Time dilation of moving particles

Time dilation of moving particles can be determined by lifetime or decay time measurements of particles. The time dilation according to the special theory of relativity states that if a clock C between two synchronized, resting in a laboratory clocks A and B is moved, she pursues in time from the two clocks. Since, in principle any process can be referred to as a periodic clock, for example, this is true for the lifetimes and decay times of unstable particles such as muons. That is, moving muons would have a longer lifespan than rest. To demonstrate this effect measurements in the atmosphere as well as in particle accelerators are carried out with different types of particles, all results confirm the time dilation. Other experiments on the time dilation belong to the Ives - Stilwell experiments ( see also Tests of special relativity ).

• 2.1 Time Dilation and CPT theorem
• 2.2 twin paradox
• 2.3 Watches hypothesis

Atmospheric tests

Theory

It is measured that arise when impinging muons of cosmic radiation on the molecules of the upper atmosphere in 9 to 12 kilometers altitude. You are one of the main components of the secondary cosmic radiation, and move towards the surface at near-light speed. Since the same scenario must be present in all inertial systems, the place of origin in a particular layer of the atmosphere and the simultaneous position of the Earth must be calculated. Thus, this experiment depends on the ratio of two all parameters: a) the life of the relatively moving the ground muons and b) the extension of the upper to the lower layer of the atmosphere ( at the surface). This measurement situation allows the use of valid in all inertial systems in accordance with the principle of relativity formulas for time dilation and length contraction, the relevant objects for this experiment, namely the atmosphere at rest in S, and the muon at rest in S ':

Length of the atmosphere: the contraction formula is where L0 is the rest length of the atmosphere and L is their move - contracted length. Since the atmosphere rests in S, is considered γ = 1 and it is their resting length L0 measured. Since they in S ' is moved, shall γ > 1, and it is their contracted length L' measured.

Lifetime of the muon: The Zeitdilatationsformel is where T0 is the proper time of a comoving with the muon clock, and the average lifetime of the muon corresponds in its rest frame. Since the muon in S ' at rest, is considered γ = 1 and it is their own time T'0 measured. As it is moved in the S applies γ > 1, from which it follows that their proper time relative to the time t is dilated. ( For comparison purposes, can another, rest on the earth muon are considered. Consequently, the decay time of the stationary muon -S is faster than the moving muon -S in S ', whereas in S' is exactly the reverse. )

• In S muon S ' a greater life span than muon -S. Thus, muon -S ' to have enough time to the rest length of the layers of the atmosphere to penetrate to the earth's surface.
• In S ' has a greater life span Myon -S as muon -S'. However, this is not a problem, because the atmosphere is moving here and thus contracted in relation to their resting length. This even extends to the lower life of muon - S ', to the lively atmosphere pulled over and the earth's surface has arrived.

The muon produced at local zero (event A) by collision of the radiation to the upper end of the atmosphere. The muon at rest in S ', its world line is the ct' axis. The top of the atmosphere at rest in S, its world line is the ct- axis. On the x -axis and x'- axis contains all events that occurred simultaneously in S and S ' with the Myonenentstehung. For event D to earth and muon hit. Because the earth is at rest in S, its world line ( identical with the lower end of the atmosphere) by D drawn parallel to the ct- axis until it intersects the x 'axis and the x-axis.

Time: The time interval between two events that are on the world line of a single clock is called the proper time. She is one of the fundamental invariants of the theory of relativity. Since the emergence of the muon at A and the encounter with the Earth in D are located on the world-line of the muon, only one can comoving with the muon and thus in S ' clock at rest the proper time T'0 = AD Show. Due to the invariance of the AD Myonenuhr also in the Earth system S must show exactly the same time between events, and because the Myonenuhr is moved here, is T'0 = AD with respect to the rest in S watches dilated. This can be based on the much longer, indicated by the S- watches parallel to the ct- axis periods T = BD = AE are detected.

Lengths: Event B where the world line of the Earth intersects the x - axis corresponds to S in the position of the Earth at the time of Myonenentstehung. Event C where their world line intersects the x 'axis corresponds, in S' the position of the Earth at the time of Myonenentstehung. Length L0 = AB in S is thus significantly longer than L ' = AC in S'.

Experiments

By a special filter arrangement, it is possible to limit the measurement to such muons, moving at a certain speed. The comparison of the measured numbers makes it possible to determine the half -life of the fast moving muons. This is 1.3 · 10-5 s many times higher than the half-life of muons at rest with 2.197 · 10-6 s

Bruno Rossi and David Hall (1941 ) conducted the first experiment, where the number of muons that arrive at different heights was measured. The relativistic time dilation was confirmed qualitatively.

A similar experiment was carried out with increased accuracy by David H. fresh and Smith ( 1963). About 563 muons were observed at a rate of 0.995 c with which they moved over the height difference of 1907 m between Mount Washington and Cambridge in 6.4 microseconds per hour. Of these, about 412 muons per hour arrived at the goal, which is only a Zeitdilatationsfaktor of 8.8 ± 0.8 was possible, in good agreement with the predicted factor of 8.4 ± 2

Since then, those experiments that determine life time and time dilation of muons in the atmosphere, carried out routinely in experiments for Undergraduate Studies.

Accelerator tests

Time dilation and CPT theorem

Tests of Teilchenzerfallszeiten however carried out mainly in particle accelerators, which also confirm the time dilation with great accuracy. In addition, it was also confirmed by comparing the lifetimes of positive and negative particles, the CPT theorem. It states that the disintegration times of particles and their antiparticles must be equal. Failure to do so would result in a violation of Lorentz invariance and thus of special relativity result.

Corner house et al. (1965)

Nordberg et al. (1967)

Greenburg et al. (1969)

Ayres et al. (1971)

Nordin (1961 )

Boyarski et al. (1962)

Lobkowicz et al. (1969)

Ott et al. (1971)

Skjeggestad et al. (1971)

Geweniger et al. (1974)

Carithers et al. (1975)

Meyer et al. (1963)

Corner house et al. (1963)

Balandin et al. (1974)

In modern particle accelerators time dilation is already confirmed routinely together with the relativistic energy - momentum relation, and is necessary in the analysis of collision experiments.

Twin paradox

Bailey et al. (1977 ) examined the lifetime of positive and negative muons in the storage ring at CERN. They sent the particles into a circular path so that they repeatedly came back to the starting point. The obtained in this experiment confirm the time dilation is also a confirmation of the twin paradox, namely the statement that one coming back to the starting clock against the backward clock is slow. Further tests also measure the time dilation caused by gravity, Hafele - Keating experiment see and repetitions.

Watches hypothesis

In the experiments mentioned above, the dilation was measured during Teilchenzerfalls, as the particles were not subjected to acceleration. However Bailey et al. (1977 ) also confirmed the so-called "clock hypothesis " according to which the acceleration does not affect the time dilation. In their experiment the muons a permanent transverse acceleration of up to ~ 1018 g were exposed, yet they were given the same value for the time dilation as in the other experiments. This was also reported by Roos et al. (1980 ) confirmed subject which decompose Σ - baryons a longitudinal acceleration between 0.5 and 5.0 × 1015 g, and also received the usual value for the time dilation.

Links and literature

• T. Roberts; S. grinding; JM. Dlugosz: What is the experimental basis of Special Relativity? . In: Usenet Physics FAQ. University of California, Riverside., 2007. Accessed on May 21, 2011.
• Time Dilation - An Experiment With Mu - meson