Extra: What about not-physics?

I am doing this resigned of the test I will do tomorrow. I may sound pissed or something, but it is not because of the subject, far beyond that, I find it quite interesting (I'm only like this because tomorrow I will have to wake up really early). 

Most subjects I've had were either physical, mathematical or some weird juxtaposition of biological or chemical concepts for physicists or people who work with physics, so having Economics has been a blast. Being able to look at underlying mecanisms that are behind our policies, and that have influenced much of history. And the debates, where you have different ideologies clashing each other, as if you were in a japanese anime with a villain and a hero (Dragon Ball Z is a good example, the classical shounen genre) were both of you were villains on each other's eyes. I am not an economist, nor will I be one, as far as I know, which is why I cherish this subject I am having right now, because I know I will likely work on it again, but I am very certain I will be working with it, whether it be as an engineer or as a physicist.

Sure, the current dynamics of your society shows everyone in bubbles, more or less isolated from each other, none standing each other. It's kind of sad actually. I am specially sad for the so-called "far-left and far-right activists" in our social media. Sure, classifying political ideologies as being binary is about as stupid as classifying sexuality as such. There is a whole spectrum, and it should even be one-dimensional. Now, we pretty much assume that if you are pro-LGBT and pro-choice, you automatically are a leftist, a socialist (or as any right-wing in the US would say, communist "UUUUuuuuhh the commies are coming, and they are coming hard"). And I pretty much thought of myself as such as well. Now, while I still consider myself as progressive, I don't think of everything as black and white anymore. There are many sides to one issue, some with more validity than others.

No sides are equal, but if we notice a logical flaw we shouldn't just shut it down. As something that kind of pisses me off, a good example is astrology. I may think that an astrologer is a legalized con-artist, but I won't shut down someone for believing stars millions of miles away will have any influence in their lives. I even enjoy reading the horoscopes to my "alleged" signs. It's quite funny actually what they think of Taurus. But if  you don't go with a sceptic eye, you might start thinking, "Hey, I am like that too. This thing really can say something about me.". Heck, even as a sceptic, I noted some things were the same for what I thought was my personality. I am pretty sure some psychologists have studied this, if you know who they are, please leave your comments down below.

Here's a dilemma we were talking about on class. Something about an huge oil reserve in Alaska, worth something like 700 billion USD. To give you perspective, you know how many countries have a GDP below that value? Pretty much all of them, besides the 18 wealthiest countries (Not counting the European Union as a single economic entity, although it is a single economic entity). So naturally there is an huge interest in exploiting the resources. But the debate was not because this oil reserve was found, but because of the location. It happened to be on a natural reserve, I think, where there are some animals who might be endangered, and the method that was being discussed for extracting the oil could put that ecossystem in jeopardy (not the game) so obviously you had two sides in the issue.

One side (the proxy republicans) obviously thought that 700 billion dollars was too much to let go to waist, and specially after the wealthy people tax cut, they should probably find money to cover for government expenses, because these poor people can't even afford their healthcare anymore. The other side (the environmentalists) were already against this before the debate started, for the simple reason that our planet is FUCKING DYING and we should go solar before it's too late. After that, they also thought about the endangered species, I mean, at least think of the children, will they even know what these animals were in the future, if they go extinct? It's a matter of patrimony.

In the end, the debate remained unconclusive, because we still had two many people in both sides. But, a third group appeared. I started as an environmentalist and ended in this group, because ignoring our feelings, and destroying our emotions we decided to look at this from a survival and economic perspective. Something that would allow us that have a sustainable future, while still enjoying the benefits from that oil. Maybe we could still exploit the oil, with a method that wasn't so damaging to that environment. Sure, you could argue, that is not gonna help the planet. But realistically, it is the best option. Our energetic needs right now, or at least, those of the US, which is the country that matters for this particular issue, can't really be suplemented by solar alone, so even if all governments decided to start replacing every fossil fuel energy with renewable, it would still take decades to fully replace everything. So if that oil is gonna sit there, it may as well be used. On the same time, let's admit that maybe use a better, safer method, and while many say they are not even sure if the oil reserves are that big or if the terrain allows to use that method, the Secretary of Interior, the "geologist", I think his name was Zinke, still allowed for using that controversial method. We believe that yeah, maybe use the oil, but at least, make sure to look like you give a shit about the environment.

That was a fun day, and we had other debates, most of them about issues affecting our own Portuguese reality, so I don't think it would of much interest to you guys. It was cool, we were able to exchange ideas, oppose ideas, have a bit of conflict (I secretly like chaos) and even change your own personal beliefs. Economics not only taught me how to make decisions (it is literally the science of decision-making) but it also taught me how to change my decisions if they happen to be stupid, and to find if they are stupid by sharing them with someone you disagree with. Again, this doesn't mean you should take it as a subject.

The core message I wanted to share from my experience was that maybe discussing your ideas with people outside of your echo-chamber is not a bad thing. And yes, you will find out you are wrong in many things, and yes, you will be pissed about it, but you will thank it, one day.

Sorry about not posting lately

Sorry guys, I couldn't keep the blog updated these months, since I am currently in my 3rd year in college. That is not a good excuse, but I haven't been able to carefully prepare the next post of the "So on Special Relativity..." series and that is really pissing me off, and probably you too, I assume. But I will make sure to make it up to you guys, even though this summer will also be tough. I will make sure to keep you updated. You can still comment on the other posts, I regularly go check them out. 

What do physicists whine about most?

I wouldn’t say whine. I have never seen a physicist whine. We are too high on coffee to do that, we just tear things apart, ripping the fabric of space-time. But I can tell what a physicist may feel uncomfortable with, and will use myself as an example for a couple of those.

One thing I believe we’re not comfortable with is when people assume we are geniuses just because we are doing physics. Don’t get me wrong, I am talking about the kids (and by kids, I mean mentally immature, not an actual minor. We have to specify everything, or else the internet crucifies you, like "someone" was allegedly... I am digressing) on the internet who say things like “Hey look, I have an IQ in the 99th percentile, look at me”, and also, physics does demand a lot of work to be understood, but I don’t like when I see people using things like “I read Quantum Mechanics books because I am very smart”. Like, many people think Einstein achieved what he did just because of his intellect, and I think that is an offense to Einstein, by disregarding the efforts he did. Sure, having an IQ of 200 is great, but if you don’t make at least the effort to learn something you will definitely not achieve anything. That being said, there are various examples of physicists you could describe as being prodigies, like Von Neumann, Dyson or Witten. But most physicist that go to work on the field, do it because they love what they are working on, and not because they feel like “With my intellect, this is the least I could do to you, mere lesser minds (Who speaks like this?)”. Again, I am not generalizing. Maybe there are geniuses who are also selfish pricks, and yes that sounds contradictory, but we are humans, contradiction, dichotomy materialized in flesh. Just so we can be clear, I looked up for dichotomy in the dictionary before using it. In the same, even best physicists today will still look for work done by those before him. Not only because we want to learn what they discovered, but for more trivial reasons, like plagiarism. Who cares if you found a new cure for cancer? If you don't quote those who did a prior work on that, who may have had come close to reaching your conclusion, a lawyer is coming up in your ass with a lawsuit. And you will lose credibility, and the scientific community will pretty much ignore you, and we don't want our brightest minds to go to waste, just because of some silly pride. So yeah, that is one frustration for me. Sure, we can say, that it may also be because I am stupid, and I take it. Yeah, I am stupid. Which is why I try to find ways to not be stupid anymore.

And also, really important, all this new age bullsh*t about quantum this, quantum that, magnetic something something, usually related to some biological or medical principle, like quantum mind (Now there is quantum biology, and that is a legit science)… The reason this ticks me of is because it affects my field. Whenever someone hears medical physics, or biophysics they start saying, oh yeah I heard about your field. I am like, “Really? I thought mine was a darkhorse in the different subfields of physics”, and then I just hear a “I’ve reading specially a lot on the quantum nature of consciousness” (Now again, we can use the mathematical methods in quantum mechanics and apply it to neurophysics, but in no way we assume brain activity to have a quantum feature) or “Do you work on magnetic therapy?” (We do use magnetic fields in medical and biological physics, but as far as I am aware, only in imaging and spectroscopy)*. I guess it is the same with astronomers and astrophysicists when they get asked “I was born in April, do you know the effects Jupiter has on me?” (While this is a hypothetical, I do know a friend of mine who went through this). Sure, these people are not at fault, they were just misinformed, my real frustration is with those gurus that spread these false statements as factual. We physicists do enjoy a bit of pondering and philosophy, but when you take that thought experiment and turn it into something “factual”, not only you have gone out of physics, you left the realm of science altogether.

I mean, today I was talking about it with this friend of mine. She is more tolerant to them, and even sometimes we joke around with astrology, but that is because most of us have already accepted astrology as a pseudo-science. And those who go there, don't think they will actually meet with a scientist. However, those who go to homeopaths, actually believe they are meeting with a respectable doctor. And that is dangerous. 

Sorry for my long rant, but these are things that I think could possibly make us whine a lot. And to all other physicists, if you think I exagerated on some parts or if you think I left something out, please tell me.

*An update to that, actually we can use magnetic fields for therapy, but definitely not in the way they are talking about it.

What are the different types of physicists?

So in the last two posts I was talking about how experimental and theoretical physicists may complement each other, and how the future of physics and science as a whole may be doomed if we leave everything at the ends of lobbyists and legislators. But then it occured to me that we don't really know how many kinds of physicists are there. This is an oversimplified version of many colleges, and universities curricula in way to properly say what the consensus for different types of physicists.

Now there are many ways to answer that. First, we need to go with conventions We start by answering at a more fundamental level, you have two types of physicists, fundamental physicists and applied physicists. What is the main difference between the two? Arguably the same as a theoretical mathematician and applied mathematician. Which means, that while both applied and theoretical physicists can work on the same subject, an applied physicist would work on a subject in order to find a pratical use out of it. Now while this seems similar to engineering, it is not exactly the same thing, since an applied physicist will most likely be doing research on the physics of some thing, and later may find some use for it. A good example would be physicists Lauterbur and Mansfield, which applied the physics of nuclear spin and magnetic resonance to medical imaging, completely revolutionizing the field. On the same note, a fundamental physicist would also be researching the physics behind some particular phenomena, while not being particularly interested in the use it may have, they would doing research just for the sake of knowledge and physics. Using spin again, a good example would be physicists Bloch and Purcell, which found a mathematical model that could describe the behavior of nuclei under magnetic fields, and the phenomena of magnetic resonance that would occur.

When 80 years of work and anything between 7 to 9 Nobel Prizes, from Physics to Physiology & Medicine, led to this wonder of a machine.

Besides of fundamental physics and applied physics, you may divide physics in two other (maybe three) types of physicists. You have the theoretical physicist, the experimental physicist, and while many believe a computational physicist to be a theoretical physicist, some argue that it may be a type of its own. A theoretical physicist would as the name implies either develop mathematical models to describe phenomena that were observed experimentally, or to predict outcomes that will be observed experimentally (nowadays it is mostly the latter, technology is lagging behind), while the experimentalist usually would try to verify results predicted by the theoretician, or just would do a random experiment and see what happens. (Before, most physicists were both experimentalists and theoreticians, but today most physicists like to dedicate to one thing or the other) Also, experimentalists would also work on ways to make the observations more reliable or statistically significant, or to be able to make experiments in different, or more extreme conditions. Sometimes, developments on experimental physics will be applied by applied physicists in other fields (like how they are now using the detector tech developed to detect the Higgs boson in other fields like nuclear medicine or in telecommunications). A computational physicist would pretty much run simulations of the theories in computers to try and see what the results could be. Now this is important, because nowadays physical experiments are expensive, so instead of doing experiments everytime we come up with a new hypothesis, we run simulations on computers. If the simulations are good, or what we expected, cool, if not, we have to change something. While this may seem something that a theoretician would do, and many do, a computational physicist would be working on various other things. They could, for instance, work on computational methods that allow for better, faster simulations, and those things are hard to do. Believe me. And that is why many are now believing that computational physics is a type of physics distinct of pure theoretical physics. (And also applied physicists may also be computational or experimental physicists just saying).

This is what a theoretical physicist would be doing. Although nowadays they are a bit more tech savvy, they would probably be writing on glass or something. I don’t think there is any practical use to that, but there a whole lot of things written in glass on some places.

And the exciting life of a experimental physicist. Imagine if one of those cables are not conducting, the struggle to find the one.

And the day-to-day life of a computational physicist, in that moment the code finally compiles, after 3 full bottles of coffee and 6 hours.

Now the part everyone cares about, the divisions of fields in physics. Truth be told, it is very hard for a single person to be working on various fields at the same time nowadays, so it became important to make distinction between those fields.

First, we have Nuclear and Particle Physics, which is like the poster child of modern physics (I mean, literally every person thinks that a modern physicist is either a particle physicist or astrophysicist). And they usually worry with the fundamental forces and constituents of nature. It was started with the discovery of the nucleus by Rutherford or with the discovery of radioactivity by Becquerel, about a 100 years, and right now, it is the field where such hot topics like the Higgs Boson, Supersymmetry, quantum gravity, GUT and string theory are extensively researched. On the applied field, there is a surprisingly high number of applications of Nuclear Physics, like the entire field of Medical Imaging and Radiotherapy, being pretty much Applied Nuclear Physics (with knowledge of physiology and anatomy), and let’s not forget Nuclear Energy, and Nuclear Bombs. As for particle physics, I don’t think we will have an application for it so soon.

Look at how beautiful this image is. I don’t know what they collided, but I can just imagine the excitement generated by the results. “Maybe it was just a flutuation” is what they will likely say, since NPPhysicists are usually those whose scientific experiments need to be the most statistically precise. And by precise, I mean 1 chance per billion of being wrong, p = 0.0000001. How about that? And you with your pitiful p = 5 or 1.

We also have Condensed Matter Physics, that studies condensed matter (like liquids and solids, and everything in between) and their physical properties. They study things like phase transitions and distributions of energy and states, something statistical physics, I guess. And they apply various fields of both classical and modern physics, like quantum mechanics. This field overlaps with others like Chemistry, and Biophysics (an applied physics) and has some cool things to be studied like superfluidity and supercondutivity, and topological phase transitions. Usually the field is subdivided in Solid State Matter Physicsand Soft Matter Physics. Now, while Physics doesn’t have a industry of its own (like the Chemical Industry) you can say that arguably, the most important field of Modern Physics to industry is CMPhysics, specially SSMatter Physics, because all of modern electronics is based on research in CMP. So, you can imagine that the applications usually involve nanotechnology, semicondutors, and oddly enough, or maybe not, even MRI (which kind of makes sense, thanks to superconductivity)

A Bose-Einstein Condensate. This a phase of matter where the state distribution of particle follow the Bose-Einstein statistics. Particles who follow this statistics are called Bosons, and they all have integer spin.

Am I forgetting something…

Right, we still have atomic and molecular physics and astrophysics and classical physics, that while not being a research for physicists anymore, are still very researched in engineering and mathematics, because of the so-called chaos theory. Right now, I will stop right here, but I will complete this latter. I am feeling lazy right now, sorry AMPhysicists and Astrophysicists, but don’t worry, your turn will come.

EDIT: So now, I am supposed to finish this, huh? Oh boy!

So, we also have AMO Physicists, which stand for Atomic, Molecular and Optical Physics. And their name is kind of self-explanatory, but I will make an effort. They are usually worried with interaction between matter and light, or just matter-matter, or even light-light (I don’t know, the possibilities are enormous). And they are also divided in (you guessed it) Atomic physics, Molecular physics and Optical Physics. Atomic physics is concerned with studying the physics of a system composed of electrons and a nucleus. While it may seem they do the same thing as nuclear physicists, that’s hardly the case. They usually are concerned with the system of electrons and the nucleus and their interactions, while nuclear physicists usually deal with atomic nuclei and their properties, disregarding their interaction with electron for most fundamental models. As for molecular physics, it is less about the inner workings of atoms, and more with how molecules interact with each other. As you can imagine by that, there are fields like physical or theoretical chemistry which are concerned with pretty much the same thing, so they hang out together a lot. Optical Physics is primarily studying light. The nature of light, the behaviour of light, the interactions of light with itself, interactions of light with matter, it’s all tied to light. Now when I say light, I mean electromagnetic radiation, they study all the electromagnetic spectrum, not just visible light.

Lasers… Enough said. I am still for those light sabers, though.

Now let’s go to the sexiest physicists out there. Astrophysicists! If I didn’t put them down here, probably the guys would just read this part and leave without caring for the rest. Now astrophysicists are just worried about one thing: The nature of heavenly bodies and the physics (and chemistry) behind all astronomical events. That is their "thing". Astrophysicists are usually seen (or maybe I am the one who seems them like that) as one of the two extremes in physics, dealing with the physics of the very large, while particle physics deal with the physics of the very small. And considering the scale and variety of things to work on, obviously it also has subdivisions. I mean, you have Planetary Physics, with Geophysics specifically focused on Earth, that studies planets and their physical properties, including extrasolar planets. You have Solar Physics that studies the heavenly bodies in the Solar System and their interaction, studying things like the motion of bodies inside of the solar system, which is not easy because you have a multiple body system where all those bodies interact with each other and generate their own gravitational field. You have Stellar Physics that study the physics of stars, like star formation, stellar activity and stellar death, the Heliophysics specifically studying the Sun. They also study things like Black holes and Neutron Stars. (I don’t know if you realised but the trend is to keep getting bigger in scale) You have galactic physics that studies the physics of well galaxies, how stars interact with each other inside a galaxy, how a galaxy forms, what is the physics behind galaxy conformation, and other questions. You even have extragalactic physics, that study interactions between galaxies, the distribution of galaxies in a group, and extragalactic bodies, like quasars or pulsars. And finally the crown jewel, Cosmology that studies the fundamental and cooler stuff in astrophysicist (from a pop science POV). They study the entire universe, its evolution, its beginnings, and its possible end. Also they study the nature of spacetime, like the existence or not of wormholes, multiple universes, Dark Matter, Dark Energy and Gravitational Waves (There are definitely some Metal bands with at least one of these names). As for applications, there are way too many, and this article is getting way too long.

The main thing you need to know is that physics is very diverse, and you could do things that would change the world, but most important of all, no matter how hard you may think of it, physics is something you should do only if you like it enough. If you are willing to work on the same problem, sometimes for decades, just to get that one confirmation of a fundamental truth. You may not win a Nobel, but damn, you would feel joy in working on this amazing field. Scientia Prima as some would say.

Also, just leave a comment below or anything, so I can have a feedback from you guys, I don't want to talk to a wall.

What is wrong with modern physics?

I will rant a bit about my personal frustrations and hopes for the future of modern physics. Now, sure I ain't shit, but to be honest neither are most future physicists. As of right now, we are only prospect physicists, many of us will work on the tech industry, many in the financial market, and many will give up to insanity and start talking nonsense like "quantum mysticism". But if we want to start, if you are talking about concepts in modern physics, well, is the fact that it is incomplete. Why that is? Well, for many reasons. For one, right now, we are trying to understand physics at the most extreme environments in the universe, many of which we will probably never be able to reach. Before an hypothesis has been well established you already have a new, better hypothesis (which is great, so that is actually what is right with modern physics).

But the main problem is the fact that our technology can’t keep up. Many of the theories in Modern Physics can only be confirmed if they are verified experimentally. Before when Physics was mostly done by people who had their own wealth, experimentalists would take a year or two to dismiss or prove some hypothesis, but nowadays, while it is easier to become a physicist than ever before, it is also harder to do physics, so hard that only budgets of countries could afford to do so.

And then we reach another problem, countries may not be that interested in investing in physical research, because while research in chemistry and biology have a clear practical use, usually it takes 60 to 70 years for one to find any sort of use from physical principles. I mean, many of the technologies we take for granted today are based on physics from 60 years ago, to say the least. And lawmakers aren’t interested in investing in things at such long scales (F*ck why do you think many of them don’t believe in Climate Change?). I mean, in the 30’s and 40’s they at least had the motivation of nukes.

But still we are doing some advancements every year, and I understand your feelings, if you compare to last century and how fast physics seemed to advance, in a couple of decades, entire paradigm shifts occurring, it was a joy to be alive back then. But it is not all that bad today. As I said, we have more people working on physics now than ever before, even though many people are dropping out. So while we may not have a generation of physics wonders, we do have an entire army of physicists working not only in fundamental research, but also on applied physics, so we can directly improve your life, and so those lawmakers can see that “Hey, maybe we should invest a bit more on this, and less on our behemoth of an army”.

I let my anti-war sentiments slip there a bit, but I hope I answered your question.

Who is smarter between theoretical physicists and experimental physicists? - A personal take

So this was a question asked by someone on Quora, and I found it interesting enough to answer not because I am a theoretical or experimental physicist and I am butt-hurt or similar. But because  many outside of the scientific community seems to think there is some sort of rivalry between physicists of different approaches or fields. So this is my take on that. In the time, I will try to look for someone who has actually worked for more than a decade as a physicist, they would have a lot more to say than me. But to start...

I guess it really depends on what you mean by smart.

For instance, the usual definition of smart, is someone that is quick-witted, someone is quick to take decisions, but also intelligent, so a smart person is someone that has quick-witted intelligent. Just because you are intelligent, wouldn’t mean you are quick-witted and vice-versa. Now it is true, that in American english, smart is synonymous with intelligent, so I guess what you mean is who is more intelligent. And going by that, an intelligent person is someone who is able to acquire AND apply knowledge and skills. 

And we can assume both theoretical and experimental physicists would need to be able to acquire knowledge and apply such knowledges, for the sake of obtaining new knowledge. Now as for who is more intelligent, that depends on what you need, what knowledge or skill you are considering. Pure logical or mathematical reasoning may seem like the bulk of a theoretical physicist’s work, but they also need to be able to interpret new results obtained by an experimentalist, in order to either reject or change their previous theory. On that same note, an experimentalist would need to know how to obtain and analyze the results of an experiment, but also would to know enough about the theory to either dismiss the results as nonsense or an artifact, or to actually challenge the theory itself (or hypothesis, if the theory has yet to be established as such). And actually, many physicists end up working a certain time of their careers in both sides, so trying to say one is smarter than the other may be tough, with this mass flip-flopping around the pond.

But anyway, here are some famous physicists from both sides (Not including Einstein, because well, you know him)

Experimentalists:

• Michael Faraday (which is actually interesting, albeit not having formal education in physics, and being kinda sloppy in mathematics, actually was such a brilliant experimentalist that he was one of the forefathers of the classic theory of electromagnetism)
• Wilhem Roentgen - The first Nobel Prize in Physics, for the discovery of X-rays
• Ernest Rutherford, known as the father of nuclear physics, and the greatest experimentalist of his time, since Faraday. Also he discovered the nucleus, for which he was awarded a Nobel Prize in Chemistry. Also, he has an element with his name (Cool!)
• Enrico Fermi, creator of the world first nuclear reactor, and called by some as the “architect of the nuclear age” (or the atomic bomb). He is actually one of those physicists who are great both experimentally and theoretically, making advancements in quantum theory, nuclear and particle physics and statistical mechanics. Also a Nobel Prize winner.
• John Bardeen, also a physicist and electrical engineer, who has part of the trio who made the first transistor (which revolutionized the world, I mean, the entire modern computation can stem its hardware to that pivotal moment) with Shockley and Brattain, and also the guy who made the first formal theory of superconductivity (also known as BCS theory, for Bardeen, Cooper and Schrieffer). He is actually the ONLY physicist to have won two Nobel Prizes in Physics. (Marie Curie won one in Chemistry. Of course, she was a great experimentalist as well)

Theoretical Physicists (I tried to pick those who are not Nobel Prizes, so that you don’t think only Nobel physicists are great):

• Leonhard Euler (everyone knows him first as a mathematician or a god of mathematics, but did you know he was also a physicist? There are literally entire books with his achievements.)
• James Clerk Maxwell, a mathematical physicist (like Einstein). He is considered by many physicists as being as important as Einstein and Newton, due to his pivotal contributions. He was the second great unifier of physics, joining electricity, magnetism and light onto a single theory of electromagnetism. And his equations were pivotal enough that led to the formulation of the special relativity by Einstein, so you know he is a big deal. And his works were fundamental to the developments of fields like Special Relativity and Quantum Mechanics. Which is why he is held with such respect by the scientific community, albeit not the same by those outside of it.
• Georges Lemaitre, a physicist and catholic priest who was the first one to derive the theory of universe expansion, and the first proponent of the Big Bang Theory.
• Ettore Majorana (look about him. There’s a whole conspiracy theory surrounding him)
• Roger Penrose, the co-author of Penrose-Hawking Singularity theorem and a bunch of other things.

In truth, we can’t really say who is smarter, because as you can see we have plenty of great physicists on both sides. The core message I want to take is that both are instrumental for the advancement of physics and science as a whole.

And also, I will make sure to talk about Majorana more in the future, so sorry for the cliffhanger

So on Special Relativity, Special De-Tour - About lights and waves

So now, I want to talk about light. And more specifically, about electricity, magnetism and how they come together. And I will be honest, I will gloss over a lot of detail, because this is a series on special relativity not electromagnetism, so I won't go in detail. But here are the things you may need to know:

- High school mathematics, specially derivatives

- And hopefully, some pre-calculus, like integrals and such. I would recommend you watch 3blue1brown's series on calculus, because it gives you an intuitive understanding of what a derivative or integral means.

I will use mathematical expressions to summarize the ideas, but I will make an effort to give a written explanation of what they mean, after all, my point for you right now is not for you to understand the math behind it, but to understand that maths give sense to physical conclusions, no matter how unconventional they may seem.
Also, a couple of considerations here. To avoid complexity, I will consider mostly point-like bodies when talking about these equations, because let's be honest, I don't really want to put that much detail into things.

So, the first thing we will talk about today is about Coulomb’s Law, a law that describes the interaction between charged bodies:
 
Now, let me give a quick explanation of what does this expression mean. First, let’s explain the constants, you have your classic π, and then you have this symbol ε_0, which in physics is called electric permittivity of the vacuum. It is a physical constant that expresses how vacuum permits electric fields. Now this permittivity may seem a complicated concept, but it essentially says if a certain space is resistant to electric fields (similar to the concept of electric resistance in an electric circuit) and in this particular case, the vacuum permittivity is a constant (at least, we think it is, but is a whole new discussion), it has a specific value, of about 8.854∙10^(-12)  m^(-3) kg^(-1) s^4 A^2 (with A being ampere, the unit of current). And four is a number, so we usually just consider all constants assembled in a single constant:

, which we call Coulomb’s constant, and which value is 8.99∙10^9  Nm^2 C^(-2). We can simplify the expression as: 

Now, the q_i  ,i=1,2, are the charges of the bodies, as of now you can think of them as a fundamental property of matter like mass. And r is the classic distance. So what this expression says is: If you have two bodies with electric charge, they will exert a force on each other that decreases with the square of the distance. Let’s consider their initial distance is A, and they feel a certain force F. If they are at twice the distance A, the force is four times weaker. If they are at half the distance, the force is now 4 times stronger. As for the arrows, as you now, the force is a vector, so it has a direction. And that’s what the last term represent, it shows that for two bodies 1 and 2, the force goes from 1 to 2, and vice-versa. Now if you pay attention, you will see that the formula we have above is like Newton’s Gravitational law:

 , that describes the interaction between massive bodies. And this is a good way for you to notice a couple of properties for the Coulomb’s force:
First, the intensity of the force does not depend on the direction, but only on distance. Which means it doesn’t matter if you are in any specific point in space, if you are at the same distance, you feel the same strength. That is what we call radial symmetry, and it is something that the gravitational force also presents. Also, you may realize something in the equation, that Newton’s law has a negative sign. Here is something we know in physics (it is more of a convention actually), when forces have negative signs it means they are attractive, while when forces have positive signs they are repulsive. Now, as of right now, we have never found anything with negative mass, so we can be sure Newton’s law is always attractive, but we can’t say the same for Coulomb’s law. We do now there are positive and negative charges, and that means the electrostatic force can be negative and positive depending on the charges, more specifically on the product q_1 q_2. If it is positive (if both charges are positive, or both charges are negative) then the force is repulsive, and they push each other apart. If it’s negative, they have opposite charges, and attract each other.

 And that pretty much describes all of the fundamental interactions between charged particles. By the way, the gravitational constant G has a value of like 6.6⋅10^(-11)  Nm^2 kg^(-2) which means that Coulomb’s force is like 10^20 times stronger than gravitational force. That's 1 with twenty zeros behind it. Which is why we don’t perceive gravitational force in small scales, like the ones we experience daily, and why all our molecules are bound to each through electrostatic interactions.

Also, I would like to point out about electric fields. As you see from the expression above, force can be described as an interaction between two charged bodies. But it can also be described as an interaction between a charged body and the electric field of another body. This description is particularly useful if our body has some weird shape and consequent charge distribution. We don’t really want to deal with complex integrals that much, but only when necessary. So we can define the force as:

This expression is especially good if you know what is the value of the field, but don’t know where it is coming from, or if you don’t know the source. By the way, you can also describe Newton’s gravitational law as a field equation, like this:

 which also has units of acceleration in this case. For Earth’s surface, our gravitational field is approximately 9.8 N/kg or 9.8 m/s^2, the unit of acceleration. So, you can see how useful it is for us to use fields instead. And this is useful if we want to go to the next section. If you want to describe the acceleration caused by an electrostatic force, it would be:


Which means the body would feel an acceleration in the same direction of the electric field. By convention, this is how we show the electric field lines of a charged particle. 

Now that you know about electrostatic forces and electric fields, you know one of the main things in electromagnetism. The other thing you need to know is about magnetism. Now the existence of magnetism was known for a long time, ever since Ancient Greece. In Ancient China, compasses were already used as a reliable mode of orientation. And yet it lacked a way for us to properly describe it. No one knew why certain things would attract metals, or why the compasses would always point to the north. The first expression to describe the magnetic field’s behavior has this one:

Now, we have a couple of different things displayed on this expression. First, now we have the velocity appeared, as v, which means the body 1 is moving, and we have this new thing, B. That B is the magnetic field. A current as we know is a collection of moving charges so, what this expression is saying is that a moving charge inside of a magnetic field feels a force that is proportional to both how fast it is moving, and to the strength of the magnetic field it crosses. Now as you see there is a cross product between the two quantities. I hope you already know what a cross-product is but the short explanation I can give is that if you have two vectors and you make a cross-product of them, what you get is another vector perpendicular to both. What this means is that force vector is perpendicular to both the direction of the magnetic field and of the velocity of the particle.  Visually, it would probably be something like this.

Now, to be truthful, if it was a negative charge it would be pointing in the opposite way, but this is just for you to visualize what a cross-product mean. Which brings me to another point I want to make that the cross-product as its maximum value if v is perpendicular to B, and its minimum value if v is parallel to be. For you to understand this more intuitively, there is the formula for the absolute value of the force:

, where the θ represents an angle between the vectors velocity and magnetic field. If they are parallel to each other, then the angle between the two vectors is zero, which means sin(θ) and by extension, F, is null. But if they are perpendicular, then θ is equal to π/2 which means sin(θ) is equal to 1, and:

, its maximum value. And if you look, the direction where the force points is always perpendicular to the motion of the body, which means that this force changes the direction of motion. 

Remember when I told you about current? Well, let me just explain it real quick. Current is formally defined as being the variation of charge over time, or:

Which means, in some cases, charge can change over time. So in our previous expression:

If instead of you having a constant charge moving a certain displacement l, you had a certain constant path l where charge would change over time (example: a wire), you could write the expression above as:

You could say that expression describes the strength of a magnetic field on a conducting wire, also called Laplace force.

But there is still a mystery left. Where does the B come from? We know that the electric field E comes from a body with a charge q, but we don’t know the source for B yet. As it turns out, there is an answer for that. Two French physicists, Jean-Baptiste Biot and Felix Savart, where the ones to find a first answer to this question, in a law we now call Biot-Savart Law:

Like with the time we were analyzing Coulomb’s equation, let’s break this one down a bit. First, let’s see which one of these are constants: we have our usual 4 and π, and this time, instead of ε_0, we have µ_0, which is called the magnetic permeability (not permittivity) of the vacuum. It is kind of like permittivity, but instead of determining how resistant (or permissive) is a space to electric fields, it determines how permeable is a space to magnetic fields. And you also have that common factor q/r^2 which means the fields is proportional to the charge that is generating it, and to the distance from that source, like the electric field expression. But the main difference here is on that last term. On the electric field expression, we only had the vector direction u_r that meant the field had radial symmetry over the source. But here we have a cross product between the vector v and the unit direction vector. If you have a cross-product between them can only mean that the field generated is perpendicular to the velocity vector and to the direction. It would look something like this:

If it was a positive particle, the magnetic field would be pointing in the opposite direction.

So while it still holds the radial symmetry of the electric field, the magnetic field has some really interesting characteristics of its own. Like, it is generated by a moving charge, which means that in a place where charges aren’t moving you will not find magnetic fields (not exactly true, but not exactly false either, I just don’t wanna explain more). Now this is most you need to know before we talk about Maxwell and you will finally understand why maybe Galilean Relativity was not the best relativity.

Damn it, this was way longer than I expected. But this is what happens when you try to study half a semester worth of Electromagnetism in one day. Luckily this is not my first encounter with it, and honestly I think it is really important for me to talk about this basic concepts in EM, because we will soon talk about Special Relativity, and then the birth of quantum mechanics. I understand many wouldn't feel comfortable with this much content at once, but you don't have to take it at once. This is not a test, so you don't to be very attentive and fast on learning. But it is important for you to learn if you want to understand anything that may come behind this. Anyway, thank you for your time in here and remember to comment or send me an email at this adress rafaelhoppfer97@gmail.com, for critic or any suggestions you may have. 

Some references for you to learn more about this:
- Physics for Students and Engineers (with Modern Physics), Serway & Jewett: Part 4: Electricity and Magnetism, Chapters 23 (23.4-7), 29 (29.1-3), 30(30.1)

For a little more advanced description, we also have this:
- Electromagnetic Fields and Waves, Lorrain & Corson: Chapter 3: Electric Fields(3.1-3)
Chapter 18: Magnetic Fields (18.2)

Also, Wikipedia may give a good introduction on the topic. These books also happen to have a bunch a exercises you can use to pratice, so I highly recommend you to try and solve them, and email me your answers to certain problems, if you are having difficulties.