Quantum Weirdness

Quantum Weirdness

Or What the Hell is this Going On?

We all know that Quantum Mechanics is weird; weird doesn’t begin to explain what it really is, but all we can say is weird. Even physicists agree that Quantum Mechanics is weird. It all starts with a simple thought experiment; just put a cat in a box.

Take a cat and put it in a box along with a Geiger counter inside which is contained a bit of a radioactive substance whose atoms have a 50% probability of decaying, and 50% probability of not; in such a case where it does decay, it is connected to a hammer that will break a vial of hydrocyanic acid that will result in instantly killing the cat. Now, when this system is left all by its lonesome without any outside interference, the cat has an equal probability of being alive and dead. In Quantum Mechanics, any system is defined by a Psi-Function: and this describes the state of the system. So, in the case of this cat, the psi-function is in a superposition of the two possible states of the cat – dead, and alive. So yes, the cat is, in fact, both dead and alive in the box, in layman’s terms.

The only way to solve the problem is opening the box and seeing what state it is in; doing this constitutes a measurement – making an observation – and this collapses the wave function, causing the cat to be either dead, or alive.

So, what this actually implies is that a system exists in that particular state only after we observe it, or make a measurement.

Now, you could very well argue that this is absolutely absurd, and that’s not how reality works – you don’t need to observe something to make it exist in that state. But if we follow the Quantum Mechanical interpretation of the world, then that is how everything is.

Before we go on, lets define a couple of terms.

In Quantum Mechanics, the Observer is quite the same as a measurement apparatus; the act of making an observation is synonymous with quantum measurement, which in itself is difficult due to the Uncertainty Principle; and an Observable is anything that you measure.

In Classical Mechanics, you can very accurately describe the state of a system by stating its position and momentum. The quantum mechanical analogue to this is a quantum state, which is made up of several probabilities, but, unlike in Classical Mechanics, we cannot describe the state in terms of its position and momentum accurately; there is some inherent uncertainty in defining its position and momentum.

When we talk about Collapse of a Wave function, we mean that the function that describes the system has been found to be in one state, rather than any other, upon measurement. A system is described by a wave function, which could refer to any number of possibilities; think of a system before observation as a cloud of possibilities, it could be absolutely anything and everything. So when you make an observation, and see that it is in some state 1, rather than any of the other states, it is said to have collapsed into that state. This cloud of possibilities mentioned before is the superposition of states.

Quantum Mechanics is hugely successful because it manages to predict things very well; the mathematics of it work wonderfully, but the problem is the theory. The theory of Quantum Mechanics is incomplete, some would say, and this leaves a lot to interpretation and this gives us several interpretations of Quantum Mechanics itself.

The most famous interpretation of Quantum Mechanics is the Copenhagen Interpretation of Quantum Mechanics. This interpretation says that physical systems don’t have definite properties unless they’ve been measured, and hence causing the wave function to collapse. Niels Bohr and Werner Heisenberg developed this version between 1925 and 1927.

The Copenhagen interpretation is the most widely accepted and widely taught version, but it’s not safe from criticism. One of the major critiques of this interpretation is that it is a bit ad hoc; take the example of Schrodinger’s Cat that was mentioned before, and now add a human in the same box as the cat. Now, for the outside observer, the cat is in a superposition of states – that is dead and alive; but the human inside sees the cat to be alive. This leads us to having two different wave functions for the same cat, and you might very well be in a position to ask: “What the hell is this going on?”

Copenhagen has a nice work around; it now creates a distinction between the inside observer and the outside observer. There is something called a Heisenberg Slit, which is, in theory, an interface between he Quantum Mechanical system and the observer. So, the Copenhagen Interpretation says that if the two observers are on the same side of the slit, it’s a measurement. But if they’re on either side, then for the one on the same side as the cat, it isn’t considered a measurement.

What this basically boils down to is the seventh commandment of animalism in Animal Farm. At the beginning, the pigs say, “All animals are equal.” But later, the pigs amend that (and others) to make way for their “law breaking”: “All animals are equal, but some are more equal than others.

Another major critic of the Copenhagen Interpretations was Einstein himself. Einstein, Nathan Rosen and Boris Podolsky published a paper that came to be known as the Einstein-Podolsky-Rosen (or EPR) paradox that states that Quantum Mechanics is an incomplete description of reality.

The paper stated that this interpretation was incomplete and hence there is a possibility of a more complete theory being developed in the future. It states that if Quantum Mechanics were a complete description, then there must exist some local hidden variables to help account for the some of the other, inaccessible variables.

In what theorist Sean Carroll calls the “most embarrassing” poll in the history of physics, physicists attending a conference called Quantum Physics and the Nature of Reality were asked which interpretation of Quantum Mechanics they subscribe to and 40% said that, despite its many pitfalls, flaws and its ad hoc nature, they subscribe to the Copenhagen Interpretation; the rest couldn’t find an alternative theory to follow.

Another way of looking at Quantum Mechanics is the Many Worlds Interpretation. Taking the example of the famous cat, since it has only two possible states, reality splits into two – one where it is alive, while another where it is dead. So, we have two universes created, one in which the cat is dead, another where it is alive. The reason this isn’t that big is because it implies that the whole universe is defined by a single wave function, which is a hard truth to digest. But this interpretation, as with many other substitutes for the Copenhagen Interpretation, create more problems than they hope to solve.

Now, one of the biggest flaws of the Copenhagen interpretation is of a more existential nature. As mentioned before, the reason, according to this interpretation, that anything exists is due to observation. So, that begs the question: How do we exist?

Common sense dictates that if this were, truly, an accurate representation of reality, then something must have observed the original system, to cause a collapse into our state – the one in which we live, breathe and exist. We simply could not exist unless some measurement had been made to allow the wave function that described our universe to collapse.

Who is observing us? What caused the wave function that described our universe collapse?

Short answer: No clue.

Long Answer: Not the slightest idea.

So, really, what the hell is this going on?

Holding Back Gravity

(This is something I wrote a while back for my University)

Take a look at the night-sky and what do you see? Stars, constellations, a moon, the occasional planet, maybe a shooting star, but everything else is dark. Theory and several observations suggest that the Milky Way, the galaxy in which our humble solar system lies, has millions and millions of stars. Not just that, we have observed several other galaxies with millions of stars. Then, one can ask, why do we not see all, and just a handful? If the universe was static, and infinite, as many believed it to be, then the night sky should be bright and full of wondrous stars, rather than dark abyss that we see. This contradiction between theory and observation is called the Olbers’ Paradox. This Paradox has many solutions, as is standard for paradoxes. Many of them are absurd, as is expected, but I shall focus on exactly one – The Inflationary Model.

Hundred years ago, Albert Einstein was formulating his General Theory of Relativity and the equation he formulated described a universe that is constantly expanding. At that time it was assumed that the universe was static, and not expanding, so Einstein introduced the Cosmological Constant, denoted by Λ (Greek: Lambda) to counteract this expansion. Around the same time Edwin Hubble discovered through observations of galaxies that the universe was expanding, as described by Einstein’s original equation sans the constant. According to George Gamow, Einstein called his failure to recognize the accuracy of his equations the “biggest blunder” of his life. Many assumed the cosmological constant to have a zero value, and this led to a conclusion that the expansion of our universe was decelerating. But observations of galaxies showed them receding away from us at an accelerated rate. This led to the cosmological constant to be brought back, and this constant was said to have a positive value to account for the accelerated expansion.

So, why is the universe expanding at an accelerated rate, and what is resisting and counteracting the attractive nature of gravity all around us? The answer is that something is pushing it and that something is Dark Energy. Dark Energy is this hypothetical “force” that exists in the form of negative pressure causing this accelerated expansion and works against gravity. This constitutes the so-called ΛCDM – Model (Lambda- CDM; and CDM is an abbreviation of Cold Dark Matter), which takes into account Dark Energy as well as Dark Matter.

Dark Matter is that hypothetical substance that occupies a large amount of space in our universe, and it is used to explain the gravitational effects (like gravitational lensing) of very large-scale structures, which cannot be explained by ordinary matter. Cold Dark Matter is a form of Dark Matter, which travels at speeds much smaller than the speed of light (hence the name cold). Dark Matter is described as “non-baryonic” that is to say that it is made up of elementary particles that are not protons or neutrons; dissipationless – that is it cannot cool itself by radiating photons; and collisonless – that is it interacts with each other, and ordinary matter through gravitational forces or the weak force, but not directly.

It is estimated that the total energy density in our universe has the following distribution: Dark Energy – 70%, Dark Matter – 25%, and Ordinary Matter (stuff we are made of) a mere – 5%.

The ΛCDM – model includes a single originating event – the Big Bang or a Singularity where there was no bang but a sudden and unexpected appearance of an expanding space time with a temperature of around 1027 K. The very next instant, about 10-29  seconds after it came into existence, it started expanding at an exponential rate and this is what is known as Cosmic Inflation. For the first several hundred thousand years it was very hot (around 10,000K) and this is detectable through the Cosmic Microwave Background (CMB) Radiation. Cosmic Background Radiation is what is observed in the microwave spectrum in the dark between galaxies where there are no stars.

This Inflationary Model tries to provide a solution to The Horizon Problem. Imagine standing somewhere in space. To your left, at about 10 billion light years away (1 light year is the distance traveled by light in a year) is a galaxy. To your right, again at 10 billion light years is another galaxy. Armed with the knowledge that the universe is 13.8 billion years old, one would assume that, since nothing can travel faster than the speed of light, the two galaxies would not have had any opportunity to communicate with each other as light could not have traveled sufficiently far to reach the other galaxy to transfer information. Here “information” refers to some form of physical interaction.

Now, let’s take something basic like heat transfer. The Zeroth Law of Thermodynamics states that heat from a hot body, keeps flowing into a cold body until they reach thermal equilibrium, and only if they are in thermal contact. That is heat flows from a hot body, to a cold body until they are at the same temperature and the bodies would have to be in some form of physical contact with each other, without which no heat transfer can happen.

The two galaxies that were mentioned before have never been in physical contact and light wouldn’t have travelled fast enough to transfer any information. So, one would expect these galaxies, and the whole universe to have different properties. But this is contrary to the observations made.

Our Universe is highly isotropic, meaning it has roughly the same properties throughout; and it is homogenous, which means that matter is spread quite evenly throughout. The CMB radiation that fills the universe is roughly the same temperature: 2.728 K. The difference in temperature is extremely minute and only recently has human kind developed the technology to detect these differences.Inflation helps resolve this problem.

The universe, at the very beginning was very small, very dense and was causally connected. It is at this stage that all the properties evened out and then there was a very brief period of exponential expansion, which led to an increase in the size of the universe by a massive factor. This didn’t eliminate any irregularities, but greatly reduced them.

This theory of Inflation (originally proposed by Alan Guth in 1980), though it manages to solve several problems that have plagued the field of cosmology, was not welcomed with open arms by everyone. Roger Penrose, a world renowned physicist, is one of the most vocal critics of this theory. He says that for this theory to be a valid explanation, the originating events must have had highly specific initial conditions, and this is otherwise known as the Fine-Tuning Problem.

Andrei Linde of Stanford, another major contributor to the Inflationary Model, proposed something called Chaotic Inflation, a more general theory of inflation (also called Eternal Inflation). He is also responsible for proposing the theory on how matter was created (in a process called reheating that took place right after the inflationary stage). Linde made a prediction that the inflationary model of the universe would inevitably lead to the creation of a multiverse. He suggested that the inflation will go on, in certain parts of the universe, endlessly and this will lead to creation of pocket universes that will be independent of ours. So, our universe, instead of being like a balloon, will be like a huge fractal.

The ΛCDM – Model and the Inflationary Model try to provide an explanation as to why the night sky is dark, instead of bright. The acceleration of the universe is causing something known as redshift. To put it simply, redshift is what causes the emitted light to increase in wavelength, hence pushing it beyond the visible spectrum and into the microwave range, which our eyes cannot register. This redshift causes the energy to reduce by a factor of 1100 and so the light fades into the Cosmic Background Radiation. This causes the night sky to look dark, and not bright, as theory would suggest. Hence providing one of the most beautiful, and plausible explanations to the Olbers’ Paradox.