 You'll recall from our segment on the microscopic in the How Small Is It? video book that momentum is mass times velocity. Another interesting consequence of the speed of light being a constant for all observers is that the momentum of an object increases without bound as its velocity approaches the speed of light. This increases the amount of energy it takes to increase its speed even more. Our best example of this is the Large Hadron Collider at CERN where the Higgs boson was found. To begin with protons are accelerated down a linear accelerator. By the time they reach the first cyclotron they're traveling at one third the speed of light. We can use this as the starting momentum. If we had used Galilean transformations we would be off by 5% and the linear accelerator would not work. The first booster accelerates the protons to 91.6% of the speed of light. This speed more than doubles the momentum. The protons are then flung into the proton synchrotron. They circulate here for 1.2 seconds reaching 99.9% of the speed of light. At this speed their momentum has increased by more than 60 times. The protons are then channeled into the super proton synchrotron. This is a huge ring almost 7 kilometers in circumference. The best that it can do is to increase the velocity of the protons by around 8%. To 99.9998% of the speed of light. The proton's momentum has now jumped by over 1,400 times its momentum at the end of the first acceleration. Finally, the large Hadron Collider accelerates these incoming protons to 99.999964% of the speed of light. The proton's momentum tops out at 10,562 times its original momentum. At this level Galilean transformations would be off by over 99.9%. The fact is that as the velocity gets closer to the speed of light the momentum increases without bound and the energy required to get it even closer to the speed of light grows to be more energy than exists in the universe. This is one of the reasons why we say that nothing with mass can ever reach the speed of light. The operations of the Large Hadron Collider at CERN confirm this relativistic momentum increase just as the operations of GPS satellites confirmed relativistic time dilation and cosmic ray created muons confirmed relativistic length contraction.