Frames of Reference and Fast Neutrinos: Misinterpreted Findings?
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.
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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