The Particles with velocity more than the speed of light

 Around 27 months ago, I wrote an article of "Analysis and Design Open Oscillatory Systems with Forced Harmonic Motion" posted on link: http://www.emfps.org/2014/02/analysis-and-design-open-oscillatory.html

According to the conclusion of above article and using of Newtonian mechanics, it can be proved that there is some systems with velocity more than the speed of light.

Let me tell you another example about the kinetic theory of gases.

In the reference with below links, Physicists at CERN generated ions with temperatures of more than 1.6 trillion degrees Celsius. At the Brookhaven National Laboratory in Upton, have set a new record for the highest temperature ever measured: 4 trillion degrees Celsius.

https://www.insidescience.org/content/hottest-temperature-universe-measured/1169

http://www.dailygalaxy.com/my_weblog/2011/06/cern-lhc-creates-temperatures-1000-times-hotter-than-center-of-sun.html

Assume, we have a 0.500 mole sample of hydrogen gas at 1.6 - 4 trillion degrees Celsius.

By using of Maxwell–Boltzmann speed distribution function, we can calculate number of molecules with velocity between 300000 km/s to 400000 km/s at 1.6 trillion degrees Celsius which is equal 1.01326*10^21. It means that about 0.34 % of total molecules of hydrogen have velocity more than 300000 km/s. At 4 trillion degrees Celsius, number of molecules which have velocity between 300000 km/s to 700000 km/s, is equal 4.23143*10^22. It means that about 14.05% of total molecules of hydrogen have velocity more than 300000 km/s.

In record of CERN, it has been stated: "… ions together at close to the speed of light…"

The question is: Had all (100%) ions the velocity close to the speed of light?

Therefore, we have only two alternatives:

1. If the answer to above question is positive, then all reference books should apply the limited velocity of 300000 km/s for Maxwell–Boltzmann speed distribution function.

2. If the answer to above question is negative, then we can use from special theory of relativity only as a simulation model in which limited speed of light is an assumption of this model.

Of course, previous experiments showed that Newtonian mechanics is contrary to modern experimental results and is clearly a limited theory in which velocity of the particles in the Universe always remains less than the speed of light.

But, here there is a strange case and the interesting point. Because this temperature which has been generated by Physicists at CERN (1.6 trillion degrees Celsius), is approximately the boundary between using of the Maxwell-Boltzmann distribution and Maxwell–Jüttner distribution. It means that all particles (100%) in temperature less than 1.6 trillion degrees Celsius have velocity between 0 to less than 300000 km/s and we can still use from Maxwell-Boltzmann distribution instead of Maxwell–Jüttner distribution.