Does my shipboard computer slow down as I approach light speed?

Question

This question about time dilation got me thinking.

The speed of an electron through copper is a whole heckofa lot slower than the speed of light, but if I understand the limits of relativity correctly, the electron can never travel faster than the speed of light anyway.

Now, let's ignore the ultra slow drift velocity (<<0.01c) and stick with signal propagation, also known as the velocity factor (~.95c). If you're not aware of the difference, consider a Newton's Cradle. The middle balls hardly move (drift velocity) but the last ball in line goes winging off into space (velocity factor).

So, if my ship is traveling at 0.95c then the "ball at the end" of my Newton's Cradle is moving at the same speed as the ship, and since I'm dealing with relativistic problems, it's standing still, right?

Which means, if I'm correct, my computer is at a standstill.

Am I correct? Will humanity need to come up with a non-EM logic board to perform course calculations for relativistic ships? Or will relativistic speeds always be limited by the computational speed required to make course corrections? (Making massively parallel computing a very desirable thing).

Answer 1

This is a pretty interesting topic, and one of the things that makes special relativity so mind blowing. But the answer is:

From your perspective on board the ship, the computer will function just as fast as it would if you were using it on Earth. After all, physics doesn't care about which inertial frame of reference you're in, so it wouldn't make any sense for the computer to work in some frames and not in others. However, from the outside perspective of a "stationary" observer, your computer would indeed be running slower -- though not at a standstill. Note: I put the word stationary in quotes because in special relativity, there's not really such a thing as stationary. All motion is, well, relative. What I should really say is "an observer moving quickly with respect to the spaceship", but that's not nearly as catchy.

These seeming paradoxes are explained away with the help of time dilation, length contraction, and the relativistic velocity addition formula. I might go more in depth here later if I have the time, but suffice it to say that the main place your thinking is going wrong is that you're unconsciously assuming that time and space are absolute. In reality, they start stretching and contracting when you move between different reference frames, and the end result is that the computer works just fine for the astronauts using it, but looks like it is running slow for outside observers. As an analogy, note that all biological processes take place at sub-light speeds, yet the astronauts will not perceive themselves as slowing down.

EDIT: Here's a slightly more math-y explanation, for those so inclined.

To truly channel the spirit of Einstein, rather than spaceships and electrons I'll talk about trains and baseballs. The concepts are exactly the same, but this is perhaps more concrete. Anyway, suppose little Jimmy is standing on top of a speeding train throwing his baseball, as kids are wont to do. Say the train is moving at $20 m/s$, and from Jimmy's point of view, he's throwing the baseball at $20 m/s$ in the direction the train is moving. Now, how fast will old man Jenkins, who's standing on the platform, see the baseball travelling? Why, $40 m/s$, of course! How do we know? Well, we simply added the velocity of the train and the velocity Jimmy throws the baseball at, since the baseball is already traveling at $20 m/s$ just by virtue of being on board the train.

Now, suppose the conductor got bored and told the engineers to speed the train up to $0.95c$, while Jimmy undergoes intense physical training to get his fastball up to $0.95c$ as well. Now suppose Jimmy has lived on this train his whole life. From Jimmy's point of view, he's just standing on a stationary train throwing a fast ball at $0.95c$. No biggie. From his point of view, the Earth is the thing moving really fast, while he's standing still and throwing the fastball at sub-light speeds. So there's no problem from his end.

But what about old man Jenkins? Surely, he'd see the fastball moving at $0.95c+0.95c=1.9c$, violating the speed of light, right? Wrong! Due to some clever arguments (that actually only require basic trigonometry to follow, if you're interested), old man Jenkins will actually see everything Jimmy is doing being done slower than normal and squished along the direction of travel. The net effect is that to Jenkins, the velocities of the baseball and train won't add in the usual way. Instead they'll follow the relativistic velocity addition formula: $$u = \frac{v+u'}{1+(vu'/c^2)}$$ where $u$ is the speed of the baseball old man Jenkins measures, $v$ is the speed of the train, and $u'$ is the speed of the baseball measured by Jimmy. Plugging in the numbers, we get $u=0.9986c$, rather than the $1.9c$ we would naively expect.

Now go back and mentally replace every instance of the words "baseball" and "train" with "electron" and "spaceship", respectively, and I think you'll find the answer to your question.

Answer 2

Approach the speed of light with respect to what?

Right now there is an electron flying around in a synchrotron somewhere which is moving at an appreciable fraction of the speed of light with respect to you and your computer: which means that you and your computer are moving with an appreciable fraction of the speed of light with respect to that electron. So, has your computer become slower because of this?

The point is that all movement is relative, and all the laws of physics are the same in all inertial frames. There is no aether, there is no fixed space. We are all moving at relativistic speed with respect to some frame of reference; this cannot possibly affect the laws of physics in our frame of reference.

Answer 3

From all of the answers and the comments therein, I think the issue is simply a lack of understanding of relativity, so this answer is mostly just going to be a primer in how to think about it.

I am not a teacher, nor a physicist. Forgive me if I make errors, and point them out so I can correct them. However, I am friends with an excelent physics teacher, and I got the privilege of sitting in on his class when they were learning relativity. He started out with a few of the more interesting thought experiments, like the one with two flashing lights on a train. He kept going and going, and you could watch the students getting more and more perplexed. Finally one student slammed his hand down on the table and yelled "Bull-----!" My friend did not miss a beat, and immediately replied, "Good! Now class can begin!" If the claims of relativity do not bug you at first, that means you are not paying enough attention. They should bug you. They're freaking weird!

Now I am just writing this text as I go. I don't have the privilege of waiting until I hear you shout "BS!" at me, so I have to take a different approach. I find it's effective to make sense of relativity from a historical perspective. The original investigators got to think the same sorts of naive theories that we all think of, and as relativity evolved, they tried to call BS, but couldn't because the evidence showed that the universe was actually that weird.

Before Einstein, there was Maxwell. Maxwell's equations were a very effective set of equations for modeling the propagation of EM waves. They predicted basically everything we could test when it came to EM waves. However, there was a catch. In Maxwell's equations there was a really natural derivation of a "wave velocity," that is the velocity that an EM wave propagates in. Now if we do any of the standard experiments where I stand on a train and throw a baseball or something, we're used to the idea that I perceive the baseball as traveling slower than you perceive it when you're on the ground. But Maxwell's equations only offered one wave velocity for EM radiation, c -- the speed of light.

The natural assumption that many scientists made in that age was that light traveled through some sort of medium, just like soundwaves travel through air. Thus the natural "privileged frame" for defining the speed of light was the frame of this medium, called the Aether. And, of course, we expected it to behave similar to how air does, with doppler shifts and shock waves and what-not. There were other theories too, but Aether is the most fun to talk about, and it lines up directly with your concept of an electron traveling at a high velocity with respect to a ship that is traveling at a high velocity.

At some point, scientists started experimenting to try to pin down this Aether's frame. They did many experiments, the most notable was the Michaelson-Moorley experiments. The idea behind these experiments was that the Earth is clearly orbiting the sun, so its velocity with respect to the Aether should change over the course of a year. The experimenters just had to look at the velocity of light waves in a couple directions, and see how they differ. Then we could make calculations about our movement through the Aether.

When they compiled their data, they noticed a really strange thing. The velocity of light was the same in all directions. It didn't matter if you pointed the light with the orbit of the Earth, or against it, or if the Earth was on one side of the sun or the other. The measured speed of light was the same every time. This meant one of a few things:

• The Earth really was the center of the universe, being connected directly to this heavenly Aether.
• The Aether was somehow being "drug" along by the Earth so completely that we couldn't even detect any relative velocity (they couldn't fly experiments in space at that time)
• Maxwell's equations were incomplete.

Eventually it was found that the Aether drag, or whatever other effect was occuring, caused EM waves to exhibit what is known as the Lorentz Transform. They found that if you took Maxwell's equations in one frame and modified them using the following 4 subsitutions:

$t^\prime=\gamma(t-\frac{vx}{c^2})$
$x^\prime=\gamma(x-vt)$
$y^\prime=y$
$z^\prime=z$

Where $v$ is the relative velocity between this frame and the next frame in the x axis, you got numbers which lined up. This transform "fixed" the equations so that they matched the data. Science is good about that: always make sure your model matches the data, even if the data looks schizophrenic.

Now I don't think you need to appreciate exactly what those equations are. What you have to appreciate is that they are messy. Physicists hate messy. Messy usually means we didn't understand the problem fully. This transform at least meant our physics wasn't provably wrong, but that doesn't mean the physicists had to like it. This transform has all sort of peculiarities. For example, we see time dilation and length contraction here, written right into the equations for $t^\prime$ and $x^\prime$.

Also note that by twiddling with time, we broke simultaneity. Remember the story my physics teacher friend started with, with the train with flashing lights? It turns out that you and I can disagree on what order lights flash in, based on where we are standing. There may be some "proper time" order for the "correct" observer, but EM didn't provide any way to identify where that "correct" observer was.

Einstein's brilliance was in the idea that all inertial reference frames were the "correct" one. He threw away the idea that simultaneity had any meaning at all, and started from the principle of relativity:

If a system of coordinates K is chosen so that, in relation to it, physical laws hold good in their simplest form, the same laws hold good in relation to any other system of coordinates K' moving in uniform translation relatively to K.

Okay, maybe Einstein's own words aren't quite so clear to the layman. Let's use a thought experiment with a train. If I'm on the train and you're on the ground, and the train is traveling at a constant speed with respect to the ground, then the laws governing the speed of light are equally valid in both my frame and your frame. I'm allowed to see that the speed of light is $c$ in all directions, and you are allowed to see that the speed of light is $c$ in all directions, even if I am the one holding the flashlight, while traveling really fast on the train.

Sound messed up? Of course it does. Relativity is wierd! But what Einstein proved was that if you start from this principle of relativity, you naturally derive the Lorentz transform from that principle. The horribly ugly math of the Lorentz transform was still valid, but now it had a simple explaination: the laws of physics remain the same while changing frames.

And indeed time dilation was a major factor in the cementing of relativity as "the right theory." Once we had clocks accurate enough to experiment with this, we found that, indeed, this kooky theory was right. Time was not absolute*. Time could progress differently for different frames, and there was no global concept of simultaneity.

So in your relativistic space ship, computers work just like normal, because in their frame, light is traveling at light speed, so electric waves can travel at 0.95c without breaking any speed limits. If those electrons were viewed from the ground, they would be seen as going at 0.9986c, which is faster, but still not faster than light speed. The stretching and contracting of our concepts of time and space would account for all the oddities that arise from that, and if you want to see the equation which you can use to calculate that 0.9986c, I recommend reading el duderino's answer, which is where I stole that number from. His answer also has the equation used to calculate that.

So when you are doing relativistic spaceship thinking, always remember that every frame is a privileged frame for EM radiation. Light travels the same speed no matter what frame you are in, so you can always solve problems by simply picking the most convenient frame. In this case, it's the frame of the space ship.

Answer 4

Your question falls into a frame of reference fallacy category.. The electrons are travelling at 0.95 c in the ship's frame of reference. This is irrespective of whether the ship is stationary *relative to whatever) or moving at any any velocity and it doesn't matter if it's moving backwards or forwards or even sideways. It will remain the same: the electrons are travelling at 0.95 c in the ship's frame of reference.

To an external observer the ship can zip past at 0.95 c. OK, so that takes of the ship. Now granting the external observer some form of hand-waved, "magic" super-duper observing instrumentation to be able to observe what the electrons are doing.

Will the external observer see the electrons are stationary? Absolutely not! The external observer will observe the moving at a higher relativistic velocity than 0.95 c. So the electrons in the computer will still be moving. However, it requires calculations passed on the sum of relativistic velocities. The electrons will be time dilated but the amount of time dilation will be determined in terms of their relative motion.

The proposition the electrons are stationary in a moving ship only makes sense if the electrons were, for example, fired out of an electron gun at 0.95 c in the stationary frame of reference, which can be described as external to the ship itself, and the ship and the electron will be stationary relative to each other. However, the electrons running inside the computer on the ship will still be moving at 0.95 c in the ship's (internal) frame of reference.

Note: the electron fired out of the electron gun is best considered to be outside the ship and the electron gun is at rest with respective to the ship which is moving away at 0.95 c in the electron gun's frame of reference. So from the ship's frame of reference, the electron gun is receding at 0.95 c

Like most apparent contradictions of special relativity things go wrong, conceptually, when people mix up the wrong frames of references. This is definitely the case here.

Answer 5

I see a lot of (good) answers that all go into Relativity and its consequence, but none actually answers the question of the OP:

Will humanity need to come up with a non-EM logic board to perform course calculations for relativistic ships?

That answer to that is: Yes. And no - it is not physically possible to come up with something else that will work faster. The reason has nothing to do with relativity - as others have pointed out, the computer in your spaceship will work at normal speed from your perspective. But things in the universe will be coming towards you at a very fast speed. And you will only see them at the last moment because light only travels a little faster. So you will simply have a very short time to react.

Let's take an example. Suppose you have good sensors/telescope and can detect small objects as far away as the Sun, that is, 8.5 light minutes away. And suppose you are traveling at 99% of light speed. From your perspective, that means that these objects are traveling towards you at 99% of light speed. And due to relativistic length contraction, they are actually not 8.5 light minutes away, but more like 1.2 minutes. So the light of these objects takes 1.2 minutes to reach you, but the objects themselves take only 1.212 minutes to reach you. Therefore, your reaction time must be better than 0.73 seconds. And this is inclusive the time it takes to move the ship out of the way...

To add to that, you would want to get out of the way as well, because the objects will have enormous kinetic energy. If I calculated it correctly, a 1 gram object will hit with approximately the energy of an atomic bomb.

Answer 6

Your ship runs fine

Everything on board your ship operates exactly as it always does; there is absolutely nothing out of the ordinary going on. You don't even look that unusual to the people you pass by.

Despite the popular description, time dilation isn't really that "things slow down". Instead, time dilation is about the fact that when people take divergent trips and then meet back up, their watches don't agree. Time dilation is an obstacle to synchronizing distant clocks.

The usual idea of time dilation is really about a single POV deciding upon a convention for a universal time standard (there is no physical basis for such a standard). If they are sufficiently inertial, then by this specific standard, that person's clocks will run faster than anyone else's.

But any other person can establish the same convention with them at the center instead, and (if they're sufficiently inertial) it's their clocks that run the fastest.

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The better way to think about the situation is simply that the trip will go by more quickly. A human sitting on Earth has to wait 8.5 years for a light signal to make a round trip from Earth to Proxima Centauri and back, but a space traveler travelling at 0.95c (as measured by the people on Earth as you leave and return) will make the round trip in merely 2.7 years, as measured by their own clock.

A noticeable difference in elapsed time to be sure, but it's not even an order of magnitude in effect.

Answer 7

The idea of a course corrections at the speed of light is the point of failure, not the computer which is "handling it". Once your ship is proceeding forward at the speed of light, the light which it is receiving from "up ahead" will be too old to be relevant.

For example, a particle of dust which becomes visible at a distance of one light second will hit the ship one half second after it is first seen. The light which reflected off of it as it first came into sensor range will meet the incoming ship midway through its one light second perimeter. Even if the computer decides instantaneously to evade the particle, that still leaves no useful time for evasion.

We will have to bully our way across space once we reach light speed and beyond. Captains screaming "Correct Course" or "Evasive maneuvers" will be quaint misconceptions from the scifi of our distant past.

Answer 8

Why work so much, when you can just make a nice, fast computer with quantum entanglement? If your story characters can manage 0.95c, that should be a lot easier.

However, to answer your question, for you, the computer will work JUST fine. You will detect no change in the computing speed. However, for someone outside, the computer will appear to move a lot slower.

Answer 9

I think that once spaceships get going that fast, better computers will be in place. Supercooled superconductors, or maybe room temperature superconductors, or maybe just light being conducted, will allow calculations to be done at the speed of light. So electrons in copper is perhaps not the right way to be thinking of this.

Answer 10

Yes.

Work this problem backward with a simpler example.
Let's say your computer is a ramp with a marble that hits the stop button. You start going the speed of light with the marble going down the ramp and without external influence you will never stop. I like to think of momentum at relativistic speeds as a energy parasite. Not chemical energy so things freeze. All energy so things stop.

External influence is important here because that's the only way you will stop or turn. An external EM source will be needed to shut down your engines.

Dialing this back to 0.95c makes it so you don't need to collide with some radio single that originated from somewhere besides your ship. Your computer will be very slow but space is very big so you'll have time. Just be ready to slam on the breaks when that planet starts getting bigger.

Edits based on feedback:

Example 1: If an Earth based turret and a ship based turret going 0.95c start targeting each other at the same time the earth base one would shoot first. The computer at relativistic speeds has a clock that ticks slower so it calculates slower so it fires the lasers later. If Earth and the ship are close enough together Earth could hit the ship before the ship fires and the ship would think "Oh my god how did they target us so fast".

Example 2: Your 0.95c ship buzzes a planet and asks them to do a calculation. The planet will do the calculation faster than the ship thinks possible. Or the reverse might happen - "Sir they haven't responded to the order. Oh they are still decryption the message."