The physics world as of today is in chaos. Theories, which were once glorified for their accurate explanations, are now battling the anomalies that are being fired at them by the universe. Be it the fine structure constant or the magnetic dipole moment of electrons, with newer ways of observations comes newer predictions, which demand a drastic change in the existing explanations. This time it is the very famous Hubble constant which is playing its game.

Hubble constant, what is it?

In the1920s, Edwin Hubble, who had just found a new way to estimate the distance of cepheids (special stars whose luminosity rises and falls regularly) from Earth, noticed that everything in the universe moved away from Earth and the speed at which they were moving out increased with their distance. That means that farther away an object is, faster it would be moving. This would mean either of two possibilities – Earth was the centre of the Universe, or the entire Universe was expanding. Hubble theorized that it was the Universe expanding, and gave the very famous constant which still bears his name.

The constant problem with the constant…

Ever since Hubble gave his constant, it has always been a topic for debate. This is because Hubble has errors in his data and had derived the constant which was approximately 10 times the actual value. And ever since then, new methods have been devised to accurately predict the Hubble constant. And to everyone’s surprise, every method gave entirely a new number. No two methods had matching readings. 
One method is to work on the existing datasets on cepheids and accurately calculate the constant. It has been worked up and the value came to be 50,400 mph per million light-years (73.4 km/s/Mpc). 

Astronomers also devised a new method to determine this constant – the cosmic microwave background, CMB. CMB refers to the radiation emitted during the Bigbang. This has all the information about the initial universe. The Planck satellite of the European Space Agency – ESA has spent 10 years in gathering data about the CMB. The calculated value of the constant from this data comes to be 46,200 mph per million light-years (67.4 km/s/Mpc).

These two numbers may look close, but there is a very huge difference, even after considering their error margins.

If the value calculated from cepheids is correct, there is something entirely wrong with our perception of the universe. This would mean that we need to introduce new and exotic physics into our models of the universe. 
If the value from Planck satellite is correct, then astronomers have been always calculating distances in space entirely wrong.
Either of the two possibilities is scary and requires us to change our perception of the universe.

A possible explanation for this anomaly…

There is one more thing this could mean. The universe’s expansion may be accelerated, and the universe is expanding faster now than it was earlier. But this would still require radical transformations of our theories. Many possible explanations have been provided for this anomaly, let’s have a look at few of them.

1.Decaying Dark Matter:

Dark Matter is one of the fundamental ingredients of the universe, but very little is known about it. So the very first thing to get tampered is obviously this. One of the theories proposed says that the dark matter particle decay into a lighter particle and something called the dark photon. This causes the gravitational force exerted by the dark matter to decrease with time and hence accelerating the expansion of the universe. 
But the very important drawback of this theory is that for explaining one discrepancy, we are introducing two new unknowns, the lighter dark matter particle and the dark photon. And this is the reason why such a theory makes physicists uncomfortable.

2.Variable Dark Energy:

Dark Energy is another mystery which was introduced to resolve the existing mysteries of accelerated expansion of the universe. Theories constructing models for varying dark energy could explain this discrepancy. They do this by stating that the excess of energy present in the early universe provided pressure required to accelerate the expansion. And that is the reason why we see an accelerated expansion today. 
But again no perfect model is present for the dark energy, thus any changes would again lead to much more discrepancies.

3.Modified Gravity:

In the standard method, all of the universe’s energy and matter content is fed to Einstein’s equation and the universe’s fate is determined. But some people have tried to modify the recipe itself instead of modifying the contents of the recipe, i.e. tried to modify the theory of gravity itself. William Barker, PhD student at the University of Cambridge believes that a theory of modified gravity could help in explaining this anomaly. The modified gravity could behave as if the universe had excess radiation in the early stage which added to outwards pressure, accelerating the expansion of the universe  In the preprint, the authors acknowledge that the model requires more analysis.

This anomaly could be an inadequacy in our observations, or it might be a flaw in our theories, all we can do right now is wait and watch what will be the fate of the universe. But cosmology never stops entertaining us, nobody knows what the universe has in store for us. Anything could be anticipated any day and no surprise is really a surprise because uncertainty is the only certainty in the universe.

The story of quantum mechanics is a very weird one. Because that is how the quantum world is, totally counter-intuitive, absurd, and nonsensical. The reason why it is so is that our brains are adapted to understand the world as we can see it, and whatever we see is only the classical approximation. Humans tend to search for logic in a statement based on their experiences. The quantum mechanical absurdity seems unreasonable because there is no way we can experience these in our classical perception. Spin too is one of such phenomena we stumble in understanding.

The Story of Spin

In the initial formulations of quantum physics, things were relatively easy. You wanted to explain an electron, just take the mass and charge and you had the complete description of it. Nothing else was required to explain an electron. But unfortunately to the physicists, the tables got turned when Stern-Gerlach performed their silver atom experiment.

What they did was heat some silver atoms in an oven, and collimate the silver atoms from the oven forming a single beam and then pass it through a magnetic field, say in the z-direction. 

To oversimplify the model, the silver atom is entirely neutral, and it has a magnetic moment which depends only on the outermost electron.
Since the orientation of all the atoms is random, the expected outcome is a spread along the z-axis with a gaussian distribution. This is what anyone with their right minds would expect.
But the result totally revolutionised the world of physics. The beam had split exactly into two parts. About half of the atoms had gone upwards and the other half downwards.

This could only mean that the electron had an angular momentum of its own causing a magnetic moment. This angular momentum was discrete, i.e only in two possible directions, either upwards or downwards, and nothing in between. Since this angular momentum was as if the electron was spinning independently about an axis of its own, it was called the spin. This spin can indeed exist in any possible direction, but upon measured, we get only one of the two possible directions.

By then another physicist, sir Wolfgang Pauli, while trying to explain the structure of an atom and the states of the electron, gave his exclusion principle and also stated that the two electrons possible in a given orbital had opposite spins thus making them non-identical and hence allowing the exclusion principle to be satisfied. 

Click here to read more about the exclusion principle.

What is it and Where does it come from?

Spin is the property of all particles just like mass and charge are. Angular momentum is a conserved quantity, and so is spin. Also, the total angular momentum for a system is not conserved unless we count in the spin. This is the reason spin is associated with the intrinsic angular momentum of particles. It is also responsible for the magnetic moment of these particles. 

The mathematical description of quantum mechanics in the early stages had no signs of spin. This is because initially, it was as if it had no reason to exist mathematically. It was something that was introduced only to explain the phenomenon like the Stern-Gerlach experiment, or the states of electrons in an atom and so on.
But when P.A.M Dirac amalgamated relativity with quantum physics, it was soon noticed that spin was an essential requirement of the relativistic quantum theory. It arises from the rotational symmetry of nature.

Spin and Symmetry

As stated above, the spin arises out of the rotational symmetry of fields in nature.

Consider a scalar field, where every point in space is associated with a scalar quantity, or to put simply, with a number. If you take the field at any point and rotate it by any angle, the number at that point does not change. This scalar field is called spin-zero field. The Higgs field is an example of the spin-zero field.

The vector field has every point in space associated with a vector. Now if you take a vector at some point and rotate the coordinate system, the components of the vector do change. But a rotation by 360° brings back the original vector. Thus the vector field is invariant under rotation by 360°. This vector field is called a spin-one field. The electromagnetic field is an example of the spin-one field.

There are fields in nature which are invariant under rotation by 180°. These are called tensor fields, with each point in space associated with a tensor. These tensor fields are called spin-two fields. The gravitational field is a tensor field and hence is a spin-two field. 

From QFT, every particle has an associated field and vice versa. So the particle corresponding to the scalar field will have zero spin, the one corresponding to vector field will have spin one, and the one corresponding to the tensor field will have spin two.

Thus the Higgs Boson is a spin-zero particle, photons spin-one, and gravitons spin-two. 

What we can notice here is that spin-one field is invariant under rotation by 360°, spin two is invariant under 180°, and so on. So from the same pattern, it is obvious that a spin “n” field would be invariant under rotation by (360/n)°. Thus a spin ½ field should be invariant under rotation by 720°. Such a field is called a spinor field, with every point in space associated with a spinor. A spinor is a “weird” type of vector, which upon rotation by 360°, gets reversed. The electron field is a spinor field, invariant under 720° rotation. Thus the corresponding electron has spin one half.

The Physical Meaning of Spin

Most people believe that the electron is actually spinning about some axis to generate the spin angular momentum.
This is entirely wrong because the electron is considered a point particle, and for a point particle to generate a finite angular momentum, it should be spinning infinitely fast.
If you argue saying that electron is a wave packet with some finite size, say the Compton wavelength,  then too, the electron’s surface must be spinning at a velocity greater than that of light. So the intuitive of an electron spinning is a wrong one and should be discarded.
But what about fields, fields can have angular momentum. And any particle is an excitation of its underlying field. So a possibility is that the spin of particles as we see it could be, in fact, the angular momentum of the corresponding field. The angular momentum carried by the electron field could be present to us as the spin of the electron and so on.
But all of this is still only a hypothesis. No concrete idea is present for the physical meaning of spin. That is why it is not a wonder that it is one of the most confusing aspects of quantum mechanics.
To conclude, it is best to quote Feynman,

” I think I can safely say that nobody understands quantum mechanics.
If you think you understand quantum mechanics, you don’t understand quantum mechanics.”

Quantum physics is a jungle of paradoxes. Any direction you go you end up with a paradox, waiting to pounce on you, its claws ready to slash through your common sense, making you wonder what is actually real, and ridiculing at your inability to comprehend it. Most of these paradoxes are not really paradoxes but they just showcase our inability to perceive quantum physics. Be it the Schrodinger’s cat paradox or any other, ultimately they have an explanation. Generally, we oversee and ignore it, until one day when we finally realize that we are completely wrong in our perception of it.

Quantum Zeno effect is a very interesting consequence of the mysterious quantum world. Before diving deeper into the effect, have a look at the classical counterpart of the same.

The Zeno Paradox:

Zeno of Elea was a Greek philosopher. He gave paradoxes which went against one’s common sense and made one question about the reality of his perception. One of his famous paradoxes is the arrow paradox:

If everything, when it occupies an equal space, is at rest at that instant of time, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless at that instant of time and at the next instant of time but if both instants of time are taken as the same instant or continuous instant of time then it is in motion.
— as recounted by Aristotle, Physics VI:9, 239b5, Wikipedia.

Zeno states that for the motion to occur, the object must change its position which it occupies. For an arrow in flight, at a given instant of time, it can not be moving at all because time is not elapsing. Hence it must occupy the same position always. Thus if everything is motionless at a given instant, and if time is composed of many instants, then no motion must be possible.

In short, he states in his paradox that a flying arrow that is being observed can never fly.

This, even though it is counterintuitive, it is only a vague attempt to crack open our common sense. Ultimately it is just an argument and not a firm physical statement.

The Quantum Zeno Effect

This has inspired a beautiful effect in quantum physics, the quantum Zeno effect: An observed water pot in the quantum world never boils. Or to be put in a better way, a quantum system cannot undergo any changes while it is being observed.

This is not a paradoxical statement like Zeno paradox but is actually an observed and proven quantum effect. But to understand this paradox, you first need to know what is meant by observation in the quantum world, and how states evolve with time.

Quantum states and their evolution:

Consider a quantum system, which upon observed or measured gives one of the two possible values, either A or B. The state of the system is represented by |𝜓〉. Let us say that the system is in state |A〉if the measurement gives the value A and it is in state |B〉 if the measurement gives value B.

Quantum Superposition, which is the heart of quantum mechanics states that at any time, the system is in a superposition of all possible states. Mathematically it can be written as  |𝜓〉= C₁|A〉+ C₂|B〉, where C₁ and C₂ are two complex numbers, subject to the condition C₁² + C₂² = 1.

The system which is in the state |𝜓〉, when measured, wavefunction collapses. The collapse of wavefunction means that the system which is in superposition goes back to one of the pure states |A〉or |B〉. Thus, upon measurement, the system goes back to state |A〉 with probability |C₁²|, and to state |B〉with probability |C₂²|.

If you start with the state |𝜓〉=|A〉, the energy content of the system drives it towards superposition. So at a later time t, the system will be in state |𝜓〉=C₁(t) |A〉+ C₂(t) |B〉. This is how systems evolve in quantum mechanics.

The Zeno Effect

Now coming to our Zeno effect, let’s take a radioactive atom. This atom can be in either of the two possible states – Decayed or Undecayed. Let’s represent the decayed state by |D〉and the undecayed state by |U〉. Once we observe the system, we see either the atom is undecayed (in state |U〉) or it is undecayed (in state |D〉).

Initially, we take an undecayed atom. The atom is in state |𝜓〉= |U〉. Since the atom has some energy, it evolves continuously, ending up in the superposition state |𝜓〉=C₁(t) |U〉+ C₂(t) |D〉. Thus a measurement at a later time will give a decayed atom with probability |C₂(t)²| and undecayed atom with probability |C₁(t)²|.

Suppose initially the radioactive material was in an undecayed state, i.e C₁(t=0) =1and C₂(t=0) =0 . Now if we make a measurement on it after a very short interval of time t, then the system is most likely to be in the same undecayed state. This is because a very short period of time has elapsed and the system has not evolved much, meaning C₁(t) ≈1and  C₂(t)≈0.

So, each measurement you make will take the atom back to its undecayed state restarting the whole process. Which means that continuous measurement at small intervals of time will restrict any changes in a system. Even a radioactive atom having a mean life of 5 seconds, can be prevented from decaying for as long as we want, for minutes, hours, days or even years.

So indeed in the quantum world, observed water pot never boils. A system can never undergo any changes when it is being observed continuously at short intervals of time. Even though it seems to be totally weird and wrong, it is indeed a physical effect which has been proven experimentally. But this effect requires distinguishable quantum states, and this is not the case in the classical world, where all states are continuous. Thus this effect is not observable in the classical world.

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