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Testing the Validity of the Lorentz Factor Y Wang, X Fan, J Wang Et Al Physics Education PAPER • OPEN ACCESS Related content - A MRPC prototype for SOLID-TOF in JLab Testing the validity of the Lorentz factor Y Wang, X Fan, J Wang et al. - Prototyping a 2m × 0.5m MRPC-based To cite this article: H Broomfield et al 2018 Phys. Educ. 53 055011 neutron TOF-wall with steel converter plates M Röder, T Aumann, D Bemmerer et al. - Aging test of a real-size high rate MRPC for CBM-TOF wall View the article online for updates and enhancements. Y Wang, X Fan, H Chen et al. This content was downloaded from IP address 128.141.192.149 on 04/01/2021 at 10:56 IOP Physics Education Phys. Educ. 53 P A P ER Phys. Educ. 53 (2018) 055011 (10pp) iopscience.org/ped 2018 Testing the validity of the Lorentz © 2018 IOP Publishing Ltd factor PHEDA7 H Broomfield1, J Hirst1, M Raven1, M Joos2,4, T Vafeiadis3, 055011 T K Chung1, J Harrow1, D Khoo1, T Kwok1, J Li1, H Mandelstam1, J Martin-Halls1, R Perkins1, A Singh1, H Broomfield et al J Southwell1, A Tsui1, K Tsui1, D Townsend1 and H Watson1 1 Colchester Royal Grammar School, Colchester, United Kingdom Testing the validity of the Lorentz factor 2 CERN, Geneva, Switzerland 3 Aristotle University of Thessaloniki, Thessaloniki, Greece Printed in the UK E-mail: [email protected] PED Abstract The CERN Beamline for Schools Competition gives high school students the 10.1088/1361-6552/aaccdb opportunity to perform an experiment of their design using the T9 facility. Our team, ‘Relatively Special’, was fortunate enough to be joint winners of this global event and travel to CERN for a unique adventure. This paper gives 1361-6552 an account of our story including the application, preparation, experience and the overall effect which it has had on us. We also detail our proposed experiment (Proposal from Relatively Special and Video) which aimed to Published test the validity of the Lorentz factor with two methods: the time of flight (TOF) of various particles and the decay rate of pions at different momenta. 9 Due to the high sensitivity required for the second method the results were inconclusive, therefore we report only on the results of the first method. We focus on the techniques we used, the setup of detectors, and how they 5 function. Introduction This seemed like an incredible opportu- One morning in 2015, a tweet from CERN began nity, and 17 of us, aged 16–18, quickly formed to stir excitement among students in our school, a team to tackle the challenge. Meeting weekly, Colchester Royal Grammar School. we worked together to write the 1000 word pro- posal and create the 1 min video needed to submit “CERN is offering high-school students from a complete application. around the world the chance to create and Our early meetings focussed on deciding perform a scientific experiment on a CERN which experiment to choose. Researching in accelerator beamline [2] . ” small groups, we explored ideas ranging from 4 matter-anti-matter symmetry to deep inelas- Author to whom any correspondence should be addressed. tic scattering. Each group regularly presented Original content from this work may be used their findings to the team and through a demo- under the terms of the Creative Commons cratic process we decided to investigate Special Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the Relativity. After this, the team name ‘Relatively work, journal citation and DOI. Special’ was quickly proposed and chosen. 1361-6552/18/055011+10$33.00 1 © 2018 IOP Publishing Ltd H Broomfield et al Composition of positive beam Composition of negative beam 1.0 1.0 – π e– 0.8 0.8 p 0.6 e+ 0.6 0.4 0.4 + 0.2 π 0.2 Fraction of total beam Fraction of total beam – + K K pbar 0.0 0.0 0246810 0246810 T9 beam momentum (GeV c−1) T9 beam momentum (GeV c−1) Figure 1. Composition of the beam in T9. Our enthusiasm for the topic quickly inspired machine entirely in one-take and then submitted more research, and our teachers were a use- the video along with our research proposal to ful resource for discussing conceptual details. CERN [1]. Another helpful resource was the CERN website, In May of 2016 we discovered that we had where we found specific information about the won the Beamline for Schools competition, along detectors and resources on offer. This helped us with another team from Poland called ‘Pyramid design our experimental method, which aimed hunters’. This was the exciting beginning to our to test the validity of the Lorentz factor with two journey. methods: the time of flight (TOF) of various parti- cles at different beam momenta and the changing decay rate of pions. Preparing for CERN Having a variety of interests within the team The wait between learning the amazing news and was incredibly beneficial and led to valuable dis- travelling to Geneva was livened by the com- cussions at each step of our journey. This was munication with one of the support scientists. especially true while writing our proposal, since He updated us with the work which CERN had we each investigated different aspects of the been doing to determine the feasibility of our experiment and then shared our findings. This experiment. We were informed that simulations process helped us develop our ideas, which we had been carried out using the Geant4 software, eventually collaborated to form our final proposal. which highlighted some of the limitations of For our 1 min video we decided to design, the setup which had not been considered in our build, and film a Rube-Goldberg machine (an experimental proposal. Methods were discussed ingeniously and unnecessarily complicated series to overcome the problems while maintaining the of devices which are linked together to produce general aim of the proposed experiment. a domino effect). We knew this was ambitious, The initial proposal [6] detailed a plan to sin- however, we were excited to pursue such a unique gle out the pions of the beam and compare their idea. Our school was incredibly helpful by regu- theoretical velocity at varying beam momenta larly rearranging classrooms to provide us work- with their measured actual velocity (method 1). space, and even teaching around our construction We also planned to compare this to a velocity when this was not possible. They also equipped obtained from measuring different decay rates us with the tools and resources that we needed due to time dilation (method 2). It was decided to build the machine. The members of our team that it would be best to separate the two meth- had a diverse skill-base, which proved useful ods into different runs, due to a variety of rea- when milling custom MDF components and film- sons, including the fact that a positive beam was ing with a self-stabilising camera. We filmed the preferred for method 1 and a negative beam for September 2018 2 Phys. Educ. 53 (2018) 055011 Testing the validity of the Lorentz factor Velocities of different particles at different momenta 1.0 0.8 −1 c Positrons Pions Muons Velocity 0.6 Kaons Protons 0.4 0.5 1.0 1.5 2.0 2.5 3.0 Momentum /Gev/c Figure 2. Velocity of the particles composing the T9 beam. method 2. This was owing to the different beam Figure 1 shows estimations for the respective compositions (figure 1). proportions of particles at each momentum. The Concerning method 1, as a result of the small beam momentum could be set between 0.5 and mass of pions, muons and positrons, the range of 10 GeV, delivering bursts of up to 106 particles their TOFs would be too little for the detectors in 0.4 s. 1 to distinguish over the possible 0.5–10 GeV c− momentum span. This led us to consider these Method particles as one group so that we would obtain an increased count rate. On the other hand, the The Lorentz factor, γ, describes the relativistic proton’s mass is large enough so that it could be change in properties of an object that is moving distinguished from the other particles, thus these with respect to an inertial frame at velocity, v. As were used as another TOF validation. We were particles travel close to the speed of light, c, in also informed that new, more precise detectors, particle accelerators, the effects of special relativ- namely the MRPCs and smaller 1 × 1 cm2 scin- ity become significant enough to measure. This tillators, had been built which would be used in includes the effect of mass increase. the setup. 1 Concerning method 2, alterations were γ = 2 (1) 1 v made to the experimental method before our trip. − c2 However, due to the high sensitivity of measure- ment required, the results obtained at CERN were p = γm0v. (2) inconclusive. Equation (2) describes the relativistic momentum, p, of a particle with rest mass, m0. T9 Beamline From the previous two equations using the time, t, to travel a distance, d, in the inertial The experimental area encompasses an area of 5 frame’s perspective, equation (3) can be derived: m by 12 m in which different detectors [3], out- lined below, can be positioned. The beam enter- 2 2 2 d m0c + p ing the experimental area is composed of positive t = . (3) or negative particles. The positive beam con- pc tains protons, pions, kaons and positrons and the Using the facility at CERN, a beam of a particles negative contains their respective antiparticles.
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