Jingly Bells and Big Bangs

Hohoho, Christmas  must be in the air and as always, we have some religious nuts going around complaining about secularism. Now I try to maintain my stance as irreligious in this debate, so I don't usually argue with them, but a really funny question popped up. 

"Why do people still believe in the Big Bang Theory when it's been disproved by the Bible?"

Sorry, but if you in some way agree with that reasoning, I am pretty sure you are not a Catholic. Or you are a really terrible one.

No, not because I think that Catholics are heretic whose only real thing they have going is the fact they are around for pretty much two millennia and for a large portion of that time, were the most powerful corporation in the planet.

And also not because I think not being a catholic means you are an heretical protestant that should receive the wrath of Inquisition, as the good old days of the Holy See as the overseer of the world (as opposed to the modern US, which I am also going to assume you are from)

Now, the reason why I know you’re not a catholic is because, as a former catholic, I know one of the things we would pride ourselves is in the fact that the catholic church and/or catholic individuals were innovators in various fields of science. And every catholic likes to brag about it to their protestant and atheist friends. I used to be like that.

Some of the greatest astronomic discoveries were made by catholic priests like the fact that the Earth revolves around the Sun, by Copernicus, which if I recall, is also in contradiction to the Bible (Actually later, Galileo got in some hot water with the Holy See because of this same heliocentric view). Another catholic priest, Mendel, is known as the father of genetics, which, along with many other things, have been used to prove that evolution is an actual thing (again in contradiction to the Bible). And the topic of your question, the Big Bang theory, was first proposed by a Belgian catholic priest, Lemaitre.

So, you have the biggest christian church in the planet, where its members have made discoveries that well may contradict the Bible, which is like the constitution of Christianity. Now you have a few options on what to believe:

A - You take the catholic approach, that is to say that while it may seem like it contradicts the bible, in reality, it doesn’t contradict it at all, since in essence, even though Bible is the word of god, they may have taken some literary liberty in some descriptions. I mean, if you think about it, while the bible doesn’t say anything about evolution, it doesn’t say anything against it, just like with Big Bang. If anything, the only suspicious “theory” here is that the Earth revolves around the sun, when Genesis clearly says the sun was made as a lighter above the firmaments. Although I do think the Catholics are really good with Jedi Mind tricks and Doublespeech.

B - You take my approach, and assume that a Book written (allegedly) over the span of two millennia with multiple writers none of them with the scientific knowledge we have today, and as such, on a bad trip, assumed to have met a “god” who told them words of wisdom. You know, like when Marduk slayed Tiamat and with her body created the world (you should know about them, they were part of Abraham’s first religion, back when he was just Abram). Fairy tails.

C - Or you take the fun approach, the planet X approach, or the flat-earther approach, believing that the catholic church has somehow allied itself with the scientists and the Muslims (even back when they were killing each other in the crusades) in a massive conspiracy to promote heretical teachings that contradict their own word, for the purpose of… making frogs gay with chemicals in the water? On that note, should we open an inquiry on the subject of heliocentric solar system? It seems like Sun worship to me.

Yeah, this isn’t about the scientific reason, because we both know we wouldn’t understand. The reason why I believe in the Big Bang, is because believing in it wouldn’t really hurt me in any way. And if I believe that the Earth revolves around the sun in an elliptical path, then it’s not much of an stretch to believe that the universe is expanding.

So long, and happy Holidays everyone!!

Parity in Physics

Something that always confused when I was first studying physics was the concept of parity, parity transformations, parity conservation... So I figured that a good way to properly understand the concept of parity and in a way to help others in doubt, is to talk about it in a informal way.

A good analogy for parity would be for you to imagine yourself in a mirror. Your mirror image looks exactly like you, except for the fact it’s inverted. Try raising your right hand, your mirror image raises the left, and so forth. You could that the mirror you is the you who suffered a transformation, where your front is now your back, and your left is your right, so in mathematics, something like

(x,y,z)⇒(−x,−y,z)$(x,y,z)\Rightarrow (-x,-y,z)$

x and y represent respectively your left-right and front-back direction. Now that is almost like parity. If your mirror image is also upside-down, then it is a true parity transformation. In short, a parity transformation is essentially a transformation that flips the sign of your coordinates. Something like r⃗ −→P−r⃗ .$\overrightarrow{r}\stackrel{\mathcal{P}}{\to }-\overrightarrow{r}.$

So yeah, it’s just that in essence. An inversion operation under all spatial coordinates. And yet it is very important in physics. Let’s say you have a physical quantity dependent on spacial coordinates, and let’s say that quantity suffers a parity transformation. Then if

f(−r⃗ )=f(r⃗ )$f(-\overrightarrow{r})=f(\overrightarrow{r})$

the quantity is said to have even parity. Examples of classical quantities with this property are energy, mass, the electric potential, usually scalar quantities. Else if

f(−r⃗ )=−f(r⃗ )$f(-\overrightarrow{r})=-f(\overrightarrow{r})$

the quantity is said to have odd parity. Examples being those like the position (seems rather obvious), force, or the linear momentum.

Now, those things are not really what we care about in quantum mechanics and nuclear physics. But with this part, you hopefully understand what we mean by even or odd parity.

In nuclear physics specially, the concept of even or odd parity is important to describe gamma decay (or isomeric transition) and nuclear stability. The quantum state of each nucleon has either odd or even parity. I am not gonna prove this, but the parity operator can be represented by its eigenvalue as show below:

P|ϕl>=(−1)l|ϕl>$P|{\varphi }_l>=(-1{)}^l|{\varphi }_l>$

That l is a quantum number equivalent to the angular momentum (but not necessarily being an actual angular momentum). So you can pretty much define the parity of a nucleus by the product of the individual nucleons. If both Z and N (number of neutrons) are even, then the parity of the nucleus is even. If (Z+N) is odd, then the parity is determined by the “valence nucleon”, the nucleon at the highest energy level, you could say. If (Z+N) is even, but Z and N respectively are odd, well, there is no way for you to know. The parity of the nucleus determines its stability, so you can see there is importance in this detail.

The parity is also important for isomeric transitions, or gamma decay. But I will come back later to edit it.

So on Special Relativity: What is mass, according to physics?

Mass, uh? This is an interesting topic.

The classical definition of mass is essentially how much matter is contained in a body. Like how much stuff is in you. It also determines the strength of the gravitational force you exert over other materials and they exert over you.

In the past, you three kinds of masses. The inertial mass, that represents the resistance of a body to an applied force. You can think of it this way, for the same force, a body that has more mass, would move less, because it would suffer a lower acceleration. That is all condensed in Newton’s second law of motion: F⃗ =mia⃗   
$\overrightarrow{F}=m_i\overrightarrow{a}$.

The other kinds of mass are called gravitational masses. Active gravitational mass of a body is the strength of gravitational force exerted by that body, or F⃗ g=Gmr2Mg${\overrightarrow{F}}_g=\frac{Gm}{r^2}{M}_g$. And Passive gravitational mass is the gravitational force exerted on that body in a gravitational field or Fg→=mgg⃗ .$\overrightarrow{F_g}=m_g\overrightarrow{g}.$

For quite a long time, physicists were trying to figure out whether inertial mass and the gravitational masses were the same. Einstein proved that there was no real difference between inertial mass and gravitational mass, so there was no real experiment that could differentiate the two. To think of it in a different way, assume you were stuck in a box, and you had no way of actually knowing what was outside that box. Now assume you were in a place in space, too distant to suffer significant gravitational force from anything. If we put rocket boosters in your box, with acceleration = 9.8 meters per second (about the same as the Earth’s gravitational acceleration), would you be able to notice the difference? Einstein concluded that you couldn’t, and that principle is called the equivalence principle, being the basis for General relativity. Also Einstein showed a equivalence in mass and energy, in Special Relativity (specifically Rest mass and Rest energy), because the true expression for a moving body is E2=m2c4+p2c2$E^2=m^2{c}^4+p^2{c}^2$, with p being the momentum of the body. If the body is not moving, p is equal to zero, and you get the famous E=mc2($E=m{c}^2$. Now this other equivalence is very important, because, considering that inertial mass is equivalent to gravitational mass, and inertial mass is equivalent to energy, that means that bodies without mass can also suffer gravitational force (i.e. photons).

As for where does mass come from, the modern quantum field theory says that is comes from the interaction of quantum fields of different particles with the Higgs field. You see, for the modern quantum field theory, all of the particles can be described as actually being oscillations in quantum fields, which are massless in their nature. In order for them to gain mass there needs to be a coupling of the respectively quantum fields with a Higgs field, breaking the symmetry of the system and getting this mass, as far as I understand the subject, which is not a lot. But we should definitely go back to this subject when we finally reach QFT.