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Archives for: June 2009 - Ask Dr. Volt!
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The Pauper's Theater
  
Ask Dr. Volt!
 
Befuddled by physics?  Stymied by science?  Then ask Dr. Volt!
 
Dr. Volt, certified Mad Scientist, will take your questions, scrutinize them over a Bunsen burner, and post the answers here!  You can also search the archives for answers to past questions.
 



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The Theory of Relativity


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Jacob H. asks, "I understand that causality is no longer valid with the theory of Relativity. Can you please explain this?"

Ah, Jacob, this certainly is one of the more peculiar aspects to Relativity! First, however, let us start by establishing a few basics of Einstein's Theory. In Relativity we deal with what are called inertial reference frames, which are simply the frame of reference for any observer moving at a constant speed (a non-inertial reference frame, on the other hand, is a reference frame that is accelerating, and things there become much more complicated). One of the key concepts of Relativity is that while the physical laws are the same in all reference frames, there is no frame of reference that can be said to be at absolute rest. All we can say is that one reference frame is moving relative to another, and whether we choose frame A to be moving relative to frame B or the other way around, it makes no difference, both are equally valid. We can easily visualize this principle when we are riding in a car. To someone standing on the road it appears that they are at rest and we in the car are moving. To us in the car, however, it feels as if we are at rest and the person on the road moves past us. According to Relativity this is more than a mere perception and it is perfectly valid to say that we in the car are in fact the ones at rest with the whole of the world moving relative to us.

Now at normal, everyday speeds this still doesn't make much of a difference for us, but if we are moving at speeds that approach the speed of light, things become much more interesting. For example, the closer we go to the speed of light, the slower time moves (what is termed time dilation) and a clock held by a moving observer will tick more slowly compared to one help by a stationary observer. This can even be seen at relatively slow speeds - an atomic clock on an airplane will eventually run slow as compared to a similar atomic clock that remains on the ground. The different will be incredibly small, but real, and is a result of the clock's motion while sitting on the airplane and not any fault of the timepiece.

"But wait, Dr. Volt, didn't we just say that there isn't any absolute reference frame? We did, as long as it's not accelerating. While the plane is in the air, moving at a constant speed, it will appear to someone on the plane that it is the clock on the ground that is moving and thus running slow. But because the plane must eventually stop on the ground (thus entering the reference frame of the ground clock) it will at some point experience an acceleration which ultimately allows us to say more absolutely that the plane's clock is the one running slow.

So now let's let look at the issue of causality. When one inertial frame is moving near the speed of light relative to the other, then each frame can legitimately say that they are the frame at rest. Now let's imagine that in frame A we have a garage with a door on both ends, and in frame B we have a vehicle. Furthermore, the garage doors are automatic such that as soon as the car reaches one it will instantly open, and as soon as the car has passed through it will instantly close. Now, when both frames are at rest relative to each other the car is longer than the garage. However, another strange feature of Relativity is that when an object moves close to the speed of light its length contracts. So let's assume that the car in frame B is moving fast enough that it's length contracts to a point where it is now shorter than the garage. When it drives through the garage in frame A, an observer in frame A will see the car at some point fully contained within the garage. But wait! The driver of the car in frame B can say that he is the one stationary with the garage moving past him. In that case it is the garage that is moving close to the speed of light and thus becomes shorter, and the driver in frame B will never see a moment in which the car sits entirely within the garage.

We have here a seeming paradox - two observers making fully accurate observations cannot agree on what actually occurs. Either one of them is wrong or our assumptions are incorrect. Relativity says that both observers are correct and that it is indeed our assumptions that are wrong. Specifically, our assumption that events that happen at the same time for one reference frame (i.e. the events of both garage doors being closed) happen at the same time for all observers. The solution to our paradox lies in the fact that they do not. In this example the two observers see the same events happen at different times because the large relative speed between them causes events that are simultaneous in one reference frame to not be so in another. A consequence of this is that there can be certain events in one reference frame which cannot affect certain events in another reference frame because while the "cause" may happen before the "effect" in one reference frame, in another it may be the "effect" that happens first!

So as you can see, Jacob, the world of Relativity is a both fascinating and perplexing place, but I hope this has given you (and our other readers) a taste of this intriguing theory. Its elegance, and dare I say beauty (which you must delve into the mathematics to fully appreciate), speaks volumes of Einstein's great genius.

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What is the periodic table of the elements?

Kate S. asks, "Dr. Volt, can you please explain the periodic table of the elements? Why does each element have a different atomic mass?"

An excellent topic, Kate! Let's start with the question of atomic mass and the related atomic number. Each element has a unique atomic number which gives the number of protons (positive charge) found in its nucleus. The simplest element, hydrogen, has only one proton and thus an atomic number of 1. Atomic mass takes into account both the number of protons in an atom, but also the number of neutrons (no charge). Atomic mass, however, is not necessarily the same for all atoms of an element, because many elements have different isotopes, which means they have a different number of neutrons. For example, most carbon atoms have an atomic mass of 12 - 6 protons and 6 neutrons. But some carbon atoms have more neutrons, for a total of 8. These atoms then have an atomic mass of 14, but still an atomic number of 6. Carbon-14, as it is called, is radioactive and will ultimately decay, and thus is not found in as large of quantities as everyday Carbon-12.

So why is the periodic table arranged as it is? To start with, in addition to the protons and neutrons in its nucleus, an atom also consists of one or more electrons which orbit the nucleus. The electrons are negatively charged, and so to balance out the atom's total charge an atom will normally have the same number of electrons and protons. The chemical properties of a particular element are greatly affected by the way that the electrons are arranged. Quantum mechanics tells us that no two electrons in an atom may exist in the exact same state, and this leads to the electrons arranging themselves in different "shells," or layers. The first electron shell can hold up to 2 electrons. Hydrogen, with just 1 electron, thus has its electron shell half full, while Helium, with 2 electrons has its shell completely full. The third element, Lithium, has its first shell filled with 2 electrons, followed by 1 electron in the next shell, and so on with all the other elements.

The number of electrons in an elements outer shell are a major facto in determining the element's chemical properties, as atoms "like" to have their outer electron shell full. Thus an atom with just 1 electron in the outer shell will bond most easily with an atom whose outer shell is missing 1 electron. The first atom can then share the electron with the second, and they both then are "happy" with what looks to them like a full outer shell. Elements such as Neon, however, where the outer electron shell is completely full, are chemically inert as they don't feel the need to share their electrons with anyone else.

So as you move horizontally across the periodic table, this corresponds to the filling of the electron shells: the first element in a line has just 1 electron in the other shell, the last in a row has a full outer shell. The elements in each vertical line on the table are thus chemically similar because they have the same number of electrons in their outer shell. There are other factors, of course, which also affect the chemical properties of an element, but it is the filling of the electron shells which gives the periodic table its basic shape.

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Why does music sound different in different parts of a concert hall?

Mary Kay S. asks, "Dr. Volt, why is the sound different in different parts of a concert hall? Where should I sit to get the best sound?"

Ah, it all has to do with acoustics - the physics of how sound, well, sounds in a particular space. Every surface, be it the walls, the seats, and even the audience, will absorb or reflect the sound in a particular way. Concert halls are designed in order to maximize the quality of the sound, both for the listeners, but for the performers as well. If, for example, all the sound is absorbed by the walls, the ceiling, etc. before it ever has a chance to reach the audience's ears, then you can bet they will soon be making a very lively march towards the box office for a refund! The key is to create surfaces in the hall such that the sound is evenly distributed over the entire hall, but yet doesn't reverberate too long (else it will interfere with the sound still to come). It is also important that enough sound bounce back to the performers, so that they are able to hear one another. Otherwise while the audience may hear very clearly, the performance may not turn out to be worth hearing! As you can imagine this all poses a very difficult puzzle for the acoustical engineers designing the hall, further complicated by the fact that you have to take into account how the hall will sound when people are filling all of the seats.

The ancient Greeks were geniuses when it came to acoustics. Their amphitheatres were designed such that an actor on stage could be heard clearly by thousands of spectators all at once, a feat which proves a challenge even for our modern engineering.

As for the best place to sit, that I think is left in "the eye of the beholder." A well-designed concert hall should have excellent sound wherever you sit, and thus it all comes down to your own personal preference.


The Greek ampitheatre at Epidaurus

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What's the big deal about potential energy?

Patty B. asks, "Dr. Volt, what's the big deal about potential energy?"

Ah, potential energy, one of my favorite concepts, for really, where would we be without it? But let's start at the beginning with energy in general. There are two primary types of energy: kinetic energy and potential energy. An object's total energy is the sum of the two and will always remain constant.** Kinetic energy is an object's energy of motion, given by Kinetic Energy = ½mv2. Here m is the object's mass and v is the object's velocity (or speed). All other forms of energy are potential energy, which simply means that they have the potential to become energy of motion. Gravitational potential energy would be a common example. As a lift an object up (that is, away from the Earth) it gains potential energy due to gravity. When I release the object, and gravity pulls it back to Earth, that potential energy is transformed into kinetic energy.

But perhaps a more mad sciencey example is in order. Another form of potential energy is chemical potential energy, which is how batteries work. In a battery a chemical reaction inside creates an electric current, which is simply electrons in motion, i.e. kinetic energy. But a much more exciting example is this:

  

That's right, it's our old friend trinitrotoluene, better known as TNT. TNT is a chemical that contains a great deal of chemical potential energy, enough so that when that potential energy is released the results are quite, well, explosive. Chemical potential energy is also found in many fuels that we use, such as oil or coal, not to mention the food we eat in order to gain the energy to pursue our dreams of world domination (I am quite partial in this regard to banana splits).

So you see, Patty, potential energy is all around us and is quite a big deal indeed! For more information on potential energy I suggest you attend my Mad Scientist Training Academy this summer (Assistant's note: see Schrödinger's Cat Must Die!). I think you shall find it most enlightening!

**All right, technically it is the mass and energy combined that remains constant, as shown by Einstein in his famous equation Energy = mc2 where c is the speed of light. Show off.

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