Quantum Mechanics
Sara Earnest, Alisha Gosain, Daniela Nemi, Savannah Spencer, and Ava Tillmann
Have you ever wondered how light works? Does physics perplex you? Well during these past two weeks, at Girls Talk Math, we learned about vectors, energy, polarization, photons, quantum entanglement, and waxed philosophical behavior of photons in polarizers as well.
Trigonometry is a large part of the foundation for quantum mechanics problems. Our curriculum contains problems relating to initial and final light intensity after being polarized. Polarizers have specific transmission axes, which requires trigonometry to figure out how much light is able to pass through at specific angles at which the polarizer filter is rotated.
Quantum mechanics, put simply, is the mechanics of matter and light in terms of the very small: thinking of things on the atomic or subatomic level. But before we could get into the quantum-specific details, we first had to understand some basic concepts in physics. The first of these was vectors and trigonometry.
We started out by learning that vectors are quantities that have magnitude and direction, which can also determine the position of one point in space relative to another. After learning this we began to apply the vector rules. For example, vectors which are moving in the same direction add, whereas vectors moving in the opposite direction subtract. As seen in the image the first two vectors have a magnitude of 5, and because they’re both moving to the right, both their magnitudes are added—magnitude is the amount of force that a vector has. However, as seen in the image, the 2nd row of vectors demonstrates two vectors moving in opposite directions. Because both their magnitudes are 5, but one vector is moving to the left and the other one is moving to the right, then they will cancel out creating a net force of zero. The net force is the resultant of adding or subtracting all the force vectors.
Now why did we learn about vectors? Simple, vectors are extremely important for many important concepts in physics. For example, Energy! Energy can be a vector or a scalar, thus why it was important for us to understand vectors. There are different types of energy, such as potential, kinetic, and elastic potential energy. However, energy as used in waves is kinetic, when the wave is in motion. Additionally, a result that follows from the mathematical theory of waves is that the energy contained in the waves is proportional to the square of the amplitude. This holds true for the electromagnetic waves and material waves. The energy formula can be denoted as:
Energy = |E₀ | ²
For an electromagnetic wave equation for energy can be given by:
Energy = E₀ sin (ω t)
However, the energy relates directly to the intensity of light.
A photon is the smallest discrete sum or quantum of electromagnetic radiation. It is the essential unit of all light. Photons are dependably in movement and, in a vacuum, travel at a consistent speed to all eyewitnesses of 2.998 x 108 m/s. This is normally alluded to as the speed of light, indicated by the letter c.
The basic properties of photons are as follows:
Photons have no mass, and never rest, so they can only exist in as state of motion. They also are not made up of smaller particles, which means photons are “rudimentary particles”. They are neutral, having no electric charge.
Light also has wave particle-duality. This means that they display qualities of both a particle (exemplified by photons) and a wave. The wave-like property of light allows it to be polarized in different directions, and allows polarized sunglasses to be effective by blocking out a specific polarization of light waves, making the light that hits your eye less intense. This prevents blinding glare when you’re driving.
Whenever you see a Polaroid picture, do you ever wonder what causes the tiny photos to come out so well, despite the amount of sunlight in the sky? If, so, you’re in luck. When trying to block the sun, polarizers will be your best friends because polarizers are actually filters that allow only specific light waves to pass through them, leaving both your pictures and eyes unaffected by those annoying other light waves. Wait a second, eyes? What do polarizers have to do with my eyes? You see, one of the main products that incorporate polarizers are sunglasses. Sunglasses, similar to the Polaroid camera lenses, block out that unwanted light because those polarizers are hard at work removing polarized light.
The last topic we learned about was quantum entanglement. Which, at first glance, sounds very complex. Probably because it has “quantum” in the name. However, the explanation can actually be relatively simple. All you need is some socks and a little imagination.
The analogy is like so: imagine you know that I have a bunch of pairs of socks in my sock drawer of various colors. Also imagine you catch a glance of the sock on my right foot and see that it’s green. By that knowledge, you know that the other sock on my left foot must also be green. My left foot could be any distance away, but you would still know that it must be green. This is similar to how entangled photons behave. When two particles are entangled, the quantum state of one cannot be described independently of the other, no matter the distance between them. Similar to the sock analogy, if you determine something about one particle in an entangled pair, you know that information pertains to the other particle regardless of where it is spatially. If you observe something about an entangled particle, the other will instantly change its properties as well.
Quantum entanglement is interesting as well because it appears to break a fundamental rule of physics, which is that nothing can travel faster than light. Entangled particles, however, seem to instantaneously pass information back and forth regardless of their distance from each other. It is a phenomenon that can relate to many other sci-fi sounding concepts. Einstein even called entanglement “spooky action at a distance”. One recent breakthrough has to do with the fundamental question in entanglement which is how big in scale can we go? Usually entanglement can only be observed in tiny particles, but recently scientists have managed to entangle objects visible to the naked eye (i.e., not microscopic).