Reality

š

šš Quantum physics is our modern understandingš of atoms and molecules, including their structure and chemical behavior. A particle, e.g. electron is not a a geometric structural point like billiard ball but is only describable by a wave function, Y (psi). The wave-particle duality idea has been introduced to explain the particle-like behavior of light in terms of photon to explain phenomenon such as the photoelectric effect which gained Einstein his Nobel prize and its wave-like nature in phenomena like diffraction and interference. This idea was extended by Prince Louis de Broglie in 1932š to encompass matter and particles. The proof lies in the Young double slit interference experiment. When this experiment which was originally for the study of the behavior of light as wave was extended by substituting light with some particles like neutrons and electrons, the same interference pattern as light was shown. Since only wave shows such properties, this clearly shows that particles are behaving like waves in this experiment. Anyway, according to him, any moving particle or matter has a matter wave with a specific wavelength, known as de Broglie's wavelength, l, determined by its mass, m and velocity, v:

l = h/(mv)

where h is a constant known as the Planck's constant with a value of 6.63 x 10^-34 J s. Note that if the speed of an object is close to the speed of light, the more general equation which has to be used would be

l = h–[1 - (v / c)²]/(mv)

in accordance with Einstein's theory of relativity.

šAssuming you weigh 60 kg at rest (rest mass), running on the field with a speed of 7 m/s, then the calculated de Broglie wavelength is approximately 1.58 x 10^-36 m. You would have a noticeable wavelength if you lose some fat or move extremely slow as in 1.1 x 10^-35 m/s but how do you know that you are walking at that speed? The wavelength of a moving electron is detectable since its mass is relatively small. Thus, the properties of large objects including its motion are best described by considering its particulate aspect, ignoring its wave. But it becomes important when we consider the subatomic world. de Broglie's suggestion was confirmed and is of extreme importance as it gives us a hint on a grand unification, similarity and symmetry in nature, composed mainly of matter and radiation, including light.

šš The wave-particle duality idea was further developed when Erwin Schrödinger formulated his wave equation, now called Schrödinger wave equation.š We must know how does the wave describable by a wave function, Y (psi) governs the particle and how does it propagate.š In the same way as the wave mechanics in classical physics, the same line of thought should follow that there must be a wave equation governing a particle. It was found that the equation for the wave function is complex, i.e. it has a real part and an imaginary part. The real part stands for real number like 1, 2, 1/4 and 0.5. The imaginary part contains imaginary number, i.e. a real number multiplied by i (i =š–-1) like 4i. This is a clear difference from a wave function in classical mechanics governing mechanical wave or any similarity to the formation of ripples in a pool of water when you drop a rock into it since it contains an imaginary part which has no physical meaning in this case. Imaginary numbers^* have a mathematical meaning but not a physical one. Thus, the wave function has no physical existence. But what is it about? One scientist, Max Born suggested that the square of the wave function^*, y² was to be interpreted as the probability density. The probability or chances of finding a particle in a certain region at any moment is given by y². It holds true till today. Predictions of quantum physics is statistical and only provides a probability of determining a particle's position. Nonetheless, this does not mean that quantum physics is incomplete because they must account for the fact that there is a fundamental uncertainty principle that governs all of us but more importantly the microscopic world.š

imaginary number*

šImaginary numbers have no physical meaning generally. But, in some modern fields of mathematics, such as fractal and chaos theory it is extremely important. Fractals are able to reproduce nature and natural objects with only mathematics and are now being widely used.

š

square of the wave function*

The square of the wave function does not mean the multiplication product of two Y (Y²). Instead, the square refers to the multiplication product of the wave function, Y and its complex conjugate, Y*. Thus, it was written as y².

š