Particles recorded moving faster than light

[starslayer]

In order:

1. The speed of light has been measured to very high precision, and is in fact how we now define the length of a meter. If you doubt this measurement at all, you can get an approximate result using a chocolate bar and a microwave oven.* It has never been determined from first principles, at least not in terms of things that are not themselves measured fundamental constants.

2. No they are not. The quantum foam is a relatively recent idea from the last 20-30 years, as I recall.

3. Through matter, yes. You are correct in that since photons readily interact with atoms, in most matter they quickly interact with one and are absorbed or scattered. Thus, a wavefront of photons moves more slowly through matter than a similar one of neutrinos, and both move more slowly through matter than they would through a vacuum. However, in between interactions, the individual photons which make up the wavefront are moving at c, their speed in a pure vacuum. This is because the space between atoms is just as empty as that in a pure vacuum - it's just that in a solid, for example, there's a lot more stuff taking up some of that space.

4. Yes, light can propagate through a true vacuum. As I noted above, it does so all the time, since the space between atoms in bulk matter basically is a true vacuum anyway. Whether they "experience" the passage of time is not clear, since the equations all diverge as you get close to the speed of light for things with mass. From our perspective, which is really what matters in this case, the photons exist when they exist (sounds tautological, I know, but I'm having trouble coming up with some good wording for this), not just when they hit something.

*To measure the speed of light using a microwave, remove the turntable and put the chocolate bar in the middle of it, aligned parallel to the back of the oven. Open the door and turn the microwave on for, say, 30 seconds or so. You may have to experiment to find the right amount of time. What you want is for some portions of the chocolate bar to melt (there should basically be even stripes of semi-melted chocolate if you've done this correctly). Measure the distance between the middle of one melted band and the next one over; this is the wavelength of the microwaves. Now read the frequency off the back of the microwave and multiply those two numbers together, since from wave mechanics, the speed of any wave is just wavelength*frequency. You should get about 300 billion cm/s, which is the speed of the microwaves. Since microwaves are a form of light, and air has an index of refraction very close to one (i.e., from light's perspective is actually close to a vacuum), you have just measured c.

[Surlethe]

We might make the "experience" of time precise by defining "time experienced" to be proper time (arc length, I believe) along a curve. Since photons follow null geodesics, the arc length of the curve is zero and it follows that proper time elapsed for any interval along a null geodesic is zero.

I'm sure Kuroneko will be along shortly to correct me.

[Kuroneko]

We might make the "experience" of time precise by defining "time experienced" to be proper time (arc length, I believe) along a curve. Since photons follow null geodesics, the arc length of the curve is zero and it follows that proper time elapsed for any interval along a null geodesic is zero.

Yes, that's exactly what happens in relativity. You don't need to base your conclusion on mass and how the quantities behave as mass approaches zero, because both energy and momentum are more fundamental (being generated by temporal and spatial translation symmetries). In a relativistic context, mass is just the length of the four-momentum [E;p], i.e., m² = E² - p², so instead of defining four-momentum as mass times the four-velocity (as is usually done in textbooks), it's quite possible to consider mass derived from it instead.

4. Yes, light can propagate through a true vacuum. As I noted above, it does so all the time, since the space between atoms in bulk matter basically is a true vacuum anyway. Whether they "experience" the passage of time is not clear, since the equations all diverge as you get close to the speed of light for things with mass.

It's pretty clear that they don't, at least for reasonable interpretations of "experience."

From our perspective, which is really what matters in this case, the photons exist when they exist (sounds tautological, I know, but I'm having trouble coming up with some good wording for this), not just when they hit something.

That's true, but even that is a matter of interpretation, because there can't be a position operator for a massless particle of non-zero spin. You always need some sort of interaction to talk about the position of a photon; on its own it's a semi-classical fiction. Unless it's producing some sort of effect, asking for location is not meaningful.

Classically, there's an alternative interpretation of electromagnetism which completely lacks fields altogether, the Fokker-Tetrode action, in which every observable field effect is a direct interaction between charges instead. This only makes sense because spacetime has null geodesics, so in a very literal sense, you can have events that are zero distance apart even though they're separated both spatially and temporally. I've no idea of whether this would work quantum-mechanically, though.

[starslayer]

Ah, I see. Thanks for the correction, Kuroneko and Surlethe.

[Anacronian]

I'm a layman no doubt about it so take this idea with a grain of salt.

But could Neutrinos be moving faster because they are so small - I mean it in the way is it possible that photons are large enough that they bump into dark matter(or is it dark energy?) on their way while Neutrinos are small enough to not have collisions so often?

[Kuroneko]

I don't think it's possible. If we're around about the speed of light being the invariant speed in spacetime, we can't be off by much, since experimental bounds on photon mass are of order 1E-18 eV.

That means compared to the typical visible light, with photon energies on order of ~1eV, we need a Lorentz gamma also around 1E18. So the speed difference between the 'effectively massive' photon and the invariant speed would be v = 1 - sqrt(1-1/γ²) = 1/(2γ²) + O(1/γ[sup]4[/sup] ~ 10[sup]-36[/sup]. That's over 30 orders of magnitude too low to explain the relative error in speeds this experiment is getting.

Maybe there's some loophole, but I'm not seeing it.

[HMS Conqueror]

To go a bit further as to why the following is not true:

If effect doesn't necessarily follow cause, the entire predictive nature of the scientific method ceases to function. It also would seem to imply the possibility of paradoxes. If you still don't understand why it should be a big deal, the wikipedia page should be your next port of call.

Uncountable numbers of "experiments" are done every single second that support our current understanding of causality (and physics).

This is why almost no physicist thinks causality is actually violated. But if it were shown to be, it would blow an enormous hole in the philosophy of physics.

[Freefall]

The speed of light in a vacuum has been mentioned and my first thought was why do we assume that we know what the speed of light is? Has the speed of light ever been determined from first principles? Or has it only been measured?

Not exactly, but you can get the speed of light out of Maxwell's equations, which govern electromagnetism and were developed much earlier and independently of our understanding of light. Basically, you can perform some basic mathematical operations on them to change some of the standard Maxwell's equations into the "wave equation." When you do this, the term in the resultant wave equation that corresponds to velocity is a constant, that just happens to be exactly what we get for the speed of light in vacuum. If my history isn't too muddled, I think this was actually evidence that lead scientists to identify light as actually being electromagnetic waves in the first place. I'm sure Surlethe and Kuroneko understand it better than me though. It's been a while since I looked at that derivation.

[CaptainChewbacca]

You can actually measure the speed of light with a microwave and a candy bar.

A fun experiment.

[Surlethe]

The speed of light in a vacuum has been mentioned and my first thought was why do we assume that we know what the speed of light is? Has the speed of light ever been determined from first principles? Or has it only been measured?

Not exactly, but you can get the speed of light out of Maxwell's equations, which govern electromagnetism and were developed much earlier and independently of our understanding of light. Basically, you can perform some basic mathematical operations on them to change some of the standard Maxwell's equations into the "wave equation." When you do this, the term in the resultant wave equation that corresponds to velocity is a constant, that just happens to be exactly what we get for the speed of light in vacuum. If my history isn't too muddled, I think this was actually evidence that lead scientists to identify light as actually being electromagnetic waves in the first place. I'm sure Surlethe and Kuroneko understand it better than me though. It's been a while since I looked at that derivation.

You pretty much nailed it. I'd just add that the speed of light was independently measured with greater and greater accuracy between the seventeenth and nineteenth centuries. Meanwhile, experimentalists in the nineteenth century measured the electric permittivity and defined the magnetic permeability of the vacuum. As you said, vacuum solutions of Maxwell's equations are solutions of the wave equation with velocity c = 1/sqrt[(permeability)(permittivity)]. When you plug in what you believe to be permeability and permittivity, you get a number that is suspiciously close to the measured speed of light. IIRC, this lead Maxwell to argue that light was, in fact, propagating electromagnetic waves. It also introduced the big electrodynamical question of the late nineteenth century: through what medium did light propagate?

The answer to that, of course, was: that is a meaningless question. Enter special relativity.

[Mr. Coffee]

Kuroneko, could you briefly explain what you mean by "four-momentum" and such in a way that I could kind of understand?

[Darth Yoshi]

According to wiki, in special relativity four-momentum is momentum in terms of spacetime. Normally, we think of objects as moving in three dimensions, with a momentum vector corresponding to each dimension. Four-momentum is just that, but with an additional vector factored in for time.

[Surlethe]

Kuroneko will give a better description. To tide you over until he gets here ... an 'event' has to be specified by 4 coordinates: three space and one time. A particle with mass traces out a path of events in spacetime. You now ask "how fast is the particle going." Answer: 4 more numbers, how fast each of the 4 coordinates is changing. Because physicists are classy, this is called the "4-velocity." The particle has mass, so to get a measure of its oomph, multiply how heavy it is by how fast it's going. This quantity is, creatively, known as 4-momentum.

In coordinates, BTW, the 4-momentum is, IIRC, (-E/c, p) where E is the particle's total energy and p is the particle's 3-momentum.

[Number Theoretic]

A new development, which might be of interest: Seems, they forgot
to take earth's precise "potato-shaped" gravity distribution into account.

"Two weeks ago, researchers claimed particles called neutrinos were travelling faster-than-light and violating the laws of special relativity. But now it looks as though general relativity might be behind the experiment's unusual result. An independent analysis claims that the original experiment, known as OPERA, failed to take into account differences in earth's gravitational field between the neutrino source and the OPERA detector. As Nature News reports, gravity can distort time according to Einstein's theory, and the effect could explain why neutrinos appear to arrive 60 nanoseconds ahead of schedule. The OPERA team is now reviewing the new analysis."

[Sriad]

A new development, which might be of interest: Seems, they forgot
to take earth's precise "potato-shaped" gravity distribution into account.

"Two weeks ago, researchers claimed particles called neutrinos were travelling faster-than-light and violating the laws of special relativity. But now it looks as though general relativity might be behind the experiment's unusual result. An independent analysis claims that the original experiment, known as OPERA, failed to take into account differences in earth's gravitational field between the neutrino source and the OPERA detector. As Nature News reports, gravity can distort time according to Einstein's theory, and the effect could explain why neutrinos appear to arrive 60 nanoseconds ahead of schedule. The OPERA team is now reviewing the new analysis."

I once used differences in Earth's gravitational distribution as an excuse for being late to a Physics lab. They were sufficiently amused.

[Kuroneko]

Kuroneko, could you briefly explain what you mean by "four-momentum" and such in a way that I could kind of understand?

I'm not sure that a more exact definition would be fruitful, so allow me to add some intuitive motivation to Surlethe's post. Say you have a clock with some velocity, 50 m/s in the x-direction (let's consider only one spatial direction for simplicity). There's a variety of ways you could represent that in spacetime--imagine drawing a vector on a (t,x) plane.

You could say the velocity is [Δt;Δx] = [1s;50m]: v = (50m)/(1s). Or equally well say it's [0.5s;25m]: v = (25m)/(0.5s), or indeed any positive multiple of that whatsoever*. In spacetime, velocity is a direction, the length of the vector is irrelevant to it. What matters is the ratio of spatial to temporal components, so what you do with the extra degree of freedom is up to you.

If we're talking only about velocities of a massive clock (particle), the most convenient choice is taking the the length of the vector to be 1 (in units of c=1), which is equivalent to taking the rate of change of position in spacetime with respect to the proper time of the traveling clock (i.e., the time lapse it measures). That's the standard four-velocity in relativity. But another choice is scaling so that the components correspond to the energy and momentum of the particle instead. One finds that energy is actually just momentum in the time direction.

What I was talking about earlier is making this kind of definition primary: there turns out the be a very precise mathematical sense in which momentum is a measure of how the system responds to being kicked a little bit in some spatial direction, and energy to time directions. Intuitively, energy conservation is a statement that the outcome of an experimental setup is independent of when you perform it, momentum conservation of where you perform it, and angular momentum of which way you orient your experiment in space.

[Kuroneko]

A new development, which might be of interest: Seems, they forgot
to take earth's precise "potato-shaped" gravity distribution into account.

Perhaps I'm being dumb, but I don't believe it at all. Unless OPERA has been very incompetent in synchronizing their clocks, you just can't get that kind of relative error from GR corrections. GPS clocks are in reference to the "potato-shaped" ideal geoid, a particular surface of constant gravity potential (gravitational potential + centrifugal potential), and all clocks on it tick on the same rate. The potential here is tiny, even hundreds of kilometers inside the Earth's surface, it's still on the order of 7E-10, and the potential differences are smaller still.

For those interested, I've discussed GR corrections with publius on another forum: [1] [2].

Basically, if you start out GPS-synchronized, then you can't get relative errors of more than a few parts per billion. If the neutrino speed is faulty, that's four orders of magnitude less error than they got. Unless they allowed the relative drift between the two clocks to compound over a long period of time. That could be true, but it would be a rather embarrassing error that I've trouble believing they would make.

[phongn]

Perhaps I'm being dumb, but I don't believe it at all. Unless OPERA has been very incompetent in synchronizing their clocks, you just can't get that kind of relative error from GR corrections. GPS clocks are in reference to the "potato-shaped" ideal geoid, a particular surface of constant gravity potential (gravitational potential + centrifugal potential), and all clocks on it tick on the same rate. The potential here is tiny, even hundreds of kilometers inside the Earth's surface, it's still on the order of 7E-10, and the potential differences are smaller still.

OPERA's said that Contaldi's challenge is the result of a misunderstanding.

[Terralthra]

A new potential explanation...

It's now been three weeks since the extraordinary news that neutrinos travelling between France and Italy had been clocked moving faster than light. The experiment, known as OPERA, found that the particles produced at CERN near Geneva arrived at the Gran Sasso Laboratory in Italy some 60 nanoseconds earlier than the speed of light allows.

The result has sent a ripple of excitement through the physics community. Since then, more than 80 papers have appeared on the arXiv attempting to debunk or explain the effect. It's fair to say, however, that the general feeling is that the OPERA team must have overlooked something.

Today, Ronald van Elburg at the University of Groningen in the Netherlands makes a convincing argument that he has found the error.

First, let's review the experiment, which is simple in concept: a measurement of distance and time.

The distance is straightforward. The location of neutrino production at CERN is fairly easy to measure using GPS. The position of the Gran Sasso Laboratory is harder to pin down because it sits under a kilometre-high mountain. Nevertheless, the OPERA team says it has nailed the distance of 730 km to within 20 cm or so.

The time of neutrino flight is harder to measure. The OPERA team says it can accurately gauge the instant when the neutrinos are created and the instant they are detected using clocks at each end.

But the tricky part is keeping the clocks at either end exactly synchronised. The team does this using GPS satellites, which each broadcast a highly accurate time signal from orbit some 20,000km overhead. That introduces a number of extra complications which the team has to take into account, such as the time of travel of the GPS signals to the ground.

But van Elburg says there is one effect that the OPERA team seems to have overlooked: the relativistic motion of the GPS clocks.

It's easy to think that the motion of the satellites is irrelevant. After all, the radio waves carrying the time signal must travel at the speed of light, regardless of the satellites' speed.

But there is an additional subtlety. Although the speed of light is does not depend on the the frame of reference, the time of flight does. In this case, there are two frames of reference: the experiment on the ground and the clocks in orbit. If these are moving relative to each other, then this needs to be factored in.

So what is the satellites' motion with respect to the OPERA experiment? These probes orbit from West to East in a plane inclined at 55 degrees to the equator. Significantly, that's roughly in line with the neutrino flight path. Their relative motion is then easy to calculate.

So from the point of view of a clock on board a GPS satellite, the positions of the neutrino source and detector are changing. "From the perspective of the clock, the detector is moving towards the source and consequently the distance travelled by the particles as observed from the clock is shorter," says van Elburg.

By this he means shorter than the distance measured in the reference frame on the ground.

The OPERA team overlooks this because it thinks of the clocks as on the ground not in orbit.

How big is this effect? Van Elburg calculates that it should cause the neutrinos to arrive 32 nanoseconds early. But this must be doubled because the same error occurs at each end of the experiment. So the total correction is 64 nanoseconds, almost exactly what the OPERA team observes.

That's impressive but it's not to say the problem is done and dusted. Peer review is an essential part of the scientific process and this argument must hold its own under scrutiny from the community at large and the OPERA team in particular.

If it stands up, this episode will be laden with irony. Far from breaking Einstein's theory of relatively, the faster-than-light measurement will turn out to be another confirmation of it.

It's a plausible explanation, on its face, though I think that would be a rather glaring error on OPERA's part to overlook.

[Psawhn]

That reminds me of something else that might contribute to - ionospheric delay. Free electrons in the ionosphere cause errors in GPS position due to absorption and re-emission of the radio waves (it delays phase velocity and advances group velocity, if I remember correctly).

I'm a bit wary of the article's linking of the 55-degree orbital plane and the path of the neutrinos, however. The satellites' paths over the ground may not always be parallel to the direction between CERN and L'aquila. (Actually... just looking at their latitudes, I really doubt it. CERN is about 44N, and L'Aquila is about 42N. A satellite directly overhead will be passing more of an west-east direction). That's not to say that relativistic effects can't be a source for the errors - I don't know enough about this stuff to say whether or not that's an issue.

[Beowulf]

Bump with semi-new result:

Neutrino experiment affirms faster-than-light claim - November 18, 2011

dario.jpgIt is a remarkable confirmation of a stunning result; but most physicists remain skeptical. That seems the most probable outcome of a release of new data expected on 17 November from researchers with the Italian OPERA collaboration, who say they have confirmed their controversial finding that flighty subatomic neutrinos can travel faster than light.

“It’s slightly better than the previous result,” says OPERA’s physics coordinator Dario Autiero of the Institut de Physique Nucleaire de Lyon in France (pictured). He adds that most of the members of the collaboration who declined to sign the original paper because they wanted more time to check the result have now come on board. One of these is Caren Hagner of the University of Hamburg in Germany. She says not only has the experiment's precision been improved, the statistical analysis is more robust and has been replicated by different groups within OPERA not just the original team. “We gained much more confidence,” Hagner says.

OPERA (which stands for Oscillation Project with Emulsion-tracking Apparatus) made headlines in September with a claim to have clocked neutrinos traveling faster than light, a result at odds with Albert Einstein’s well-established Special Theory of Relativity, which sets light as the ultimate cosmic speed limit. The group used a pulsed beam of neutrinos produced by a particle accelerator at CERN near Geneva which traveled some 730 kilometers to Gran Sasso near L’Aquila, Italy where the particles were detected.

The result was highly statistically significant but following Carl Sagan’s well-known mantra that “extraordinary claims require extraordinary evidence”, most physicists expressed doubts. While OPERA appeared to have conducted its data-taking and analysis carefully, there was rampant speculation about possible sources of error and some made claims of mistakes that the collaboration brushed off.

One set of concerns centered on the relatively long timescale – 10.5 microseconds, or 10.5 millionths of a second – of the proton pulses produced at CERN that result in the neutrino pulses OPERA detects. OPERA did not know whether individual neutrinos received at Gran Sasso corresponded to protons early or late in the proton pulse, creating uncertainty around their detection of them. In October OPERA therefore asked CERN to generate shorter proton pulses lasting just 3 nanoseconds. They have now recorded 20 events in the new data run and say that they have reached a similar level of statistical significance to the first time around, with the neutrinos again reaching Gran Sasso 60 nanoseconds faster than a light beam would do.

OPERA expects the new result to rule out uncertainties due to the long timescale of the proton pulses. But concerns about the experiment’s use of the Global Positioning System to synchronize clocks at each end of the neutrino beam are unlikely to be as easily allayed, The use of GPS is novel in the field of high energy and particle physics and the same system was used for both the original experiment and the new run. Hagner also adds that she’d like to see the time measurement checked using another part of the detector, to increase confidence further.

For most physicists outside the collaboration, however, the key test will be replication by an independent experiment. The one best placed to independently confirm or refute OPERA’s result is MINOS (the Main Injector Neutrino Oscillation Search) at Fermilab in Batavia, Illinois. In response to the latest OPERA result, MINOS issued a statement saying it is upgrading its timing system to match OPERA's precision and might have preliminary results obtained using the existing system that are relevant to assessing OPERA's results as soon as early 2012.

"OPERA is to be congratulated for doing some important and sensitive checks but independent checks are the way to go," says Rob Plunkett, co-spokesman for MINOS.

Note that this result still is dependent on the GPS system. The consistency of the result is encouraging though.

[phongn]

Preprint paper available at arΧiv

[CaptainChewbacca]

Well, its probably the satellites then. The fact that its the same 60 nanoseconds every time, which is almost exactly the computed error compensating for motion, is a great example of verifying a result.

[phongn]

ICARUS says no FTL neutrinos

[D.Turtle]

That was submitted in the middle of October. If it were that conclusive, wouldn't we have heard of it before?