If I ask myself what pushes me to write, my answer would most likely lack clarity. Writing is a complex field. It has a certain amplitude (A), the reach, I mean; there would be certain boxes in the reader's mind that I'll be able to squeeze myself into. But that's of course, not all about writing. Every thing that comes out of me, represents a phase. Make no mistake, this phase is too real, even though the output as a whole might be complex in general. Simply put, this is what writing (W) is :
W = A exp[i P] .
The quantity of interest for me is the phase P(x,t). In usual notations, x is space and t refers to time. So you see, P is a function of space and time.
Caution : If you're a physicist, don't let your arrogance get the better of you at this moment. You would probably do better to submit. Flow with my lines. It's going to be a journey for us; you and me.
Let's get back to P.
Time : If you ask me, P doesn't really have a global structure in time. It's too local in that sense. Though each fluctuation in time leaves its signature, most time-correlations eventually turn out to be short-ranged. Most.
Space : This really is vital. Let me be absolutely clear about P. It is NOT a Goldstone mode. The reason it cannot be, is simple : A Goldstone mode represents a low-energy excitation. These modes appear when the ground state has a continuous symmetry that gets spontaneously broken. One can then move from one ground state to another through small excitations (these fancy modes). But I have a single ground state! End of story. Any symmetry that might appear in W (carrying all elements of entertainment for the reader), must carry signatures of excited states.
Okay! The article seems to be on the right track.
To answer the original question, i.e., what makes me write, is/are excitation(s). Of all mysteries of nature, here's a well known one. Any system has a 'natural' (for the lack of a better word) tendency to be in its ground state. Put the system in an excited state and it will do whatever it can to part with the excess energy. This is what I do. Every thing that I have written so far, is only me saying to society, "Take back what you have pumped into me."
Ground States : Oh! the sad dilemma! With choices aplenty, we have nurtured a habit of living in a make-believe universe, where we feel powerful enough to set the rules. We let ourselves believe in the existence of multiple ground states. While obviously, there are some systems with this degeneracy, it is of course not the norm. Sure, you have the liberty to define any model for your own system, but you know what, Nature is sarcastic. You being bad at mathematics has no relevance on the actual laws that Nature has written for itself (Herself? Himself? Excuse me.). Sooner or later, the ground state will kick out any hallucination that you dream of holding on to forever. As for the degenerates (not a judgement call here, just wordplay), you either have domain walls or Goldstone modes.
Domain Walls : The ground state has a discrete degeneracy and this symmetry gets broken at a certain point. Now, the mimicking ground states are so far apart that no low-energy excitation can ever take you to the other states, once you have collapsed into one. A domain wall is a separation between the equivalnet ground states. The widths of these walls tend to mostly diverge at the transition point.
Goldstone modes : Here we are then! The curious case of multiple options! No poet has ever figured out whether more is actually merrier. In a system, when a continuous symmetry exists, the game submits itself to God. Think of it! All interactions have performed their respective duties, even the system has gotten rid of the outer excitations. Yet, it falls on a dicey platform. There are infinite states, all equivalent. And right at this moment, God, Nature does play dice! It is at this point that the system wonders about the fluctuations it feels! And it has no idea. It has no mathematics to rescue itself anymore. Each throw of the dice makes it hop to a new state. To those with the magnifying lenses, the system appears erratic, mad (Brownian ? - risky statement). But who understands what the system feels? We debate on whether the system has no peace at all. But what is peace really? Remember, I told you that Nature loves sarcasm. You see, equilibrium is a strange thing. What seems to be the most peaceful state of all, is in fact associated with maximum randomness (call it disorder, entropy, chaos, love).
My Ground State : Did I lead you to the thought that love is chaotic? Well, I now claim that love is all about peace. And you know what, I will make a case for my peace.
What is randomness?
It only represents the amount of choice a system has. The more choices it has, the more random we call it. Yes, equilibrium is indeed associated with maximum amount of choice. This is probably one of the deepest statements that Nature makes; and as a consequence, Nature is only telling us, "To each its own".
I have a single ground state. It's composed of an expensive chunk of space-time. Hence, there's no fancy domain wall or Goldstone mode in my ground state configuration. Equilibrium though, doesn't make separate rules for me. There was only one realization that waited for me all this while :
The maximal entropy that maintains my equilibrium is zero.
Did you get the point of this article then? It doesn't matter what I write. I am only a river, propagating through life. Each droplet within me will escape the interactions and transform into free hydrogen. Each electron will free itself and so will the quarks. There awaits one P for me, when the sacred boundary condition of fields vanishing at infinity will apply. In eternity's normalized measure of randomness, with certainty the Universe will be mine.
W = A exp[i P] .
The quantity of interest for me is the phase P(x,t). In usual notations, x is space and t refers to time. So you see, P is a function of space and time.
Caution : If you're a physicist, don't let your arrogance get the better of you at this moment. You would probably do better to submit. Flow with my lines. It's going to be a journey for us; you and me.
Let's get back to P.
Time : If you ask me, P doesn't really have a global structure in time. It's too local in that sense. Though each fluctuation in time leaves its signature, most time-correlations eventually turn out to be short-ranged. Most.
Space : This really is vital. Let me be absolutely clear about P. It is NOT a Goldstone mode. The reason it cannot be, is simple : A Goldstone mode represents a low-energy excitation. These modes appear when the ground state has a continuous symmetry that gets spontaneously broken. One can then move from one ground state to another through small excitations (these fancy modes). But I have a single ground state! End of story. Any symmetry that might appear in W (carrying all elements of entertainment for the reader), must carry signatures of excited states.
Okay! The article seems to be on the right track.
To answer the original question, i.e., what makes me write, is/are excitation(s). Of all mysteries of nature, here's a well known one. Any system has a 'natural' (for the lack of a better word) tendency to be in its ground state. Put the system in an excited state and it will do whatever it can to part with the excess energy. This is what I do. Every thing that I have written so far, is only me saying to society, "Take back what you have pumped into me."
Ground States : Oh! the sad dilemma! With choices aplenty, we have nurtured a habit of living in a make-believe universe, where we feel powerful enough to set the rules. We let ourselves believe in the existence of multiple ground states. While obviously, there are some systems with this degeneracy, it is of course not the norm. Sure, you have the liberty to define any model for your own system, but you know what, Nature is sarcastic. You being bad at mathematics has no relevance on the actual laws that Nature has written for itself (Herself? Himself? Excuse me.). Sooner or later, the ground state will kick out any hallucination that you dream of holding on to forever. As for the degenerates (not a judgement call here, just wordplay), you either have domain walls or Goldstone modes.
Domain Walls : The ground state has a discrete degeneracy and this symmetry gets broken at a certain point. Now, the mimicking ground states are so far apart that no low-energy excitation can ever take you to the other states, once you have collapsed into one. A domain wall is a separation between the equivalnet ground states. The widths of these walls tend to mostly diverge at the transition point.
Goldstone modes : Here we are then! The curious case of multiple options! No poet has ever figured out whether more is actually merrier. In a system, when a continuous symmetry exists, the game submits itself to God. Think of it! All interactions have performed their respective duties, even the system has gotten rid of the outer excitations. Yet, it falls on a dicey platform. There are infinite states, all equivalent. And right at this moment, God, Nature does play dice! It is at this point that the system wonders about the fluctuations it feels! And it has no idea. It has no mathematics to rescue itself anymore. Each throw of the dice makes it hop to a new state. To those with the magnifying lenses, the system appears erratic, mad (Brownian ? - risky statement). But who understands what the system feels? We debate on whether the system has no peace at all. But what is peace really? Remember, I told you that Nature loves sarcasm. You see, equilibrium is a strange thing. What seems to be the most peaceful state of all, is in fact associated with maximum randomness (call it disorder, entropy, chaos, love).
My Ground State : Did I lead you to the thought that love is chaotic? Well, I now claim that love is all about peace. And you know what, I will make a case for my peace.
What is randomness?
It only represents the amount of choice a system has. The more choices it has, the more random we call it. Yes, equilibrium is indeed associated with maximum amount of choice. This is probably one of the deepest statements that Nature makes; and as a consequence, Nature is only telling us, "To each its own".
I have a single ground state. It's composed of an expensive chunk of space-time. Hence, there's no fancy domain wall or Goldstone mode in my ground state configuration. Equilibrium though, doesn't make separate rules for me. There was only one realization that waited for me all this while :
The maximal entropy that maintains my equilibrium is zero.
Did you get the point of this article then? It doesn't matter what I write. I am only a river, propagating through life. Each droplet within me will escape the interactions and transform into free hydrogen. Each electron will free itself and so will the quarks. There awaits one P for me, when the sacred boundary condition of fields vanishing at infinity will apply. In eternity's normalized measure of randomness, with certainty the Universe will be mine.
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