Unit 1: English Summary – Perspectives of Modern Physics & Basic Electronics

Relativity – Experimental Background

Relativity is a fundamental aspect of modern physics, which revolutionized our understanding of space, time, and motion. We will explore the experimental background that led to the development of Einstein’s theory of special relativity.

1. Structure of Space & Time in Newtonian Mechanics

In Newtonian mechanics, space and time are treated as separate, independent entities. Space is three-dimensional, consisting of length, width, and height, and time is a continuous, linear flow. These concepts are considered absolute, meaning they are the same for all observers, regardless of their motion or position in the universe.

Newton’s laws of motion rely on the assumption of an absolute space and time framework. According to this view, the position of an object in space is described by three coordinates (x, y, z), and the time it takes for an object to move is described by a separate scalar value (t). The laws of motion are invariant under changes in velocity, meaning that they apply in the same form regardless of the motion of the observer or the object.

In other words, if two observers are moving relative to each other, the measurement of space and time by each observer would remain the same, and the laws of motion would hold universally. This framework laid the foundation for much of classical mechanics, but it would soon be challenged by new experimental findings.

2. Inertial and Non-Inertial Frames of Reference

An inertial frame of reference is one in which an object remains at rest or in uniform motion unless acted upon by a force. Essentially, these are frames of reference that are not accelerating. According to Newton’s first law of motion, in an inertial frame, an object experiences no net force and will continue its motion in a straight line at a constant speed.

Non-inertial frames of reference, on the other hand, are frames that are undergoing acceleration, whether it’s a change in speed or direction. For example, a car accelerating on a highway or a rotating turntable would be considered non-inertial frames. In these frames, fictitious forces such as centrifugal force and Coriolis force need to be introduced to account for the effects of acceleration.

The distinction between inertial and non-inertial frames is important when discussing the principle of relativity. In Newtonian mechanics, the laws of motion are valid in all inertial frames, but the equations of motion need to be modified for non-inertial frames to include the effects of acceleration.

3. Galilean Transformations

Galilean transformations are mathematical equations that describe how the coordinates of an event (position and time) change between two inertial frames moving at constant velocity relative to each other. The transformations assume that time is absolute (it’s the same for all observers), and space is homogeneous (the same throughout).

For two observers moving with a relative velocity v along the x-axis, the Galilean transformations are given by:

x′=x−vt

y′=y

z′=z

 t′=t

Where:

x,y,z and t are the position and time coordinates in one frame of reference.

x′,y′,z′ and t′are the position and time coordinates in the other frame, which is moving with velocity v relative to the first.

These transformations were built on the assumption that time and space are absolute. They form the basis for Newtonian mechanics and describe how space and time should transform when switching between different inertial frames.

4. Newtonian Relativity

Newtonian relativity is the principle that the laws of physics are the same in all inertial frames of reference. In this framework, the motion of objects is described in the same way regardless of the observer’s state of motion. Therefore, an observer in one inertial frame should observe the same physical phenomena as an observer in another inertial frame, even if the two frames are moving at constant velocity relative to each other.

This principle is consistent with the Galilean transformations, which imply that space and time remain independent and absolute. For instance, if two observers are moving with respect to each other, the velocity of an object should simply be the difference in the velocities of the object in each frame, which follows the Galilean velocity addition rule.

While this was an effective description of the physical world at low velocities (compared to the speed of light), Newtonian relativity began to encounter problems when dealing with high-speed motion or electromagnetic phenomena.

5. Galilean Transformation and Electromagnetism

In the 19th century, as scientists delved deeper into the study of electromagnetism, the limitations of the Newtonian framework became more evident. James Clerk Maxwell’s equations for electromagnetism describe the behavior of electric and magnetic fields and their interactions with charged particles. However, these equations seemed to predict strange results when considered in different inertial frames.

Specifically, the speed of light, according to Maxwell’s equations, was always constant in any frame of reference, independent of the motion of the observer. This was in direct contradiction to the Galilean transformations, which predicted that velocities should simply add or subtract depending on the relative motion between frames.

Thus, while Galilean transformations were successful in explaining mechanical motion, they failed to explain electromagnetic phenomena properly, especially the constancy of the speed of light, which posed a significant problem.

6. Michelson-Morley Experiment and the Null Result

In 1887, the Michelson-Morley experiment was conducted to detect the motion of the Earth through the “ether,” a hypothesized medium through which light was thought to travel. The idea was that, just as sound travels through air, light would travel through this ether. By measuring the speed of light in different directions relative to the supposed motion of the Earth through this ether, they expected to detect changes in the speed of light based on Earth’s motion.

However, despite all efforts, the experiment produced a null result — the speed of light appeared to be the same in all directions, independent of the motion of the Earth. This result was a major puzzle, as it contradicted the prevailing understanding of light and motion based on the ether and Newtonian mechanics.

The null result of the Michelson-Morley experiment played a key role in the development of special relativity. It suggested that either the ether did not exist or the laws of motion were different from what had been assumed in Newtonian mechanics.

7. Einstein’s Postulates of Special Theory of Relativity

In 1905, Albert Einstein proposed the theory of special relativity, which resolved the issues raised by the Michelson-Morley experiment and the limitations of Newtonian mechanics. Einstein’s theory was based on two fundamental postulates:

The Principle of Relativity: The laws of physics are the same in all inertial frames of reference. This means that no inertial observer has a privileged position, and all observers will observe the same physical laws.

The Constancy of the Speed of Light: The speed of light in a vacuum is constant and the same for all observers, regardless of their relative motion or the motion of the light source. This postulate directly contradicted the Galilean transformation, which implied that velocities should add up or subtract based on relative motion.

These two postulates led to profound changes in our understanding of space and time. They implied that space and time were not absolute entities but were relative and could change depending on the motion of the observer. The constancy of the speed of light meant that the concepts of simultaneity and absolute time needed to be reconsidered.

Conclusion

The experimental background leading to Einstein’s special theory of relativity was shaped by key experiments, including the Michelson-Morley experiment, and the limitations of Newtonian mechanics. Einstein’s theory introduced a radically new understanding of space and time, where these concepts are not absolute but are relative to the observer. The Lorentz transformations that followed from these postulates described how space and time coordinates change between moving observers, marking the beginning of a new era in physics. Special relativity has since become one of the cornerstones of modern physics, influencing not only the study of motion at high speeds but also the development of quantum mechanics and the understanding of electromagnetic phenomena.