There's been a lot of news lately about measurements from CERN that apparently show neutrinos traveling faster than the speed of light. This would seemingly overturn decades of experimental verification of the theory of relativity, which predicts that nothing can possibly go faster. It might be going faster than the speed of light, but if faster than light particles are real, then they would seem to lead to a time travel paradox. Here's why I think that:
Einstein's Though Experiment:
In 1887 it was discovered that the speed of light is constant for all points of view in the universe, regardless of how fast an observer is moving while doing the measurement. Albert Einstein came up with several thought experiments to try to imagine what reality must be like under these circumstances. Here's one of them that describes what happens:
A person standing in a train station sees a train moving at high speed. At the moment the train passes the center of the station, they see two lightning flashes at exactly the same time, equally far away from the center on opposite sides.
From the stationary person's perspective, if the lightning flashed simultaneously when the train was passing in the center, then the train would move forward slightly in the time it took the light to get to it. The light in front would have a shorter distance to travel and the light from behind would have to travel farther, so they see the light reaching the front of the person in the train before it hits them from behind.
To the person on the train, the perspective would be slightly different. Instead of seeing both bolts of lightning at the same time, they actually would see the one coming from the front first. They would appear to be happening at different times. (On the other hand, if the person on the train saw both lightning bolts at once, then the person on the ground would have to see them flashing at different times in order for the light to hit the train at the same time.)

The speed of light is constant for each observer, but the distance and time of the lightning flashes would not agree. Another person in a different train moving in the opposite direction would see it with the order reversed.
The shape of space and time is altered for each observer in a symmetrical way: The person in the station sees the train shortened from front to back with time moving slower, and the person on the train sees the world outside the train foreshortened and with slower time.
Here is an animation from Wikipedia that visualizes this:


It is a timeline where time is vertical and space is horizontal, with the future on the top. You can see exactly how the space-time perspective "shifts" as the velocity changes.
Each person sees a different view of events, but they are both equally valid vantage points of the universe, viewed from a different perspective. The order of events at each specific location remains the same. This has all been measured experimentally, and it is how space and time actually work.
Moving faster than the speed of light:
One of the consequences of the theory of relativity is that it is impossible to travel faster than light (the math predicts it would take infinite energy.) But what would happen if you actually could send a signal faster than light?
Let's go back to the thought experiment. Suppose you are the "stationary" observer and you see two things happening at the same time on opposite sides. Now suppose you had something that could travel faster than light. Imagine it's REALLY fast, so if you send a signal exactly as the lightning flashes you will see it reach the other location immediately after the flash.
Now all of the same space and time transformation is still in effect, but it has an extra effect on the faster-than-light object: To someone moving in one direction, the object appears to be moving slower (but still faster than light.) To someone moving in the opposite direction, the object appears to be moving BACKWARDS IN TIME. It starts off at the destination and then moves backwards faster than light until it reaches the source. According to relativity, moving faster than light is literally equivalent to time travel.

And that's where the paradox comes in:
Suppose you alter the faster-than-light neutrino somehow to represent information. You can measure a bit of information (0 or 1) by the particle's orientation, position, number of particles, etc.
Now change the experiment so the faster-than-light object actually is sending a signal. It will either send a "red" neutrino or a "blue" neutrino (terms I made up) depending on how it is programmed. The device can be programmed to fire either red or blue by sending it a signal before it fires.
One of the moving observers sees the signal going backwards in time. If they can measure the state of the particle, then they know whether it's red or blue before it appears to have been sent. It would still be impossible to notify the sender moving slower than light, but we've already established that it's possible to go faster. So this observer can now send a faster-than-light neutrino to program the sender before the information is sent.

Now all you have to do to create a world-ending paradox is send the opposite signal of whatever you receive. If you see a blue neutrino, send a signal back to make it turn red, and vice versa. Now each situation causes the opposite one to happen and propagate backwards in time somehow, over and over again until you destroy the universe or something.
This is why I have no trouble believing that it's impossible to go faster than light. It's doesn't just require infinite energy, it actually violates the order of cause and effect.
So, it's possible that we just discovered neutrinos moving faster than light and we need to overturn all we know about physics, but I'm putting my money on the "faster than light" measurement being caused by something completely different.
Einstein's Though Experiment:
In 1887 it was discovered that the speed of light is constant for all points of view in the universe, regardless of how fast an observer is moving while doing the measurement. Albert Einstein came up with several thought experiments to try to imagine what reality must be like under these circumstances. Here's one of them that describes what happens:
A person standing in a train station sees a train moving at high speed. At the moment the train passes the center of the station, they see two lightning flashes at exactly the same time, equally far away from the center on opposite sides.
From the stationary person's perspective, if the lightning flashed simultaneously when the train was passing in the center, then the train would move forward slightly in the time it took the light to get to it. The light in front would have a shorter distance to travel and the light from behind would have to travel farther, so they see the light reaching the front of the person in the train before it hits them from behind.
To the person on the train, the perspective would be slightly different. Instead of seeing both bolts of lightning at the same time, they actually would see the one coming from the front first. They would appear to be happening at different times. (On the other hand, if the person on the train saw both lightning bolts at once, then the person on the ground would have to see them flashing at different times in order for the light to hit the train at the same time.)

The speed of light is constant for each observer, but the distance and time of the lightning flashes would not agree. Another person in a different train moving in the opposite direction would see it with the order reversed.
The shape of space and time is altered for each observer in a symmetrical way: The person in the station sees the train shortened from front to back with time moving slower, and the person on the train sees the world outside the train foreshortened and with slower time.
Here is an animation from Wikipedia that visualizes this:


It is a timeline where time is vertical and space is horizontal, with the future on the top. You can see exactly how the space-time perspective "shifts" as the velocity changes.
Each person sees a different view of events, but they are both equally valid vantage points of the universe, viewed from a different perspective. The order of events at each specific location remains the same. This has all been measured experimentally, and it is how space and time actually work.
Moving faster than the speed of light:
One of the consequences of the theory of relativity is that it is impossible to travel faster than light (the math predicts it would take infinite energy.) But what would happen if you actually could send a signal faster than light?
Let's go back to the thought experiment. Suppose you are the "stationary" observer and you see two things happening at the same time on opposite sides. Now suppose you had something that could travel faster than light. Imagine it's REALLY fast, so if you send a signal exactly as the lightning flashes you will see it reach the other location immediately after the flash.
Now all of the same space and time transformation is still in effect, but it has an extra effect on the faster-than-light object: To someone moving in one direction, the object appears to be moving slower (but still faster than light.) To someone moving in the opposite direction, the object appears to be moving BACKWARDS IN TIME. It starts off at the destination and then moves backwards faster than light until it reaches the source. According to relativity, moving faster than light is literally equivalent to time travel.

And that's where the paradox comes in:
Suppose you alter the faster-than-light neutrino somehow to represent information. You can measure a bit of information (0 or 1) by the particle's orientation, position, number of particles, etc.
Now change the experiment so the faster-than-light object actually is sending a signal. It will either send a "red" neutrino or a "blue" neutrino (terms I made up) depending on how it is programmed. The device can be programmed to fire either red or blue by sending it a signal before it fires.
One of the moving observers sees the signal going backwards in time. If they can measure the state of the particle, then they know whether it's red or blue before it appears to have been sent. It would still be impossible to notify the sender moving slower than light, but we've already established that it's possible to go faster. So this observer can now send a faster-than-light neutrino to program the sender before the information is sent.

Now all you have to do to create a world-ending paradox is send the opposite signal of whatever you receive. If you see a blue neutrino, send a signal back to make it turn red, and vice versa. Now each situation causes the opposite one to happen and propagate backwards in time somehow, over and over again until you destroy the universe or something.
This is why I have no trouble believing that it's impossible to go faster than light. It's doesn't just require infinite energy, it actually violates the order of cause and effect.
So, it's possible that we just discovered neutrinos moving faster than light and we need to overturn all we know about physics, but I'm putting my money on the "faster than light" measurement being caused by something completely different.
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