Faster-than-light-neutrinos

Transcription

1 Faster-than-light-neutrinos Karlstads universitet Fakulteten för teknik och naturvetenskap Avdelningen för fysik och elektroteknik 19/ Sofie Yngman

2 Table of content Background 3 Neutrinos 3 Past results 4 Special relativity and the speed of light 4 Experiment 5 Creating the neutrinos 5 Underground 5 The detector 6 Time measurement 6 Length measurement 7 Creation of neutrinos revisited 7 Conclusion 8 What if it is wrong 8 Possible explanations if the result is correct 8 The third option 9 References 10

3 Background In september 2011 the Oscillation Project with Emulsion-tRacking Apparatus (OPERA) published an article in which they present results saying that they have found neutrinos travelling faster than light 1. This created lots of discussions and debate world wide since it, if correct, might violate the way of which we know the theory of special relativity. The OPERA group was mainly designed to investigate neutrino oscillations. They aimed to detect the tau neutrinos transmuted from muon neutrinos during their 730 km trip from CERN, Geneve Switzerland to LNGS, Gran Sasso Italy. During these experiments the neutrinos travel underground, through earth and were detected under the Gran Sasso Mountain. But already all facilities were in place to do a speed measurement this was also done and it is this experiment that gained all the attention in media lately. Neutrinos The neutron is one of the elementary subatomic particles. It has no charge so it is not affected by electromagnetic forces. It is a fermion, and all known fermions are affected by the weak force but they have no color charge so they are not affected by the strong force. The neutrino also has a mass, though very small, which makes it affected by gravity. These properties make them rather unsocial particles which most of the time travel through matter without interaction. There are three different types, or flavours, of neutrinos as we know it: electron neutrinos, muon neutrinos and tau neutrinos. Figure 1 The three flavours of neutrinos in their place in the elementary particle diagram.

4 The flavour of the neutrino may change when the neutrino is travelling through matter and this is what the OPERA experiment is designed to study. The beam used in the OPERA experiment was an almost pure muon neutrino beam with an energy average of 17GeV which transmuted into an almost pure tau neutrino beam. The contamination when detected was about 2% muon neutrinos and 1% electron neutrinos 2. Past results The speed of light and of neutrinos has been investigated before. In 1987 the neutrinos and light from a supernova hit earth 3. The neutrinos did arrive to the earth about three hours before the light did, but this was due to the head start they got when escaping the exploding star. Since the neutrinos do not interact with matter very much they could flee before the light could. If they would have travelled at the speed suggested by OPERA they would have reached earth about 4 years before the light. So calculations did not indicate, this time, that the neutrinos had travelled faster than light but rather a little below light speed as expected. Though this were electron neutrinos with an energy of 10 MeV while those created and used by OPERA was muon neutrinos with a different energy. Another project concerning the speed of neutrinos is the Main Injector Neutrino Oscillation Search (MINOS) project 4. This project was also designed to study the oscillations or transmutation of neutrinos. Here the neutrinos with energies of about 3 GeV were shot from Chicago to northern Minnesota and the flavour composition of the beam was detected at both places. They also tried to study the time of flight of the neutrinos. Their conclusion was that the speed of the neutrinos was below the speed of light. Their uncertainty was much higher than that of the OPERA experiment and they could not completely rule out speeds above the light speed. MINOS will now redo their experiments to see if the OPERA results are reproducible. For a long time an unsolved problem in physics was that the neutrinos detected from the sun was about one third fewer than expected by theory. The assumption was made that the neutrino did not have any mass. When realising that the neutrino actually has a small mass also the realisation that transmutation is possible came. Before this only the electron neutrinos were detected. Now when detecting all three types of neutrinos the numbers were correct. Special relativity and the speed of light In the beginning of the 20 th century Einstein published an article connecting the mass of an object to its energy and to the speed of light. The well known equation for relativistic energymomentum gives a restriction to how fast a particle with mass can move. E 2 = m 2 c 4 + p 2 c 2 (1) Here E is the total energy, m is the rest mass of the particle, c is the speed of light and p is the momentum. If rearranged and assumed that the momentum is conserved so that it can be expressed as equation (1) can be written as pc = E*(v/c) (2) E 2 = (mc 2 ) 2 +E 2 *(v 2 /c 2 ) (3)

5 It is not only implausible but actually impossible to break this speed limit as when the energy approaches infinity the speed approaches c asymptotically. This means that in order to have a speed equal to the speed of light the particle must have infinite energy. Experiment There are several parts of the experiment that need to be examined thoroughly and the most important are presented below as described in the OPERA article 5. Creating the neutrinos The first important part is the creation of the neutrinos used in the measurements. The neutrinos are produced by accelerating protons to 400GeV/c in the CERN Super Proton Synchrotron (SPS) and letting them hit a graphite sheet. Reactions between the protons and the target create. The pions and kaons decay, producing neutrinos, which are focused to LNGS. The protons are extracted from the accelerator in bunches as shown in figure 2, where the intensity is plotted against the time. In the right part of figure 2 the resolution is shown. Each of these wave packages is 10.5 μs long and it is not possible to know which proton in this package produced the neutrino detected at LNGS. Instead the time distributions of protons, for each extraction from the accelerator for which neutrinos are observed, are summed together and normalized to give a probability density function (PDF). And this PDF is compared to time distribution from the detector. Figure 2 Left: A proton waveform after extraction from the SPS. Right: A blow-up of the waveform showing the resolution. Underground The neutrinos travel through the earth as depicted in figure 3 6. They arrive at LNGS in Italy about 4 ms after they leave CERN. LNGS is situated inside Gran Sasso mountain providing a 1400 m shelter from cosmic background radiation which otherwise could affect the measurements.

6 Figure 3 The path travelled by the neutrinos. The detector The detector consists of layers of bricks of photographic films and led sheets and is shown in figure 4 7. There are also scintillators in order to detect the neutrinos and magnetic muon spectrometers to establish the spin and charge of the detected particles. The scintillators also detect the exact time that the neutrinos hit the detector. Figure 4 The detector at LNGS with its led sheets. Time measurement One of the key points in the experiment was to be able to measure the time with high accuracy. The GPS system used at CERN and LNGS only gave an accuracy of about 100 ns so a new system had to be used. For the experiments two identical GPS receivers as well as a

7 Cs atomic clock were installed at CERN and LNGS. The time was not measured by starting and stopping these clocks in a conventional manner. Rather the time of the start and the time of detection were noted by the two GPS receivers and compared to each other. The difference between the time bases in the two receivers was calculated to be 2.3 +/- 0.9 ns. In figure 5 a schematic set up of the time measurement is shown. Figure 5 Schematic set up of the time measurements. Length measurement Another key point is to know the distance between the point where the proton time structure is measured at CERN and the detector in LNGS. The distance is about 730 km but in order for the calculations to be valid the distance must be known down to the centimetre or preferable even millimetre scale. GPS was used to pin the coordinates of the key points in the experiment. The total distance travelled by the particle was divided in two, the distance between the BCT and the focal point and the distance between the focal point and LNGS. For the first one the position of the beam line was known down to millimetre accuracy and when this position was related to the global geodesy frame the coordinates are still known down to 2 cm. One thing that should be noted is that the position where the parent meson decays and produces a neutrino is unknown. It is somewhere in the decay tunnel, but the decay tunnel is 1 km long. Even though this may seem like a big uncertainty it will only affect dt with about 0.02 ns. This is because the parent mesons are ultra-relativistic. The distance between the OPERA reference frame and the target focal point was measured in detail in 2010 and the uncertainty was 20 cm. GPS are used to continuously monitor movements of the earth crust (only about 1 cm/year) and also to register the effect of earthquakes. Also tidal effects were considered and accounted for, making it possible to compare results obtained at different times. Creation of neutrinos revisited

8 Instead of sending several bunches of protons to the graphite target the OPERA group also tried sending only one bunch at a time. This was done in order to secure that a detected signal at LNGS is associated with the correct proton bunch at CERN. These experiments were performed during late October and early November 2011 and the result was added to the main article. The time found using this technique was t = (62.1 ± 3.7) ns as compared to (57.8 ± 7.8) from the earlier measurements. The gain in knowledge of the exact bunch observed, and therefore the exact time it left CERN, was paid by lack of intensity of the beam which now was about 60 times lower than during previous measurements. Conclusion The first thing to mention is that the OPERA team did not draw any conclusions nor did any speculations of their result. They simply wrote: In conclusion, despite the large significance of the measurement reported here and the robustness of the analysis, the potentially great impact of the result motivates the continuation of our studies in order to investigate possible still unknown systematic effects that could explain the observed anomaly. We deliberately do not attempt any theoretical or phenomenological interpretation of the results. But a lot of speculations have been done since the result was published. There are basically two possibilities. Either there is something wrong with the measurements or the result is correct. It will take a lot of time and effort to figure out what was actually observed and establish the speed of the neutrinos. For now two research teams, MINOS in USA and T2K In Japan has agreed to redo the experiment to see if the result is reproducible. What if it is wrong A lot of people doubt whether the results are really accurate or if there is something wrong with the measurement or the techniques of measurement. The next step is therefore to let other research groups redo the experiment to see if the results are reproducible. The MINOS group mentioned before has agreed to do it as well as a Japanese team called T2K. The results from these two groups are not expected to be published any time soon. One article that highlighted the time issue was Measuring time of flight using Satellite-based clocks by Ronald A.J. van Elburg 8. He suggests a lack of the correction for first order Doppler effects of the clocks, used for time measurement, in OPERAs report. One needs to consider where the clocks are located, on the ground or on the satellite, in order to place the system in the correct reference frame. This may sound as if it should not matter too much since in Galilean physics time is invariant under a change of reference frame. However it is important to realise that the special relativity does not preserve time and distance separately. To solve this, Lorentz transformations have been performed on space and time. When accounting for these effects a large part of the unexpected time difference is corrected. This may sound like the solution to the problem but it is important to emphasise that OPERA did take effects like this into account but not in the same manner as Ronald A.J. van Elburg. It is not obvious which the correct approach to the problem is. Possible explanations if the result is correct Even though the sources of errors are many the result of this experiment is clear and the possibility of it being legit should not be disregarded. After the publication of the article a lot of theories were published.

9 One interesting point of view was brought up by Christopher White in a lecture given after the result was published 9. He points out that there exist more solutions to the relativistic energymomentum equation: E 2 = m 2 c 4 + p 2 c 2 (1) than only the positive one. Here E is the energy, m the mass, c the speed of light in vacuum and p the momentum. When taking the square root of both sides of this equation two solutions appear, one positive and one negative. The negative solution is usually considered unphysical and is disregarded. If plotting both of the solutions we get curves as in figure 6. Figure 6 A plot of the relativistic energy-momentum formula for both the negative and positive solution. Above the speed of light, c, the Tachyons are supposed to exist. Here it seen that the positive solution asymptotically approaches the speed of light but never exceeds it. To exceed it is not mathematically possible. But what about the negative solution. This curve is all located above c. Here some other particles are already suspected to exist namely the tachyons. The tachyons have never been observed experimentally but is said to be a particle that always moves faster than light. Could neutrinos possible be Tachyon-like? The third option There is also a third option allowing for the particles to travel below the speed of light but still arrive at their goal quicker than light in vacuum would. This, what seems to be a paradox, can be solved by string theory and is explained briefly by Prof. Michael Duff here 10 and is also explained in another article 11. According to this theory our universe can be seen as a bread slice in a loaf of bread usually called a membrane. Light is confined to move only inside each membrane and not in the bulk. Normally particles cannot move from inside a membrane to the bulk. But if they for some reason did this and the membrane is curled it would give observers in a membrane the impression that a particle travelled faster than light.

10 References: 1 The main article from OPERA: ( ) 2 The main article from OPERA: ( ) 3 ( ) 4 P. Adamson et al. (MINOS Collaboration) (2007). "Measurement of neutrino velocity with the MINOS detectors and NuMI neutrino beam". Physical Review D 76 (7) 5 The main article from OPERA: ( ) 6 The OPERA experiment official presentation: ( ) 7 The website of OPERA: ( ) 8 Measuring time of flight using Satellite-based clocks: 9 Dr Christopher White, coordinator at MINOS: ( ) 10 Prof. Michael Duff briefly explaining string theory: 11 Neutrinos travelling in extra dimensions: ( )