Uncharted Territory

October 18, 2011

Not so fast neutrinos – how CERN have got it wrong

Filed under: Neutrinos, Physics, Relativity — Tim Joslin @ 2:07 pm

Uncharted Territory: “E pur il muove…” [And yet it (the Earth) moves]
CERN: “Mea culpa!”

From Galileo’s Dialogues, 2020 edition, recently received by NeutrinoMail(TM).

This post supercedes my previous effort, since it includes an updated version of my paper on the CERN-OPERA neutrino velocity measurement experiment.  It complements my two earlier posts on the fast neutrino problem, the first being a general discussion of my explanation for the detection of apparent superluminal neutrinos and the second a detailed look at Einstein’s train thought-experiment.

They say a picture’s worth a thousand words.  I can tell you that’s a massive underestimate.  I could have bashed in 5,000 words in the time it took me to conceive of the following diagram, construct it in Powerpoint (is it really totally pants, or do I need a training course?) and most of all, tinker with it. And I’m still not sure it’s clear enough (comments welcome):

In Fig 1, I’ve shown a schematic of the neutrino velocity measurement experiment. It’s very simplified as the neutrinos were not sent exactly from the GPS at CERN. Similar errors may have occurred there as I am about to describe at the OPERA neutrino detector end of the experiment.

The aim of Fig 1 is to show that, over most of the neutrino flight path, all timing measurements were “one-way”:

  • The neutrinos were transmitted from CERN to OPERA.
  • GPS timing signals, used to synchronise the two GPS points shown, travel at light speed, which we perceive to be the same in all directions.
  • Distances were measured either with reference to the GPS signals, or physically the old-fashioned way, in both cases within the Earth system of reference (ES) where we perceive distance to be equal in all directions.

But, crucially over part of the neutrino flight path, the experimenters have used the two-way light speed to determine the expected neutrino flight time. They had to do this because the OPERA neutrino detector is inside the Gran Sasso mountain to protect it from cosmic rays.

The question is whether the light “thinks” it moves at the same speed in all directions with respect to us here on Earth.

The answer is it doesn’t. Why would it? The Earth isn’t even a speck of dust over the distance light and neutrinos can travel. Light speed is nearly 30,000 times the Earth’s escape velocity. Neutrinos go through planets like bullets through tissue-paper. I could go on.

Fig. 2 attempts to show why light doesn’t “think” it moves at the same speed in all directions with respect to our experimental equipment.

First, Fig. 2a shows part of our planet as we perceive it. We perceive distances and therefore time the same in all directions. We set our clocks the same everywhere and assume that light simply takes d/c (the distance divided by a constant speed of light) to get from A to B, or CERN to OPERA in this case.

But, in fact, the Earth is moving, as shown by the fact that distant objects, such as what I recently saw a cosmologist term the rest frame represented by the cosmic microwave background (CMB) (this link has some good CMB schematics, too, btw), appear blue-shifted in the direction we’re moving in – the relative motion causes the photon waves to appear closer together – and red-shifted in the other direction. The CMB appears blue-shifted, not due south, but in a southerly direction (this is important).

Now, the fact that the planet is moving matters. Its speed relative to the CMB is about 600km/s or 1/500th light speed, which is significant when you’re trying to measure neutrino flight times to the nearest nanosecond (ns) or so.

I’m going to digress and explain why movement matters. Here’s another diagram (you really are being spoilt today!):

All we have to do is imagine we’re on a mission to Mars. Mission control are really sweating us – sending people to Mars is not cheap – but have said that we can have precisely one hour off each day to watch the 60 minute episodes of the second series of Firefly we’ve been waiting for for decades. After all, improved morale will increase efficiency.

Unfortunately, the PVR broke on landing so we can’t record the show or fast-forward through the ads. We have to be at the TV to catch the actual broadcast.

Now, if the show is broadcast at 8pm on Earth the time it will reach Mars depends on how far away we are at the time. Light takes 8 minutes to reach Earth from the sun, so I’m guessing that, during our mission, Mars could vary from being, say, 3 light minutes away from Earth to, say, 15, as illustrated in Fig 3.

Hopefully it is apparent that if we have a clock on Mars set to Earth time, we will have to adjust it continually as Mars moves further away from and closer to Earth as the two planets follow their different orbits around the Sun. The rate at which clocks appear to move on Earth as seen from Mars varies continually.

There is no absolute time, a common misconception.

Rather, relative time depends on distance and the relative rates at which time seems to pass depend on relative motion.

Returning to a consideration of Fig 2a, note that I have used no colour within the Earth part of the diagram. OPERA does not appear red-shifted to CERN even though OPERA is moving at 500km/s to the right in the diagram, because CERN is also moving at 500km/s to the right.

Now let’s consider how all this appears from the point of view of a neutrino (or light). Now, light can’t move at greater than the speed of other light. Such faster than light travel would effectively be the same as going back in time.

So light (and neutrinos) always travel at the speed of light, c, in empty space. If other objects are moving then they will perceive light to be red-shifted in the direction they’re moving from and blue-shifted in the direction they’re moving. The light waves are stretched (red-shifted) or squashed up (blue-shifted). As will be seen, it’s only by convention that we don’t instead consider the Earth as squashed up or stretched, which in fact might be a better fit to how the Universe actually is – as usual (sigh!) our perception is Earth-centric.

In Fig 2b, then, I’ve put the neutrino in the middle of its journey from CERN to OPERA (it might have been less confusing to have put it at the end, but the view forward is also interesting). Looking back, the neutrino would see CERN coming towards it at ~500km/s, due to the motion of the planet – the distance it has had to travel to OPERA is shortened (blue-shifted) by the Earth’s motion. This is true when the neutrino arrives at OPERA, so the neutrino has travelled less distance because of the motion of the Earth. It is not moving relative to the planet, but relative to all the other light in the Universe. It has to, otherwise some light would travel faster than other light, and that’s not what we observe.

Now to confuse the issue (probably a good job neutrinos can’t really see!). Looking forward, the neutrino sees OPERA moving away (red-shifted), but after it covers that distance, where it currently is (and CERN) will look blue-shifted. Got it? If it’s any help, this is exactly analogous to the discussion of Einstein’s train thought-experiment where, you will recollect, Bob was able to warn Alice, even though it seemed to Xavier that Agent Zero could reach her in less than d/c time in his near-light speed ship inside the train moving towards her, than the d/c he knew it would take Bob to warn her along the platform.

If the Earth is really moving, then, why don’t we reckon time to take account of that fact? Well, consider how awkward it would be (Fig 2b). Light would still travel at the same speed in all directions, but we’d dispense with the idea of time being the same in different places. Instead of having time constant everywhere and assuming that distances are the same in all directions, as we perceive, we’d have to assume time is different everywhere, and that it varies with distance depending on the motion of the Earth system. Or alternatively, we could keep an idea of time as the same over the whole planet and have distances vary depending on which direction we’re going in (as shown by the red-shift and blue-shift)!

Because we’ve forgotten these points that were long ago demonstrated in special relativity, and followed the convention to assume our time can be used to measure the speed of light and neutrinos travelling in all different directions – which it can’t – we’ve observed the neutrinos travelling as faster than they actually are.

The expected arrival time of the CERN neutrinos at OPERA should have been calculated taking into account the motion of the Earth, vE, as:

t=d/c – dvE/c^2

(or to be precise t=d/c – (dvE/c^2)/SQRT(1-v^2/c^2), but the denominator is insignificant at Earth’s velocity).

This can simply be understood (ignoring the complex version of the formula) as the distance the Earth would have moved in the time light travelled a given distance, divided by the speed of light.  It works out to about 5.6ns/km.  This is a maximum value, if the experiment were oriented directly in line with the Earth’s motion.

The precise distance that was measured without taking special relativity into account is uncertain, but the paper describing the experiment notes that there is a 8.3km optical fibre cable at San Grasso, though it’s the distance as the neutrino flies that is important.

The neutrinos appeared to arrive 60ns early.  Do the math.

——————
I’ve discussed this issue in much more detail in a paper Analysis of Flawed Fibre Time-Delay Calibration Methodology in CERN-OPERA Experiment v0.3 (pdf). I’d really like to post this on the open physics site, ArXiv, but I need to be endorsed by someone with the right credentials to do so. If anyone reading this can help, please contact me via this blog.

Here’s the Abstract for v0.3 of my paper (pdf):

The OPERA neutrino experiment at the Gran Sasso Laboratory, [1], obtained a measurement, v, of the neutrino muon velocity with respect to the speed of light, c, of (v-c)/c = (2.48 ± 0.28 (stat.) ± 0.30 (sys.)) ×10-5, that is, in excess of c by about 1 part in 40,000. Over most of the neutrino flight path from CERN to OPERA, distances and timings were established by GPS signals to within 2cm and (2.3 ± 0.9)ns respectively. These measurements are not problematic. The Gran Sasso Laboratory is underground, however, and a significant part of the measurement of the expected flight time at c was established using two separate fibre delay calibration procedures, both of which are based on the two-way speed of light rather than the reference-frame dependent one-way speed implicit in the GPS and the velocity of neutrinos over the (one-way) flight path from CERN to OPERA. The two-way light speed measurement ignores the moving frame of reference (the Earth system (ES)) in which the experiment was conducted and introduces errors of the same order as the early arrival time of the neutrinos (60.7 ± 6.9 (stat.) ± 7.4 (sys.)) ns. Similar problems affect all attempts to measure the one-way speed of light [2]. This paper explains these problems, with reference to Einstein’s train thought-experiment and suggests how the expected one-way speed of light in a moving frame of reference such as the ES could be derived using the cosmic microwave background (CMB) as a stationary frame of reference. This problem is additional to the clock synchronisation issues described in [3], and can be traced to a flaw in a procedure, [5], which may have been used at CERN on other occasions, so may affect other experiments involving the accurate measurement of particle velocities approaching or at c. The experiment may yet prove to be important as it would, in fact, have measured a one-way neutrino (and hence one-way light) velocity and, by identifying a stationary frame of reference (possibly that defined by the CMB) with respect to light (and neutrino) transmission, perhaps shed light on cosmological questions.

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October 14, 2011

Analysis of Fibre Delay Calibration Error in CERN-OPERA Neutrino Speed Experiment

Filed under: Neutrinos, Physics, Relativity — Tim Joslin @ 12:57 am

Following on from my previous two informal posts discussing the apparent measurement of superluminal neutrino velocities in transit between CERN and OPERA, I have drafted a paper on the topic (pdf), which I hope to submit to ArXiv, the open physics online journal.

The paper is a little more precise than the previous blog posts, but makes the same general point. I’d appreciate any comments. Here is the Abstract:

“The OPERA neutrino experiment at the Gran Sasso Laboratory obtained a measurement, v, of the neutrino muon velocity with respect to the speed of light, c, of (v-c)/c = (2.48 ± 0.28 (stat.) ± 0.30 (sys.)) ×10-5, that is, in excess of c by about 1 part in 40,000. Over most of the neutrino flight path from CERN to OPERA, distances and timings were established by GPS signals to within 2cm and (2.3 ± 0.9)ns respectively. These measurements are not problematic. The Gran Sasso Laboratory is underground, however, and a significant part of the measurement of the expected flight time at c was established using two separate fibre delay calibration procedures, both of which are based on the two-way speed of light rather than the reference-frame dependent one-way speed implicit in the GPS and the velocity of neutrinos over the (one-way) flight path from CERN to OPERA. This ignores the moving frame of reference (the Earth system (ES)) in which the experiment was conducted and introduces errors of the same order as the early arrival time of the neutrinos (60.7 ± 6.9 (stat.) ± 7.4 (sys.)) ns. Similar problems affect all attempts to measure the one-way speed of light. This paper explains these problems, with reference to Einstein’s train thought-experiment and suggests how the expected one-way speed of light in a moving frame of reference such as the ES could be derived using the cosmic microwave background (CMB) as a stationary frame of reference. This problem is additional to the clock synchronisation issues described in Carlo Contaldi’s paper, and can be traced to a flaw in a procedure which may have been used at CERN on other occasions, so may affect other experiments involving the accurate measurement of particle velocities approaching or at c.”

October 10, 2011

Einstein’s Train Thought-Experiment, Fast Neutrinos (and One-Way Measurements of the Speed of Light)

Filed under: Neutrinos, Physics, Relativity — Tim Joslin @ 12:58 am

My previous, somewhat rambling, post attempted to explain the recent experimental observation of neutrinos apparently travelling faster than light. I concluded that an adjustment needs to be made to the clocks used to measure the neutrino time of flight to compensate for the absolute motion of the experiment, i.e. in relation to the cosmic microwave background radiation (CMB). Observations suggest the Earth is moving at ~600kps (~1/500th light speed) relative to the CMB.

This post attempts to prove that conclusion by a thought-experiment.

Let’s remind ourselves of Einstein’s train thought-experiment (figures from Wikipedia, copied here purely for convenience):

What Einstein demonstrates here is the relativity of simultaneity. Events (say light emitted at the centre of the carriage reaching the two ends) which are simultaneous in one frame of reference (top, from within the train) are not simultaneous in another frame of reference (bottom, from the platform).

I’d like to extend this slightly.

There’s even a little story. Xavier, in his hyperspeed train, has lured Bob to the train platform under the pretext of performing a relativistic experiment. He hopes to distract Bob for long enough to send Agent Zero to shoot Alice, who is also standing on the platform:

Consider a scenario where Xavier is at the centre of the train, and Bob is standing on the platform, each with their atomic clocks. Bob’s colleagues are also standing on the platform with their atomic clocks at the precise points where there are clocks on the train. Clearly, if set correctly, each pair of clocks would, for an instant, show the time in the other frame of reference – T1(train) would be the same as T1(platform) and so on.

Xavier doesn’t just want a pretext for his evil scheme. He also wants to perform an experiment. He wants to impress Bob by displaying Bob’s correct time on clocks at the ends of his train when he passes Bob on the platform. Bob’s clocks are synchronised by signals from T1(platform) so reflect light speed transmission delays in Bob’s frame of reference. Unfortunately for Xavier, he doesn’t know how fast his train will be moving relative to the platform at the moment he passes Bob.

How can Xavier get his clocks to show the same as Bobs’? There are two possibilities. He could either send a timing signal to each of the clocks at the ends of his train or he could walk the clocks from his position in the centre to each of the two ends. In the first case, the clocks would show the same as T1(train) adjusted for the transmission delays at the speed of light in the train. But we know from Einstein’s thought-experiment that these clocks will not show the same times as those on the platform. In the second case, the clocks would initially show the same as T1(train) but to show the same time as the corresponding clocks on the platform would have to be adjusted to reflect light transmission delays in Bob’s frame of reference. The adjustments would be different for the two clocks (the clock at the front of the train would have to be adjusted by more than the transmission time for light in the train and that at the rear by less).

It is evident from Einstein’s thought-experiment that neither method will yield the times on Bob’s clocks on the platform (Xavier would need to know the exact speed of his train relative to the platform and apply some equations from special relativity).

Signals sent at light speed to the clocks at the front and rear of the train will set them too early and late, respectively, since Bob sees events at the front of the train later than those at the rear. Similarly, walking the clocks from the centre of the train would ensure T1(train)=T2(train)=T3(train), but if adjustments are made to set T2(train) and T3(train) to be in synchrony like T2(platform) and T3(platform), T3(train) at the front would be behind T3(platform) and T2(train) at the rear would be ahead of T2(platform).

Xavier would either have to assume the speed of light was different in each direction or that time at the front of the train was delayed relative to time at the rear (and middle) of the train.

Let’s consider further what would happen if, on seeing Bob on the platform, Xavier told Agent Zero to set off in his near-light speed ship within the train (did I mention it was a big train?) in the direction of travel of the train, towards Alice, who Xavier knows is standing further along the platform in order to help Bob with the experiment.

Now, Bob is nobody’s fool, and sees Zero setting off (did I mention that the train is transparent?) and transmits a message to Alice: “Duck!”. She does so just before Zero arrives at T3(platform) (before he reaches the end of the train at T3(train)) and he misses. Obviously if Zero had reached Alice before the message from Bob, Zero would have travelled faster than light in Bob’s frame of reference. This is not possible, says Einstein.

Similarly, Bob might retaliate by sending Charlie in a similar near-light speed ship to shoot Yolanda at the rear of Bob’s train (which, again, he would reach before he came to the end of the platform). In this case, Xavier would be able to warn Yolanda.

The critical point is that both Bob and Xavier see light travelling at the same speed in both frames of reference. Apologies if you knew this already, but I enjoyed telling the story.

Not shown on my diagram is that Bob would have the same problem with clocks if he was also moving (did I mention the platform is a movable construct in space? – thought-experiment technology really has moved on since Einstein’s day!). If he passed Harry’s Bar on the Intergalactic Highway, he would have the same issues as Xavier (and if Harry also tried to shoot Alice in the same way – after all, he is simmering with jealousy after she ran off with Bob – Bob would also be able to warn Alice). Bob would have to assume either that clocks on his ship were delayed or that light travelled at a different speed along and against his direction of travel.

It follows that it is impossible to measure the one-way speed of light in any frame of reference since you either have to assume there is an error between all clocks in line of motion (proportional to distance) or that light travels at different speeds in different directions.

Unless, of course, you know that your frame of reference is stationary or exactly how you are moving in relation to a stationary frame of reference.

Now, Big Bang theory* tells us that the cosmic microwave background radiation (CMB) was all generated simultaneously. The CMB was generated throughout the Universe and what we see now is what’s reaching us from those regions in all directions that happened to be 13.7 billion light-years away at the time of the Big Bang. Clearly, therefore, the anisotropy (or redshift and blueshift) of the CMB is due to the motion of the Earth rather than that of the CMB itself.

The CMB therefore represents a stationary frame of reference.

As an aside, note that if neutrinos did travel faster than light, they’d eventually (in around 500 trillion years or so, based on the magnitude of the superluminal neutrino velocity reported for the CERN-OPERA experiment) reach a region of space where the Big Bang was still in progress, potentially interfering with their own creation. I don’t think the Universe would allow that, somehow. Alice would be miffed.

I therefore propose that if we adjust the fast neutrino timings to allow for the motion of the experiment, relative to the CMB, during the time the atomic clock was** moved between the GPS at San Grasso and the point where the neutrinos were detected, we will determine the true speed of neutrinos (which I predict will be that of light, c, within the limits of experimental error).

Note that the GPS timings and distances in the fast neutrino experiment do not contribute to the error, since all these are distorted in the same way (i.e. they are consistent within our frame of reference, or, to put it another way, systematic errors cancel out) due to the motion of the Earth (I may put up another post on just this point).

——-
* Just in case anyone assumes I’m an unreconstructed Big Bangian, I want to point out that I’m not entirely comfortable with Big Bang theory, but we can explain the difficulties of one-way lightspeed measurement and, by extension, fast neutrinos, within the paradigm. Obviously any replacement theory would have to explain all the Big Bang predictions (and more – but “more” doesn’t include fast neutrinos, since, just to be crystal, that phenomenon can already be explained) just as Einstein explained Newton’s.

** Postscript (15/10/11): It is incorrect to suggest that the time when the clock was moved (or clocks were synchronised) is important. My brain must have shorted at around the point I came up with that idea last weekend. In fact, the fibre time-delay calibration procedure (which uses two techniques based on the same misconception, one of which involves a transportable caesium clock) always gives the same result for the time-delay (excepting small measurement errors) based on an implicit two-way lightspeed measurement. The (one-way) neutrino flight time is on average greater than that expected based on the fibre time-delay calibration procedure (in this particular experiment, probably due to the N-S component of the CERN-OPERA neutrino flight-path), but dependent on the experiment’s orientation with the CMB when they are sent and detected (the change in orientation, as opposed to the motion, of the planet during their flight time is seriously insignificant). More detail on this point is included in the paper I have subsequently drafted on the erroneous superluminal neutrino result.  (Also made one unrelated wording change in the text, to clarify that the 500 trillion year estimate is based on the reported CERN-OPERA superluminal neutrino flight time).

Frames of Reference and Fast Neutrinos: Misinterpreted Findings?

Filed under: Neutrinos, Physics, Relativity — Tim Joslin @ 12:32 am

There are much more pressing problems I should be looking into, but I find it more than a little distracting when my understanding of how the universe operates is publicly and loudly challenged. I refer of course to the recent experiment which appeared to determine that the velocity of neutrinos is faster than light (by about one part in 40,000) (hereafter “the fast neutrino experiment”). So I’ve had a look at the paper describing the fast neutrino experiment (Autiero et al), sampled the discussion as to what might really be happening, and even listened to the seminar of 23rd September announcing the findings from CERN.

Here’s my take on the whole business.

Note: After drafting this post I’ve come up with a systematic demonstration, by thought-experiment, of my assertion here that a correction needs to be made for the motion of the experiment relative to the stationary frame of reference represented by the cosmic microwave background (CMB) signal. When it’s complete I’ll jump in my neutrino-drive time-machine and add a link to it here.

Abstract

I’m convinced the neutrinos are not travelling faster than light, though the findings may tell us something useful. I believe the results have been misinterpreted or the experiment misconceived. It is not possible to validate the speed of neutrinos in the way attempted. I don’t believe the results are due to an experimental error as such. The problem is with the concept of synchronised time, necessary to establish a frame of reference for an experiment. The experimenters have synchronised time measurements over most of the distance over which they measured the speed of neutrinos by reference to the speed of light (via the GPS system). But over a significant distance they used a method involving the transport of timing devices. Such a method does not compensate for the motion of the local frame of reference and has introduced measurement errors leading to the apparent superluminal speed of neutrinos. Although we perceive the speed of light (and neutrinos) to be constant, time is distorted by the motion of the local frame of reference in relation to the rest of the universe (hence we see distant objects red-shifted or blue-shifted depending on their motion relative to us). The neutrinos have not agreed to be unaffected by the rest of the universe. The results could, however, be used to partially test the hypothesis that the frame of reference of the neutrinos (and, at least, light) is the whole universe, i.e. that they only appear to be travelling at equal velocity in all directions if this is measured against the cosmic microwave background (CMB) or average motion of the universe as a whole.

A Doubly Ambitious Experiment

The fast neutrino experiment measured the one-way speed of light (implicitly, by trying to establish the simultaneity of events) and then (explicitly) that of neutrinos, determining the latter to be in excess of the former. Now, the one-way speed of light has not previously been successfully measured. There are fundamental reasons for this which I will try to explain.

The fact that the literature which exists on the difficulty of one-way light-speed measurements is not discussed in Autiero et al suggests that this is the area in which the problem lies.

First, a little background.

What are Neutrinos Anyway?

I think it’s fair to say neutrinos are fundamental particles comparable in some ways to photons. If the fundamental property of photons is that they carry energy, maybe we can consider neutrinos to carry another form of energy (which we understand less and are less able to manipulate). Under certain circumstances the neutrino form of energy can be exchanged for the more familiar form of energy (so we can measure neutrino energy). I make this comparison and simplification to stress that our current level of knowledge suggests neutrinos should behave in some ways like photons. At least that should be the null hypothesis we should be aiming to falsify.

Why the Fast Neutrino Result must be false: (1) SN1987a

We already know neutrinos travel at the speed of light, to a very close approximation. Neutrinos from a distant supernova observed in 1987 (SN1987a) arrived 3 hours before light believed to have been emitted simultaneously, and there are reasons why the light might have been delayed. In any case, if the neutrinos had been travelling as fast as those in the fast neutrino experiment they would have arrived several years earlier. It’s therefore necessary to suppose there is something different about the fast neutrinos, such as their energy, even though there is no theoretical reason to suppose that this would be the case – the speed of light is not affected by its energy (which affects instead its wavelength). In fact the energy of the neutrinos in the fast neutrino experiment was several orders of magnitude greater than those from SN1987a. The obvious thing to do is to repeat the fast neutrino experiment with different energies. The critical question was asked about 1 hour 49 minutes into the CERN seminar (slide 83), by which time everyone was a bit tired. The answer was that no significant effect of energy on neutrino velocity had been determined. Referring to the fast neutrino paper (p.20), it’s clear that limited analysis, with significant uncertainty, has been carried out on only a small range of energies (varying by less than an order of magnitude and divided into just those of more than 20GeV and those of less than 20GeV).

Why the Fast Neutrino Result must be false: (2) Relativity

Relativity is not generally well-understood, but even Dara O’Briain on last week’s Mock the Week (a light-hearted UK current affairs TV show) noted that light doesn’t experience time. As far as light is concerned it travels instantaneously from point A to point B, assuming Einstein is right. Time passes only for stationary or at least slow-moving observers. In other words, time is associated with space, not with light itself. This is fundamental.

Simultaneity, Time and Frames of Reference

There’s some astonishingly good stuff on Wikipedia. I recommend the entries on Relativity of Simultaneity and Inertial frame of Reference. The point is we can only discuss events happening simultaneously within a closed system within which the relative velocities of objects are known. A frame of reference is not a property of the universe. Rather it’s something we need to define in order to apply physical laws. If we can assume we are taking measurements within a frame of reference, that is, that the phenomena (time, position, velocity, acceleration and so on) that we wish to relate are not independent of one another, then we can apply physical laws. For example, the fact that the solar system is hurtling round the Milky Way which is itself hurtling through space does not need to be taken account of in calculating a trajectory to land on the Moon.

And it’s only within a frame of reference that we can invoke a concept of simultaneity. Again, this is not a property of the universe, but something we need for our convenience. A concept of simultaneity allows us to relate time in different places.

Establishing a Frame of Reference: Conventions

Time always involves conventions, even when relativity doesn’t come into it. But when we want to make very accurate measurements we need further conventions. The main issue is how to deal with delays caused by the apparent speed of light. Consider a mission to the Moon. The communication delay is only a couple of seconds, but how does the astronaut know precisely when to expect a communication from Earth? There are a couple of sensible possibilities. The clock on the Moon could be arranged to show the time a message would arrive from Earth. The astronaut would not miss even a second of his favourite TV programme. A broadcast sent at 12 midday from Earth would arrive at 12 midday on the Moon. But when the reverse communication was attempted there would be a delay. Messages sent at 12:00:00 Moon time would reach Earth at over 2 seconds (the round-trip time delay) past 12 on Earth.

Less confusing is to pretend the time is the same on the Moon as on Earth. Messages sent at 12:00:00 from the Moon to the Earth will arrive at 12:00 and a bit over a second Earth time, and messages sent at precisely midday from the Earth will arrive at a bit over a second after midday Moon time.

Once relativity comes into it conventions have to be used to manage time even within a frame of reference. Or rather, a better way of thinking about it may be that conventions to manage time are required to establish a frame of reference. Remember, the universe doesn’t know anything about our frames of reference. They are just a means for us to apply physical laws somewhat more easily. We should always ask whether all the phenomena we are measuring are in fact entirely relative to our frame of reference. Otherwise we are not measuring what we think we’re measuring. It’s a failure to question the validity of the frame of reference that lies behind the apparent anomaly of “fast neutrinos”.

The fast neutrino experiment relied on a convention whereby all clocks indicate the same time as on a master clock (i.e. they simply tried to determine Coordinated Universal Time (UTC) with great accuracy at both the sending (CERN) and receiving points (the OPERA detector at Gran Sasso Laboratory in a mountain 730km away)). So the convention for communication is that all transmissions received appear delayed by a time dependent on the distance from sender to receiver (i.e. distance divided by the speed of light, c). At least, that is the aim, but as I hope to explain, this was not achieved. It is the limitations of this approach (rather than any errors in execution) that I believe causes the fast neutrino anomaly.

Establishing a Frame of Reference: Issues with Synchronising Clocks

There are a number of aspects of relativity that need to be considered when synchronising atomic clocks. These are well known from the experience of the GPS system (PDF), which relies on all satellites being synchronised to UTC. The fast neutrino experiment could not just rely on GPS, though, because the OPERA facility is underground. They also used “a two-way fibre procedure” (I don’t know what this is and neither does the internet) and, most importantly, “a transportable Cs [caesium] clock… yielding the same result” for a substantial distance (“an 8.3km long optical fibre” along which a timing pulse is transferred every millisecond).

There’s plenty to go wrong and some of the issues are discussed in a short paper by Carlo Contaldi (although written when it was not yet clear that GPS time synchronisation was used for the bulk of the transmission path, the points Contaldi makes are applicable to the residual time synchronisation). I agree with Contaldi that the fast neutrino experiment paper should have discussed this issue in much more depth, but am willing to assume that relativistic effects have been correctly accounted for, since two Metrology Institutes (Swiss and German) were involved. Whilst the level of accuracy may have been unusual, no new principles were involved.

One particular relativistic effect may be surprising. It turns out that simply moving atomic clocks, however slowly, introduces an error as a result of the Sagnac Effect. If you synchronise two clocks next to each other and move one from west to east (e.g. from CERN to OPERA) it gains time, i.e. a signal from CERN would take a little longer to reach OPERA. This is adjusted for in the fast neutrino experiment (and in GPS) by adding a correction to signal arrival times (you can’t just adjust the clocks because if you kept doing that right round the planet you’d end up with a clock around 200ns ahead or behind the one you started with). At the fast neutrino experiment seminar one person asked if they had “corrected for the Earth’s rotation”. One way of looking at the problem is that the light (or neutrino) is slowed down or speeded up by the Earth’s rotation against or in the direction of travel. But the light always appears to arrive at the same speed. So, even though the problem is resolved by adding a correction factor to each signal received, we have to think of the Sagnac Effect as a time distortion arising from trying to create a rotating frame of reference.

Extending Sagnac: What’s Been Overlooked

The Sagnac Effect is clearly a special case of a general effect. It’s not the result specifically of the Earth rotating, but of the Earth moving and taking with it the frame of reference we are trying to construct. If you were trying to measure the velocity of neutrinos instead in a space laboratory (with synchronised atomic clocks at each end, say), then you’d have to make a similar adjustment for the velocity of the laboratory.

Hang about! The velocity of the laboratory in relation to what? The experiment is being conducted in a closed space.

Well, to cut to the chase, my money is on the frame of reference for light and neutrinos being the whole universe. It’s unlikely to be something as small as the Earth or the Solar System, since most of the billions (trillions?) of neutrinos created at CERN will travel for light-years – only a hand-full were detected at OPERA (I heard that if you could shine a beam of neutrinos at a light-year thickness of lead, most of them would pass through).

Now, although the fast neutrino experimenters may have corrected for the Sagnac Effect (which GPS also corrects for) when moving their Cs clock, it may be the case that they didn’t correct for the Sagnac Effect motion of the Earth around the Sun, the Sun around the Milky Way or the Milky Way about the local supercluster. These are not corrected for in the GPS system, because these motions affect all the clocks (and light transmission between them) simultaneously (though I can’t help pointing out that small errors would arise if they failed to correct for the rotation of the Earth-Moon system about it’s the centre of gravity over a lunar month, but maybe they do!).

Most importantly, the red-shift/blue-shift dipole in the cosmic microwave background radiation (CMB) suggests the Earth is moving at about 6ookps (about 1/500th or 0.2% lightspeed).

Let’s come back to that.

Sources of Confusion 1: How could the motion of the Earth affect the neutrino speed measurement?

I’m confused so I expect you are too!

As with the Sagnac Effect, the motion of the Earth does not affect the speed of light or passage of time we perceive. It does, though affect time on Earth as perceived by an external observer (say one at rest in relation to the CMB). They would observe time running faster on Earth if it was coming towards them and going slower if it was receding. The time between pulses of light from Earth would vary and they would be blueshifted or redshifted.

Most importantly (as in Einstein’s train analogy), events that appear simultaneous on Earth do not appear simultaneous to the external observer.

The neutrinos (and light) are like the external observer. We might think clocks are simultaneous, but the neutrinos do not.

Sources of Confusion 2: Why don’t we notice this effect, say in the GPS system?

As in the case of the Sagnac Effect, the problem only occurs when you try to synchronise clocks. Once clocks are synchronised, then they all run slower or faster, as does every other physical process, as perceived by an external observer, as they change velocity relative to the external observer, e.g. as the Earth rotates and orbits.

Individual clocks may appear (to the observer) to speed up or slow down as they change orientation, as in the Fizeau experiment. Fizeau measured the difference in speed between light beams travelling through water flowing in opposite directions. If you were in one of Fizeau’s flows (but couldn’t detect the water flow – this is a thought experiment, OK?), it would be impossible to set two clocks to measure the speed of light without knowing the speed of the water flow.

Similarly, the errors in an experiment to measure the speed of light or neutrinos on Earth will depend on the orientation of the experiment with respect to the planet’s motion (such as its speed of 500kps relative to the CMB) at the time the clocks are synchronised.* (This has got a little chicken and egg, as we want to measure the speed of light and neutrinos to determine whether their frame of reference is the CMB. Try not to forget that the speed of light is not some external quantity, but actually determines time within a frame of reference, so appears constant, i.e. using time differences to measure the speed of light is circular. What the fast neutrino experiment was trying to do, of course, was measure the speed of neutrinos, by trying to calculate what the speed of light would have been had it been able to travel through the Earth with the neutrinos).

The GPS system synchronises time by the exchange of signals. These travel at the speed of light, which is common for the whole frame of reference. GPS doesn’t need to know about the motion of the planet as a whole (except for its rotation), since all positions are calculated relative to each other within the Earth system.

In the Fizeau thought-experiment, if instead you used the speed of light to synchronise clocks within the water flow, you could then use them to determine positions just as in the GPS.

Sources of Confusion 3: the Aether versus Frames of Reference, Mitchelson-Morley versus Sagnac and Fizeau

I’ve noticed that a number of people have pointed out on blogs that errors might have arisen in the fast neutrino experiment because of the motion of the Earth. They’ve been slapped down by others saying there’s no “aether”, as supposedly shown by Mitchelson and Morley (M&M). The idea of the aether was that there was a substance through which all objects move, which some argued exerts a drag in a preferred direction. Mitchelson and Morley showed this was not the case by demonstrating that light travelled at the same (2 way) speed in perpendicular directions.

This helped Einstein develop a theory without the aether concept. But he nevertheless needed to explain findings like those of Sagnac and Fizeau which appeared to show the existence of an aether.

The Real Meaning of the Fast Neutrino Experiment

When I thought the fast neutrino experiment had involved transporting clocks over 730km, I calculated the error as too large – up to 730km/500 (assuming the Earth is travelling at roughly 600kps or 1/500th light speed relative to the CMB, as discussed earlier) or 1.46km distance or around 4900ns early, as against the actual 60ns. To have had only 60ns error (of course other timing errors may come to light) would have been to assume the OPERA clock was synchronised when the experiment was somehow moving only slowly in relation to the CMB (maybe perpendicular).*

But with only 8.3km to worry about (actually there are other segments where the same error might be made), the maximum possible error is around 8.3km/500 or 16.6m or around 55ns, around that which was observed. Trouble is, this assumes the experiment was oriented directly in line with the motion of the Earth in relation to the CMB. If records of exactly how and when clocks were moved* still exist and/or it is possible to repeat the experiment, it should be possible to determine orientations wrt the CMB, and hence expected timing errors, assuming there’s anything in all this.

Maybe the fast neutrino experiment has not proved that neutrinos travel faster than light, but rather suggests ways in which we might measure the direction and velocity of motion of the Earth with respect to the frame of reference of neutrinos (meaning the frame of reference in which they appear to travel at the same speed in all directions). Maybe this will turn out to be the whole universe (and therefore in agreement with CMB redshift/blueshift measurements), maybe not.

* Postscript (15/10/11): It is incorrect to suggest that the time when the clock was moved (or clocks were synchronised) is important. My brain must have shorted at around the point I came up with that idea last weekend. In fact, the fibre time-delay calibration procedure (which uses two techniques based on the same misconception, one of which involves a transportable caesium clock) always gives the same result for the time-delay (excepting small measurement errors) based on an implicit two-way lightspeed measurement. The (one-way) neutrino flight time is on average greater than that expected based on the fibre time-delay calibration procedure (in this particular experiment, probably due to the N-S component of the CERN-OPERA neutrino flight-path), but dependent on the experiment’s orientation with the CMB when they are sent and detected (the change in orientation, as opposed to the motion, of the planet during their flight time is seriously insignificant). More detail on this point is included in the paper I have subsequently drafted on the erroneous superluminal neutrino result.  (Also made one unrelated wording change in the text, to clarify that the Sagnac Effect is just one example of a general phenomenon).

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