Massive and Mass-less

Krish Ramkumar

4/15/2015

                                                       

Why does the Higgs field provide masses to only certain particles in the standard model? For instance, why does the photon not have any mass? Is the Higgs field constant throughout the universe?

These are the primary questions that I want to address in the following blog. I must specify that since I have very limited mathematical knowledge in the area of QFT, My final hypothesis is built purely on conjecture.

Before I write about my hypothesis, I feel the need to consolidate the present theories associated with the above questions for the sake of continuity.

The standard model of particle physics has established a strong framework to classify particles existing in the universe and has narrowed down their respective functions.

There are two main families of particles namely, fermions and the bosons. All elementary particles fall under the family of fermions (Quarks that make up the protons and neutrons, leptons (electrons, neutrinos etc)) and the bosons are carriers for the 4 fundamental forces (EM, G, Weak nuclear, strong nuclear) we see in the universe. In order for these forces to be transferred from point a to point b, some kind of mediator is required. Bosons act as mediators. The electromagnetic force is carried across with the help of photons, the weak nuclear force through W&Z bosons and the strong nuclear forces with particles called gluons. We are not entirely sure about the force carrier associated with the gravitational force at the moment. Although physicists think that a mass-less and charge-less boson particle called ‘gravitons’ might be particles to carry the ripples (gravitational waves) in space-time. This will make the standard model more complete.

 Each of these particles has some mass or no mass and the reason they inherit this mass is due to the Higgs field mechanism. It has been established by great minds and partial observations that right after the big bang, the universe started to cool down and a field (Higgs field) was switched on giving rise elementary particles with their set values. But what was the mechanism behind each of these particles getting their respective masses? What went on when the Higgs field was switched on? These questions were answered by looking into the effects of the fundamental forces.

While the EM force and the gravitational forces weaken gradually with distance from the source (Inverse sq law), the nuclear force disappears suddenly within a short distance. Why does the nuclear force behave differently from the other two fundamental forces?

The reason behind this conundrum is the Higgs mechanism and the mass associated with the force carriers of the respective forces.

At this point I would like to paraphrase a great analogy put forth by physicist Sean Carroll. The following analogy makes this profound problem more understandable.

Think of a lantern in the dark. As the lantern moves away from you the light from the lantern weakens gradually following the inverse square law thereby validating what happens in the case of gravitation and EM. But if you think of the lantern as a source of nuclear force, the lantern quickly disappears within a short distance. How does this happen? It might happen if there is a shutter around the lantern that completely shuts of the light from escaping (gluons that mediate the strong nuclear force interact such that they create a shutter around the source) or if the air around the lantern is filled with dense fog which shields the light from propagating thorough the air. This fog is the Higgs field. The Higgs field prevents the carrier of the weak force to propagate by providing resistance (inertia) thus giving mass (a measure of resistance on an object in motion) to the force carriers (W&Z Bosons).

But how does the Higgs field decide to provide resistance to the W&Z bosons and not the photons (or gravitons) is the question of interest as stated in the beginning?

The Higgs field seems to have no effect on certain particles thus allowing them to move freely and are unperturbed under the influence of the field. This goes to say that the field provides zero net resistance to these particles thereby making them mass-less. Under the assumption that the Higgs field is a constant field throughout the universe, the particle, in my opinion must provide some kind of “counter resistance” or anti resistance that enables it to balance the resistance offered by the field. Working with this logic, massive particles should have “counter resistance” that does not balance the resistance of the field.

Since we measure the quantity of a field by its effects and not the field itself, we could measure the effects of the Higgs field by measuring the effects of the mass-less particles moving through it. The different masses of particles might be due to the amount of some kind of “exotic anti- resistance” offered by the particle itself on the Higgs field and not the Higgs field alone. Perhaps this will bring us closer to dark energy?

The Beginning

                                            The Beginning 

The superposition principle in quantum theory states that if a system is observed to be in one of several states, then it could exist in a combination of states at one given time. The Schrodinger cat experiment illustrates this principle.

In this experiment ,the cat is placed in a sealed box along with a radioactive substance, some poison and a Geiger counter.  Once the radioactive substance has decayed, the counter detects it and unleashes the poison in the box which eventually kills the cat. But the beauty of this thought experiment lies in the radioactive substance. Since the decay is a random process, it is not possible to predict the process and hence the actual state of the cat. If we analyse this experiment, we realize that before we observe the cat, the cat can be in two different states both dead and alive at one given instant of time. It is only after the observation that we conclude with one of the states.

This is a great experiment that allows us to incorporate the quantum theory for large objects such as the cat and the observer in this experiment lies outside the system (box).If the observer lies inside the system under scrutiny, the integrity of the experiment is automatically destroyed. From my understanding about system and observer, my being inside the system will bring in extra variables which in turn will affect the original experiment to start with.  

Although this experiment enables us to think about macroscopic objects in terms of quantum states, if the system is the entire universe (Which we are a part of) becomes a problem since we are inside the system.

Several years of mind bending experiments from great minds and classical logic suggests that observer must be outside the system under study to keep it consistent and not ruin the integrity of the original system. Since we do not know what is outside the observable universe (for now) i.e. beyond 13.5 billion years of the universe or in other words- The Big Bang, logic dictates that we need a model that allows for the observer to be outside the system and yet inside.

The model from my amateur understanding on the subject should look something like in the figure below.

 This model suggests that quantum fluctuations in a black hole could result in a separate cone that is outside the realms of the present universe (maybe another dimension) and yet originating from the same universe. This way we, as observers ,are outside. The objective of this model is to understand the mechanism of the universe before the big bang in terms of quantum states by observing black holes. Although studying the black hole for such clues is a task that is unimaginably difficult. Perhaps the universe that we live in resulted from one such quantum fluctuation inside a black hole. We would never know.

I would also like to emphasize that the above fig does not denote a geometrical model of the universe but built on conjecture.


References - Three Roads to quantum gravity- Lee Smolin 
Krish Ramkumar

The boundless set of concentric spheres

The boundless set of concentric spheres

The Big bang theory, as we know it, seems to work beautifully in explaining the present universe and the origin of the observable universe. We tend to use the word observable rather loosely but it does have a subtle importance to it because the universe is very different from the universe we observe, in my opinion. The big bang theory takes us back to the beginning of the observable universe and the age is estimated to be around 13.7 billion years. This estimation comes from the fact that the radiation emitted after the big bang has taken this long to cool to this present temperature that we see.

When we look deep into the sky and look at a star X which is Y light years (distance travelled by light in one year) away, we are looking at the star, Y years ago in the past. This star might not exist now for all we know. When we look at the sun we are looking at the light that was emitted 8 minutes ago. When I look at the screen in front of me, I am looking at it a billionth of a second in the past. Our senses are such that we need a medium to observe and that medium is light. The very innate property of light having a cosmic speed limit restricts us to view the universe only in one direction, the past.

Past, present and future might be coexisting in different frames of references. For instance, my past in space-time can be the future that is yet to be unraveled by an inhabitant in some other part of the universe and the future that we unravel as we travel through the passage of space-time might be overlapping with another inhabitants’ past.

From the scientific findings, we have come to a consensus that the big bang originated from some primeval particle that was extremely dense. This particle exploded giving rise to the universe that we have come to know of. However, it is not clear how this particle came into existence. Some of the greatest minds have suggested that it was due to random quantum fluctuations. If this were the case, taking into account the expansion of the universe, the model in my opinion should be a collection of concentric spheres with the origin as the primeval particle or the big bang. According to this model, the observers are on the surface of the sphere. The sphere that we exist in would be the sphere with a radius of 13.7 billion light years. It would be impossible for someone to travel from one point on one of the concentric spheres to a diametrically opposite point because by the time we get there the sphere would have increased in size.General relativity,however allows that trough wormholes. There also might be spheres that exist beyond the realms of the present sphere and it would also impossible to get to that sphere because we always look into the past as we look farther into the cosmos. Perhaps the sphere is some sort of a cosmic snow globe which allows /gives us the illusion of travelling far and yet never reaching the edge of the so called universe. However we can reach spheres that have smaller radii than ours but inhabitants on the smaller sphere may have no idea that we even exist since we would be beyond the realms of their observable universe. Similarly we might not know about any inhabitants that might exist beyond our sphere. This is why the term observable becomes so important. The universe that might exist beyond the observable universe can never be observed just like the concept of infinity.

Krish Ramkumar

Free Will

   Krish Ramkumar                                                            

                                                                Free Will

The ability of species to make choices based on consequences could be simply called as free will. Is this free will really a choice that we make or is it simply an illusion? There is no way to know. Free will to me seems like a deterministic approach to reality. But there are quantum uncertainties that are present at every nook and corner of the universe. We as humans, I think can be sure that the free will is simply a decision that originates in our brains. We also know that the brain consists of several neurons that are ultimately made of electrons. After all, every entity in the observable universe is made up of electrons or quarks to be more precise. Let us for now take electron as the elemental particle. From quantum mechanics, we deduce that these particles are highly uncertain and it is impossible to pinpoint their path. To put it simply they are random and unpredictable which makes them non-deterministic. When the most elemental process of making decisions is based on such uncertainty, why is it that we think free will as deterministic? This aspect of reality really confuses me because it seems like the very act of decision making is completely random. If this is the case, the universe by itself is completely random. 

Infinite or finite

Krish Ramkumar

2/18/13

Is the universe infinite or finite?

This question has been the age old conundrum in all of theoretical physics and philosophy. What was there before the big bang? Although string theorists have come up with a theory that explains the origin of the big bang, the question “what was there before that” remains unanswered. If the universe were in fact finite, mankind might be able to arrive at a universal theory that explains everything through science. But, What if the universe were infinite? The fact that the universe is never ending seems extremely dissatisfying and unconvincing to me.

On the contrary, mankind did not create the universe which implies that the universe need not function according to the laws of physics or under any other philosophical theory for that matter. We are insignificant subjects that are merely trying to; in a way decipher GOD’s own cosmic code. Whether this is really possible or not, I don’t have a clue. But from the aspect of theoretical physics, we certainly are getting closer to cracking “some” code.

For all we know, the universe might actually be infinite, albeit unconvincing. To get a feel for this idea, let us look at 2 points x and y separated by a “finite” distance. We all know from basic logic that there are infinite number of points between points x and y. The word finite loses its meaning when we talk about distance between two points. The entire number system by itself was created by mankind so that we didn’t have to deal with the concept of infinity. For instance take the famous Achilles and tortoise paradox. Achilles and tortoise agree to race with tortoise getting a 10 m head start. As the tortoise reaches the 10 m mark, Achilles also begins to run. Since Achilles is 10 times faster than the tortoise, by the time he reaches the 10 meter mark, the tortoise has travelled only 1 m ( tortoises’ speed is 1/10^th that of Achilles). When Achilles reaches the 11 m mark the tortoise also has travelled another one tenth of a meter (11.1m) and so on. As the infinite series continues, it is impossible for Achilles to catch up with the tortoise.

The most elemental quantity in the universe seems to be infinity. If there could be an infinite number of points between two arbitrary points x and y then why can’t the universe at large be infinite.

Achilles eventually winning the race makes this one of the most interesting paradoxes. Infinity as a concept could be the fundamental idea behind the universe. 

The Claim

Krish Ramkumar

Claim:

What if the universe was to contract, or goes in the direction of the big crunch, is the arrow of time then reversed for the inhabitants in that universe?

Stephen Hawking argues that the inhabitants in this particular universe will have their psychological arrow of time (How we perceive time) reversed and that it points in the same direction as the thermodynamic arrow of time as the thermodynamic arrow of time essentially determines the psychological arrow of time.

(Note : some parts of this blog are repeated from my previous post for the sake of completeness)

According to the 2^nd law of thermodynamics, entropy (randomness) increases with time and the arrow of time points in the direction of higher entropy. If the arrow of time in the present universe is in the direction of higher entropy (unordered state), then the formation of stars, star clusters and galaxies seem to be a paradox, if we consider stars as closed systems (since the law is valid only in closed systems). The law does not lay any restrictions on how one must choose a “system”. In that case I could choose a star as a closed system and that would be an anomaly from the 2^nd law. These anomalies are small fluctuations in the ever expanding universe which are compensated by very high entropy at various other parts of the universe. But the important question is even if the net entropy of the universe is increasing, why are stars formed in the first place? If randomness were to increase with time in the universe, even the formation of molecules and atoms at the quantum level seem like a contradiction to the 2^nd law. Energy dissipated by a closed system is probably the answer to this paradox. Perhaps energy dissipated into the environment by a star (The star could be considered as the closed system) during its formation is so high that this increases the entropy in the universe and overshadows the increase in order (lower entropy) within a star. In other words, if I break a solid plate (low entropy) and try to fix it with glue, I will be exerting a lot of energy into the environment thus increasing the net entropy of the universe. As per the 2^nd law, entropy of the universe as a whole can only increase but the entropy of the system as such can increase or decrease (system + environment= Universe).

The arrow of time could be defined as the direction in which the entity called “time” progresses. The arrow of time of our universe points in the direction of increasing randomness as stated earlier. This also means that “future” points towards expansion.

Since the claim is very abstract, one cannot accept or disregard this claim immediately. Science is always subject to change or addition in theories. Take for instance the period Copernicus. People in that era thought the earth was flat. This is just to show how far science has come in the past 500 years. So when asked if the source is reliable or not, in my opinion ,even though the claim might not be proved anytime soon the person making the claim, Prof. Stephen hawking is considered as one of the most brilliant minds since Einstein. Since I am an ardent believer of science I would only want to explore this further and not have a bias in my opinion as weather it is right or wrong.

Theoretical physics is mostly based on sensationalist claims that are backed up by mathematical evidence, thereby making such claims rather common. Prof Stephen Hawking being a savant in this field has made several claims that make our minds reel and many that have been backed up mathematically.

However Roger Penrose's Emperor’s New Mind discusses the big crunch and why the arrow of time would not turn backwards, even after the universe was collapsing on itself.  Since I am no expert in this field I don’t quite know how the idea was discredited partially.

Hawking in the Brief History of time argues that the thermodynamic arrow of time will always point in the same direction as the psychological arrow of time which brings us back to the basis of his claim. This means even during the contraction of the universe, the thermodynamic arrow of time points in the direction of the psychological arrow of time. Claim seems to be intuitive as to where the arrow of time must point but certainly not obvious. However if there were to be inhabitants in the contracting universe they will perceive the world in an entirely different way which probes me to say that it does not fit the way we look at the present universe but  the claim certainly has theoretical backup.

As stated earlier it is not very easy to disprove or prove this claim completely but several scientists have come up with ways to perceive this idea and I think that the majority of them have not paid much importance to the “Big –Crunch” phenomena itself because as per the current state of the universe, the speculation is that the universe is accelerating. But we still don’t know the cause that drives this phenomenon (Dark matter).  This goes to say that there is no observational evidence as of now for the “Big Crunch”.

Hawking certainly approaches the problem with strong logic. Take our present universe for example, according to the 2’nd law the arrow of time points in the direction of increasing entropy. This means that we don’t normally see broken cups or plates coming back together on their own.  The innate property of everything in the universe is to go to an unordered state.  If the universe were to contract, the thermodynamic arrow of time is reversed and hence reversing the psychological arrow of time. In other words, this means that the inhabitants in this universe will not remember the broken cup as an effect but as a cause, perhaps.

This claim however is a thought experiment rather than something that can be backed up with observational evidence.  If the net entropy of the universe were to decrease (Big Crunch--> High Order) the arrow of time is reversed but the Net Entropy of the universe cannot decrease according to the 2nd law. The question here really is why do we need the universe to obey the 2^nd’d law? The law has been derived from a series of observational evidence’. This in no way restricts the universe to behave in a particular way. This means that not obeying the law does not necessarily make this a paradox; it only means that from the point of view of how our present universe works, it is a paradox.

Hawking’s claim on the arrow of time is in fact the perfect example of a scientific claim as it has no confirmation bias what so ever. It goes against the normal traditional way of thinking about the universe and perceiving something that might or might not be true. But on the contrary I would not say that this is a good theory from the scientific reasoning as there is no observational evidence as of now to prove it wrong. Nevertheless it could be proven wrong or right through mathematics. Then again the proof offered by mathematics takes into account the 2^nd law of thermodynamics which as stated earlier does not have to agree with the idea.

Arrow of Time

Krish  Ramkumar

                                                                 Arrow of time

Is the arrow of time a consequence of the 2^nd law of thermodynamics or the law is due to the defined arrow of time? This question is a little hazy to me as the entity “time” is undefined in the law. If the law does in fact define a particular arrow of time in the universe, we need to define “time”.

According to the 2^nd law of thermodynamics, entropy (randomness) increases with time and the arrow of time points in the direction of higher entropy. If the arrow of time in the present universe is in the direction of higher entropy (unordered state), then the formation of stars, star clusters and galaxies seem to be a paradox, if we consider stars as closed systems (since the law is valid only in closed systems). The law does not lay any restrictions on how one must choose a “system”. In that case I could choose a star as a closed system and that would be an anomaly from the 2^nd law. Maybe these anomalies are small fluctuations in the ever expanding universe which are compensated by very high entropy at various other parts of the universe. But the important question is even if the net entropy of the universe is increasing, why are stars formed in the first place? If randomness were to increase with time in the universe, even the formation of molecules and atoms at the quantum level seem like a contradiction to the 2^nd law. Energy dissipated by a closed system is probably the answer to this paradox. Perhaps energy dissipated into the universe by a star (The star could be considered as the closed system) during its formation is so high that this increases the entropy in the universe and overshadows the increase in order (lower entropy) within a star. In my understanding, the same reason could be applied to star clusters as well.  To me this question is still hazy. If the universe did have some kind of innate property of moving towards randomness (higher entropy), this brings me back to my previous question- why are stars formed in the first place?

The arrow of time could be defined as the direction in which the entity called “time” progresses. The arrow of time of our universe points in the direction of increasing randomness as stated earlier. This also means that “future” points towards expansion. This is a way of understanding what happened before, what we call the past. The arrow of time has most certainly enabled man to trace back to his celestial ancestors. After all we are all star dust, remains of the Big Bang.

What if the universe were to contract, or go in the direction of the big crunch? The arrow of time then is reversed for the inhabitants in that universe. This simply means that what we call as “future” would be their past. This illustrates that the contracting universe is moving in the direction of lower entropy or high order. Perhaps the human brain is developed only to realize and perceive the arrow of time we are experiencing, which points towards higher entropy. We are probably trained to analyze only those phenomena that are directed toward an unordered state. Will man be able to perceive the universe if the arrow of time were different than what it is in our present universe? Will man be able to understand the universe if the universe were moving toward a state of lower order? Imaginably, our senses that have enabled us to understand the universe so far become an obstacle in understanding the universe after a certain point.

What happens to the arrow of time in the vicinity of a highly ordered structure? Is this how gravity is related to time at the most fundamental level? Possibly! Highly ordered structures have lower entropy. These objects also curve the space-time around them depending upon how massive they are. The curvature in space-time is considered gravity and this entity called gravity drags time (Einstein’s General -Relativity). In other words, if I were to go close to a black hole, just close enough that I’m in the orbit but not too close that I might get pulled into the singularity and then go around the orbit for a while and return back to earth, I would have actually travelled to the future. Time in my perspective slowed down when I was orbiting around the black hole (assumption is that a black is a highly ordered system as the density is concentrated at a single point). Does this mean highly ordered systems typically drag time? What I seem to infer from all this is that the arrow of time in the vicinity of a highly ordered system is not the same as what it is elsewhere in the universe.

References-

 Brief History of time - Stephen Hawking.

Einstein’s Universe- Nigel Calder