Our galaxy is over a hundred thousand light years across. A distance so vast that it defies ordinary understanding. Even humanity's earliest radio transmissions hurtling through space at the speed of light would still only have washed over less than 1,000,000th of the stellar population. The cosmic speed limit, the speed of light, is so diminutive compared to a galaxy that any aspirations we might harbor for galactic exploration or even just communication seem impossible, at least within human lifetimes.
But humanity has long wondered, could there be a cheat code? Could there be a way to exceed that cosmic speed limit? Could we go faster than light (FTL)? There is no other technology that I so keenly wish could be realized than FTL. Since childhood, I've looked up at the stars and dreamt of one day reaching them, of exploring the ocean of space, the zoo of worlds, the menagerie of life. It almost seems like a cruel cosmic joke that the universe be arranged in such a way that we are able to look out and glimpse its wonders and yet are trapped here by the speed of light, fated to only peer through the bars of our cosmic prison and dream.
And so, it's no surprise that human ingenuity and aspiration has raged against Einstein's cosmic speed limit. After all, we've never been so good at doing what we are told. To be clear though, we currently have no way of building or even conceiving of a practical FTL system, be it for travel or just for communication. But there are threads that physicists pull out that it is hoped one day might bear fruit.
For example, we know that Einstein's speed limit only truly applies to travel through space, but that space itself has no such constraint. For this reason, there are parts of the universe receding away from us faster than the speed of light as the fabric of the cosmos itself expands in all directions. Could we one day learn to manipulate space then and somehow use this to travel faster than light? The hypothetical Alcubierre drive is perhaps the most famous example of this concept. Inspired by Star Trek's warp drive, Miguel Alcubierre showed that there exists a solution within Einstein's relativistic field equations that, in principle, could allow FTL. By expanding space behind itself and contracting it ahead, a bubble of space could cruise between the stars at arbitrarily fast speeds.
The idea has certainly faced many challenges though, such as requiring the use of exotic matter, enormous energy requirements, and even obliterating the destination through the buildup of radiation gathered up by the bubble. Yet optimists might argue that none of these are truly show stoppers, merely engineering challenges. A more pressing problem is folding in quantum effects into the Alcubierre drive. In 2009, Finazzi showed that the warp drive bubble leads to exponentially increasing Hawking radiation on the inside of it. This isn't just a hazard to their crew, the exponential buildup destabilizes the bubble itself. It's important to remember that we don't have a good theory of quantum gravity yet, and the Alcubierre drive is conceived in its absence, just using general relativity alone. These kinds of quantum concerns don't just plague warp drives. Wormholes, another hypothetical FTL system, have also been criticized as being possibly unstable due to these quantum effects ignored by general activity. Ultimately, we can't truly prove whether wormholes or Alcubierre drives are allowed or not until we have solved quantum gravity or built a working example of one.
The other problem with assessing the feasibility of FTL is that there are multiple ideas out there, such as tachyons, craznic optubes, quantum tunneling, and entanglement. And each one of those has a diverse number of flavors proposed. For example, the Alcubierre metric has been tweaked many times to reduce the energy requirements in various ways. And of course, physicists will continue to conjure up new varieties in the future. As a result, it seems somewhat hopeless that we'll ever be able to completely exclude FTL as a possibility.
On the one hand, our hearts might rejoice because it means that hope persists and the dream will always be alive. But on the other hand, our minds complain because after all, this is science and we want definitive clear objective answers, not eternal maybes that will forever be unfalsifiable.
So, is there anything that we can definitively say with existing knowledge? Well, it turns out, yes. Despite the fact that we don't have a theory of quantum gravity, despite the fact that there are countless variants and ideas about FTL systems, there is a definitive statement that we can make about all FTL systems. They all allow for causality-breaking time travel.
When you hear that FTL implies time travel, you might think about sci-fi portray
Understanding the Space-Time Diagram
The space-time diagram represents the world line, which defines the time axis as perceived by those following it. By adding the null line, we can observe that the space axis is a flip of the time axis around the null. This orientation helps us in dealing with more complex scenarios.
FTL Messaging System
Let's imagine an FTL messaging system between Earth and Vega. When a supernova occurs closer to Earth, the radiation travels at the speed of light, following a null line. Earth sees the supernova first and decides to send a warning to Vega. Due to the nature of FTL lines, Vega would receive the warning before actually seeing the supernova.
Order of Events and Causality
Examining the order of events, we see that causality is preserved. The supernova occurs first, then Earth sees it, followed by Earth warning Vega, and finally Vega sees the supernova. Everything seems fine with FTL travel so far.
The Role of STL Ships
However, when we introduce slower than light (STL) relativistic ships into the diagram, things start to become problematic. The world line of the STL ship defines its own time axis, which is different from Earth's. Additionally, the space axis bends to accommodate the constancy of the speed of light. Examining the order of events from the perspective of the ship's crew, we find that Vega receives the warning before Earth even sends it. This breaks causality.
The Problem with FTL and Relativity
Removing the FTL messages, we still find no causality violation. The problem lies specifically with FTL itself, not with the theory of relativity. This disagreement about the order of events has profound implications and could potentially allow the crew to break the universe.
The Grandfather Paradox
Modifying the scenario, we imagine the crew intercepting the FTL message and sending a reply back to Earth. However, in Earth's frame of reference, the reply message seems to be traveling backwards in time. This creates a paradox where Earth receives the reply before sending the message, leading to contradictory outcomes. This is similar to the concept of killing our grandfather before we were born, resulting in a paradox.
