MUON LIFETIME WOULD DEPEND OF ITS ENERGY

MUON LIFETIME WOULD DEPEND OF ITS ENERGY by: o.serret@free.fr ABSTRACT : Only the theory of Relativity would explain that the short life of muons allows them to reach ground level. However, this explanation can be criticized on the fact that it assimilates the time measured in a terrestrial frame to the proper time in muon frame, and mainly that it confuses lifetime of a muon and dilation of the time. Therefore, another explanation is proposed based on the CERN results: muons lifetime would be proportional to gamma factor, indirectly to their speed or energy level. It is then shown that restless muons can reach ground level. This explanation registers within the framework of neo-newtonian mechanics, which makes it possible to explain phenomena at a very high speed and which is compatible with Quantum Mechanics. RESUME : Seule la théorie de la Relativité permettrait d expliquer que la faible durée de vie des muons leur permette d atteindre le niveau du sol. Cependant cette explication peut être critiquée sur le fait qu elle assimile le temps mesuré dans un «référentiel terrestre» au temps propre dans le «référentiel du muon», et surtout qu elle confond «durée de vie» d un muon et dilatation du «temps». C est pourquoi il est ici proposé une autre explication basée sur les résultats du CERN : la durée de vie des muons serait proportionnelle au facteur gamma, c est-à-dire indirectement à leur vitesse ou à leur niveau d énergie. Il est alors montré que les muons qui ne sont pas au repos peuvent alors atteindre le niveau du sol. Cette explication s inscrit dans le cadre de la mécanique néo-newtonienne, qui permet d expliquer les phénomènes à très grande vitesse et qui est compatible avec la Mécanique Quantique. Keywords: muons lifetime, variable time, Frisch & Smith, CERN, wrong Relativity, neo-newtonian mechanics. I. INTRODUCTION One of the irrefutable proofs in favor of the theory of Relativity and the dilation of time is the relativistic muon travel. Their number decreases exponentially as a function of time. Proponents of Relativity say their average lifetime would not reach the ground according to Newtonian mechanics. And using the dilation of the time of the theory of Relativity, it is possible to explain that they reach the ground. However, based on measurements, we will pick up what seems to us an abuse of language in the September 2 nd, 2018 O. Serret @ Millennium Relativity 1/6

theory of Relativity and then propose an interpretation compatible with Newtonian mechanics, or neo-newtonian mechanics. This neo-newtonian mechanics makes it possible to explain the other phenomena at a very high speed (see Related Articles) and is compatible with Quantum Mechanics, especially on the course of the time. II. MEASUREMENT Concerning the lifetime of the muons, there were two main types of measurement: a) In 1962, David Frisch and James Smith took measurements on muons in two different places, of which the following are the main results [1] of which are shown in Table 1. Let's remember that: - the half-life is the duration after which the population is divided by two - the average life is twice the half-life - if the speeds taken are different according to the altimetry, it is to consider the energy loss of the muons by ionization of the atoms with which they interact in their travel, which leads to a four times greater speed range at Cambridge than at Mount Wilson. Note that the average lifetime at sea level has not been measured. b) In 1976, CERN measured the lifetime of muons in a synchrotron. The results [2][3] are shown in Table 2. III. RELATIVISTIC EXPLANATION The muons are created between 10 km and 30 km of altitude. At 2 km above sea level Frisch and Smith measured 568 muons and their average lifetime was 2.2 μs. To travel the remaining 2 km to the ground at a speed close to light, this requires 7 μs using Newtonian mechanics. According to the law of exponential decay, we should not find more than 30, while there are 412 at sea level: 13 times more, the order of magnitude is radically different. Using the theory of Relativity, their average proper lifetime is multiplied by the Lorentz coefficient equal to 10, their average proper lifetime is (2.2 * 10 =) 22 μs. This is three times more than the 7 μs needed to reach the ground; that would be why we find practically as many muons at Cambridge as at Mount Wilson. This would be proof of the dilation of time. Table 1: Firsch & Smith s results Table 2: CERN results September 2 nd, 2018 O. Serret @ Millennium Relativity 2/6

Critique of relativistic explanation is double: - firstly, the average lifetime of the muon at rest was not measured in the muon own frame but rather in the terrestrial frame. - secondly, it is not because the lifetime of the muon is greater than expected that the time itself has been dilated. IV. NEO-NEWTONIAN EXPLANATION Taking up the results of the experiment made by CERN [4] from 1976 to 1979, it appears that the lifetime (in the terrestrial frame) of the muons is proportional to the gamma factor: (. ) = ( ) = ²!².. = 29 = 29 (1.a-b) That is, in the speed range between 0.9950 c and 0.9954 c of Mount Wilson where the gamma factor was 10, these muons have an average lifetime of 22 μs (and not 2.2 μs which is lifetime at rest ), three times more than the 7 μs needed to reach the ground. V. PROPOSAL OF EXPERIMENT In the Frisch and Smith s experiment, muons were slowed down to determine their average resting life at Mount Wilson at +2 km. At Cambridge level at +0 m, their average lifetime was not measured! According to the theory of Relativity, their average lifetime should be lower than the Cambridge level, and should be higher at their creation in the upper atmosphere. Muon lifetime is decreasing with their travel. If their lifetime in Earth frame is 2.2 μs at +2km, at sea level it should be lower and equal to (2.2-7/10=) 1.5 μs. According to neo-newtonian mechanics, their lifetime at rest should be equivalent (see Table 3). CERN experiments have shown that the lifetime of muons at rest at ground level is 2.2 μs too, which would invalidate the theory of Relativity. To discriminate both explanations, it would be necessary to measure lifetime of muons at different altitude levels. That is why we find practically as much in Cambridge than in Mount Wilson. This means that the lifetime of muons is proportional to the gamma factor, and therefore indirectly to their speed or energy level. There is no need to imagine a dilation of time (see Diagram 1, next page). Table 3: Muons lifetimes September 2 nd, 2018 O. Serret @ Millennium Relativity 3/6

VI. CONCLUSION Concerning the irrefutable proof of the dilation of time according to the experience over the lifetime of the muons, we have noted two misuses of language. Firstly, that assimilating the lifetime in the muon own frame to the lifetime recorded in the terrestrial frame. Secondly and mostly, the assimilation of the muon lifetime to the dilation of the time itself. This is why the relativistic demonstration appears to be doubly open to criticism. Moreover, supported by the CERN experiment in 1967, assuming that the muon lifetime is proportional to the gamma factor, we give a plausible explanation in the context of Newtonian and neo-newtonian mechanics. In the Frisch and Smith s experiment, the lifetime was not measured according to the altitude. Let us suppose that the lifetime at rest is independent of altitude, as the CERN experiment at low altitude tends to show, which would invalidate the relativistic explanation. The advantages of neo-newtonian mechanics are that it explains the phenomena at a very high speed and that it is compatible with Quantum Mechanics, particularly for a universal time. Diagram 1: Processing data September 2 nd, 2018 O. Serret @ Millennium Relativity 4/6

VII. RELATED ARTICLES / NEO-NEWTONIAN MACHANICS EXPERIMENTS Lorentz derivation Velocity Addition How to Demonstrate the Lorentz Factor: Variable Time vs. Variable Inertial Mass http://file.scirp.org/pdf/jmp_2015022510573131.pdf Velocity Addition Demonstrated from the Conservation of Linear Momenta, an Alternative Expression http://file.scirp.org/pdf/jmp_2015050609513342.pdf An improvement of the accuracy of Fizeau s experiment http://gsjournal.net/science-journals/research%20papers-relativity%20theory/download/7247 Force in Synchrotron Muon Lifetime OBSERVATIONS Mercury perihelion Light deflection Net Force F = γ 3 ma at High Velocity http://file.scirp.org/pdf/jmp_2016042814580505.pdf Present article About the ovoid orbits in general, and perihelion precession of Mercury in particular (2) http://www.mrelativity.net/papers/51/ Mercury%20Millennium%20Serret%205%20janvier%202018.pdf Hipparcos did not measure directly the light bending! http://gsjournal.net/science-journals/research%20papers- Mechanics%20/%20Electrodynamics/Download/6998 Gravitational Light Deflection: could Relativity be Invalidated by GAIA? http://mrelativity.net/papers/51/light%20deflection%20serret%20millennium%20aout%202018.pdf Shapiro time delay Shapiro Time Delay derivates from Refraction http://www.mrelativity.net/papers/51/shapiro%20serret%20millennium%20juillet%202018.pdf Pioneer Anomaly Dark Matter Dark Energy The Pioneer Anomaly explained by the Processing of the Doppler Effect http://gsjournal.net/science-journals/research%20papers-relativity%20theory/download/7330 The flat rotation curve of our galaxy explained within Newtonian mechanics https://physicsessays.org/browse-journal-2/product/1240-7-olivier-serret-the-flat-rotation-curve-of-ourgalaxy-explained-within-newtonian-mechanics.html Gravity vs. Dark Energy, about the Expansion of the Universe http://file.scirp.org/pdf/jmp_2018011714405269.pdf Gravitational waves Gravitational waves or particle radiation? https://www.physicsessays.org/browse-journal-2/product/1588-12-olivier-serret-gravitational-waves-orparticle-radiation.html CRITICISM OF RELATIVITY Lorentz derivation Reply to A Simple Derivation of the Lorentz Transformation http://file.scirp.org/pdf/jmp_2017121915203275.pdf September 2 nd, 2018 O. Serret @ Millennium Relativity 5/6

VIII. REFERENCES [1] Magnien P., Désintégration du muon: une horloge relativiste, http://www.lerepairedessciences.fr/terminale_s/3mecanique/chap10/horloge-muons.pdf [2] Villegas, Les muons du CERN, (2013), http://europhys.stav.free.fr/termt_ds6_physiquespecifique.pdf [3] Comprendre la relativité du temps, https://www.ac-orleans- tours.fr/fileadmin/user_upload/physique/lycee/terminale/eei/5- Orleans_TS_COMPRENDRE_Relativite_du_temps.pdf [4] Bailey & Al, Final report on the CERN muon storage ring, (1979), https://doi.org/10.1016/0550-3213(79)90292-x More Articles Millennium Relativity home page September 2 nd, 2018 O.Serret @ Millennium Relativity 6/6