## November 19, 2011

### Jitter

Here’s an old riddle, that some of you may have heard.

François lives in Lyons, and has two girlfriends: one in Marseilles and another in Paris. He can’t seem to choose between them, so he decides on the following strategy. The trains to Paris and to Marseilles both run once-an-hour. He decides to show up at the railroad station at random times, and takes whichever train comes first.

After several weeks, François finds that, on average, 9 times out of 10, he ends up visiting the girlfriend in Marseilles. Clearly, the Fates have chosen for him, so he dumps the girlfriend in Paris and proposes to the girl in Marseilles.

What’s going on?

The answer, if you think about it, is obvious. Both trains run once an hour. But the one to Marseilles leaves on the hour, while the one to Paris leaves at 6 minutes past the hour. If François arrives at random times (a uniform distribution) during the hour, he is 9 times more likely to find that the next train is the one to Marseilles.

The OPERA experiment has released a revised version of their “superluminal” paper. Among the improvements, they give more details on their timing. One factoid jumps out at us: their clock runs at 20 MHz, which means that there’s an irreducible jitter (or granularity) in their timing of events, of 50 ns. Tomasso Dorigo asks if there’s an effect which could bias that jitter in one direction.

I suggest that he consult with François.

Posted by distler at November 19, 2011 11:46 AM

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### Re: Jitter

The truly unfortunate thing is that the public will now think that the experiments have been validated, which of course they haven’t. Independent reproduction anyone?

### Re: Jitter

It’s not obvious to me that your train riddle applies to the timing in OPERA… wouldn’t the train schedule which is more analogous be the train to Marseilles leaving on the hour and the train to Paris leaving on the half hour… Francois’ problem would still not be solved.

Posted by: Guest on November 21, 2011 5:56 PM | Permalink | Reply to this

### Re: Jitter

Think of each train as a clock that “ticks” once an hour (instead of once every 50 ns). Think of François as a neutrino, whose arrival time is uniformly distributed over the span of a clock cycle (of either clock).

I’ve just explained how, even with such a uniform distribution, there can still be a statistical offset (by one tick) of the arrival time recorded by one of the clocks.

I am not saying that’s what’s happening at OPERA. But I am saying that — whenever clock jitter is an issue — you can get a systematic bias, of the sort experienced by François.

Posted by: Jacques Distler on November 21, 2011 6:21 PM | Permalink | PGP Sig | Reply to this

### Re: Jitter

Yes I see…. but then I suppose that a systematic bias will only happen if the neutrinos are always arriving just after the “correct tick” (that is the one which should be consistent with sub-luminal speed) and are then always have their arrival time shifted up by 50 ns… it is unclear to me why this would happen… it seems that they should just as often arrive just before the correct tick…

the issue with the train analogy is that the time interval between the Marseilles train leaving and the Paris train leaving is much less than the time interval to the next Marseilles train leaving…

Posted by: Guest on November 21, 2011 8:01 PM | Permalink | Reply to this

### Re: Jitter

I’d like to know what evidence there is, that neutrinos are slower than light. Even the SN1987a neutrinos got here first.

Posted by: Mitchell Porter on November 21, 2011 9:21 PM | Permalink | Reply to this

### Re: Jitter

I’d like to know what evidence there is, that neutrinos are slower than light.

Huh?

At 10-40 GeV, neutrino masses ($\lesssim 0.1$ eV) are completely negligible.

Posted by: Jacques Distler on November 21, 2011 9:59 PM | Permalink | PGP Sig | Reply to this

### Re: Jitter

Huh?

The issue is simple: is there any experimental evidence that neutrinos are ever slower than light?

Before OPERA, MINOS measured superluminal velocities, but it was not a statistically significant result. The square of the neutrino mass has repeatedly been measured as negative. There seem to be very few experiments which directly measure neutrino transit times, and all they told us in the past is that the neutrinos moved at very close to the speed of light; they don’t tell us the sign of the difference in speeds.

Yes, I know that the “dark neutrino” loophole in the Cohen-Glashow argument can’t work here, because the known neutrinos do feel the weak force. Nonetheless, it would be desirable to know what neutrino data actually allows us to infer about their velocities.

Posted by: Mitchell Porter on November 21, 2011 11:39 PM | Permalink | Reply to this

### Re: Jitter

The issue is simple: is there any experimental evidence that neutrinos are ever slower than light?

I know some experimentalists who want to measure the endpoint of the tritium β-decay spectrum and, thereby directly measure the electron neutrino mass (by seeing that it has $|\vec{p}|\lt E$).

It’s an incredibly hard experiment and, no, I don’t think anyone has succeeded. But that’s the best shot at the evidence you seek.

Posted by: Jacques Distler on November 21, 2011 11:48 PM | Permalink | PGP Sig | Reply to this

### Re: Jitter

Thanks, Jacques.

Posted by: Mitchell Porter on November 22, 2011 12:01 AM | Permalink | Reply to this

### Re: Jitter

doesn’t your analogy provide a mechanism by which jitter could give rise to a delay in the recorded arrival time, but not a mechanism by which the recorded arrival time could be earlier than the true arrival time? in other words, it seems like a mechanism by which the experiment could give rise to spuriously slow neutrinos, not superluminal ones. or have i missed it?

Posted by: guest on November 22, 2011 8:04 AM | Permalink | Reply to this

### Re: Jitter

It provides a mechanism by which the recorded arrival time could be off by one clock-tick … in either direction.

Posted by: Jacques Distler on November 22, 2011 8:54 AM | Permalink | PGP Sig | Reply to this

### Re: Jitter

can you elaborate? i don’t get it. (insert appropriate homer simpson emoticon here)

Posted by: guest on November 22, 2011 9:52 AM | Permalink | Reply to this

### Re: Jitter

I believe such a clock must have rigourously spaced 50 ns intervals between clock ticks, to a very high accuracy, so no “short” and “long” intervals as can be observed in the little problem with the trains. But I think you remarks still make sense, because some unintuitive mechanisms can cause a systematic error. If I correctly understand the issue, detection events get a timestamp from clock ticks happening every 50 ns. That means the same timestamp is given to all events in the past 50 ns, creating an error which is systematically of the same sign (a delay, uniformly distributed in [0,50] ns). So the claim in the paper (page 15) that the jitter is +-25 ns is wrong, isn’t it? This is important because if there are some slower neutrinos arriving after the clock tick, it would be wrong to correct their time stamp by -25 ns in average. Such a jitter is a noise which can in principle get filtered by averaging, but the averaging process must be carefully designed.

Posted by: T. Mataigne on November 25, 2011 6:34 PM | Permalink | Reply to this

### Re: Jitter

I know the solution and can counter this with an analogous puzzle. Assume that Mr “W” and country “I” write papers equally often, say one per month, and these are the only papers being written. Now assume you check papers on hep-th at completely random times. And you download always the last paper that was submitted. After several months, you find that, on average, 9 times out of 10, you end up downloading papers from country “I”;. How can this be, what is going on?

Posted by: W on November 27, 2011 2:45 PM | Permalink | Reply to this

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