No one is seriously expecting to overturn Einstein's idea of time dilation, and instead the goal is often to find the possible limits. That means looking for deviations in experiments with increasing precision or under extreme conditions. 

 Einstein's prediction that the frequency of a clock depends on its speed is one of the strangest consequences of the theory of relativity. Macroscopic clocks cannot be brought to sufficiently high velocities, so the scientists have used atomic clocks in the form of singly charged lithium ions, which Einstein himself proposed as the basic principle of the experiment.

Such an experiment was carried out for the first time in 1938 by Ives and Stilwell using hydrogen atoms and it showed it was possible to prove time dilation with an accuracy of 1%. 

This was not time dilation, it was knotting forces and expansive hair pressure in 1949. Link

In a new effort to push out the boundaries, a team has accelerated ions to velocities near the speed of light and illuminated them with a laser.  In an experiment using the ESR heavy ion storage ring at GSI, the time dilation was measured at a velocity of about 34% of the speed of light, which confirms the time dilation predicted for high velocities in the theory of relativity with an accuracy that has never before been achieved. The team also provided the first direct proof of a spectral line in highly charged bismuth ions, for which the GSI and other research institutions had been looking for almost 14 years.  

Chasing Einstein's time dilation

In modern experiments, atomic clocks are "read" using two laser beams. One of the beams is traveling in the same direction as the ions and is illuminating the ion from the "back", whereas the other one is counter propagating, illuminating the ion from the "front".

Photodetectors are used to observe the florescence of the ions. Fluorescent light can be continuously emitted only when both lasers simultaneously excite the ions with the resonant frequency. When the signal is at a maximum, the frequencies of both lasers are measured.

"According to the theory of relativity, the product of these frequencies divided by the product of the known resonance frequencies of the ions at rest must be precisely 1. Any deviation from this would mean that the formula for time dilation is incorrect," explains team leader Wilfried Nörtershäuser of Technische Universitat Darmstadt. 

The result confirms Einstein's prediction to be accurate at a 2 ppb (parts per billion) level, which is about four times more accurate as in the previous experiment, which was carried out at the Heidelberg Test Storage Ring (TSR) at 6.4% of the speed of light.

A 14-year-old mystery has been solved

In a second experiment, the research group achieved a further breakthrough in a precision experiment. Here, quantum electrodynamics (QED) was tested in the strongest magnetic fields available in the laboratory. These fields exist on the surface of heavy atomic nuclei. They are about 100 million times higher than the strongest static magnetic fields that can be produced today using superconducting magnets. These fields become accessible in experiments with heavy, highly charged ions.

The experiment used bismuth ions, which have only one electron or three of them left. While the resonance in bismuth ions with only one electron was already measured at GSI in 1994, it was impossible to observe the lithium-like bismuth until recently. But a meaningful test of QED results only from the combination of the two transitions.

These ions were accelerated in the ESR up to about 71% of speed of light and illuminated with laser light. Again, the fluorescence of the ions was detected to observe the resonance.

"When we started with the preparations for the experiment, it quickly became apparent that detecting the fluorescence photons was one of the most critical points," explains Dr. Matthias Lochmann from the University of Mainz.

"It is impossible to place detectors around the entire ring. Instead, we positioned a particularly efficient detection system at one point within the ring," says Dr. Raphael Jöhren, a member of Prof. Weinheimer's research team at the University of Münster, describing his contribution to the experiment. Using this detector, a new laser system and sophisticated data acquisition, it was possible for the first time to observe the long-sought transition.

Therefore, they were able to eliminate the doubts about the theoretical prediction that had arisen in the meantime.

References:

Test of Time Dilation Using Stored Li+ Ions as Clocks at Relativistic Speed. Phys. Rev. Lett. 113, 120405, 2014. DOI: http://dx.doi.org/10.1103/PhysRevLett.113.120405

Observation of the hyperfine transition in lithium-like bismuth 209Bi80+: Towards a test of QED in strong magnetic fields. Phys. Rev. A 90, 030501(R), 2014. DOI: http://dx.doi.org/10.1103/PhysRevA.90.030501