## October 17, 2005

### is anything left in newton's world?

In case anyone is interested, here's my most recent paper which discusses what is left of the Newtonian world after Einstein. It's short so don't worry. If you're not too interested, scroll to the bottom to see my paper condensed into one sentence.

The universe as a whole has not changed much since the time of Isaac Newton, but the theories which physicists use to describe the universe have changed dramatically. Until Albert Einstein transformed the fundamental principles of physics, Newton’s principles were generally accepted as supreme in the field of physics. In the Newtonian universe, space, time, and mass are absolute. After Maxwell’s equations were postulated, the Newtonian universe began to crumble. Maxwell’s equations dictate that light travels at the same speed regardless of the observational reference frame. The realization that light has an absolute speed started a scientific endeavor that lead to the creation of the special and general theory of relativity. In the midst of special and general relativity, much, if not all, of Newton’s principles must be replaced. Newton’s principles are still quite useful at explaining the classical world, but special and general relativity are all encompassing.

The expansion of the limits of the Newtonian world can be seen in Einstein’s general theory of relativity. Newton relied on inertial reference frames to describe his law of inertia. Why give preference to an inertial coordinate system? Is one coordinate system better than all the others? In general relativity, however, all reference frames are treated as equals. Thus with general relativity, the reliance on Newton’s principle of inertia and one true reference frame is abolished.

An example of special relativity replacing Newton’s principles can be found in time dilation and length contraction. In Newtonian mechanics, space and time are Galilean invariant and therefore are not relative. However, in order for the speed of light to remain constant independent of the reference frame, time and distance must undergo dilation and contraction, respectively, under uniform translation. Time and distance dilate and contract, respectively, according to the Lorentz transformation, and thus symmetry is still present. In light of Lorentz invariance and the constant speed of light, Galilean invariance no longer applies to uniform translation, and absolute time is no longer possible.

Special relativity also predicts that relative mass depends on time dilation. Since Newton’s second law, which states that a body’s acceleration is proportional to the force acting on it, uses relative mass, the law must be thrown out. Under special relativity, mass can no longer be used as a constant of proportionality. The relativistic nature of mass also contradicts the Newtonian idea that mass is conserved. Energy is now the universally conserved entity.

Einstein’s weak equivalence principle states that inertial mass is equal to gravitational mass. As a result, light must follow a curved path in a gravitational field, and Newton’s description of gravitational interactions are no longer valid. Instead, the equations of general relativity must be adopted to correctly describe frames in which gravity is acting. Under the equations of general relativity, spacetime is distorted by objects, and geodesics describe the shortest distance between two points. The distorting of spacetime seems to indicate that space is more than just a relationship between two objects. Loosely, Newtonian physics and general relativity both imply space is substantial. It seems as if the only Newtonian idea that agrees with general relativity is that space is more than the geometrical relationships between objects.

When dealing with velocities much slower than the speed of light and with small distances, spacetime is nearly flat, and Newton’s laws can be used to approximate the equations of general relativity. Physically, the Newtonian world does not exist, but it can function as a model under certain circumstances. so don't worry.

Basically, none of Isaac Newton's laws describe the real world.