# Akano's Blog

## Equation of the Day #3

Posted by Akano Toa of Electricity , in Math/Physics Oct 26 2012 · 75 views

Just so everyone knows, I obtained the awesome LEGO Haunted House over Fall Break and have pictures that will work wonderfully in a review. You can probably expect that next week at some point (I hope). For now, let's go over another fun physics equation! This one is probably very familiar to you, though you may not have any idea what it means. I give you mass-energy equivalence:

Where
E is energy, m is mass, and c is the speed of light. It's a very simple-looking equation with only three parameters, but what does it mean? Well, it means that anything with mass – you, your cat, your house, the Earth – has latent energy stored in it, and the amount of mass determines that latent energy. For an object at rest, this correlates to the rest mass of the object. If an object is moving really fast (near the speed of light) its kinetic energy causes it to actually get heavier, since the object can never actually reach the speed of light (only objects with no rest mass move at the speed of light).

So, if we have an object sitting and doing nothing, and it suddenly glows for a split second, then stops, where did the light come from? Well, light has energy, as we know, so we could calculate the energy of the light that escapes our object. If the light emanates in all directions, then the net kinetic energy of the object is unchanged. But conservation of energy says that energy can neither be created nor destroyed! Have we violated the laws of physics with our weird glowing object? Well, no, because if you were somehow able to weigh the object pre- and post-glow, you would find that the mass of this object is actually slightly less after the light is given off.

But wait! Doesn't conservation of mass say that matter can neither be created nor destroyed? Well, yes, it does say that. So the only way for this to make sense is if the mass is converted into the energy that was emitted. We know that energy can be converted into different forms (electric, mechanical, thermal, etc.), so this must mean that mass is another form of energy that can be converted to and from! Pretty neat, huh?

Minutephysics has a cool video on this with a bit more technicality and pretty pictures of radioactive cats, but this is my text-based explanation simplified.

Another thing that may cross your mind is that this looks very similar to Newton's second law:

So, does Newton's second law equate force with acceleration? Well, no, because in the mass-energy equation, the constant of proportionality,
c2, is a universal constant; it is the same for any and all objects in the universe. The mass of an object, however, varies from object to object, and is thus not a fundamental, universal constant, so while these equations are similar and relate two seemingly different entities, they do not conceptually perform the same task.

## Equation of the Day #2

Posted by Akano Toa of Electricity , in Math/Physics, Life Oct 13 2012 · 70 views

I had a wonderful time today; I got to see old friends from my undergrad today and went exploring a corn maze; it was a lot of fun.

Also, equation of the day: Newton's Second Law

where F is the net force, a is acceleration, and m is the mass of the object in question. It's such a simple-looking equation, but it contains so much physics. Want to know the path of a free-falling object subject only to the force of gravity? You use this equation. Want to know the attractive force and classical orbit of planets/atoms? You use this equation. Want to know the physics of a car skidding on pavement? You get the idea.

This equation is a staple of physics and is used extensively in intro and classical physics. Newton, you clever devil, you.

## Equation of the Day #1

Posted by Akano Toa of Electricity , in Math/Physics Oct 11 2012 · 97 views

So, I've decided to do one of those daily-like blog entries, though I can't guarantee that I'll be able to do this every day (being a busy grad student and all). I figured that, being a physics grad student, math might be one of my stronger suits (next to reviewing LEGO sets), so I'm going to try and share an equation with you and see if I can explain it well enough for people to understand. 8D

Tonight's equation: The wave equation.

This says that the sum of the change in the change in the function, ψ, with respect to the coordinates used to represent it is equal to the inverse square of the speed of the wave,c, modeled by ψ times the change in the change of ψ with respect to time.

This equation is the governing equation for all wave phenomena in our world. Sound waves, light waves, water waves, earthquakes, etc. are governed by this mathematical equation. In one dimension, the wave equation simplifies to

which has the lovely solutions

where A and B are determined by appropriate boundary conditions, and ω/k = c. This equation governs things like vibrations of a string, sound made by an air column in a pipe (like that of an organ, trumpet, or didgeridoo), or even waves created by playing with a slinky. It also governs the resonances of certain optical cavities, such as a laser or Fabry-Perot cavity.

Since waves are one of my favorite physical phenomena, I find it very appropriate to start with this one.

## There is no gravity on the moon...

Posted by Akano Toa of Electricity , in Math/Physics Oct 06 2012 · 196 views

Or, so some of my students in my Intro Physics lab think. Hopefully when you read the title you were ready to get your typing fingers ready to disprove me. You probably would have made an argument akin to the following mini-lecture.

Gravity is a force between objects/particles proportional to the objects' mass. Newton's universal gravitation looks like this:

Fg = - G m1m2/r2

where G is a proportionality constant, the m's are the masses of the two objects in question, and r is the distance between the two objects. This is why we feel the Earth's gravity affect us, but we don't feel the moon's or sun's gravity affect us. They most definitely influence the Earth (since the sun causes our orbit and the moon causes the tides), but we don't feel the effects of their presence.

So, if we have an object with mass m on Earth in free fall, its equation of motion is determined by

Fg = m a = - G m ME/r2

where ME is the mass of the Earth and a is the acceleration of the object. Note that, if we divide both sides by m, we find that

a = - G ME/r2

which means that the acceleration of an object in free fall has nothing to do with the mass of the object. In fact, you can see a video of this on the moon at Wikipedia's Gravitation page that shows Apollo 15 astronaut David Scott dropping a feather and hammer simultaneously. Since there is no air on the moon, the feather is not afloat longer than the hammer, and they fall at the same rate and hit the ground at the same time.

Also, while I said earlier that gravity affects things with mass, it also affects light, which does not have (rest) mass. However, light has energy, and as Einstein showed with his Special Theory of Relativity, energy and mass are equivalent:

E = m c2

So, you can construct the relativistic mass of light, thereby finding the equations that govern the changing of the straight path of light in a gravitational field. Using Einstein's General Theory of Relativity, you can also view the gravitational field as a curvature of spacetime, which influences straight lines to be curved in the space near the massive object, affecting the path of light.

Another interesting thing about mass: objects actually have two different masses associated with them: gravitational mass and inertial mass. Gravitational mass tells you how much an object interacts gravitationally, while inertial mass tells you how much an object resists a change in motion. In other words, more massive objects take more force/energy to alter their paths than objects with less mass. Here's the interesting thing, though: both these masses are equal, even though there really is no physical law stating that they have to be. The only reason we know these masses are equal is because empirical evidence says they are; there is no indication that these two masses are different to an appreciable/statistical extent.

So, if you think that there are no unanswered questions in the realm of physics, you are sorely mistaken.

## Just Thought I'd Mention This...

Posted by Akano Toa of Electricity , in Math/Physics Sep 17 2012 · 111 views
Acoustics, Iridescence, Rainbow and 2 more...
Science is awesome. I am currently reading a journal article about how people are making the acoustic version of iridescence. For those who don't know, iridescence is what certain insects, jewels, soap bubbles, and CDs exhibit as that rainbow effect that changes color depending on what angle it's viewed. The sonic or acoustic version of this is creating something that varies in pitch depending on the angle at which you stand relative to it.

Awesome.

## Neutrons Bouncing on Glass

Posted by Akano Toa of Electricity , in Math/Physics Sep 13 2012 · 111 views
Gravity, Awesome, Science and 1 more...

So, today our physics department had our Journal Club, where one of the professors/grad students get to share a journal article or two that they found in the vast amount of physics literature available to academia. Today our resident dark matter-seeking professor gave the talk, and boy was it awesome.

The researchers whose papers he found were bouncing neutrons on glass and looking at their quantum states due solely to the potential energy caused by gravity. Quantum mechanics with gravity.

For those of you who don't understand how ridiculously awesome this is, let me put it in terms of Classical Mechanics: when a classical object is under the influence of a uniform gravitational potential (like that near Earth's surface), it follows parabolic trajectories. Imagine a ball bouncing on a table; it forms a series of parabolic bounces, each one smaller than the last due to friction and lost energy due to sound and such. This is essentially what this group did, but with neutrons and glass.

However, because neutrons are not classical particles and instead behave quantum mechanically, they don't bounce in parabolic trajectories. Instead, they abide by the laws of quantum mechanics, which means that there are only certain heights above the table at which they are likely to be found and certain heights that they cannot be found. So, a neutron in the ground (lowest) state of this system is most likely to be found at about 10 microns (thousandths of a millimeter) above the glass.

Also, when this was published back in 2005, it was the first time quantized energy levels due to Earth's gravitational potential alone were ever observed experimentally; the theory has been known for a while, but this is the first time anyone has in any way verified it.

Now, this group is attempting to test the properties of the force of gravity using this apparatus and their neutrons. HOW AWESOME IS THAT?!

This blog entry brought to you by SCIENCE!

## Back to School

Posted by Akano Toa of Electricity , in Math/Physics Sep 04 2012 · 60 views

So, today was the first official day of school at my grad school, but I didn't have any classes. Today was lab orientation for Monday and Tuesday lab sections (since we had yesterday off). Having nearly 50 students crammed into a room only able to seat 32 is rather entertaining.

Also, I have a talk to give on Friday on my research I did over the summer. This wouldn't be so much of an issue if I knew which part of the research to discuss, as I worked with two undergrads, and we have to split the topics of our research between us. However, one of the students worked in another lab over the summer as well, so she's probably not going to present on what the three of us did at all. Now the talk has to be divided in half.

Also, did I mention the talk was Friday? ._.

## Curiosity's on Mars

Posted by Akano Toa of Electricity , in Math/Physics Aug 06 2012 · 82 views

Yay, science! 8D

## It's A Trap!

Posted by Akano Toa of Electricity , in Math/Physics Jun 25 2012 · 45 views

A magneto-optical trap. We just got it back up and running again after many days of realigning things (which is quite a pain, but it builds character ). The image is taken from a TV screen since the collection of atoms shown (the bright, white dot in the center) scatters light very dimly in the near-infrared, so our eyes can't see them, but security cameras can. The collection of atoms in the center is just above absolute zero (-273.15°C) by millionths of a degree. I don't remember off hand what the number of atoms is in the trap, but I'm assuming it's fairly large (~106?).

## Summer: Week 1

Posted by Akano Toa of Electricity , in Math/Physics, Life May 24 2012 · 93 views

Already I'm nearly through my first week of summer research. That's kinda weird.

What I've gained from this experience thus far: aligning a laser beam so that it hits a fiber optic cord that's ~1-2 microns in diameter is tedious, painful, and annoying. However, magneto-optical traps and ultracold plasmas are awesome. I am learning a lot about optics and atomic physics despite it only being week one, and I'm sure this lab will be fun.

This weekend I hope to work on my Whirling Time Warper review (I have the pics, I just have to type and format everything) and maybe even make a new comic! Hurray for no homework and more free time!

Akano Toa of Electricity

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Name: Akano
Real Name: Forever Shrouded in Mystery
Age: 23
Gender: Male
Likes: Science, Math, LEGO, Bionicle, Ponies, Comics, Yellow, Voice Acting
Notable Facts: One of the few Comic Veterans still around
Has been a LEGO fan since ~1996
Bionicle fan from the beginning
Misses the 90's. A lot.