The Story of Physics: Part 5 – The Dawn of Modern Physics - The Institution for Science Advancement

The Story of Physics: Part 5 – The Dawn of Modern Physics

3/13/2016

Contrary to what you may believe after reading Part 4, classical physics never went obsolete. It simply could not be used answer certain questions that had emerged out of late 19th century discoveries. See it like mathematics, you can't possible solve a multi-variable differential problem with only simple arithmetics, you need calculus for that.

And similar to calculus, modern physics became more esoteric and mathematically abstract. But we'll try our best to simplify it.

"1905 is often described as Einstein’s annus mirabilis: a wonderful year in which he came up with three remarkable ideas. These were the Brownian motion in fluids, the photoelectric effect and the special theory of relativity. Each of these was of a basic nature and also had a wide impact on physics." - Jayant V. Narlikar

In Part 4, we touched a bit about quantum physics to humble classical physics, but not enough to delve into the significance of it. Similarly at around the same time, another kind of physics takes shape, one that involves things moving at cosmic speeds.

Apparently, classical physics turned out not to work when the things being studied were very, very small (around the size of atoms or smaller), or were moving very, very fast (at some fairly large fraction of the speed of light). So, around the beginning of the twentieth century, Albert Einstein worked out his Theory of Relativity and people like Neils Bohr, Werner Heisenberg. and Erwin Schrödinger created quantum mechanics.

Quantum Mechanics

Isaac Newton thought that light was a stream of particles; Thomas Young thought it was a wave. Most people at the turn of the 19th century thought of light as a wave. But in 1900 Max Planck found that he could explain the way hot bodies radiate energy only if he assumed that energy occurred as packets. He assumed that his equations were simply tricks with the mathematics and called these packets of energy quanta. The equations were useful but the underlying ideas were not taken seriously.

In 1905, his annus mirabilis, Albert Einstein published three scientific papers, any one of which was the mark of a genius. The first forms the basis of his Theory of Relativity. The second proved the existence of atoms from direct observations (an effect called Brownian Motion). The third paper is the relevant one for this topic.

In this paper, he applied Planck's quantum idea of 1900 to explain the photoelectric effect. Planck’s quanta were now being utilised to explain two previously unexplainable phenomena. However, if quanta were real, was light a wave or a particle? It was as if in some experiments (refraction, diffraction) light was clearly a wave; in others (black body radiation, the photoelectric effect) it was a particle. This effect was strange and was known as wave-particle duality.

In 1912, Louis de Broglie, suggested that if energy could behave as both particles and waves, perhaps matter could as well. He produced the mathematics and predicted that under the right conditions a beam of electrons (clearly matter made of particles) might show wave properties. Surprisingly, when the experiment was performed, a beam of electrons was found to diffract just like a wave would have done. Eureka! It looked like energy and matter could both exhibit wave-particle duality. It appeared that a moving particle had a wavelength!

In continuation, Neils Bohr decided to work out the wavelength of an electron moving around the nucleus of an atom. He found that for an electron to have a stable orbit, the orbit had to include a whole-number of the electron's wave. Orbits that include fractions of waves were impossible so the electron could not inhabit them. In other words, an electron could have a stable orbit, so that it would not lose energy and spiral in to the nucleus. If an electron absorbed or radiated energy, it would do so in discreet amounts so that it would move to another stable orbit. The analogy is a staircase. You can only stand on the steps, not in the region between steps.

So these quantum ideas explained two things. Why atoms were stable and why atoms absorbed or emitted energy in selected wavelengths. Bohr used his ideas to predict what energy could be radiated from different atoms. His theories corresponded with observation.

In 1925, Erwin Schrodinger and Werner Heisenberg separately worked out the mathematics of Quantum Mechanics. Using this new theory, scientists could understand the behaviour of atoms and subatomic particles. The wave-particle duality concept it true for both matter and energy. The 'position' of a particle like an electron is given by a probability. Electrons exist in energy states. When they absorb energy, they absorb a whole number of quanta, disappear, appearing at a different energy state. Gone is the idea of little ball-like particles. The orbit of an electron is a cloud of probability around the nucleus.

Another quantum effect is the famous Uncertainty Principle. This implies that there is a built-in uncertainty in the Universe. It is possible for something to be created out of nothing, given enough time! On a subatomic level it is impossible to pinpoint things down to an infinite precision. And not because of any technological failings: this is a constraint of the Universe itself. A zero energy is impossible since it would be a precise state. This is the reason that nothing can be cooled below absolute zero (-273.15 degrees Celcius). An atom must retain at least one quantum of energy and this keeps it from cooling below absolute zero. This means that nothing can ever be at rest.

Quantum effects are not noticeable in the macro world. They only become important as one approaches the dimensions of the atom. Nevertheless, their effects are important in all branches of science. Quantum Mechanics is used to understand phenomena like radioactivity, chemical bonding, semi-conductors, solid-state micro-chips, electronics, sub-atomic physics, radiation from black holes, and many others.

Relativistic Mechanics

The theory of relativity was developed by Albert Einstein in the early 1900s. There are two theories of relativity. The first is special relativity and the second is general relativity. Both are based on the principle of relativity, which was created by Galileo Galilei, the Italian astronomer, in the 1600s.

Special relativity (or the special theory of relativity) is a theory in physics that was developed and explained by Albert Einstein in 1905. It applies to all physical phenomena, so long as gravitation is not significant. Special relativity applies to Minkowski space, or "flat spacetime" (phenomena which are not influenced by gravitation). Einstein knew that some weaknesses had been discovered in older physics. For example, older physics thought light moved in luminiferous aether. Various tiny effects were expected if this theory were true. Gradually it seemed these predictions were not going to work out.

Eventually, Einstein drew the conclusion that the concepts of space and time needed a fundamental revision. The result was special relativity theory. This is based on the constancy of the speed of light in all inertial frames of reference and the principle of relativity: (1) inertial frame of reference: a frame of reference that describes time and space homogeneously, isotropically, and in a time-independent manner. Shorthand: space the same everywhere at all times; and (2) principle of relativity: the equations describing the laws of physics have the same form in all frames of reference. Shorthand: same equations work everywhere and at all times.

Galileo had already established the principle of relativity, which said that physical events must look the same to all observers, and no observer has the "right" way to look at the things studied by physics. For example, the Earth is moving very fast around the Sun, but we do not notice it because we are moving with the Earth at the same speed; therefore, from our point of view, the Earth is at rest. However, Galileo's math could not explain some things, such as the speed of light. According to him, the measured speed of light should be different for different speeds of the observer in comparison with its source. However, the Michelson-Morley experiment showed that this is not true, at least not for all cases. Einstein's theory of special relativity explained this among other things.

General relativity is a theory of space and time. The theory was published by Albert Einstein in 1915. The central idea of general relativity is that space and time are two aspects of spacetime. Spacetime is curved when there is gravity, matter, energy, and momentum. The links between these forces are shown in the Einstein field equations.

A central idea in general relativity is the "principle of equivalence." An example is that two people, one in an elevator sitting on the surface of the earth, and the other in an elevator in outer space accelerating at 9.8 meter/sec^2, will each observe the same behavior of an object they drop from their hand. The object will accelerate to the floor at 9.8 meter/sec^2 in either case, making it impossible for either to distinguish whether or not they are at rest in a gravitational field or accelerating upward at one g. Other versions of this type of "thought experiment" were used to show that light would curve in an accelerating frame of reference. There are several forms of the equivalence principle. These include: Newton's equivalence principle, the weak equivalence principle, the gravitational weak equivalence principle, Einstein's equivalence principle and the strong equivalence principle.

The Sun can be seen as this kind of valley in spacetime, and one of the other objects in the valley is the Earth. The Earth does not roll directly towards the Sun (or ball) because it is moving too fast. The force pulling the Earth towards the sun is about the same as a second force. This second force is called the centrifugal force. The centrifugal force exists because the Earth moves sideways. This sideways motion makes the distance between the Earth and Sun increase. Since the Earth is being pulled towards the sun and moving away at the same time, it stays at about the same distance. This is also how the Moon orbits the earth. In this second case, Earth is the ball and the Moon is the object.

General relativity has predicted many things which were later seen. These include:

As light gets closer to the sun, it bends towards the sun twice as much as classical physics (the system used before general relativity) predicts. This was seen in an experiment led by Arthur Eddington in 1919. When scientists saw his experiment, they started to take general relativity seriously.
The perihelion of the planet Mercury rotates along its orbit more than is expected under Newtonian physics. General relativity accounts for the difference between what is seen and what is expected without it.
Redshift from gravity. When light moves away from an object with gravity (moving away from the center of the valley), it is stretched into longer wavelengths. This was confirmed by the Pound-Rebka experiment.
The Shapiro delay. Light appears to slow down when it passes close to a massive object. This was first seen in the 1960s by space probes headed towards the planet Venus.
And of course the recent discovery of gravitational waves by the laser interferometer gravitational-wave observatory (LIGO).

Although recognized for his role in advancing physics, Einstein never received a Nobel prize for relativity. The committee was at first cautious and waited for experimental confirmation. By the time such confirmation was available Einstein had moved on to further momentous work, specifically his contributions to quantum mechanics through his discovery of the law of the photoelectric effect.

Ponder this

In his annus mirabilis, 1905, Einstein published three very significant papers on molecular movements, the photoelectric effect, and of course, relativity. How are these three topics related to one another? What seems to be Einstein's train of thought that resulted in something seemingly unrelated? Or is there a common factor between the papers?

There is much research currently going on to link relativity with quantum mechanics. What are the aspects in each of these theories that made physicists suspect a link between them?

Discuss

Much of the cutting-edge research in modern physics is now based on explaining classical mechanics (Newtonian gravitation, electromagnetism, thermodynamics) within the frameworks that Planck and Einstein had founded. What drives this curiosity? What are the applications? What significance do or will they have in how we view our place in the universe?