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Supposed we have a ship travelling at the speed of light, or very close to it, or over.

A second ship is travelling behind it at the same speed.

The second ship wishes to communicate something to the first ship, but they can't transmit radio waves or even fire lasers at the ship in front, as that would violate general relativity. Is there any way for them to communicate without overtaking the ship (assuming they could) and sending messages downstream?

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    $\begingroup$ I believe it will fall under the same thing as if "how am I able to talk to someone if being inside plane which goes faster than sound?" $\endgroup$ – Pavel Janicek Dec 11 '14 at 10:53
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    $\begingroup$ @PavelJanicek I'm not at all sure about that, considering that sound is pressure changes in (relatively stationary within the airframe) air, whereas this is about EM and hits against the upper speed limit of the universe. $\endgroup$ – a CVn Dec 11 '14 at 10:55
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    $\begingroup$ @roryok More detail about how the ships are able to travel at relativistic or even FTL speeds may help shape answers in a way that is more useful to you. $\endgroup$ – a CVn Dec 11 '14 at 10:56
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    $\begingroup$ There is a major misconception on the question. Speeds are not just added in Relativity. $\endgroup$ – Envite Dec 11 '14 at 11:15
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    $\begingroup$ @MichaelKjörling But the whole point of relativity is that light appears to travel at the same speed, regardless of the speed of the observer. Yes, there is a speed limit but the way that velocities are combined in relativity means that, e.g., a space ship travelling at half the speed of light and firing a laser forward neither causes the laser light to move at 1.5x the speed of light (exceeding the speed limit) or at half the speed of light (seeming to go slower so it doesn't exceed the speed limit). $\endgroup$ – David Richerby Dec 11 '14 at 12:26

11 Answers 11

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It is impossible for the ship to travel at the speed of light, it can at best travel close to the speed of light. The difference matters.

There is nothing really stopping two ships travelling at a speed arbitrarily close to c from communicating with lasers or radio. It will take the laser the same time to travel the distance as it would if you travelled at some other speed. The speed relative to some outside objects is irrelevant. In this case the relative speed is zero so there won't even be Doppler shift or weird relativistic effects.

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    $\begingroup$ Interestingly, this is true even if the ships are traveling away from each other at close to the speed of light. If ship A and ship B both depart planet P and head in opposite directions at close to the speed of light relative to P, ship B will appear to ship A as moving at a slightly faster speed in the opposite direction, but still under the speed of light. This means a signal can be sent from ship A to ship B and it will eventually 'catch up', since the relative velocity of ship B to ship A is still less than c. $\endgroup$ – Dan Bryant Dec 11 '14 at 13:45
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    $\begingroup$ @DanBryant I don't really understand that part: ship B will appear to ship A as moving at a slightly faster speed in the opposite direction. I thought that ship B wouldn't appear to A at all since their relative speed is above the speed of light. Maybe I got it wrong, but I thought this was part of the reason why our observable universe is limited (because objects outside of it are moving away from us at a relative speed greater than light speed) $\endgroup$ – Vincent Dec 11 '14 at 15:26
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    $\begingroup$ @Vincent, Yes, it's a bit counter-intuitive. If A is moving at -0.99c relative to P and B is moving at 0.99c relative to P, then B is moving relative to A at approximately 0.99995c, according to the formula for the addition of relativistic velocities. $\endgroup$ – Dan Bryant Dec 11 '14 at 15:40
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    $\begingroup$ @Phaeze: Right now it looks implausible. Quantum entanglement results in effects over distances immediately, but the effect itself is unobservable. Theres no way to use it to transmit information. $\endgroup$ – Mooing Duck Dec 11 '14 at 22:36
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    $\begingroup$ @Jonathan: Correct. The light travels a $c$ as measured by an observer in the car, and also as measured by an observer standing on the road. The relevance of that to the question is that these two spacecraft barrelling along at near-light speed, one behind the other, will each measure the signal travelling between them at $c$. $\endgroup$ – Steve Jessop Dec 12 '14 at 11:03
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With real physics, yes, they can communicate. Both ships must be travelling under the speed of light, and so any light wave (or radio data) sent from one to the other travels at the speed of light, even from the point of view of the first ship!

This means that if you have two ships travelling on a straight line at 0.99c 300.000Km apart one from the other, the communication would be perfectly normal with just a delay of 1 second. In this case, the ships are not moving one with respect the other.

If you go for Faster Than Light travel, you are on science-fiction domain, and the same means you use to have FTL engines can be used to have FTL communications.

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    $\begingroup$ For the point of view of the ships time is traveling slower, so the light seems to them to take a second to cross but that second might cover the same time as a century to an outside observer. $\endgroup$ – Tim B Dec 11 '14 at 11:37
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    $\begingroup$ @roryok No, relativity means the exact opposite of that: light travels appears to travel at the same speed, to any observer, regardless of how fast the observer is moving. $\endgroup$ – David Richerby Dec 11 '14 at 12:20
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    $\begingroup$ David, thank you. You just did more for my understanding of relativity with that one sentence than years of personal research has done. What an elegant way to put it. $\endgroup$ – corsiKa Dec 11 '14 at 14:44
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    $\begingroup$ "if you have two ships travelling on a straight line at 0.99c 300.000Km apart one from the other": Actually you would have to say whether the distance is from the ship's frame of reference of from the frame of reference of the observer "at rest" who sees the ships pass by with 0.99c. Because the latter one sees a Lorentz-contracted length, and so if he sees a given distance between the ships, then the distance as seen from the ships themselves will be much longer (at 0.99c, it will be about 7 times as long). $\endgroup$ – celtschk Dec 13 '14 at 21:57
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    $\begingroup$ @corsika look up Michelson-Morley experiment The astonishing (at the time) result that the speed of the sun's rays is the same whether you are approaching the sun or moving away from it, is what got people thinking on the track that lead to relativity theory. $\endgroup$ – M.M Dec 14 '14 at 7:53
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If the ships really are travelling at the speed of light, using known physics (which is possible, sort of — see below), then they cannot communicate.

The reason for this is time dilation: the closer to the speed of light the ship moves, the slower its proper time passes. At the limit of a ship moving at the speed of light, no proper time passes for it — from the perspective of the passengers, they arrive at their destination immediately after embarking on their journey. Thus, there will be no time for the passengers to send or receive any messages, or to do anything else, during the journey.

So, how can we make a ship travel at the speed of light using known physics? Well, according to the theory of relativity, only massless particles like photons can reach the speed of light, so we'll have to make the ship (and anything it carries) out of light (or some other massless particles, but light really is the most convenient).

In practice, such a "ship" would be more like a Star Trek transporter than anything one would normally describe as a spaceship: at the departure station, using Sufficiently Advanced Science™, the passengers will be converted into a pulse of light, which is beamed at a distant receiver that reverses the process. As far as the passengers are concerned, the process resembles instantaneous teleportation, although, of course, a year of (coordinate) time will actually have passed for every light year so travelled.

Of course, this process would be a lot more convenient if the "passengers" were already encoded into easily transmissible information — that is, if they were either AIs, or humans (or other originally biological creatures) somehow "uploaded" into software. In fact, if you want to transmit beings with physical bodies this way, the easiest way would be to first scan into a software emulation, transmit the software, and then, if desired, rebuild new bodies for them at the destination. (Hey, I didn't say it would be easy — just easier than the alternatives.)

Or, of course, you can postulate some new physics (or exotic edge cases of current physics theories, such as stable wormholes) that allow faster-than-light travel. In that case, however, you're pretty much free to assume anything you want about how in-flight communications would work (or not work, as it might be). For the specific case of wormhole travel, a reasonably plausible assumption would be that ships travelling through the same wormhole could communicate just like in normal space (after all, a wormhole is normal space, just with a weird geometry), but any signals sent from inside one wormhole to another would have to take a detour through the wormhole mouth(s).

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    $\begingroup$ Actually, since the ships have the same velocity, they have zero relative velocity with regard to each other, so they can communicate with each other with zero time dilation. $\endgroup$ – Dronz Dec 11 '14 at 17:33
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    $\begingroup$ @Dronz: The problem is that, if the ships travel close enough to the speed of light (relative to their origin and destination) and have a non-zero distance between them, they will reach the destination so quickly (as measured in their own frame) that no message has time to pass from one to the other. What's "close enough" to the speed of light depends on the distance between the ships and the distance to their destination, but travelling at the speed of light is always close enough. $\endgroup$ – Ilmari Karonen Dec 11 '14 at 17:39
  • $\begingroup$ I don't know a consistent agreed definition of travelling _at_ the speed of light, or how one would do that, since adding acceleration, according to the physics I was taught, never achieves that. As for travelling close to the speed of light, and being too close to have time to communicate before arriving, that just sounds to me like a problem of poor planning and travelling too fast. You should go slower or say your peace before you leave. Or, stop and finish your message after you arrive. None of which seems relevant to the question. i.e. There is no problem. $\endgroup$ – Dronz Dec 11 '14 at 20:35
  • $\begingroup$ You left me utterly disappointed about the future for a moment there... $\endgroup$ – matt Dec 12 '14 at 16:32
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    $\begingroup$ 'humans somehow "uploaded" into software' - Cool, I could make a backup of me. I just need to delete my Facebook account before they have "me" as well. $\endgroup$ – Markus Malkusch Dec 14 '14 at 20:19
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The important thing to realize here is that velocity is always relative to a certain frame of reference. There is no such thing as absolute velocity. (This is basically what the "Relativity" in "General Relativity" is referring to)

Imagine two astronauts floating in a vast, completely empty region of deep space. There are no stars visible to them (or whatever equipment they may have) there are no little hydrogen atoms flitting around, there is nothing but the two of them and infinite blackness.

If the distance between them is shrinking at a rate of 10 meters per second, then how could you say which one of them is moving and which one is not? You can't. The question itself is flawed. If the astronauts don't know much about these things, this is probably how they would answer if you asked them their opinions:

  • Astronaut A: I am clearly stationary and Astronaut B is moving toward me at ten meters per second.
  • Astronaut B: No way, I'm the stationary one and Astronaut A is moving toward me!

They are both right. To them, they are stationary and the things around them are moving. This is true for anything, even a spaceship moving away from Earth at relativistic (very, very high) speed. To the passengers on the ship, the situation is reversed: it appears that they are stationary and Earth is moving away from them at relativistic speeds.

In the astronaut example, there are only two frames of references we can use, astronaut A's or astronaut B's. There is no one else there whose opinion we can ask. What that really means is that there is no other frame of reference from which to answer the question. You might ask "well, how fast are they moving relative to point Z somewhere between them?" but remember, this is completely empty space. There is nothing at point Z. Empty space does not move, nor is it stationary. It doesn't exist, so of course you cannot speak of where it is.

Now here's something only God knows about the situation: the two astronauts are in a distant region of space which, due to the expansion of the universe, is moving away from Earth faster than the speed of light. Thus both astronauts are moving away from Earth faster than the speed of light.

But this doesn't matter as long as the astronauts just want to shine lights at each other or poke each other or whatever they do to communicate. Eventually they will collide with one another, just as communications between two spaceships will collide with one another (if the spaceships are moving more slowly than the speed of light relative to one another). If they want to communicate with Earth, that's an entirely different matter, and then the velocity relative to Earth would come into play (in this scenario, Earth is beyond the "Hubble Volume" so indeed, they would not be able to communicate with Earth).

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  • $\begingroup$ This answer has gone a long way toward my understanding of relativity. An excellent example $\endgroup$ – roryok Dec 12 '14 at 7:59
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Relative to each other, the two ships are stationary. Any transmission from the trailing ship will arrive at the leading ship, the same as if the two were stationary.

You can think about it this way: Consider the earth, with the moon orbiting around it. If you shine a laser from the moon to a receiving station on Earth, the light will propagate towards the Earth at light speed, taking about 1.25 seconds to arrive. Because the speed of the moon revolving around Earth is very low compared to the speed of light, there is virtually no time dilation.

Now, think of your two spacecraft traveling at 0.999999c past the Earth-moon system, with craft A in front of craft B by the same 1.25 light seconds. The time dilation between the spacecraft and Earth-moon is 707 (see http://www.1728.org/reltivty.htm), which means that if you transmit from either ship to the Earth, or from the Earth to the ships, the sound and video on your transmission will have to be sped up or slowed down by a factor of 707 in order to be intelligible.

BUT, between the two ships, the relative speed is zero. Signals traveling from ship A to ship B will propagate at the speed of light relative to ship A, so, the transmission from A to B will take 1.25 seconds to arrive, but there will be no time dilation between the two spaceships.

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    $\begingroup$ Surely that would only affect analogue signals though, digital transmission would avoid that time dilation $\endgroup$ – roryok Dec 11 '14 at 18:50
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    $\begingroup$ Nope. The bits in a typical digital transmission are encoded for data integrity. In any modulated digital transmission, you are varying a consistent analogue signal's between two discrete values, while analogue signals contain data along the full range of energy states in the transmission. Fundamentally, you're always wrangling photons, so you're always limited by their speed, that of light. $\endgroup$ – Rob Perkins Dec 11 '14 at 19:31
  • $\begingroup$ Specifically, the advantage drawn from a digital encoding over analogue is that the fidelity of the signal can be much higher. It has nothing to do with the speed of the signal or the amount of information in it. The density of the information transmitted is always limited by Shannon's Theorem (I think that's the name) $\endgroup$ – Rob Perkins Dec 11 '14 at 19:32
  • $\begingroup$ I don't buy it. If craft A took a DVD of Interstellar with them and watched it, it would play back as normal for them, taking 169 minutes. However to a person standing on earth they would appear to have watched it in 14 seconds (1/707th of the running time). If earth was to then transmit a digitized copy of Interstellar 2 - Tar's Revenge - essentially all 700mb the 1s and 0s of the DVD would be transmitted to the ship, and the ship would put them in the correct order and burn that 700mb file to a disc. You're saying when the crew watch it, it would run in hyper speed? $\endgroup$ – roryok Dec 12 '14 at 8:12
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    $\begingroup$ @roryok even digital data is sent through analogue universe. If you were transmitting to earth in your example by flashing light on and off. The length of light on segments and off segments would be shortened. You would need to slow down (stretch out) those pulses to get them back in the original format. $\endgroup$ – cmd Dec 12 '14 at 16:28
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Current physics answers no. The only potential answer to this that currently exists is found in the domain of Quantum Entanglement...a concept used by games like 'mass effect 3' that has some basis within Quantum physics is a potential option here as 'information' could potentially travel well past the speed of light.

It's a weird topic to research as there's a ton of articles claiming to 'debunk' (that's a great term) followed by articles debunking the debunk (which I believe makes it just bunk), and debunking the debunked bunk debunking?...in any case, it's important to remember that this is theory, and disputed theory at that. The brief explanation is pair particles have opposite spins, but you don't know which spin either of them have (infact, it doesn't have a spin until it's measured). By measuring the spin of one, you cause the other one to take the opposite spin...and that other one can be (theoretically) light years away, yet still take the opposite spin of the one just measured instantaneously (please realize this explanation is the equivalent of attempting to explain Schrodingers cat in 2 sentences).

The idea that 'information' can travel beyond the speed of light would solve this communication dilemma.

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    $\begingroup$ As I have likewise just learned unfortunately quantum entanglement doesn't offer an answer to communicating information. From my (limited) understanding, quantum entanglement does not allow transfer of information, please see my question and the answers. $\endgroup$ – Naftuli Kay Dec 12 '14 at 4:49
  • $\begingroup$ I learned about Quantum Entanglement years ago and was always fascinated by it. I've definitely used it as a plot device for interstellar comms before. However in this story that tech is not available to the ships - one is an older ship that has set out from earth at near the speed of light , and the other is centuries newer, and overtaking it with more advanced tech, then trying to communicate with the older ship. QE would just be too easy =) $\endgroup$ – roryok Dec 12 '14 at 8:17
  • $\begingroup$ @roryok you can still have QE if - and this is my understanding of way out of my field physics - particles have to start together to be entangled. In that case entangled particles could be a very limited resource and the older ship could have run out some time ago. Also presents interesting problems of speed- if I am going at relativistic speed and use entangled data transfer, does the data arrive at the relative speed of broadcast or the perceived speed of broadcast? This is why I don't like to think too hard on physics... $\endgroup$ – glenatron Dec 12 '14 at 15:47
  • $\begingroup$ I believe the mass effect series has two set locations that can communicate with each other and that is it...a permanent 2 way connection (no 3rd party callers...I'd hate to get QE telemarketers). @NaftuliTzviKay - If we were able to alter the spin of a pair, there is still 'theoretical' room for it to exist, however you are right...it's not possible within our current understandings. It still raises the interesting possibility that 'information' (whatever that is) can be instantaneous and not limited by the speed of light. $\endgroup$ – Twelfth Dec 12 '14 at 16:43
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If two ships were traveling at the same speed at under the speed of light, and away from the Earth, they would communicate normally. They really might not even know they are traveling that fast. For instance, we could be traveling that fast right now and we'd never know it.

Now, assume there is a third ship that is traveling so fast the first two ships think it is traveling at nearly the speed of light away from them. Now, a fourth ship traveling at what the third ship thinks is nearly the speed of light faster than the third ship.. and so on until you reach what could only be described as warp 100.

From the perspective of the Earth, all the ships are traveling at just under the speed of light and will all arrive at their destination at very close to the same time. Let's just say people of the Earth think it took two years for the ships to arrive at their destination. From the perspective of the ships, the fastest ship might arrive in what it thinks is a couple of seconds. The slowest ship might think it took a year. And, every ship in between thinks it took a different amount of time.

So, on the question of communication, each ship would communicate with the other ships in the same way, using some form of the electromagnetic or visual spectrum. There will be a shift or stretching in the wavelength and data rate between ships. So, their communications equipment will need to be capable of handling the shift.

If both ships are traveling at the same direction and speed, they will communicate normally no matter what their speed. However, when traveling close to the speed of light, time shifts exponentially. If one ship were traveling slightly faster than the other ship, they would see huge temporal differences in their own perception of time. The temporal differences between ships will cause a Doppler shift between the frequency of transmission and the frequency received. One ship may be transmitting on 2.45 Ghz. The other ship may need to receive on all frequencies (2.2Ghz, 1.9Ghz, 5Mhz, etc.) depending on the degree of the Doppler shift. When returning the transmission, one ship will transmit on 2.45Gz. The other ship would receive on some other frequency (5Ghz, 20Ghz, etc.).

The question also asked what if one ship were traveling faster than the speed of light. A ship can never accelerate itself to or beyond the speed of light. Temporal changes due to Relativity will cause the person driving the ship to think they are chasing a carrot. The faster they go, the more temporal change, and they'll always think light travels at the speed of light faster than they do. However, if something is caught in the grip of a Gravity Well which compresses Space/Time beyond the limits of the speed of light, it would be as if they were traveling faster than the speed of light. In this case, the temporal shift approaches or becomes infinity. Any transmission coming from the ship would have infinitely low hertz. If the transmission could escape the gravity well, it would take an infinity to receive the entire transmission.

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So long as the two ships are travelling at the same speed and slower than C (even by a tiny amount), there are no problems. Becasue time slows down as you speed up, a radio signal travelling at C, 0.1 m/s faster than the ship, might take a month to reach the ship in front from the POV of a stationary observer, but to the people inside the second ship, it will seem instantaneous, because they are thnking 'slowly', Similiarly, any hardware emmitting or decoding the signal will be operating 'slowly', so the message will have the correct bitrate.

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Telepathy! Thought has no mass and would therefore take no time to travel so communication would be instant. I know light is made of photons and that this means light has no mass as photons are stated as having no mass. Photons do however have a relative mass.

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  • $\begingroup$ Assuming thoughts are bound by the laws of physics, they are also bound by the speed of light. Indeed, if you take into account quantum mechanics, even tachyons cannot be used for faster-than-light communication. $\endgroup$ – celtschk Dec 13 '14 at 22:08
  • $\begingroup$ That's so daft it sounds plausible. +1 $\endgroup$ – Pharap Dec 14 '14 at 2:30
  • $\begingroup$ Thought has no mass because it doesn't exist. Thought is nothing more than the current state of chemical reactions in your brain. $\endgroup$ – Jason Williams Jan 30 '15 at 15:59
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    $\begingroup$ Hey, it works for Heinlein. $\endgroup$ – JDługosz Mar 31 '16 at 19:31
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Surprised nobody thought Orson Scott Card was correct with Enders Game. I know it's a science fiction book, but since all of the answers seem to be under the assumption that current physics is 100% correct I figured I might go outside of the box (fringe science?!). I think the theory is called supersymmetry which I guess could turn what we know upside down? I'm not sure why people are saying faster than light is impossible though. There are particles that travel much faster than light, neutrinos being one of them. I think knowing that there is something that is faster gives hope that FTL (Faster Than Light) travel could be possible. If it is possible, proving supersymmetry and possibly string theory correct, I'm going to have to go with Orson Cards solution and say the Ansible. Near instant communication across any distance, thanks to what seems to be described as a device that takes advantage of quantum mechanics or string theory to transmit communications. The movie was horrible.

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    $\begingroup$ Neutrinos do not travel faster than light. en.wikipedia.org/wiki/Faster-than-light_neutrino_anomaly $\endgroup$ – roryok Nov 11 '15 at 22:22
  • $\begingroup$ @roryok touché sir, I had not known about that thank you. However, considering the fact that I'm willingly accepting string theory and supersymmetry to be correct I don't think its that far of a stones throw to go ahead and assume FTL is possible also. $\endgroup$ – user3164339 Nov 11 '15 at 22:25
  • $\begingroup$ 1) Supersymmetry is not fringe science; it is in fact somewhat mainstream. Same goes for string theory - it is accepted by a decent part of the theoretical physics establishment as a good candidate for a theory of everything (ToE). 2) The supposed faster-than-light neutrinos were, as @roryok said, not faster than light - see the OPERA experiment. 3) Finally, Ender's Game has absolutely nothing whatsoever to do with supersymmetry. This answer is incorrect in all these aspects. $\endgroup$ – HDE 226868 Nov 11 '15 at 22:30
  • $\begingroup$ @HDE226868 WOW, maybe you should start reading things with a mind set other than 'everybody is wrong'. I was not calling supersymmetry or string theory fringe science. they are 2 seperate sentences. And you are correct, Enders game has nothing to do with supersymmetry, but again I didn't say it did. Not once. I said Enders Game had an answer to communication while traveling faster than light. I happen to agree with this possibility. Calling an opinionated question and answer wrong, is what's wrong. I thanked roryok for correcting me and admitted I was wrong there. $\endgroup$ – user3164339 Nov 11 '15 at 22:37
  • $\begingroup$ @user3164339 My mindset is not that "everybody is wrong"; my mindset is that you're answer is wrong. You absolutely called string theory/supersymmetry fringe science - or at least implied it - by saying that it is only one step away from faster-than-light travel, which is fringe science. Additionally, if you weren't saying that Ender's Game had to do with supersymmetry, then I'm the confused one, because I don't see any other way for it to tie in. $\endgroup$ – HDE 226868 Nov 11 '15 at 22:42
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Here's my 50 cents..

If a ship travelling at lightspeed would be able to reach a ship in front of it, its transmitted radio signal would have to be capable of travelling faster than the ship itself through the same medium (vacuum). In other words, the radio signal must travel faster than light. This by definition is impossible. Nothing travels faster than light.

Even if the ship would be travelling slightly slower than a radiosignal trough the same medium, the relative frequency of the radiosignal as percieved by the ship in front of it would have such a low frequency that it would be impossible to decode, or would take significant time as it arrives with high delay.

Hence, it is not possible to communicate forward when travelling at lightspeed.

Backwards is a totally different ballgame. Even though the radio signal has an absolute speed of 0, its relative frequency as perceived by the ship behind it is still at lightspeed, and still intact.

I believe optical gyroscopes are entirely built around this principle. Meaning, built around the certainty that nothing can travel fast than light, even when the light-emitting device itself has an offset speed.

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  • $\begingroup$ So suppose then that the follower ship can exceed the speed of light, but the leader cannot. Would the best method be to jump in front of the ship and pass a signal "downstream" and then return to a position behind the ship to receive the response? Or is that just complicating things - would a side-by-side position work just as well? $\endgroup$ – roryok Dec 11 '14 at 12:19
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    $\begingroup$ Albert Einstein's 50c says you're wrong. The whole point of relativity is that any observer sees light move at the same speed. If the two ships are travelling at close to the speed of light (they can't travel at the speed of light) then, when one shines a light beam at the other, they see exactly what they would see if they were stationary. $\endgroup$ – David Richerby Dec 11 '14 at 12:23

protected by bowlturner Dec 12 '14 at 20:38

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