### October 10, 2011

#### Relativity-1: Going backwards in time

Part of the reason that recent reports of the detection of neutrinos traveling faster than the speed of light aroused such excitement is because of claims that such a discovery would overthrow Einstein's venerable theory of relativity and that if you could send a signal faster than the speed of light, you could go backwards in time. Are these claims true or simply overheated? If true, what exactly was overthrown? And what does it mean to 'go backwards in time' anyway?

My initial reaction to the faster-than-light neutrino report was one of skepticism, saying that I would wait and see if the result held up but was not hopeful that it would. I did not give my reasons for this pessimism and reflecting later, I thought I should because understanding what was claimed (and why) serves as a good vehicle to understand the elements of the theory of special relativity as well as how science works., so the next series of posts will deal with these questions. (I was overdue for a series of posts on a single topic anyway.)

Let's look first at the 'backwards in time' claim. There is a simple (but wrong) way of interpreting this and a more subtle (but correct) way.

To see the simple way in which something traveling faster than the speed of light can cause things to appear to go backwards in time, think of a situation in which a man fires a gun at another man but with the bullet traveling faster than the speed of light. Nothing requires the shooting of people to understand this phenomenon but this is the customary example that is used, perhaps because a bullet is the fastest object that most people can think of (although it is still much slower than the speed of light) combined with the fact shooting someone is so dramatic and final that reversing the process seems impossible, kind of like Jesus rising from the dead.

Suppose the shooter is at point A and the person hit is at point B 10 meters away. Suppose you are standing right next to the person at B. If the bullet travels faster than the speed of light, what will you see? Remember that we 'see' something only when the light from that event enters our eyes. Since the speed of light (at 299,792 km/s) is beyond anything we are familiar with from our everyday experiences, let's greatly slow things down by assuming that it travels at (say) 1 m/s and that the bullet travels at (say) 2 m/s.

You will see the gun at A firing 10 seconds after it fires because the light from that instant will take that much time to travel the 10 meters to reach you. But one second after the gun is fired, the bullet will have traveled two meters towards B (and you), and light emitted by the bullet at that point will take only 8 more seconds to reach you. In other words, you will see the bullet at the 2 meter point 9 seconds after the gun is fired, which is one second before you see the gun firing. Similarly you will see the bullet at the 4 meter mark 8 seconds after the gun fires, at the 6 meter mark 7 seconds after the gun fires, at the 8 meter mark 6 seconds after the gun fires, and the bullet entering the person at B 5 seconds after the gun fires. Put it all together and what you see first is the person at B being hit (five seconds after the gun fires) and then in the next five seconds will see the bullet emerging from the victim and traveling back and entering the gun.

This no doubt looks like is going backwards in time. But this example is not what is meant by going backwards in time according to the theory of reelativity. After all, the victim was in fact hit five seconds after the gun was fired so there is no actual reversal of the ordering of the events. What you saw is more like watching a film run backwards, which is not really going backwards in time. This effect is an illusion, an artifice caused by the fact that light takes time to travel and your special location next to the victim. Had you observed the whole sequence of events while standing next to the shooter at A, you would not have noticed anything unusual because you would have seen the gun fire right at the beginning, the bullet at the 2 meter mark after 3 seconds, at the 4 meter mark after 6 seconds, at the 6 meter mark after 9 seconds, at the 8 meter mark after 12 seconds and hitting the person at B after 15 seconds. Everything would have seemed normal.

What this example does illustrate is that specifying the time at which an event occurs by the time noted by an observer is not satisfactory because it depends on where the observer is situated relative to the events. (For example, the bullet was observed at the 2 meter mark at 3 or 9 seconds after the gun was fired depending on where you were standing.) We will also see later that in addition to the location, the state of motion of the observer (if you were observing the events from a moving train, for example) also affects the time at which they see events.

It is in trying to unambiguously pin down exactly when something happens that we arrive at a deeper understanding of Einstein's theory of relativity and what we really mean by going backwards in time.

Next: The CERN-Gran Sasso experiment

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To supplement your explanation, I have a simple one using graphic illustration:

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Posted by Christopher on November 8, 2011 01:16 PM