Classical vs. Newtonian Physics
Classical Physics is often incorrectly referred to as Newtonian Physics. The theory of Electromagnetism developed by Maxwell in 1856, also falls within the domain of classical physics. Newton was particularly interested in the dynamics of matter, energy, and particles within the classical scope of length, mass, and time. Therefore, it is important to classify Newtonian Physics as a branch of classical physics involving the mechanics of particles. The Special Thoery of Relativity, however, explains the behavior of objects in motion relative to each other. The theory states that the speed of light is the same for all observers, regardless of their relative motion, and that the laws of physics remain the same in any inertial frame of reference.
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Breakdown of Newtonian Mechanics at High Speeds
The remarkable success of Newtonian Mechanics, compared to Electromagnetism, made it a rigid foundation for the rest of physics. This means that, even if a better theory were to be discovered in the future, Newtonian Mechanics would still need to be encompassed within it. Einstein realized that the measurement of mass, length and time were inherently dependent on the use of light. When the velocity of an object approaches the velocity of light, it became clear that Newtonian Mechanics failed badly. For example, consider an electron accelerated by a potential difference of 10 million volts and moving at a velocity of 0.998c. When it is further accelerated by four times, its velocity does not equal 1.98c as it should have been according to the Newtonian mechanical relation. It was discovered experimentally that the speed of an electron was equal to 0.999c. This defied the laws of Newtonian dynamics, posing a paradoxical situation. Paradoxes, however, are one of the most significant aspects of science. Without them, and our relentless curiosity to resolve them, humanity would still be in the forests as hunter-gatherers or even worse.
Paradigm Shifts and the Need for Special Relativity
Thomas Kuhn uses the term ‘paradigm shift’ in his book ‘The Structures of Scientific Revolutions’. A paradigm shift is a fundamental change in how a system works or operates, typically in response to a new or changing environment.. It was a time for a paradigm shift when Einstein realized the need for a complete revision of entities like length, mass, and time. He did this by reformulating the idea of space and time to space-time. By doing this, Einstein was confident that the paradoxes would be resolved while still preserving the Newtonian Mechanics.
Galilean Transformation and Newtonian Relativity
The mathematical background for Newtonian Mechanics is the Galilean transformation. Under Galilean transformation, the acceleration of a body is invariant, though the quantities like velocity, momentum, and kinetic energy are not. This means that the laws of mechanics (not the laws of Physics) are invariant in all inertial systems. For example: the magnitude of kinetic energy could be different for observers in different inertial frames of reference. But if conservation of Kinetic energy holds in one inertial frame, it holds in another inertial frame as well. An inertial frame of reference is the one which is at rest or at motion with constant velocity with respect to the fixed system of distant stars. For convenience, any frame of reference can be taken as an inertial one if it is at rest or at motion with constant velocity relative to Earth.
The Flaw in Newtonian Relativity: Absolute Time
The invariance of laws of mechanics under a Galilean transformation explains why it is impossible to identify the state of rest or motion (with constant velocity) of a spaceship by observing the behavior of an apple within the system. The state of rest or motion can only be known by visually comparing the position of the spaceship with respect to the outward objects. Now, let us assume, a supernova explosion took place within the viewing range of the spaceship and the Earth. The passengers on the spaceship and we (on the Earth) as different observers in different inertial systems, will certainly not agree with our measurements. Clearly, the equations of Galilean transformation are at work here. But, the laws of physics will remain the same in both the systems. Both observers will reach the same conclusion regarding whether conservation of momentum has taken place or not. No observer is preferred over the other since all inertial observers are equivalent; this law, that every observer is equivalent and that there is no such thing as absolute measurement, is often referred to as Newtonian Relativity.
The only flaw with the Galilean transformation system and hence with the Newtonian Relativity is the bold assumption that ‘time for all inertial observers is the same’ i.e. ‘Time is an Absolute quantity’. Now, lets look at different consequences of this assumption. If time was really an absolute quantity and independent of the motion relative to an inertial observer, then, any event occurring at a given duration of time would also be the same for all inertial observers. This implies that the distance is also an invariant quantity. The distance is basically due to the two events happening in space at an instant of time. for example: the length of a fish is the distance between the points of strike of a pulse of light at its head and tail at a given instant. So if, Galilean transformation is taken for granted, the length of a fish and hence distance, would also be an absolute quantity for all inertial observers. This showed that simultaneity is an immediate absolute property of the universe.
The Velocity of Light and the Fall of Newtonian Mechanics
Soon Einstein realized the failure of Newtonian Mechanics as its inability to incorporate the velocity of light. So, he came up with an ingenious idea that the velocity of light is same in all inertial systems and given by ‘c’. He further tried to set up the equations of motion so that the constant velocity of light is preserved for all inertial observers. He used Lorentz Transformation system (developed decades before him) as the background mathematical structure. In doing so, not just mechanics but all laws of physics (laws of mechanics including electromagnetism) were conserved for all inertial observers. This is obvious since he used light, an electromagnetic wave, for the foundation of his theory.
This new theory of Einstein showed that the length, mass and time aren’t absolute quantities as conceived earlier but variational properties of space-time depending upon the motion of inertial observers. Now, simultaneity also became a relative concept. Two events that were simultaneous in one frame mightn’t be so in another inertial frame. Thereby a new term ‘relativity of simultaneity’ came up. Relativity of Simultaneity has been experimentally verified by time dilation experiments of atomic clocks. Thus Einstein’s special theory of relativity is a solid mathematical formulation of the dynamical relative quantities like length, mass and time.
The equations of motion under a Lorentz Transformation yield the same Galilean transformation equation for low velocity cases. However, for higher velocities, Einstein’s Theory of Relativity provides a new set of equations that modify the classical Newtonian laws. This was demonstrated by Maxwell’s classical theory of Electromagnetism, which was found to be consistent with Einstein’s theory. Thus, Einstein’s Relativity can be seen to be an extension of Newtonian laws to incorporate the effects of high velocity cases.