# Could a series of spacecraft, all approaching the speed of light, propel one another to faster than the speed of light?

This question assumes a number of (let's say 10) small, light-sail spacecraft connected in series which have been propelled from earth by a laser and are currently approaching the speed of light.

Each craft itself has a laser which is used to propel the craft in front of it.

Considering the speed of the craft, despite their small size, their momentum would be sufficient that the reactive force of the photons when they fire their lasers would not impact their velocity considerably (correct me if I'm wrong there).

Suppose the craft, starting with the rearmost, turned their lasers on in series to propel the one in front of it:

• Could the leading craft be accelerated to faster than the speed of light?
• Are there any hypothetical scenarios in which this would be "technically" possible (the speed of light is preserved, but the object could still reach an arbitrary destination faster than light could from the same starting point)?
• Nothing can travel faster than the speed of light, no matter what contraption you dream up. – Gert Mar 12 at 17:58
• @Gert I understand under any circumstances we currently know it is impossible, I've added to my question as I'm more curious about hypothetical circumstances like frames of reference. – SentientFlesh Mar 12 at 18:06
• Hypothetically you could travel at $\infty$ speed but what good does such a speculation do? – Gert Mar 12 at 18:08
• @Gert I meant hypothetically within the realm of physics, even if it is extremely speculative. I have a good understanding of general physics but am very interested in "sci-fi" solutions like EM Drive, etc. Constants are constant until they aren't; "asking what good does speculation do?" is like asking "why not just accept everything as it is?" There's been no evidence against general relativity yet, but we have ∞ years to find some, and that's a long time. – SentientFlesh Mar 12 at 21:02
• It's Sci-Fi my friend, nothing more. Good luck anyroads. – Gert Mar 12 at 21:05

The answer to "can X be accelerated to faster than the speed of light?" is always no.

No matter what reference frame you're in, the photons shooting out of each spacecraft are all traveling at the exact same speed, regardless of how fast the craft is moving. That speed is c, and is constant in all reference frames. Putting a laser on a spacecraft moving at high speeds is no different at all from putting a laser on a stationary spacecraft - both lasers will fire photons with speed c. Photons always travel at speed c, they don't move with speed c + the speed of the spacecraft. Nothing can travel faster than c.

Intuition from classical mechanics doesn't hold up here. If you throw a ball off a moving train, the ball moves at the speed of your pitch plus the speed of the train. If you shine a flashlight off a moving train, the photons move at c, regardless of the speed of the train.

• So the lasers would always have zero net effect on any craft in front of it? – SentientFlesh Mar 12 at 18:03
• @SentientFlesh You can accelerate a craft with a laser, but daisy-chaining spacecraft of increasing velocity doesn't accomplish anything at all. The photons from the stationary earth laser are traveling at the exact same speed as the photons from a spacecraft-mounted laser moving at 0.9c. The situation is no different from trying to accelerate one single spacecraft beyond c by shooting a laser at it - you can't. – Nuclear Hoagie Mar 12 at 18:08
• Since the limiting factor is that the photons are always moving at c, if the spacecraft is moving at 0.99c, would an observer be able to watch the photons travel to the craft in front of it after being fired? (i.e. would the speed of the laser appear to be moving slower than if all bodies are at rest) – SentientFlesh Mar 12 at 18:17
• @SentientFlesh An observer at rest relative to the spacecraft would see the photons move away from the craft with a relative speed of 0.01 c (since the photons move at c and the craft moves at 0.99 c). But someone on board the craft would see those photons move away at c, not 0.01 c. No matter what speed you're moving at or what reference frame you're in, photons always move at c. Observers in different reference frames can observe different things - everything is relative. – Nuclear Hoagie Mar 12 at 18:20
• If you throw a ball off a moving train, the ball moves at the speed of your pitch plus the speed of the train. Not exactly. The relativistic addition-of-velocities formula holds here. But it gives an answer that is very close to the simple classical sum of velocities (which even at low speeds is just a very good approximation). – G. Smith Mar 12 at 18:47

No. From the point of view of a craft firing a laser, each photon transfers less and less momentum to the next craft as it approaches the speed of light, because the speed of the photon relative to the next craft becomes smaller and smaller. And each photon it sees from the craft behind is more and more red shifted as the relative speed of the two craft increases, so has less and less momentum to transfer too.

• Thank you for diving deeper into momentum, I completely overlooked redshift, which I still find fascinating. Years ago in uni, I had a long discussion with a professor about a craft beaming a song on continuous loop back to earth and what it would sound like as it continued away. – SentientFlesh Mar 12 at 21:06