$" just isn't feasible unless you're willing to use up a ridiculous amount of fuel. Unless you consider $0.01c$ to be a very high fraction.

Let's work out an example of an actual "very high fraction of $c$", using an Ohio-class submarine as our starting point. It has a length of 170m and mass of 18750 tonnes. If we scale that lengthwise by 20 we get 3.4km, in the range of your "several kilometers". If we double the cross-sectional radius to make it at least a little bit more cozy, we've now increased the total volume by factor of 80, for an approximate mass of 1.5 million tonnes. I don't know how this compares to what you had in mind for your spaceship, but this is a very long but narrow spaceship. Now how much energy does it require to get this to "a very high fraction of $c$"? To get this ship to $0.99975c$, you need around to convert almost $6*10^{24}kg$ of mass into kinetic energy for the ship. That's the mass of the Earth.

In short, if you're not working with unobtanium/applied phlebotinum/magic you're not likely going to be able to get close to $c$.

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  • $\begingroup$ I have heard of some ideas of using a really really powerful laser pointed at your ship to transfer energy from a source outside of the ship. This could solve a lot of the problems you're describing. Also it shouldn't be too hard to reach 0.9something c, given that you can prevent deceleration due to friction and accelerate slowly. $\endgroup$
    – Florian Wendelborn
    Commented May 13, 2016 at 17:43
  • $\begingroup$ @Dodekeract there's still the problem of decelerating before reaching your destination. My main point is that it takes a ridiculous amount of energy to get close to light speed. 0.9something c can be infeasible regardless of what is supposed to be doing the propulsion - see the example I just added. $\endgroup$
    – Rob Watts
    Commented May 13, 2016 at 18:14
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AndreiROM is right, thanks to our friend inertia the only time you'd notice anything is while the ship is actively thrusting during acceleration and deceleration, or if you turned really sharply.

This actually has something of a beneficial nature because you could build the ship to where the floor is "down" during thrusting, and so you get something like gravity.
Imagine the ship is sitting on it's drive in Earth gravity. Build the decks so that the floors are where gravity is pulling, and have lifts/ladders to get between decks.
While the drive is operational it will be pushing the floor up toward your feet with the net effect that it will feel like there is gravity. How much gravity depends on how hard the ship is thrusting.

It would be more like a several kilometer high skyscraper instead of a several kilometer long ship. If the decks are laid out parallel to the direction of travel then you will be pushed back toward the back of the ship any time the drive is going, and this would severely limit the amount of thrusting you could do to get up to your desired speed, unless artificial gravity is a thing.

This question has some interesting numbers when it comes to travel times, in case it helps you any:
https://space.stackexchange.com/questions/840/how-fast-will-1g-get-you-there

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One rather big problem that you haven't mentioned is the impact of material in the interstellar medium. While gas and dust in space is extremely diffuse, at near-light speeds even a few hydrogen atoms, let alone dust particles or micrometeors, will carry significant energy that will wear away the hull of the ship over time. You're going to want to put some sort of shielding up at the front of the ship to absorb the damage. Also, unlike slower ships which can be shaped like anything, it actually benefits near-light-speed ships to have a streamlined shape to reduce friction and damage.

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