March 13, 2018
1. Waves involve the transport of energy without transport of matter. When you drop a pebble onto a water reservoir, you can see the ripples move out. There is no displacement of water from one place to another; but the disturbance moves out.
- Therefore, a wave can be described as a disturbance that travels through a medium, transporting energy from one location (its source) to another location without transporting matter.
- On the other hand, a particle can move and therefore transfer matter. The most important characteristic of a particle is that its position is localized at any given time, and it is detected as a single detection event or a “single click”.
- Those are the ways waves and particles were expected to behave before the advent of quantum mechanics. But starting around the year 1900, our ideas about waves and particles became somewhat confusing, due to many drastic changes that took place for many years.
2. The fundamental concepts in quantum mechanics (QM) were worked out between roughly from 1900 to 1930. A good description of the evolution of QM within this period and beyond is given in the book “Einstein, Bohr and the Quantum Dilemma” by Andrew Whitaker (second edition, 2006).
- That book describes how the key words like waves, particles, and wave functions related to QM evolved. Some of the old — and unnecessary — concepts like “wave-particle duality” linger on because of the impressions made at that time.
- Experiments carried out within the past 20-30 years (some key experiments within the past few years), show that such lingering ideas on “wave-particle duality” are really an obstruction to grasping the reality revealed by QM.
3. For a long time, it was thought that light is a wave, specifically an electromagnetic wave. That idea still linger on.
- Light consists of particles (photons) was firmly established only in 1986. We will discuss the next post.
- The most distinguishing characteristic of a particle is that its detection is recorded as a single event (“a click”) at the detector.
4. However, the motion of a particle — including a photon — can be represented by a wave function, which is a mathematical function, not a wave. A wave function is extremely useful for calculating experimental results, but it is not something that is physically real.
- It is easier to see the differences among the terms waves, particles, and wave functions by looking at what happens when waves and particles go through two adjoining slits.
5. When normal particles that we are familiar with go through two slits and fall on a screen to make their imprints, we will see two “line images” as shown on the left in the figure below. On the other hand, a wave (like a water wave) will give rise to “fringes” as shown on the right.
- In normal life we will see particles (say marbles) going through two large slits leading to those marbles hitting the screen as shown on the left
- With a water wave going through two slits we will see ripples giving rise to water wave crests as shown on the right.
Those are the scenarios with normal particles and normal waves.
6. If quantum particles (like electrons or photons) are going through two slits where slit opening are LARGE (say a cm or more), then we will again see the “normal particle pattern” shown on the LEFT.
- However, if quantum particles (like electrons or photons) are going through two slits where slit opening are SMALL (say less than a mm), then we will see the “wave pattern” shown on the RIGHT. If the aperture dimensions are of the order of h/p (where h = Planck’s constant and p is the momentum of the particle), then such diffuse wave patterns can be expected.
- In such cases, those experimental results can be CALCULATED by using wave functions to represent the motion of such particles.
- However, a particle is never spread out. A given particle will always be detected at a certain point within that diffraction pattern. One needs to repeat the experiment with a single particle many times to get that diffraction pattern.
We will discuss this in detail in upcoming posts, together with the following related issues.
Light is a Wave or a Particle?
1. In the early days, Newton’s concept of light consisting of particles prevailed for a long time. But Newton’s corpuscular theory of light was abandoned around 1850 because it could not explain interference and diffraction phenomena, and Young and Fresnel showed that the wave picture could explain those experimental results.
- However, a wave needs a medium to support it. A water wave propagates in water, and a sound wave can propagate in a solid or a liquid, and needs at least air to propagate. Still, light can travel in a vacuum, and therefore the existence of a yet unknown “aether” was proposed as the all-pervading medium through which light could propagate.
- The “aether theory” itself ran into several objections, and finally was abandoned after the famous Michelson–Morley experiment performed in 1887, which conclusively proved the absence of an aether.
2. Now we know that light doesn’t need a medium through which to travel. Furthermore, the speed of light is constant and is independent of the movement of the source or detector or the direction in which it travels, as shown by the theory of relativity of Einstein (discovered in 1905).
- Therefore, light is not a wave. This was confirmed without any doubt by an experiment conducted with single photons in 1986, which we will discuss in the next post. I just wanted to present the background in this post.
Matter as Waves?
1. While the debate was going on about whether light is a wave or a particle between 1850 to early 1900’s, and even up to 1986 to some extent, another related development came with the early studies in quantum mechanics beginning around 1900.
- The issue was whether solid particles can be treated as waves.
2. After Planck, Einstein, Compton, and others established that light behaved as particles (photons), Bohr in 1913 came up with an idea to quantize the energy levels of a hydrogen atom. He was able to explain why discrete lines in the spectra of hydrogen.
- The reason why Bohr’s idea worked was clarified by a yet another ground-breaking hypothesis put forth by de Broglie in 1924. He proposed that just like photons can be represented by a wave (specifically with electromagnetic wave equations of Maxwell), the motion of electrons can be represented by a “wave”. At that time it was not fully clear what this “wave” would be. Now, we know that it is a wave function.
3. Light had been considered to be a wave for a long time, as we discussed above. But the idea that electrons with no-zero rest mass could be represented by waves was an unanticipated one.
- Then in 1927, Davisson and Germer produced clear diffraction patterns for electron scattering from a nickel lattice, just like a diffraction pattern due to light. This led to the speculation that maybe particles sometime behave as waves.
- That is how the idea of “wave-particle duality” evolved in the confusing period of 1900 to about 1930. Even though an accepted “quantum theory” had been established by around 1930, the idea of “wave-particle duality” lingers to the present.
- Nowadays, those diffraction patterns seen with electrons can be explained via the wave functions that represent the motion of electrons. However, a given electron can be found only at one location at a given time.
Heisenberg Uncertainty Principle
1. To make things even more complicated, in 1927 Heisenberg came up with his famous uncertainty principle. This principle says that the uncertainty of the position of a particle (σx) multiplied by the uncertainty of the particle’s momentum ( σp) must be larger than what is known as the Planck’s constant, ℏ:
σx . σp ≥ ℏ
- Planck’s constant is extremely small; it has a value of about 10-34 Js.
- For any particle that we can see with our eyes, any uncertainty in particle’s position will be much smaller than the size of the particle. Therefore, we don’t notice this in our normal lives.
2. However, when it comes to microscopic particles like electrons, the uncertainty in position is normally very large. If you have seen a pictorial representation of the orbit of an electron in a hydrogen atom, it is shown as an area; the electron could be anywhere within that area.
The following picture shows some examples of such electron orbitals. An electron could be anywhere within a given orbital at a given time.
- Therefore, the key point to remember is that the uncertainty in the position and the momentum (or velocity) of a particle become significant only for small particles like electrons and photons.
3. We can make the following statements about the location of such a “quantum particle” at a given time.
- The significance of this uncertainty is that we cannot say precisely where such a small particle to be found. We can only say that it should be located within a certain region and calculate the probability for it to be found at a given point within that region.
- But that does not mean “the particle is spread out in that volume”. At any given time, the particle is located at only one point. It is just that we cannot say precisely at which point due to the uncertainty principle.
I hope you can see the difference. Some people make the grave mistake of saying a quantum particle is “spread over space” just like a wave. That is grave mistake, and is a key reason why people have a hard time understanding quantum mechanics.
Any questions on these QM posts can be discussed at the discussion forum: “Quantum Mechanics – A New Interpretation“.