It is indeed speculation, however apparent from information which may lead people to believe that the use of them were necessary after reptiles assumed an upright "standing" position.
T. rex evolved enormous jaws with which to attack its prey. Its arms therefore became smaller in order to keep it balanced on its legs.
Nicholas is talking absolute nonsense. Salamanders are amphibians, not reptiles. Dinosaurs evolved from four-legged reptile ancestors similar to lizards - they all had forelegs used for walking. These became smaller when the first dinosaurs evolved an upright posture, with long hind legs. When quadrupedal species evolved, the forelimbs elongated again in order to support the front half of the body.
I think the reason is because they didn't really need them. They used their back legs and jaws for grabbing. Even some birds that became gigantic lost their arms (wings) just like T-rex. A bird like a hawk is a good example of how it can function pretty well without the front arms. A road runner for example can chase down prey very effectively without really using it wings.
T-rex do has little arms because big arms would do has only gotten in the way.
How do you know they evolved from salamanders?