Content uploaded by Wilfried Flegel
Author content
All content in this area was uploaded by Wilfried Flegel on Aug 07, 2014
Content may be subject to copyright.
Abstract
The lifetimes of both positive and negative relativistic (gamma = 29.33) muons have been measured in the CERN Muon Storage Ring with the results tau+ = 64.419 (58) µs, tau- = 64.368 (29) µs The value for positive muons is in accordance with special relativity and the measured lifetime at rest: the Einstein time dilation factor agrees with experiment with a fractional error of 2×10-3 at 95% confidence. Assuming special relativity, the mean proper lifetime for mu- is found to be tau0- = 2.1948(10) µs the most accurate value reported to date. The agreement of this value with previously measured values of tau0+ confirms CPT invariance for the weak interaction in muon decay.
... Experimental tests of time dilation have never directly compared linear and circular accelerators. Muon decay experiments in circular accelerators have consistently matched the velocity-dependent predictions of Special Relativity (Bailey et al., 1977). ...
... Special Relativity successfully predicts time dilation (Einstein, 1905), however all direct muon decay experiments have been conducted in circular accelerators (Bailey et al., 1977). No controlled test has compared these results in a linear accelerator, leaving open the question of whether acceleration or cumulative distance affects proper time. ...
... Special Relativity treats time dilation as a function of velocity alone. Bailey et al. (1977) confirmed SR's predictions in circular accelerators, where muons travel repeated paths. However, no test has been conducted in a linear accelerator, where muons experience only a single, unidirectional motion. ...
Experimental tests of time dilation have never directly compared linear and circular accelerators. Muon decay experiments in circular accelerators have consistently matched the velocity-dependent predictions of Special Relativity (Bailey et al., 1977). However, no controlled study has tested whether identical muons at the same γ-factor exhibit the same decay rates in a linear accelerator. While SR assumes time dilation is dictated by velocity alone, alternative models suggest additional dependencies, including acceleration exposure (Feldman, 2023) or cumulative spatial history. If time dilation is purely velocity-dependent, muons in circular and linear accelerators should experience identical decay rates. However, if hidden variables modify relativistic time, a measurable discrepancy could emerge. We propose a direct experimental test to compare muon decay rates in both configurations, offering a novel probe into potential deviations from Lorentz symmetry.
... Previous experiments, such as Rossi & Hall (1941) and Bailey et al. (1977), have confirmed relativistic time dilation by measuring muon decay rates at high velocities. However, these studies implicitly assumed time as the controlling variable. ...
... However, time is never measured directly, it is inferred from movement (Bailey et al., 1977). ...
... In standard relativity, a traveling twin ages slower due to time dilation (Bailey et al., 1977). ...
We propose a reformulation of Special Relativity in which time is not a fundamental dimension but a derived effect of movement through space. This hypothesis builds upon the foundational works of Einstein (1905) and Minkowski (1908) but challenges the assumption that time dilation represents a fundamental warping of time. Instead, we reinterpret time dilation as a function of velocity-dependent distortions in distance measurement, aligning with the principles of Lorentz transformations (Lorentz, 1904). By reframing time dilation in purely spatial terms, we propose that biological aging and decay rates should correlate with spatial traversal rather than elapsed time. This idea is testable: if decay rates in high-velocity systems are measured relative to distance traveled rather than time elapsed, they should still match relativistic expectations. Previous experiments, such as Rossi & Hall (1941) and Bailey et al. (1977), have confirmed relativistic time dilation by measuring muon decay rates at high velocities. However, these studies implicitly assumed time as the controlling variable. We propose an experiment using particle accelerators and high-speed biological samples to test whether decay rates can be fully described by spatial traversal alone, providing an alternative interpretation of relativity.
... «Наблюдение за движущимся телом из удалённой точки имеет ещё одну особенность: воспринимаемый наблюдателем ход времени на движущемся теле отличается от хода времени по часам наблюдателя. Это следует из формулы (2). Допустим, что тело приближается к наблюдателю и на этом теле происходит некоторое событие длительностью ∆t. ...
... Кроме того, сразу же отметим, что, записывая переход от формулы (2) к формуле (7), авторы либо сознательно по-новому переобозначили штрихами входящие в эти формулы времена, либо здесь произошла какая-то путаница при печати. Каждый может это проверить сам, попытавшись получить (7) из (2). Но кроме этой досадной детали других неточностей в работе авторов нет. ...
... Поскольку авторы уравнение (7) выводят из уравнения (2), то посмотрим, как они это делают. Пусть t1 есть время какого-то первого события, например, излучения импульса света на движущемся теле, а t2 есть время какого-то последующего за первым второго события, например, излучения второго импульса света на этом же теле. ...
Об изменениях темпа течения времени в специальной теории относительности в связи с явлением запаздывания света.
The paper studies the effect of the objectively existing physical phenomenon of light retardation on changes in the rate of flow of visible (registered) time in the frame of reference of a stationary observer.
It is proven that visible (registered) time in this frame of reference is kinematic time, which is one of the physical aspects of the Einstein kinematic configuration of a body, time that changes with an increase in the speed of movement, the rate of flow of which, deceleration or, conversely, acceleration, depends both on the direction of movement of the body in relation to the stationary observer, and on whether the event associated with the moving body occurs at one or two of its points.
It is shown that when carrying out the procedure of physical observation, visible (registered) time by a stationary observer is the result of his perception of light images of events on a moving body, events lasting in time, and therefore visible (registered) time is a kind of light display of the proper duration of events, recorded in the proper frame of reference of this body.
It is shown that the proper time of a moving body, fixed in its own frame of reference, is a Lorentz invariant, therefore it is invariable with the change in the velocity of the body and is one of the physical aspects of the Einstein geometric configuration of the body.
Since the theoretically detected visible (registered) acceleration of the rate of flow of time by a stationary observer is the result of the combined action of the indisputable physical phenomenon of light retardation and the strictly mathematically proven trigonometric transformations of space and time that form a group, it is obvious that the theoretically detected phenomenon of visible acceleration of the rate of flow of time must take place in physical reality.
It is proven that the phenomenon of light retardation plays a dual role in the process of physical observation of the relativistic motion of a body. When the body moves away from a stationary observer, due to the action of this phenomenon, the visible (registered) rate of flow of time by a stationary observer slows down, while when the body approaches, on the contrary, it accelerates.
Based on this phenomenon, the so-called “twin paradox” is theoretically eliminated from physics, which appeared in STR as a result of the lack of consideration of the phenomenon of light retardation.
В работе изучено воздействие объективно существующего физического явления запаздывания света на изменения темпа течения видимого (регистрируемого) времени в системе отсчета неподвижного наблюдателя.
Доказано, что видимое (регистрируемое) время в этой системе отсчета есть кинематическое время, являющееся одним из физических аспектов эйнштейновой кинематической конфигурации тела, время, изменяемое с ростом скорости движения, темп течения которого, замедление или, наоборот, ускорение, зависит как от направления движения тела по отношению к неподвижному наблюдателю, так и от того, происходит ли событие, связанное с движущимся телом, в одной или же в двух его точках.
Показано, что при осуществлении процедуры физического наблюдения видимое (регистрируемое) неподвижным наблюдателем время есть результат восприятия им световых изображений событий на движущемся теле, событий, длящихся во времени, и потому видимое (регистрируемое) время является своего рода световым отображением собственной длительности событий, фиксируемой в собственной системе отсчета этого тела.
Показано, что собственное время движущегося тела, фиксируемое в его собственной системе отсчета, является лоренцевым инвариантом, потому неизменно с изменением скорости движения тела и является одним из физических аспектов эйнштейновой геометрической конфигурации тела.
Так как теоретически обнаруженное видимое (регистрируемое) неподвижным наблюдателем ускорение темпа течения времени является результатом совместного действия неоспоримого физического явления запаздывания света и строго математически доказанных тригонометрических преобразований пространства и времени, образующих группу, то очевидно, что теоретически обнаруженное явление видимого ускорения темпа течения времени должно иметь место в физической реальности.
Доказано, что явление запаздывания света выполняет двойственную роль в процессе физического наблюдения за релятивистским движением тела. При удалении тела от неподвижного наблюдателя из-за действия этого явления видимый (регистрируемый) неподвижным наблюдателем темп течения времени замедляется, тогда как при приближении тела, наоборот, ускоряется.
На основе этого явления из физики теоретически устраняется так называемый «парадокс близнецов», который и появился в СТО как результат отсутствия в ней учета явления запаздывания света.
Key words: light retardation, Lorentz transformations, time dilation, time acceleration, special theory of relativity, trigonometric transformations of space and time, geometric configuration, kinematic configuration, duration of events, twin paradox, muons, Hafele-Keitting experiment, orbital motion of satellites.
Ключевые слова: запаздывание света, преобразования Лоренца, замедление времени, ускорение времени, специальная теория относительности, тригонометрические преобразования пространства и времени, геометрическая конфигурация, кинематическая конфигурация, длительность событий, парадокс близнецов, мюоны, эксперимент Хафеле – Киттинга, орбитальное движение спутников.
Copyright © Платонов А.А. 2025 Все права защищены
... Кроме того, сразу же отметим, что, записывая переход от формулы (2) к формуле (7), авторы либо сознательно по-новому переобозначили штрихами входящие в эти формулы времена, либо здесь произошла какая-то путаница при печати. Каждый может это проверить сам, попытавшись получить (7) из (2). Но кроме этой досадной детали других неточностей в работе авторов нет. ...
... Здесь ∆t есть релятивистская длительность события (1), ∆t' есть видимая длительность того же события, измеренная наблюдателем (2). Ясно видно, что с увеличением скорости v видимая длительность события ∆t' У М Е Н Ь Ш А Е Т С Я . ...
Псевдонаучные мифы СТО. Замедление собственного времени
движущихся объектов.
The paper studies the effect of the objectively existing physical phenomenon of light retardation on changes in the rate of flow of visible (recorded) time in the frame of reference of a stationary observer.
It is proven that visible (recorded) time in this frame of reference is kinematic time, which is one of the physical aspects of the Einstein kinematic configuration of a body, time that changes with an increase in the speed of movement, the rate of flow of which, deceleration or, conversely, acceleration, depends both on the direction of movement of the body in relation to the stationary observer, and on whether the event associated with the moving body occurs at one or two of its points.
It is shown that when carrying out the procedure of physical observation, visible (recorded) time by a stationary observer is the result of his perception of light images of events on a moving body, events that last in time, and therefore visible (recorded) time is a kind of light image of the proper duration of events, recorded in the proper frame of reference of this body.
It is shown that the proper time of a moving body, fixed in its own frame of reference, is a Lorentz invariant, therefore it is invariable with the change in the velocity of the body and is one of the physical aspects of the Einstein geometric configuration of the body.
Since the theoretically detected visible (registered) acceleration of the rate of flow of time by a stationary observer is the result of the combined action of the indisputable physical phenomenon of light retardation and the strictly mathematically proven trigonometric transformations of space and time that form a group, it is obvious that the theoretically detected phenomenon of visible acceleration of the rate of flow of time must take place in physical reality.
It is proven that the phenomenon of light retardation plays a dual role in the process of physical observation of the relativistic motion of a body. When the body moves away from a stationary observer, due to the action of this phenomenon, the visible (registered) rate of flow of time by a stationary observer slows down, while when the body approaches, on the contrary, it accelerates.
Based on this phenomenon, the so-called “twin paradox” is theoretically eliminated from physics, which appeared in STR as a result of the lack of consideration of the phenomenon of light retardation.
В работе изучено воздействие объективно существующего физического явления запаздывания света на изменения темпа течения видимого (регистрируемого) времени в системе отсчета неподвижного наблюдателя.
Доказано, что видимое (регистрируемое) время в этой системе отсчета есть кинематическое время, являющееся одним из физических аспектов эйнштейновой кинематической конфигурации тела, время, изменяемое с ростом скорости движения, темп течения которого, замедление или, наоборот, ускорение, зависит как от направления движения тела по отношению к неподвижному наблюдателю, так и от того, происходит ли событие, связанное с движущимся телом, в одной или же в двух его точках.
Показано, что при осуществлении процедуры физического наблюдения видимое (регистрируемое) неподвижным наблюдателем время есть результат восприятия им световых отображений событий на движущемся теле, событий, длящихся во времени, и потому видимое (регистрируемое) время является своего рода световым отображением собственной длительности событий, фиксируемой в собственной системе отсчета этого тела.
Показано, что собственное время движущегося тела, фиксируемое в его собственной системе отсчета, является лоренцевым инвариантом, потому неизменно с изменением скорости движения тела и является одним из физических аспектов эйнштейновой геометрической конфигурации тела.
Так как теоретически обнаруженное видимое (регистрируемое) неподвижным наблюдателем ускорение темпа течения времени является результатом совместного действия неоспоримого физического явления запаздывания света и строго математически доказанных тригонометрических преобразований пространства и времени, образующих группу, то очевидно, что теоретически обнаруженное явление видимого ускорения темпа течения времени должно иметь место в физической реальности.
Доказано, что явление запаздывания света выполняет двойственную роль в процессе физического наблюдения за релятивистским движением тела. При удалении тела от неподвижного наблюдателя из-за действия этого явления видимый (регистрируемый) неподвижным наблюдателем темп течения времени замедляется, тогда как при приближении тела, наоборот, ускоряется.
На основе этого явления из физики теоретически устраняется так называемый «парадокс близнецов», который и появился в СТО как результат отсутствия в ней учета явления запаздывания света.
Key words: light retardation, twin paradox, special theory of relativity, proper time, kinematic time, time dilation, time acceleration, Lorentz transformations, trigonometric transformations of space and time, geometric configuration, kinematic configuration, duration of events.
Ключевые слова: запаздывание света, парадокс близнецов, специальная теория относительности, собственное время, кинематическое время, замедление времени, ускорение времени, преобразования Лоренца, тригонометрические преобразования пространства и времени, геометрическая конфигурация, кинематическая конфигурация, длительность событий.
Copyright © Платонов А.А. 2025 Все права защищены
... Lorentz (1899a) proposed motion mass, which was supported experimentally first by Kaufmann (1902), and time dilation which was supported experimentally first by Rossi and Hall (1941). Many later experiments support motion mass (Rogers et al., 1940;Grove and Fox, 1953;Zrelov and Stoletov, 1959;Meyer et al., 1963) and time dilation (Frisch and Smith, 1963;Bailey et al., 1968;Bailey et al., 1977;Bailey et al., 1979;Hafele and Keating, 1972;Alley, 1981;Vessot and Levine, 1979;Vessot et al., 29 1980;National Physical Laboratory, 2005). Modern variants of the Michelson-Morley experiment also have similar null results (Essen, 1955;Jaseja et al., 1964;Shamir and Fox, 1969;Brillet and Hall, 1979;Müller et al., 2003;Antonini et al., 2005;Herrmann et al., 2005;Stanwix et al., 2005;Müller et al., 2007;Herrmann et al., 2009;Eisele et al., 2009). ...
This article examines whether a simpler theory can explain the experiments/observations that are supposed to make special relativity necessary. These include the Michelson-Morley experiment, stellar aberration, the Lodge experiment, the binary star observations, and the Fizeau experiment of relative velocities of light in moving water. The results of all these experiments and observations can be explained by simpler classical models with a postulate that the medium of light in a vacuum corresponds to the local dominant gravitational field (LDGF). The medium of light is dragged completely in the rectilinear motion of the object that provides the LDGF, but not in its rotation when it is a perfect ball. The null result of the Michelson-Morley experiment arose because the motion of its interferometer relative to the LDGF caused by the Earth's rotation is too small compared with the Earth's orbital velocity. Stellar aberrations are the refraction of light across the interface between the moving Earth's LDGF and the solar LDGF. The Lodge experiment cannot affect the LDGF. The velocity of a wave propagating in its medium will not be affected by the velocity of its source so binary stars will not have ghost images. The result of the Fizeau experiment is the consequence of water molecules absorbing and releasing light wave packets while flowing. There is no length contraction, but clocks whose mechanisms are based on electromagnetic interaction run slower when they move relative to the LDGF. Such clock slowdown is not time dilation because time refers to (the record of) the process of events in their sequence of occurrence in (some parts of) the universe or the quantitative event-ordering system used to measure this process. The mass-velocity relationship is not an increase in the mass but a reduction in the electromagnetic force exerted on the object that moves relative to the LDGF. Therefore, a simpler theory can explain these "relativistic" phenomena.
... In atmospheric muons, this effect allows them to travel greater distances before they decay, as shown by Rossi and Hall (1941). Similarly, in a controlled synchrotron environment, time dilation significantly extends the apparent lifetime of muons, as demonstrated by Bailey et al. (1977). More recently, Botermann et al. (2014) have confirmed relativistic time dilation in lithium-ion beams, providing further evidence for this fundamental prediction of Einstein's theory. ...
This work presents a thought experiment where the number of cellular duplications or generations (G) is used as a biological clock to investigate the effects of relativistic environments on biological time. We demonstrate that, although physical clocks in different reference systems measure varying times due to relativistic time dilation, biological time remains invariant and corresponds to the 'proper' time. This invariance holds not only across inertial reference frames but also extends to non-inertial, accelerated, and gravitational reference systems. The invariance arises because G is defined as the ratio of the growth time to the duplication time, ensuring that any relativistic effects influencing these time intervals cancel out. These findings challenge the classic interpretation of Einstein's twin paradox, which suggests differential ageing due to relativistic velocities. In reality, while physical clocks indicate differing times, biological time, and thus the biological age of living organisms, remains unaffected, aligning consistently with the proper time. Although bacterial cultures were used as a model in this study, the results are generalisable to all cellular systems, provided identical growth conditions are maintained. This study provides new insights into the interplay between biological processes and relativistic effects, establishing G as a reliable and invariant measure of biological time across all reference frames.
The time dilation of Lorentz-Einstein can be readily derived from the classical light clock experiment where the clock is positioned perpendicularly to the direction of its motion. The extent of dilation is given by the Lorentz factor: 1/√(1− υ 2 /c 2) where υ is the relative speed of the light clock and c is the speed of light. The muon experiment is consistent with this type of time dilation. Assuming that the Lorentz-Einstein time dilation is relevant to the light clock experiment when the clock is aligned along the direction of motion, the Lorentz-Einstein length contraction is usually derived. However, if there is no such contraction we then deal with a time dilation of the non-Lorentz-Einstein type. The amount of time dilation is now specified by the squared Lorentz factor: 1/(1− υ 2 /c 2). It appears that this type of time dilation is even much more agreeable with the muon experimental measurements than the Lorentz-Einstein type.
A historical survey of the measurements of the gyromagnetic ratio g of the muon. A brief introduction is given to the theory of the ‘anomalous magnetic moment’ a ≡ ½ (g-2) and its significance is explained. The main part of the review concerns the successive (g–-2) experiments to measure a directly, with gradually increasing accuracy. At present experiment and theory agree to (13 ± 29) parts in 109 in g, and the muon still obeys the rules of quantum electrodynamics for a structureless point charge.
A determination of the ratio of the muon to the proton magnetic moment, μμμp, is described. The precession rate of positive muons was compared to that of protons in the same magnetic field and chemical environment. Attention is given to the points which bear on the accuracy of the result: timing, magnetic field, many systematic checks, and particularly the question of the chemical environment of the μ+. It is shown experimentally that the so-called "Ruderman correction"-the ionic state in water once tentatively proposed by Ruderman-does not occur. A physical effect which excludes the possibility of the ionic state is pointed out. Consistent results were obtained in three different media: water, NaOH solution, and an organic liquid. Chemical corrections were ≤ 2 ppm. The result, including residual uncertainties in the chemical corrections, is μμμp=3.1833467±0.0000082 (2.6 ppm); in terms of the muon mass this implies mμme=206.7682±0.0005, or mμ=105.6594±0.0004 MeV. The new value for the muon moment, used with the most recent measurements of the muonium hyperfine interval, yields a value for the fine-structure constant of α-1=137.03632±0.00019, an accuracy comparable with that of the current recommended value which depends primarily on the Josephson effect. The two numbers differ by 2.2 ppm, while the standard deviation of the difference is 2.1 ppm, which is satisfactory agreement.
Recent experiments by Pound and Rebka on the temperature dependence of the Mössbauer effect in Fe57, and by Hay, Schiffer, Cranshaw, and Egelstaff using an Fe57 absorber on a rotating drum are shown to provide the first direct experimental verification of the time-keeping properties of accelerated clocks such as occur in the classic "clock paradox" of relativity. In the experiment by Pound and Rebka, the thermal vibrations of the lattice impart rms velocities of about 10-6c, and nearly continuous, randomly-oriented accelerations of the order of 1016g to both the source and the absorber nuclei. In the experiment by Hay et al. the acceleration of the absorber was 6×104g. The photon provides continuous communication of time data between the two nuclei for the duration of the "journey" (the emission time of the quantum). In each case the observed fractional frequency shift Δf/f0 which occurs between the source and the absorber is found to be -vs2/2c2+va2/2c2, where vs and va are the rms velocities of the source and the absorber nuclei, respectively. These results are in quantitative agreement with the generally accepted calculations for the "clock paradox", in which two clocks pursue independent paths (at least one of which involves accelerations) in a common inertial frame, but are compared at two or more points where they coincide in space and time. The temperature-dependent experiments also demonstrate that accelerations of the order of 1016g, arising from lattice vibrations, produce no intrinsic frequency shift in Fe57 nuclei to an accuracy exceeding 1 part in 1013.
A study is made of the radiation level in a scintillation counter following a short burst from the CERN Proton Synchrotron. The delayed background in the region of the target is ascribed primarily to γ rays of neutron capture in equilibrium with the neutron flux in the enclosure. The theory of neutron moderation and capture correctly predicts the intensity and time dependence of the radiation.The possibilities of counting single particles in the presence of this background are assessed.
A check on CPT invariance has been made by comparing the lifetimes of the charged pion and its antipion. The fraction of surviving pions in beams of pi+ and pi- which were nearly identical in their spatial and momentum distributions were measured at ten positions along the beam using a liquid-hydrogen differential Cerenkov counter. Over 100 successive pi+-pi--pi+ comparisons were made. Because of the method used, many possible systematic errors which affect an absolute lifetime measurement cancel out in determining the ratio of the lifetimes. The ratio measurement gave (tau+tau-)-1=0.0056+/-0.0028 and the absolute pi+ lifetime was found to be 26.6+/-0.2 nsec.
The interference of KS and KL in the decay KS,L-->pi+pi- has been studied by use of the KS regeneration technique. With utilization of the results for the regeneration phase presented in the preceding Letter, the phase of eta+- has been determined as a function of the KL-KS mass difference: varphi+-=(45.5°+/-2.8°)+120°(Deltam-0.5348)Deltam. The data also provide an accurate measurement of the KS total decay rate: GammaS=[(1.122+/-0.004)+0.16(Deltam-0.5348)Deltam]×1010 sec-1.
DOI:https://doi.org/10.1103/PhysRevLett.4.165
In this paper the details of a previously reported precise measurement of the K+K- lifetime ratio are described. Using a separated beam at the Brookhaven AGS, we have counted the fraction of 1.6- and 2.0-GeV/c K mesons surviving at distances up to 2000 in. The result of the measurement yields tau(K+)tau(K-)-1=-0.00090+/-0.00078, indicating no violation of the CPT theorem. No evidence for deviations from an exponential decay law or for the existence of long-lived K mesons was found. The upper limit for any long-lived K mesons in the beam is 3×10-3 at the 90% confidence level.
The velocity dependence of the lifetime of the muon is investigated under the assumption that the Hamiltonian contains a spatial form factor which in the lab frame (the frame at rest with respect to the neighboring macroscopic bodies) vanishes for distances larger than some length α. In this model there is a violation of the principles of special relativity at small distances. In particular, space-time is anisotropic at distances smaller than α. The lifetime of the muon is calculated to second order in α, and it is shown that there will be about 1% deviation from the usual formula τ(v)=(1-v2/c2)-1/2τ(0) (which holds if special relativity is valid at arbitrarily small distances) if, e.g., the muon energy Eμ=104 MeV and α∼7×10-16 cm. The measurement of the velocity dependence of the muon lifetime at high energies could thus serve as a possible check on the validity of special relativity at small distances.