The latest news from Opera is that some of their neutrinos are breaking the speed limit. That’s not only a violation of road speed limits, it’s a violation of the universal speed limit, and the laws that it breaks are the fundamental laws of physics. So let’s spend a few minutes speculating wildly about what would happen if these neutrinos are actually going faster than the speed of light. (As Katherine said in her blog post, there will be a lot of serious discussion once we have more information.)
So, why can’t anything go faster than the speed of light? When a massive body approaches the speed of light, it’s effective mass increases. That means that every time we apply a force to the particle to accelerate it, the change in momentum is the same, but the change in speed decreases. The particle asymptotically approaches the speed of light, and never goes faster. This has been tested in the lab over and over again. Fortunately the electron is extremely light, so we can see it move at amazingly high speeds. (In fact the difference in speed between a photon and an electron accelerated at LEP is one part in 1011.)
What about a massless particle? Can that go faster than the speed of light? That’s actually a trickier question than it sounds. One approach would be to take a part with mass \(m\), apply a force, \(F\) to it for an infinitesimal amount of time and make the mass approach 0. When that happens you find that the particle should go at the speed of light. But as any mathematician will tell you there’s a difference between a value approaching a limit and a value being the same as another number. The equation also looks a little suspect:
\[
\lim_{m\to 0, \delta t\to 0}\left[ \frac{F}{m}\delta t = c \right]
\]
What does it really mean to say that the time interval \(\delta t\) approaches zero in the context of quantum mechanics? If you want to make the time interval very small then the energy transfer must increase in accordance with the uncertainty principle.
You can work through the math of special relativity and come to the conclusion that going faster than the speed of light would violate causality (as well as common sense), but that’s circular logic, since one of the assumptions of special relativity is that the speed of light is a constant.
And again, quantum mechanics is at odds with special relativity, since Bell’s inequality shows that the universe “knows” what happens in regions of space that are not causally connected. The experiment goes like this: Two particles (usually photons) are created in an entangled state so that, for example, one has spin “up” and the other has spin “down”. If you measure the direction of spin of one particle with respect to a given axis you instantly know the direction of spin of the other with respect to the same axis. Now separate the spin measuring devices by a large distance and perform the experiment again. You’ll find that the directions of the spins agree (one “up” and one “down”), even though there has not been enough time for one particle to “tell” the other one what spin to have. So far it all seems fairly reasonable and even deterministic.
That is until the next step of the experiment is performed: the direction of the axis is not determined until the particles are halfway to the measuring devices. If we have two experimenters Alice and Bob, one at each measuring device, then it doesn’t matter what Alice chooses to be “up”, if Bob chooses the same axis then he’ll measure “down” whenever Alice measures “up” and vice versa. (If Bob picks an axis at 90 degrees to Alice’s then he’ll get garbage. Exactly half the time he’ll get the same as Alice by dumb luck.) By picking the “up” direction while the particles are in flight, we break any causal connection between the measuring devices. The conclusion is that Alice’s measurement determines Bob’s measurement, even though there’s no way to transfer that information without going faster than the speed of light. Quantum mechanics doesn’t respect locality, and details about a wavefunction can travel faster than the speed of light. (Quantum mechanics has an ironic sense of humor though, since this mechanism can’t be used to send real information.)
Why not look at some other massless particles to see how they behave? Unfortunately there aren’t any more that we can study, since gluons are always bound up in hadronic states, and they’re only theoretically massless. (We haven’t yet ruled out very small masses with experiment. Small masses would cause problems for QCD, but that’s a different story…) Until recently neutrinos were considered massless, but we now know that isn’t the case, and each year we get better knowledge about the mass differences of the various neutrinos.
Just to confuse things further, quantum mechanics allows particles to travel faster than the speed of light (and photons to travel slower than the speed of light) as long as the uncertainty principle isn’t violated. This is how an electron can emit a virtual photon and still catch up to it to reabsorb it before anyone notices. If you try to catch particles violating these laws by firing other particles at them, they suddenly conspire to come out with the correct masses and speeds after all.
So what can we do if these neutrinos are going faster than the speed of light? Throw out special relativity? Adjust it somehow? Appeal to quantum mechanics? We have an immense mountain of evidence in favor of special relativity, and it’s passed about as many experimental tests as any theory in the history of science. (Okay, technically we have no evidence in favor of special relativity, but we have an immense amount of evidence which has failed to falsify it!) Abandoning special relativity would also upheave huge areas of physics, notably electromagnetism, which has been through all kinds of stringent testing.
Let’s leave special relativity alone for now and see if we can extend it somehow. It’s possible that there extra dimensions curled up that we can’t usually see. If that’s the case then there may be a shorter path between Gran Sasso and CERN that isn’t available to most particles, but which can be used by neutrinos. That’s an interesting proposition as it could explain why the neutrinos couple so weakly- they could spend most of their time interacting in the other dimensions and this could “dilute” the coupling in our 3+1 dimensions.
In the distant past, after the big bang, the universe was full of neutrinos (and lots of other particles!) and these neutrinos lingered until today and they’re known as relic neutrinos. These relic neutrinos form a field that occupies all the space around us (in the same way as the cosmic microwave background radiation does.) It’s possible that neutrinos traveling through “empty” space could interact with relic neutrinos, shaking up their wavefunctions. According to special relativity these neutrinos couldn’t transmit any information faster than the speed of light, but as we already know, quantum mechanics isn’t local. Could a field of relic neutrinos account for faster than light travel? Maybe, but I doubt it, as we’d have probably seen other effects elsewhere before now.
Special relativity says that a massive particle cannot travel faster than the speed of light, and that massless particles must travel at the speed of light, but it doesn’t say anything about particles with imaginary mass. Take one of these exotic particles, known as tachyons, and apply special relativity and you’ll find that it goes faster than the speed of light! Could the neutrinos be communicating with these particles? Perhaps…
Maybe we can turn to general relativity for help. The huge gravitational field of the Earth should not be neglected when calculating the length of the path from CERN to Gran Sasso. The distance may be smaller than we think. It’s something that would be hard to verify directly, as the matter between the two points is not completely transparent to light. Calculating the true interval would require knowledge of the gross structure of the Earth and the path taken by the neutrinos, which isn’t insurmountable, but the calculation isn’t trivial. Without seeing any papers on the subject it’s hard to make a statement about it, but if the true interval is smaller than we expect by one part in 50,000 this could explain the result, and the speed of light would live to fight another day.
A lot of people have commented on the timing measurement itself. It’s calibrated with GPS, which is precise to within about 10 nanoseconds. But we need to be careful when dealing with differences in height. Once again, general relativity comes in and messes things up, and 1 second at sea level is not the same as 1 second in space or 1 second deep underground. This means that the accuracy might not be spot on, unless we take special precautions. (In fact satellites are continually updated to make sure they don’t go too far afield. Blindly trusting their on board clock isn’t enough when gravity plays around with the local time.) Synchronizing two distant clocks is a long standing problem for physicists, even in hypothetical scenarios and thought experiments. How could we guarantee that two clocks agree that lunchtime at CERN is the same as lunchtime at Gran Sasso? It’s easy to imagine sending pulses of light to a satellite and counting how many arrive between each measurement, but that only tells us about the time differences at a given site, and not about the time differences between the sites, which is what we want. I suppose the way to measure synchronicity is to perform the same experiment in reverse, making a different beam of neutrinos travel the same journey in reverse. If they arrive 60ns later than expected then it shows an asynchronicity between the clocks. But that’s hardly practical!
So the conclusion? There is none really. This is just a fun post of wild speculation, not to be taken too seriously. So let’s wait for more information and in the meantime we can finish on a joke:
So the neutrino leaves.
The barista replies “We don’t serve faster than light particles here at Gran Sasso”
A neutrino passes through a coffeeshop and asks the barista for “An espresso, and make it quick!”
Question;
But first thanks for your timely comments.
If the speed of light has been exceeded by intact particles
could this indicate an avenue to understanding dark matter /
black holes / associated gravity etc. This from a retired
A&P Mechanic / Industrial Arts Teacher & All Round Tinker
Thanks, Steve
As far as I remember from my studying days, special relativity apply locally at each point of spacetime. From a differential geometry point of view it applies to the tangent space of earch point of a manifold. So couldn’it be the effect is due to how points connect with each other? That wouldn’t break any special relativity law.
The joke in the end.. That’s brilliant…
LOL!!!
+ 1 simple question…
Whenever we say that nothing can travel faster than the speed of light, we actually measure all that using light.
Isn’t the situation like in a medieval town the highest weight measuring device is capable of measuring 10 kg so they concluded that nothing weigh more than 10 KG’s and whenever they measure anything heavier than 10KG the result also came 10Kg’s.
Similarly if we measure anything traveling faster than the speed of sound using sound as the measuring technique and not light (sight) then we will never be able to measure anything traveling faster than the speed of sound.
Please let me know if my concept is wrong.
By the way nice research by CERN guys, and i am eagerly waiting for the real conclusion.
I am in no way a physicist but things like this have always interested me, I haven’t been able to look at the research data obviously but just a question
Did they take into account the movement of the planet etc… is 732km the distance from CERN to Gran Sasso after taking into account that the planet etc is moving?
If not wouldn’t slightly shorter distance make sense with conventional physics?
If the distance between CERN and Gran Sasso is 1 part in 50000 shorter than we think, would we expect to see the same effect with photons?
Hello Steve,
It will be hard to tell before understanding exactly why do Neutrinos behave like this. Then we can start factoring this into the body of theory we have to tackle some of the issues you mentioned. I know from my course on Cosmology that neutrinos factor considerably in our estimates of the mass of the universe, so any discoveries of this scale relating to them will affect of estimates for the dark matter (supposedly the matter filling the difference between all the matter we see and the gravity we observe in the universe).
Wow, we have a lot of comments here!
Steve, faster than light travel could indicate where we need to look for new physics, but we need to be a bit careful with the conclusions we draw. There are probably quite a few theorists who have their own theories about faster than light travel, and these theories would make other predictions that are consequences of the faster than light travel. It’s very often the case that we make a breakthrough whenever we see a small discrepancy between the world around us and our theories. For example, when we observed parity violation in the 1950s we got a hint that the universe favors left-handed particles over right-handed particles. So yeah, this could be the first sign of something very new and exciting, but we make sure the theories follow where the data lead us and presuppose what answers we’ll get!
Carlo, wow, what a question! It’s been a while since I studied relativity (both special and general) but from what I remember the paths that matter are the geodesics, and those are well defined paths with mechanics that respect the limit of the speed of light and causality. I’m afraid you’ll need to speak to someone more knowledgeable if you want a fuller answer!
Vikash, the analogy of measuring the speed of sound using sound is a good one! When an object travels faster than the speed of sound it leaves a super-sonic wake in front of it (for example, the “boom” that emanates from high speed aircraft, or the crack of a whip.) We use this same principle to measure the speed of particles as they pass through a medium. If the particle travels faster that light in the medium (usually water) then it leaves a wake of light, known as Čerenkov radiation, which forms a cone shape. By measuring the angle of the cone we can measure the speed of the particle very precisely. So even though we have no way to make anything go faster than the speed of light in the lab, we can certainly see an object that does travel faster than light. (The Čerenkov radiation from a tachyon is actually a rich spectrum of light, very much like a rainbow! You can see an animation of this effect on the Wikipedia page for tachyons. Actually, the article on Čerenkov radiation is very good as well.)
Shawn, that’s exactly the kind of subtle feature of relativity that could easily fool us! I’ve been thinking it over in the back of my mind for the past few hours and I haven’t come up with a satisfactory argument one way or the other. The neutrinos take about 2.4ms to travel from CERN to Gran Sasso. In that time the Earth will have moved about 10m in space and Gran Sasso would have moved about 1m as the Earth turns. That means that maximum distance between CERN when the neutrinos were emitted and Gran Sasso when they were detected is 11m, or about 1 part in 70,000. If this is the real cause of the shortening of the path length, then we could expect to see a variation of the path length as a function of the time of day.
Emmanuel, yes we’d expect to see a shorter distance for light as well. Unfortunately the neutrino beam passes though 730km of rock which is not transparent to electromagnetic radiation at pretty much any wavelength. In order to measure the distance using light we’d need to drill a hole through the Earth!
The distance and the time interval between two events in space time are subtle concepts in general relativity, and they must be accurately phrased in terms of a specific frame of reference. Sometimes I wonder if oversimplifications are done and a Newtonian point of view is taken illegitimately.
So … has everybody caught where they goofed yet?
It is an easy one. According to the paper the distance measurement procedure use the geodetic distance in the ETRF2000 (ITRF2000) system as given by some standard routine. The european GPS ITRF2000 system is used for geodesy, navigation, et cetera and is conveniently based on the geode.
I get the difference between measuring distance along an Earth radius perfect sphere (roughly the geode) and measuring the distance of travel, for neutrinos the chord through the Earth, as 22 m over 730 km. A near light speed beam would appear to arrive ~ 60 ns early, give or take.
Of course, they have had a whole team on this for 2 years, so it is unlikely they goofed. But it is at least possible. I read the paper, and I don’t see the explicit conversion between the geodesic distance and the travel distance anywhere.
Unfortunately the technical details of the system and the routine used to give distance from position is too much to check this quickly. But the difference is a curious coincidence with the discrepancy against well established relativity.
Wow, really curious coincidence, smart observation!
I found the paper which describes how the distance was measured: GEODETIC PARAMETERISATION
OF THE CNGS PROJECT (http://www.slac.stanford.edu/econf/C0211115/papers/020.PDF)
Didn’t this whole thing start out in Fermilab,
spelling may be wrong,,,I seem to remember
them sending a beam thru Wisconsin?
a joe in Texas
I don’t see many people commenting on
what this would mean for Space travel?
Also,,couldn’t the put a target on the moon and measure that?,,”That” being the time it took to reach the target and the integrity/quality of the received data?
I’ll shut up now.
a joe in Texas
Instead of considering that neutrinos may communicate with tachyons, a more natural proposal is that this neutrino type (mu neutrino) may BE a tachyon.
Hi
When captain Kirk calls his superior boss on the earth and his 100 light years from the earth. Will he wait endless on his answer? There are rays that humans did not discover yet. Good luck with searching
Alexis
Hi Carlo, I agree, these concepts are subtle in general relativity, and that’s one reason I’m glad I no longer have to study it (or at least I thought I didn’t have to study it anymore!) Am I correct in thinking that if I send a photon and a neutrino down the same geodesic, then the neutrino should never traverse the same path faster than the photon? (Even this test is subtle, as the neutrino will have a slightly different geodesic, as it couples differently to the various fields when compared with the photon.) Unfortunately I’ve not had time to sit down and open my favorite relativity book to get a firm answer!
Tjorborn, that’s an interesting point, but I think the physicists at OPERA would have already looked into this. When the three questions are “How far apart are these two points in space?”, “How long did the journey take?” and “What happens when we divide one by the other?”, and a hundred physicists have six months to think about these questions, then they’ll think of nearly everything (or at least I’d hope so!) Thanks for your comment!
Joe, nice to hear from you, and please don’t feel the need to “shut up now” if you have things to say.
There are a few neutrino experiments based in North America that observe neutrinos produced at Fermilab. In fact, because of the way neutrinos act we need a lot of different experiments to observe them properly.
Neutrinos get produced in one flavor state (for example, if they are produced alongside an electron then they called electron neutrinos and they have “electron” flavor) but after flying for a while there is a chance they will change their flavor. We can work out how often one neutrino changes flavor into another as a function of the distance flown, and this tells us about the mass difference of the neutrinos. Each kind of flavor changing has its own characteristic flight length, so we need experiments with different lengths of baseline to measure all the flavor changing parameters. Gran Sasso is looking for neutrinos changing their flavor from “muon” to “tau”, and it just happened that they got lucky (and very skillful) with their speed measurement! The experiments that have neutrinos passing under Wisconsin are MiniBoone and MINOS.
You can see a full list of neutrino experiments on Wikipedia. As you can see, there are experiments in North America (taking their neutrino sources from Fermilab), Europe (taking their neutrino sources from CERN) and Asia (taking their neutrino sources from the J-PARC or KEK labs), as well as “neutrino observatories” which usually look for neutrinos from the sun or from the atmosphere. It’s important that we study all the possible flavor changes (there are three flavors, so there are six possible changes) and it’s also important that we study neutrinos vs antineutrinos. In some models these are the same particles, but in other models (including the Standard Model) they are distinct particles. If a process favors particles over antiparticles this gives us evidence of CP violation, and this is very closely related to the matter/antimatter asymmetry in the universe. Neutrino physics remains a very active, mysterious and rich area of research, that has potential to throw up all kinds of surprises like the one we saw this weekend!
Even though it seems like the next logical step, there are many problems associated with setting up an experiment on the moon. Ignoring all the practical problems (such as calibrating equipment, reducing the effects of cosmic rays, precise and accurate measurements of the distances and times) there are some fundamental physical difficulties which are simply insurmountable. (To be fair on the practical side, the experiments we currently operate are not significantly less difficult than a lunar experiment. Some experiments are located deep underground with special shielding, kept close to absolute zero etc. Engineers are not scared of practical problems!) The biggest problem comes from the beam spreading. As the neutrino beam passes through space it spreads out in the transverse direction. After only 730km (from CERN to Gran Sasso) a beam of neutrinos is 2km wide! If we fired neutrinos at the moon (about 380,000km away) the beam would be about 1,000km wide, and the moon itself is only 3,500km wide. We’d need to create a detector that is 500 times larger than the OPERA detector to get the same number of events.
As for space travel… well who knows what we could do with this? Let’s imagine ourselves in the distant future where we can do almost anything with neutrinos. The difference in speed we’re looking at is very small (1 part in 105) so we wouldn’t get a great head start on light. Since our bodies and spacecraft are not made of neutrinos, I doubt we could transport anything material faster than the speed of light. At best we could send information faster than the speed of light (with the correct neutrino “senders” and “receivers”) and the tiny difference in speed could be leveraged into something more significant. After all we can already turn small changes in potential energy in semiconductors into intricate computers. So in short we might be able to transfer information faster than light, but not much else. Space travel would remain either a fantasy, or it would still have to span several human generations to get anywhere useful.
Ahh, but to be able to send information faster than light would be amazing. We could virtually scan the galaxy for life and eventually the entire universe….
Hi Paul, I was considering this point earlier. If the tachyon was charged then we’d definitely see it as it would produce a visible wake as it propagated. However, since neutrinos interact so rarely we not notice the wake it would produce if it was also a tachyon. It might be worth considering the concept of imaginary mass. If we assume that a virtual particle can have imaginary mass then there’s no reason why this shouldn’t favor neutrinos (as their mass is almost zero anyway) as the difference between δ and iδ is tiny. How would a model incorporate imaginary and complex masses? It’s not obvious, but if it is the case that particles have complex mass (and hence have some amount of “tachyoness”) then these effects should be visible in more cooperative particles, such as the electron.
Alexis, let’s hope we find those rays! So far this is the first evidence we have of faster than light rays. If we find more evidence we could be in for a very exciting future!
As a scientifically interested layperson may I congratulate the contributors to this site for their open-minded comments showing interest and excitement in a possible new science.
Many other sites are full of excessive skepticism, doubt and debunking of the experiments without due respect for the hard work done by the scientists involved.
It is refreshing that with very little being known about “reality” there are still scientists willing to be scientists and search for the unknown.
Another clue is held in the hidden and neglected progress on COLD Fusion that shows another, beyond known science effect but unfortunately un-scientifically being sidetracked by science.
The speed of light and neutrino’s. Can it not just be, that we have the true speed of light wrong by 0.002. As light is slowed down by water and neutrino’s are not. This Show that neutrino’s can go faster than light were light is traveling in a medium. Is it not just that, in are local system there is such a medium that we are not yet aware of? Ether any one
Hi Edward. The problem with the neutrinos is not that they happened to beat photons in a race from one point to another (as you say, we can slow light down by forcing it to go through water, or some other medium.) The problem is that if we take the distance traveled and divide by the time take the result is faster than the speed of light, and to take an object along that path is impossible under special relativity as it would violate causality. We can slow particles down, but our theories cannot accommodate faster than light particles and still make sense. As for the speed of light, we’ve measured the speed 1,000 times more precisely than the difference that OPERA sees, so it seems unlikely that we got the speed of light wrong.
“How could we guarantee that two clocks agree that lunchtime at CERN is the same as lunchtime at Gran Sasso?”
Of course we can’t. As Ford Prefect said, ‘Time is an illusion, lunchtime doubly so.’ Besides that, lunchtime in Italy is generally later than at CERN.
I was tempted to use coffee time instead of lunch time, but when isn’t it coffee time?! CERN seems to run on coffee!
If i were to believe the constant speed of light and that nothing can travel faster according to GR theory, then light photons must have a velocity profile. It is absurd to think that a photon when emitted from a light source kicks off with an initial speed C(sub0) equal to the speed of light !!! such is not scientifically sound with the massless photon dilemma. Then, a photon must have acceleration profile as well! Waooo! so where are we now? the big question is where on the geodesic of a traveling photon, does a photon reach constant speed to satisfy GR theory? Also, does constant speed decay after what length on the geodesic or after what time? or it never decays? and travels in space time indefinitely ? do we have real solid answers to these questions ?
Hi Fluidic, can you be a bit more specific please? I’m not sure what you mean when you “velocity profile” and “massless photon dilemma”. Do you mean that the velocity varies in time? Under both special relativity and general relativity photons travel at the speed of light at all times, to all observers. This hypothesis has been tested many times and has never been violated. (At this point we have so much confidence in the constancy of the speed of light that it’s formally impossible to measure the speed of light- we use it define the unit of length!) To understand how a photon travels at the speed of light you can see what happens when you accelerate a very very light particle with a finite force. As the mass of the particle decreases the final speed gets closer to the speed of light and the time it takes to do so decreases. If you take the limit that the mass is zero then you will see that the photon must travel at the speed of light and accelerate instantaneously. Weird, but that’s how nature works.
Your questions about geodesics have some interesting answers! In the absence of mass, the light rays will travel through space until they hit an object and interact. If there is nothing to hit then the photon will continue to travel indefinitely. (In fact the cosmic microwave background radiation is made up of photons which have been traveling through space for over 13 billion years!) In the presence of mass photons can follow closed geodesics, in which case they can travel indefinitely around the same path. I’m a bit sketchy on the details, but I think it’s also possible that a photon can be gravitationally redshifted away. As a photon leaves a very deep gravitational well it loses energy. If it requires more energy to leave the well than the photon has it then it will never escape, but it must continue to travel at the speed of light. In order to do so the photons loses energy until it’s no longer visible. It essentially disappears!
It’s important to remember that our answers are only as good as the evidence that backs them up. So far there have been no experiments which have contradicted general relativity, and there have been several experiments which have contradicted alternatives to general relativity. So our answers are quite solid!
I allways like your explanations, is thre an explanation and/or similitude betwin the CHERENKOV effect and these superluminal neutrino?
I could agree with many things of what you explained. However, what pulled me little to the back is your statement <>. This also comes back to your questions on being more specific about velocity profile, and massless photon dilemma. Your concept of “accelerating instantanously” is incomplete without explaining how such a framework would generate a photon from some energy level change, starting from stationarity location (speed = 0) and then magically “instantaneously” hit speed =c. Plz let’s not hide behind, <<>> !!! OK! what i mean by velocity profile is that a transformation force generated from a change of energy quantization levels creates a photon that starts from speed=0 and within the atomic structure is accelerated to reach speed =c at some point at the atomic outermost surface whereby it travels constantly at c. You just said it yourself, that it is accelerated, and therefore there is a velocity profile or call it velocity history, starting at zero, accelerating until speed = c at outermost boundary of atomic structures then continues as we know it.
but i am thankful, because i liked your approach though.
Hi David, I’m glad you enjoy the blog! Cherenkov radiation is a special case of matter and waves interacting. When an object passes through a medium faster than the speed that waves can pass through the medium there’s a wavefront. That’s a lot of dry technical words in one sentence, so let’s think about a few examples and try to visualize what’s going on! Wikipedia has a great animation of Cherenkov radiation.
A familiar example of this effect is a supersonic aircraft. As the aircraft passes through the medium (air) faster than the speed of sound, it creates a series of sound waves. These sound waves overlap and add up to form a wavefront (just like in the animation) and the result is the sonic boom. (The reason you only hear the sonic boom once is because the wavefront only passes you once.)
The Cherenkov effect is the same but, it uses light instead of sound, and the medium is usually water. The results can be beautiful, for example take a look at the Cherenkov rings from the Super Kamiokande experiment. The colors give information about the time the wavefront is detected. These pictures give a wonderful visualization of the wavefronts as they pass through the water and are detected by the photo multiplier tubes!
The same would happen with faster than light particles. If an electron went faster than the speed of light then we’d see a wavefront of light (the “medium” would be the vacuum!) It would be an odd situation because the observer would be hit by the electron before they saw it coming, and then they would see the beautiful wavefront. In reality this effect has never been seen and instead we see radiation first, and the electron second. (A good example of radiation preceding the particle is synchrotron radiation. There’s an incredible photo of it here!)
For the case of faster than light neutrinos, we wouldn’t see a wavefront at all. Neutrinos give off almost no radiation, which is a shame. If only we could see faster than light electrons! That would be one of the most amazing sights in the world!
Maybe someone could further explain the causality implications here, because I don’t see any reason that this violates Einstein’s relativistic causality. If it travels faster than light, and you could use it to communicate, it would mean that they would receive it 1.01 times faster than light(or whatever the factor is), but they wouldn’t receive it before it was sent. This simply means that we could theoretically communicate faster than it takes the light to get there. I don’t see anything “happening before it happens” so to speak. If, for example, you could somehow shoot a neutrino into a mirror and it reflected back to you, it would be an image from the past, just not as far back as the light delay. Help please!
Hi Greg, that’s a great question! The breakdown of causality doesn’t happen in our frame of reference (a person standing at CERN or Gran Sasso would not notice anything odd happening like getting messages from the future.) The breakdown of causality would happen in a different frame of reference, and it happens in the following way. Whenever the distance between two events is larger than the time between to the two events multiplied by c, the two events are said to be causally unconnected, because nothing can communicate information between them. (In the same way, causally connected events have a distance which is shorter than or equal to the time difference multiplied by c.) Different observers traveling at different speeds will see time passing differently, so they will see different timing for the same events. However, all observers see the same order of causally connected events, so the same effects follow the same causes for all observers. This isn’t the case for causally unconnected events, so different observers can see them happening in different orders. Since one event does not cause the other, this isn’t a problem for causality.
So how do we make it a problem? Well the transformation of time coordinates for an observer traveling at speed \(v\) goes as:
t’ = γ t – βγ x/c
where t’ is the time coordinate of the moving observer (someone traveling near the speed of light from Gran Sasso to CERN!), t and x are the time and space coordinates on Earth (let’s assume Earth does not move much as the neutrinos travel, and lets line the x axis up with the line of sight from CERN to Gran Sasso.) β is the relativistic speed of our observer (β = v/c) and γ is the relativistic factor (γ²(1-β²)=1).
Let’s say that the neutrinos travel at speed c+δ (where δ is very small for the neutrinos) and perform the transformation. We can relate x and t to each other using x=(c+δ)t and then insert them into the equation. (To do this we actually need to synchronize the clocks so that x=x’=0 and t=t’=0 at CERN when the neutrinos leave, but that’s not a problem for thought experiments!)) When we do this we get:
t’ = γt – βγtc(1+δ)/c
= γt(1-β(1+δ))
From CERN’s point of view the neutrinos arrive at Gran Sasso after they have left CERN, so t is positive. We can now choose a value of β, such that 0≤β≤1 so that (1-&beta(1+δ)) is negative, and thus t’ is negative. If that’s the case then our observer sees the neutrinos arrive at Gran Sasso before they leave CERN!
Let’s take it a step further and turn it into a real paradox. To do this we need to neutrinos to go much faster, say at 2c+δ. Our observer sees them arrive at Gran Sasso and then they travel at nearly the speed of light to CERN. They have just enough time to get to CERN to tell the physicists to dump the beam and stop the neutrinos being produced! But of course, if they do this then the neutrinos never arrived at Gran Sasso in the first place, so how can the observer know when to go to CERN to tell them to dump the beam?
I guess I don’t understand the causality being linked to the speed of light part. I understand that with tachyons you will see the light from the future (or present) FIRST and the light from the past LATER, but I don’t see how this creates paradoxes, because you are only perceiving it that way. The light is still traveling through the air to hit you from the neutrinos being shot (there is NO speed that will stop the neutrinos from being seen at Gran Sasso from ‘when’ they are shot, even if they see it in reverse order). As a result, this means that Gran Sasso telling CERN to stop shooting the beam will stop them from shooting it AFTER they have already shot it, regardless of the speed (obviously we’re in CERN’s time frame here, if we’re sticking to Einstein’s relativity). It seems to me that it creates problems in perception (i.e.- not all time frames will perceive events in the same order) but I don’t see them CHANGING the events “before they happen” so to speak. It seems more like “spooky action at a distance,” or possibly instant communication, is possible, but not actually changing events that have already happened. If I’m way off, which I probably am, I would appreciate clarity :p
I’d place my bet that this is an artefact of the wave nature of neutrinos, very similar to the “faster than light” transmission of music we heard about in the 90s.
It’s easy to talk about the speed of a bullet. You just consider the center of mass movement.
However, the neutrino is – in some aspects – more like a wave. So you first have to define what you mean by “speed of a neutrino”. Since you measure statistical effects, you don’t have a handle on one particular neutrino, you can’t “shoot” it. Rather, you measure correlations. And that’s where you have to be very careful, since waves are (most likely) analytic functions. And analytic functions have some delocalized properties, so you might compare the wrong parts of a neutrino wave function while talking about velocity.
With the music transmission experiment, one could understand the paradox as follows: when you hear the first few tones of a transmitted piece by Mozart (say), you can recognize that piece and then you will immediately know all the remaining tones. Now that doesn’t mean that the information about the remaining tones has travelled with v>c. Because if someone smashed the cd player during transmission (or the performer), than you will continue to hear the undisturbed music until the information about the disturbance has traveld (with v=c) to you. It would be nice to have a similar experiment in the neutrino setting.
Hey Greg, let’s work through the example explicitly. Suppose the photons travel at speed c+δ = cΔ. We set up an abort button that our observer can press to dump the proton beam at CERN. Our observer is traveling at high speed from Gran Sasso to CERN with a relativistic speed βc. The time interval between the neutrinos leaving CERN and arriving at Gran Sasso in the Earth’s frame of reference is t. Then this time interval in our observer’s frame of reference is -γΔt. (Note how this is always negative for c+δ>c and always positive for c+δ<c) Now the amount of time it takes our observer to get to CERN is at least γx(1-β)/c where x is the distance between CERN and Gran Sasso in the Earth’s frame of reference. So if we pick β such that γx(1-β)/c<γΔt then our observers gets to CERN before the neutrinos leave! Our observer hits the abort button and the neutrinos never leave CERN.
If you prefer we can a sensor at Gran Sasso that fires a light ray towards CERN whenever a neutrino is detected, and this light ray is what hits the abort button (in this case, a light sensor.)
So, from CERN’s point of view the neutrinos leave, make their way to Gran Sasso, where the sensor triggers the light ray, the light ray comes back and aborts the beam. But from the point of view of our light ray (which we can transmit via optical fiber if you want to travel slightly slower than the speed of light, allowing us to boost into its frame of reference) the beam gets dumped first, before the neutrinos have an opportunity to leave CERN at all!
Working through the math, this outcome is inescapable, and that’s why things can’t go faster than the speed of light. When you say that it’s a matter of perception, I would only agree with you for events which are not causally connected. We can play about with the time ordering of those events, but the same does not apply to causally connected events. We can see that the two events must be causally connected (since the neutrinos went from one event to the other) to the time ordering must be respected. When we let something go faster than the speed of light we find things don’t just look as if they go back in time, they do go back in time.
Is that any clearer?
I guess what I’m saying is that CERN’s point of view is the only one that matters, because they are the only ones seeing it happen “when it actually happens,” or close enough so the difference is negligible. How others perceive the events doesn’t affect the events themselves, it only affects their perception. You agree that CERN will see things in the correct order and it will make sense. In my opinion, that is all that matters. How others “see” the events is irrelevant to what actually took place. I guess I am arguing against relative time and for absolute time, that seems to be where the disagreement is. And it would appear, if this experiment is proven to be correct in their measurements, that this is actually how things work and we need to adjust relativity as a whole. Paradoxes like these are only perceived paradoxes in my opinion. The math is obviously not correct IF the experiment is correct.
Or, perhaps, some of the assumptions behind the formulas need to be changed, i.e.- what does negative time actually mean? And in what frame do you apply it?
Hi Greg. Actually I haven’t agreed that CERN sees the “correct” version of things, because there is no preferred frame of reference. I tried to show that moving to a different frame of reference create a paradox if we allow faster than light travel. It’s a subtle point that requires a bit of knowledge of lots of areas of special relativity and it’s these concepts (simultaneity, time dilation, length contraction and so on) which are most difficult to grasp.
Now it could be possible that absolute time and absolute space exists, but whenever an experiment is performed to test these hypotheses they are always proved wrong. Experiments with interferometers show us that there is no absolute space and experiments with muon lifetimes show us that there is no absolute time either. (There’s a punchline to all this though- it turns out we can get a measure of some of our absolute motion with respect to the rest of the matter of the universe by observing the cosmic microwave background radiation. But that’s a different story.) Anyway, if you’re interested in this kind of discussion I’d recommend getting a good book on special relativity and reading about some of the fascinating “paradoxes” and consequences of special relativity. It’s the most fun you can have with Pythagoras’ theorem!
The mathematics of special relativity is a bit tricky to adjust. The framework of special relativity is “water tight” in the sense that it doesn’t allow for any exceptions or deviations. There’s no part of the theory that suggests that it’s a convenient approximation, and as long as we don’t deal with strong gravitational fields it seems to fit in with all the phenomena we see around us. To change relativity would require some very ingenious trickery and mathematical manipulation. Something which probably isn’t beyond the abilities of a smart mathematician, but something which many physicists would be skeptical of. It’s hard to change a model to allow a particular observation to make sense, without also changing it so that some other observation doesn’t make sense. (In this case we can’t just allow particles to travel faster than the speed of light without also allowing particles to travel back in time. If we’re going to allow faster than light particles then something else has to change to prevent causality falling apart, or we may need to abandon causality altogether.)
I think that peeceeph might have the right idea. This may be a quantum mechanical effect, because in quantum mechanics the changes to a wavefunction “travel” instantaneously across space. It could be the case the wavefunction of the neutrino is simply not disturbed until it interacts at Gran Sasso, and then it has the ability to deviate slightly from its expected path. If that’s the case, then we should see the same effect for photons in a vacuum (ie no other fields in the region of space at all) as the photon would propagate through space without altering its wavefunction. The uncertainty principle alone is not enough to allow the neutrino to break the speed limit, but there could be something less familiar happening.
Thanks for the reply, yeah I’ve been reading a lot on Wikipedia about inertial frames, absolute time, anti-causal systems, etc etc. I got a decent explanation (or at least easy for me to understand) about how a reply would be received before the message was sent if v > (2a)/((1+a)^2) on the tachyonic anti-telephone page. It occurred to me that this is probably what you said above phrased differently, but for some reason that one clicked for me. I understand the basic theory behind it, I’m just wondering if it is a truly complete theory given that black holes and worm holes generally need “new math” to cope with the weirdness (no time, etc). That is what gets me about this particular experiment, it seems that maybe the rules are different when v > c (don’t ask me how you get to that speed lol). My best guess would be other dimensions come into play, or perhaps something altogether new that we’ve never seen before. However, the other dimensions thing definitely plays into the hand of time-travel, an idea I’m not too fond of, except for the obvious time-dilation forward “time-travel.” Very interesting stuff, but as with most sciences it seems that the more we know the more questions we have. Maybe one day…
Hi Fluidic. To an extent this is “just the way the universe works” and it matches all the data we have looked at. It is nice when we can understand what is happening in the world around us, but ultimately our theories are only there to describe the world around us. When we take a look at the simplest parts of our world the ideas we need to describe those parts don’t feel intuitive. I agree that it doesn’t seem right that a photon should go at the speed of light instantaneously, but so far it’s the best model we have, and there would be serious problems with any other model. (To go a little further into the theory, we require that any massless object travels at the speed of light, and we also require that photons be massless because they are the particle which corresponds to local gauge invariance. All the data so far point to the photon having a mass no greater than 1e-18eV and all the data so far point to a gauge invariant universe. This doesn’t answer your question, of course, it just outlines our best model of massless particles.)
But this blog post is about having some more fun with ideas that do not fit in with the current best models! In quantum mechanics there’s no reason why an unseen photon has to be massless, and a virtual photon can have any mass it likes. In fact, experiments like those at LEP, or the B-factories relied on the virtual having photons having mass in order to produce the particles they wanted to produce! (In the case of LEP, the massive photon was a measurable effect. Its wavefunction interfered with that of the Z and physicists could make precision calculations based on this.) If a virtual photon have mass then can it also have a velocity profile? Well, in a very strange sense, yes. Photons only interact with charged particles, so to “accelerate” a photon it would have to be hit with a charged particle. Then to conserve change, the charged particle would have to bounce back, unscathed. (What would really happen is the photon would get absorbed by the charged particle, which would then emit it a short time later, because we don’t have two-photon two-fermion interactions in the Standard Model. It could get hit by a W boson, I suppose, but that’s really weird!)
So let’s imagine we’re producing a virtual photon at the BaBar experiment and the virtual photon has a mass of about 10GeV, then decays to a charm quark-antiquark pair. We could imagine the photon being produced at some speed, and then given a kick as it gets hit by a virtual electron. It would then get two speeds before decaying into the charm-anticharm pair. As long as nobody “sees” the photon, then this is perfectly acceptable. We would add the probability of that process happening to our list of possibilities and check it against the data for the rate of charm-anticharm pair production compared to, say, electrons scattering off each other. Even with all those amazing coincidences taking place we still wouldn’t have a velocity profile for the photon, since it started at one speed, moved to another speed and then decayed. The same is true for all particles, in fact. When we accelerate a proton we just hit it with a lot of photons and each one gives it an instantaneous kick.
Or does it? It could be the case that the photon gives its energy to the proton in a short period of time, decreasing its frequency in order to lose its energy. The proton would then have a velocity profile which varies smoothly in time. I’m trying to think of an experiment which would be sensitive to this kind of transfer of energy, but I can’t think of any which have been performed. (I think that the photoelectric effect may help here. If the photon transfers its energy over a short period of time it may be possible to interrupt the process of energy transfer, and then the energy would no longer be quantized. Even so, it’s hard to not picture that happening for the Compton effect.)
I suppose the only way to see a photon accelerate is to catch it “in the act” by measuring its speed. The best way to do this would be to set up an interferometer to measure how far a photon has traveled in a given time. Then as the distance is changed, the speed of the photons should very by a tiny amount, because the time they spend accelerating and decelerating would given them an overall slower speed. The kind of experiment which would be sensitive to this would be a Young’s triple slit experiment. If light from a coherent source was shone onto three equally spaced slits, the slits would cause a (symmetric) interference pattern to be formed on the other side. (We need to three slits to make sure that a tiny change in the position of the slits is not responsible for any change in pattern.) The source would then be moved further away from the slits and the interference pattern would change very slightly if the photons accelerated when they were produced. This is because the time taken to fly along each path would vary, but the time taken to accelerate a photon would be constant, so the changes in time for each path would be different.) Has this experiment been performed? Probably not. It would need to be very precise!
So to conclude, I can’t give you a firm answer other than “It agrees with our data”. Perhaps someone else knows more about it than I do. Personally I find the whole “instantaneousness” of nature a little unnerving. For example, does it really make sense to say that an electron exist in one point in space and the direction of the electric field changes instantaneously as we pass from one side of the electron to the other? That doesn’t seem right to me, and yet it’s required by the symmetries of the system.
Hello back Aidan Randle-Conde.
Indeed, it is quite enlightning, interesting, and objective what you have analyzed and explored. Indeed,
your proposed approach to detect photon acceleration by using the famous slit experiment with 3 equally-spaced slits seems quite reasonable. I agree though, it has to be performed with great precision so as to observe that slight changes in interference patterns have indeed been detected after moving the sources further away from the slits.
Based on your suggestion i very quickly set up rough setting (which i can’t even call Young’s experiment). However, I thought that monochromatic light would be more feasible in this rough-view early testing than would regular light sources. I thought this scheme would swiftly show us rough but slightly feasible pattern visualization.
I performed this virtual experimental setup few times in a very dark room at night. I can only tell you that I was starting to see extremely slight variations in the interference patterns as i started to move the laser source away more and more, but you know, I was very limited in room space and hence distance moved.
CERN scientists and physicists could carry this further with precision. Then based on my very rough (non precise) experimental setup and very primitive experimental setup, and also based your suggestion of Young’s 3 equally-spaced slits, we could start seeing something important starting to come out. Once experimentally proven, the photon “acceleration” or “acceleration profile” intrinsic property would spill over to other possibly starving electromagnetic radiation profiles. Although we do like the special relativity, but then, does it continue to hold, and under what additional contraints?
On the other hand, I have been thinking out-of-the-box of the slit experiment for little less than a decade, but for something else. The thinking process is related to how a photon and all electromagnetic radiation physically “escapes” matter, even though the standard model would offer some weird explanation. Whether the electron’s intrinsic spins we know are themselves the momemtum force that accelerates particles off the atom (or matter) causing the electron to split from matter (atom) forming the beginning of a helical motion once emitted from matter in the form of radiation.
That is, photons and all electromagnetic radiations and emissions travel in helical motion, but what we see and observe is a sinusoidal wave, because helical 3D orthogonal projection onto their 2D plane is a perfect wavefunction !!! Mathematically, and physically, the orthogonal projection of any 3D helix onto 2D plane is a perfect sinusoidal wave function. Its frequency, its amplitude, its zeros, etc are exactly those shades of the 3D helix. So, whether it is the wavefunction interference, destruction, superposition, etc. or any other physical features we have been working on for over a decade, all those still apply physically and mathematically to the helical motion.
It only makes sense, if there is an intrinsic spin, that this must be the origin kickoff of deterministic location and momentum associated with the uncertain Heisenberg’s delta(S)delta(P)>= hbar/2 for the helical path to be generated for light and other electromagnetic radiation travel trajectory.
I would greatly appreciate your deeper insights.
thanx
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Hi Fluidic! After thinking things over for a few days I’ve come up with a way we can confirm or exclude the velocity profile using existing data. Suppose we have some velocity profile over a short period of time in a given frame of reference. (This period of time needs to be sufficiently small that we wouldn’t usually notice it.) We can then boost into a different frame of reference and because of Lorentz time dilation the velocity profile would be observed over a much longer time interval. We can get boosts of 2e5 from LEP and 4e3 from the LHC. If there was a velocity profile for the photon we would have seen slow photons at LEP, but we didn’t. (Out of time photons are a good indicator of new physics.) Assuming we can see a change in timing on the order of 20ns, we can exclude a velocity profile down to 0.1ps, which is a tiny time interval! Basically, if there is a velocity profile for the photon, it’s not measurable.
Hi! If the electromagnetic energy tensor is large enough, then GTR will kick in and the velocity of light can be different from its vacuum value.
It need not harm causality if tachyons can go to earlier times (but not too early) – an objective present separating past and future can be lurking anywhere outside the light-cone: see my early paper “A program model of becoming”, mentioned under Time at my website. I developed that idea later.
We live in interesting times, anyway.
Gentlemen:
There is still hope to break the “light barreer”:
* According to Special Reltivity Theory, everything, the resting mass of which is not equal to “0″, becomes heavier and heavier, its mass increasing up to infinity, the more closer to light velocity it were accelerated.
* This is nonsense! Because in the nature there does not exist any function that really goes to infinity. All “goes-to-infinity functions” of anything break down (earlier or later) at very hight values, but nevertheless nothing “infinite”!
* I expect that the Real Special Relativity Theory also behaves so.
Matter, accelerated more and more, once will reach light velocity, having very high but not “infinite” mass.
* Accelarating such matter, at light velocity, even more it will superate the light velocity and simply disappear, like in Science Fiction, because nothing at higher velocity than light can stay in our universe, because of Relativty Theory. Such matter will break the barreer of our universe and escape from it. Where to go ? I don’t know.
* Let’s have a try in a particle accelerator, using electrons, because their resting mass is about 1,800 times lower than that of a proton. We’ll accelerate and accelerate and suddenly there iso no electron any more. Where did it got to ? Don’t know, but we succeeded.
*How much energy we’ll need ? I expect, when electron, because of its increasing mass, becomes its own Black Hole, able to break the barreer of our universe, will be sufficient. Note: not even mass increases and time slows down, near to light velocity, but the space dimensions of any object become smaller and smaller, making the object more and more compact. This will help us to transform the electron into a black hole.
* Risks ? I do not think that there are. I expect that such tiny black holes will be unstable in our universe and vanish from it, before spoiling anything on our planet.
If my theory were somehow infantile, this is, because I am a simple Ph.D in Chemistry, not in Theoretical and Quantum Physics.
Yours truly:
Toivo Willmann
Hi Tovio, thanks for your comment! You raise an interesting question about massive bodies and traveling near light speed. As you say, as objects travel faster their effective mass increases, so people sometimes say that a massive body traveling at light speed has an infinite mass, but I think that this is a little misleading. Every massive body can be accelerated in any direction, and all we need to do is apply a force to the body. The effective mass keep increasing as the body gets faster, so it gets a smaller acceleration when the same force is applied. This way the description of the universe is consistent under special relativity- a massive body can never travel at the speed of light and we do not need to worry about infinite mass or infinite energy.
You mention accelerating electrons, and this experiment has already been performed at LEP. There, the electrons have a mass of 0.5eV and an energy of 45GeV, meaning that the difference between their speed and the speed of light is extremely small. None of those electrons disappeared from reality, so it’s safe to say that if there is such an effect, it happens at much high speeds. Cosmic rays can produce even faster particles, but since we see them there’s little reason to think that particles escape the universe. Neutrinos provide even higher speeds, probing even tinier differences in speed.
(However, there is an effect where if a particle’s momentum has a wavelength smaller than the Planck length then it could vanish into a micro blackhole. Such an effect gives us an ultra-violet cutoff for some processes, but I doubt any particle has ever actually reached this energy, as it’s about 10^20eV. Interestingly the age of the universe can give us an infra-red cutoff for the same reason, since the largest wavelength we can ever measure would be the width of the universe. That could spell bad news for supersymmetry!)