Do faster than light neutrinos let you change the past?S

There's been a lot of hubbub about the possibility of FTL neutrinos. But would breaking the light barrier really be such a big deal? Hell, yes, it would! In this week's "Ask a Physicist," we'll find out why.

While I normally try to vary topics from column to column based on the questions you send me, we're going to continue the discussion from my last on column on faster-than-light technology.

Why the change? A few weeks back the OPERA experiment announced that they had apparently measured neutrinos traveling faster than light. There was an enormous amount of excitement, both here and elsewhere, but also a lot of skepticism. My position: I'm not buying it.

But are faster than light particles really such a big deal?

They sure are. FTL communication results in nothing less than being able to communicate to the past, and produces all of the complexity and paradoxes of good old fashioned time travel.

Jason Honan asks:

Even if the communication took place instantaneously, I don't see how one would use that to communicate with one's own past. Can you explain it in plain English?

Specifically, Alice and Bob want to chat, Bob sends a message and N seconds later, Alice sends a reply. Even if the transit time for the message were zero, N seconds have still elapsed for both individuals. How does a superluminal transit speed equate to negative elapsed time? Wouldn't, at best, a message have a zero delay?"

This column's going to be a bit different than the normal "Ask a Physicist" fare. While it's not going to use equations per se, I will put in a few diagrams. However, if you really want some equations, a more technical version of this discussion appears in my blog.

A Simple Tachyon Telephone

Suppose we've managed to develop a beam that travels across vast distances at faster than the speed of light. On the surface, this is exactly the result announced by the OPERA experiment, since neutrinos are so weakly interacting that they can easily travel interstellar distances without interacting with anything.

While the OPERA measurement only suggested that the neutrinos traveled at something like 2 parts in 100,000 faster than the speed of light, but basically, once the light barrier is broken, then it's only a matter of fine tuning to get any superluminal speed we like. For our purposes, I'm going to suppose we have a tachyon telephone which sends signals at 4 times the speed of light. (Again, I do not believe that the OPERA result will pan out. I just wanted to make that clear).

Jason and I stand 1 light-second from one another, and send each other messages. Normally, light would take 1 second to travel that distance (by definition), but since we're using our tachyon beam, the signal gets sent in only a quarter of a second.

Do faster than light neutrinos let you change the past?S

In a so-called "spacetime diagram", a snippet of our conversation would look like this.

The bold lines show where Jason and I are at any given time. Since we're standing still, we move through time, but not through space. The diagram tells a very boring story:

  1. I send Jason a message.
  2. He receives it and sends me a signal back
  3. I receive his message.

And what do you know? Jason was exactly right! I get his response after I send my original message.

But once we start moving, things get far more interesting.

Moving transmitters

Einstein's Theory of Special Relativity is based on two fairly simple assumptions:

  1. There's absolutely no distinction between somebody moving at a constant speed and direction, and somebody standing still.
  2. Everybody will measure the same speed of light, regardless of their state of motion.

The problem is that for both of these things to be true, measurements of time and space are very strongly related to your state of motion. We go through this with hobos in Chapter 1 of the "User's Guide to the Universe,", but the upshot is this:

Moving clocks always seem to run slow.

Under normal circumstances, this isn't a big deal. A car races by you on the highway at 100 mph, for example, and the dashboard clock only seems to run slow and the driver ages more slowly than you do — but only by about 1 part in 10^14. Even if he drives around for a hundred years, this only adds up to a delayed aging of about 30 microseconds.

But if we're traveling a good fraction of the speed of light, things become very different. This is the origin of the "twin paradox," where one twin stays on earth, and the other goes on an interstellar adventure. When the traveling twin returns, she finds that she's aged far less than the stay-at-home twin. But since she's been exposed to tons of dangerous cosmic rays, her youthful good looks are something of a Pyrrhic victory.

It turns out, though, that we'll be able to exploit different local clocks to make a phone call — (cue dramatic music) to the past!

An Anti-telephone

So here's the trick: Suppose we're flying away from each other at half the speed of light, and, just to make things concrete, he and I can send tachyon beams to one another with virtually infinite speed. If you'd like to see what happens if the signal is just faster than light rather than infinitely fast, please check out the equation-ridden version.

Do faster than light neutrinos let you change the past?

Jason and I fly past each other in our spaceships and 1 1/2 seconds later (a time chosen to make the diagram look nice), I send him a message.

Here's the weird part. Even though 1.5 seconds have elapsed on my clock since Jason and I passed one another, because of this whole "time dilation" thing, only about 1.3 seconds elapsed for him.

In and of itself, this isn't such a big deal. After all, if Jason sent me a communique by conventional means — radio signals, perhaps — I'd still get it after I sent him my original message.

However, once we look at things from Jason's perspective, they start to look seriously messed up.

Do faster than light neutrinos let you change the past?S

Remember that Einstein tells us that there's no way to tell who's standing still and who's moving. Just as I think Jason's clocks are running slow, he thinks he's standing still, I'm flying to the left, and that my clocks are running slow. Yes. This is one of the many crazy headaches that come from relativity.

From Jason's perspective, the 1 1/2 seconds that passed before I sent my first signal is more like 1.7 seconds. In other words, I sent the signal after he received it.

Do faster than light neutrinos let you change the past?S

Jason then sends me a response. It could be something as simple as, "Don't call me!" He transmits it instantaneously back to me.

Do faster than light neutrinos let you change the past?

From my perspective, I get his response before I ever sent out my original message and, if I'm not a huge fan of causality, presumably could preclude me calling him in the first place. In other words, we've got a serious paradox on our hands.

This is nuts! The simple ability to send signals faster than light would allow us, in a very real way, to affect the past. And that my friends, is why the prospect of faster than light neutrinos (or anything else for that matter) would be such a world-changing discovery.

Dave Goldberg is the author, with Jeff Blomquist, of "A User's Guide to the Universe: Surviving the Perils of Black Holes, Time Paradoxes, and Quantum Uncertainty." (follow us on twitter, facebook, twitter or our blog.) He is an Associate Professor of Physics at Drexel University and is currently working on a new book on symmetry. Feel free to send email to askaphysicist@io9.com with any questions about the universe.

Top illustration by R.T. Wohlstadter via Shutterstock