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6.2: Section 1: What is Modern Physics?

Difficulty Level: At Grade Created by: CK-12
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“The supreme task of the physicist is to arrive at those universal elementary laws from which the cosmos can be built up by pure deduction. There is no logical path to these laws; only intuition, resting on sympathetic understanding of experience, can reach them.” (Einstein 8)

Question 1: How do you see?

When you see an object, what actually is happening is light from some outside source is bouncing off the object and is reflected into your eye. The rods and cones in the back of the eye are like little receptors, and the brain interprets these stimuli to form a picture.

Question 2: Why can’t we see atoms? Objects are made of atoms and light is reflecting off of them, right? Why don’t we see the little “balls” that make up the object?

There are a few complications when trying to see atoms. Light is a wave and different colors of light have different wavelengths or frequencies. When we say wavelength, we are referring to the length of one “repeat.” That wavelength would include one crest and one trough. Frequency refers to the number of “repeats” of crests in a specified amount of time. The wavelength and frequency of a wave a related to each other: a long (short) wavelength corresponds to a low (high) frequency. Wavelengths are the key here. We actually can’t see all of the wavelengths of light. We can only see red, orange, yellow, blue, indigo, and violet. Red has the longest wavelength and violet has the shortest. There are many wavelengths that are longer than red and many wavelengths that are shorter than violet, but the cones and rods in our eyes do not detect them. The next longest wavelength beyond red is infrared and the next shortest wavelength beyond violet is ultraviolet. These segments of the spectrum should be familiar to you.

Now let’s extend the concept of light to sound waves for a moment, as they are a good parallel to light waves. Have you heard of ultrasound? You probably think of babies when you hear that word. That’s because we use ultrasound to “see” a baby. The prefix “ultra” refers to a high frequency. High frequencies have short wavelengths. The following diagrams should help clarify this.

Diagrams of waves with different frequencies and wavelengths

Diagrams of Waves with Different Frequencies and Wavelengths.

We use ultrasonic waves or sound waves with a short wavelength to “see” the baby because babies are small. If we used a long wavelength, the waves would pass right over the baby without bouncing off. We want the sound wave to bounce off the baby, like light bounces off objects that you see with your eyes. Simply put, the ultrasonic waves are small and easily bounce off a baby’s tiny frame, and then are interpreted by a computer (like your brain interprets light) to form a picture.

Let’s think about ants for a moment. Have you ever walked along a sidewalk and noticed a colony of ants all grouped in the crack? What if you wanted to step on them to kill them? Would you march around on top of them taking big steps or would you march taking tiny steps? You would probably use small steps so that you wouldn’t miss any of them because ants are small. Now, have you ever noticed dust floating in the air near a bright window? How come you can’t see the dust floating anywhere except near the window? Well, the light coming through the window has lots of different wavelengths and some of the wavelengths are small enough that they bounce off the dust and are reflected into your eye for your brain to interpret. All of the long wavelengths of that light just pass right over the dust, just like if you take a big step over a colony of ants, and just like long wavelengths of sound would pass right over the baby. All the short wavelengths of that light would hit the dust and bounce off. (Incidentally, shorter wavelengths [higher frequencies] are higher energy waves for light and longer wavelengths [lower frequencies] are lower energy waves for light.) This idea is used in (physical rather than geometric) optics: you need to much the wavelength with the size of the object in order to "see" it.

How does this relate to seeing atoms? Atoms are very tiny. Scientists have found that if you line up ten carbon atoms, they will be about 1 nanometer long. A nanometer is very small. Hold up your hands to about the size of a meterstick (close to a yardstick). If you could divide that meterstick up into \begin{align*}1,000,000,000\end{align*} (or \begin{align*}10^9\end{align*}, or a billion) little equal parts, one of those parts would be the size of \begin{align*}10\end{align*} carbon atoms lined up in a row. It’s hard to imagine a number like a billion because we don’t usually think about it. The wavelength of violet light, the shortest wavelength of visible light, is \begin{align*}400\end{align*} nanometers long, which is 400 times larger than the ten carbon atoms lined up. Metaphorically, that’s like taking steps that are two meters long when trying to kill ants that are half centimeters long. You would not kill too many ants taking steps that big, and similarly you can’t see tiny atoms shining violet light on them. The violet light is just too big and won’t reflect off the tiny atoms so you could see them. The violet light will just pass right over the atoms.

And even when we do shine light on atoms with a wavelength that is small enough to bounce off the atom and into a detector, some complications occur. It turns out that light causes changes in the atom because light carries energy.

Question 3: So how do we know atoms exist?

Consider cutting a piece of paper in half. Now cut one of the resulting halves in half again. Continue doing this. How many times can you cut it before it can no longer be cut? Is there a limit? Around \begin{align*}400\end{align*} BCE the Greek philosophers Democritus and his instructor Leucippus considered this and decided that there must be a “tiniest” part that cannot be divided and they called it an atom. They theorized that matter has whole building blocks. You can relate it to your skin cells. Your skin cells are your basic building block for your skin, and if you cut one in half, you no longer have a skin cell. The cell is the “smallest whole” of your skin. Democritus and Leucippus theorized that there must be a “smallest whole” of matter. This happened way before instruments were developed to detect atoms.

There wasn’t much in the development of the theory of atoms until much later, around the early 1800s. Summarized very briefly, chemists were taking very careful measurements of masses and ratios of combining elements (such as hydrogen and oxygen to form water) and found that the ratios of elements in compounds is fixed. This analysis is attributed to John Dalton, although he was building on Antoine Lavoisier, among other chemists. The significance of this follows: Elements combine together in specific ratios, and this must mean that there are “smallest wholes” that can be added, but you cannot add a part of a whole. For example, you can have three atoms of hydrogen, or four atoms of hydrogen, but not three and a half. Dalton found that if you have \begin{align*}1\end{align*} gram of hydrogen and combine it with \begin{align*}8\end{align*} grams of oxygen, you get water. The ratio of oxygen to hydrogen is \begin{align*}8:1\end{align*}, and this is fixed. You can also get water with \begin{align*}16\end{align*} grams of oxygen and \begin{align*}2\end{align*} grams of hydrogen, or any multiple of this specific ratio. Dalton considered this and decided that there must be atoms, or little whole chunks of matter, which give this ratio.

Now physicists can “see” atoms by using as electron microscope, which uses electrons to magnify objects.

Question 4: How do we know the basic structure of an atom?

We can “see” atoms in other ways. We can see evidence of atoms. Close your eyes and feel the tabletop. You can tell it’s a table by how it feels, right? What if you were not allowed to feel it with your hands, but could touch and poke it with a stick? Would you be able to tell that it’s a table? It might take awhile, but you probably could figure out that it’s heavy by trying to push it with the stick. You could probably figure out that it’s hard by poking it. You could probably figure out how big it is by tracing along the tabletop with the stick. You could get a pretty good mental picture by just using a stick. (You should play a little game and try this.)

Similar things have been done with atoms. In 1909, two British scientists, Hans Geiger and Ernest Marsden, took a sheet of very, very thin gold foil (like aluminum foil, except gold), and sent tiny particles toward it to detect what makes up the foil. Imagine taking a tennis ball shooter (like what tennis players use to practice their swing) and pointing it toward the chain fence that surrounds the tennis court. Instead of shooting tennis balls, shoot ping-pong balls instead. You would notice that some of the ping-pong balls would go right through the fence and some would bounce back, depending on what part of the fence they hit.

Geiger and Marsden did the same thing, except on a smaller scale. They sent alpha particles (\begin{align*}^{4}\mathrm{He}-\end{align*}nuclei) toward the foil and noticed that most of them went straight through the foil, but some of them bounced back. Please note that the momentum of the alpha particles they sent toward the gold foil was very high, and they completely expected them to pass right through. Ernest Rutherford, a scientist who used this experiment to develop his ideas on the structure of an atom describes it as shooting bullets at tissue paper. There was no reason for Geiger and Marsden to expect any reflection of the alpha particles, but that’s exactly what they observed. Because most of the alpha particles went right through, the scientists knew there must be empty space (where the electron cloud is, actually), and because some of the alpha particles were repelled back, the scientists knew there must be a dense core in the middle of the empty space. That’s the indirect evidence of the existence of the nucleus of the atom.

Question 5: How do we know there are electrons? Is it the same experiment as for the nucleus?

Not quite. And actually, the evidence for the electron came before the evidence for the nucleus.

It was J. J. Thomson in 1897 who was able to construct an experiment that helped scientists conclude that electrons are negatively charged. Thomson created a series of experiments applied to a stream of electrons (at the time they were called cathode rays) that were propagated through a vacuum tube (cathode tube). Thomson saw that the cathode rays had a negative charge, and thought he might try to separate the negative charge from the ray, but when he used a magnet, which bends negative charge, he saw that the whole ray bent, and he could not separate the charge from the cathode ray. From this and a couple of other experiments on the cathode rays he came up with the following hypotheses. His first hypothesis was that the cathode rays themselves are charged particles, because he was unable to separate the charge from the ray. His second hypothesis was that these particles were part of the atom (a smaller particle that makes up the atom), because when he calculated the mass-to-charge ratio, he found that it was much smaller than the atom. At the time most scientists thought of the atom as indivisible, so to find a smaller particle was unbelievable for many scientists. His third hypothesis was that these particles were the only building-blocks of the atom, which turns out to be incorrect, as we now know.

Thomson proposed that because the atom was known to be neutral, perhaps these electrons swam around inside a cloud of massless, positive charge. His model was sometimes called the “plum pudding model.” Of course, we know this turned out to be incorrect because Geiger and Marsden with Rutherford were able to show us the nucleus.

These days, scientists detect particles using particle accelerators. Here in Virginia, we have a particle accelerator at Jefferson Lab in Newport News (there are other particle accelerator labs in places such as Switzerland, Illinois, and California). Basically, scientists shoot particles at atoms and then watch where the particles go. Scientists can cause an electron to eject from an atom and watch its path, which helps them learn basic things about atoms and particles (particles leave “tracks” that scientists can detect).

Question 6: How do we know that there are protons and neutrons in the nucleus?

We already know that particles with opposite charges attract, like the proton and the electron. This attractive force is what keeps the electron in its orbit (or cloud) around the nucleus. It’s similar to the way the Moon is attracted to the Earth and the Earth to the Moon. The gravitational pull (from the gravitational force) between the Earth and the Moon pulls the Moon inward. Likewise, the electric pull (from the electromagnetic force) between the electron and the proton pulls the electron inward.

Particles with the same charge repel one another. For example, if you put two protons near each other, they push each other away. So, how can a nucleus full of protons stay together? Wouldn’t the protons all repel each other like they repelled the alpha particle in the gold foil experiment? What glues them together in the nucleus?

Well, it’s what physicists call the strong force, or the strong interaction. The strong force is what’s responsible for the binding energy, which is the energy that glues together protons and neutrons in the nucleus. Without the neutrons, the protons would fly apart because of the electromagnetic force (like charges repel). Therefore, the strong force has to be bigger than the electromagnetic force that causes the protons to repel each other. For example, suppose that you and your brother are pushing each other away. To keep you close together and prevent you from pushing each other apart, your parents would have to hold you together with a greater force than the force you and your brother are using to push each other apart. That force holding you together (your parents’ arms) is like the strong force that holds the protons together in the nucleus, even though they push each other apart. The neutrons provide part of this force, although protons themselves also contribute to the strong force. The strong force exists only in short range, meaning that the protons repel in general because of their charges, but if they are close enough (and they have to be very close), a different force (the strong force) attracts them together. If the nucleus just had protons, the short-range strong force would not be enough to hold the protons together, especially if it’s an atom with lots of protons (lots of repulsion force). It’s the neutrons that add enough of the strong force to keep them together because they don’t contribute to the repulsion (neutrons have zero charge and thus do not repel). The neutrons only contribute to the strong force, the force of attraction. The strong force is many more times greater than the electromagnetic force that causes the protons to repel. It’s worth mentioning again, though, that the strong force only exists at very short ranges. That means if protons or neutrons are far apart, the strong force does not affect them. Only when they are close neighbors does the strong force create a large result (Weidner \begin{align*}415\end{align*}).

Question 7: What are quarks and how do they play a role inside the atom?

You have probably heard of the term quark and are wondering how it fits in the whole picture. We can explain the quark in terms of the strong force we just learned about.

Recall how an atom is made up of smaller parts: electrons and nucleons (i.e., protons and neutrons). Electrons zip around the outside of the atom and protons and neutrons are inside the nucleus. Scientists presently think that electrons are fundamental particles, meaning that there is nothing that is smaller that composes an electron. However, neutrons and protons are not fundamental particles because there are particles that come together to create neutrons or protons. Think about it this way, just like a building is made of smaller components, such as bricks, in the same way protons and neutrons are composed of smaller quarks. The bricks are the quarks. The electron is like a brick, in that it is the smallest part. There does not seem to be anything smaller that builds an electron (so far). We call the electron a lepto (a different kind of brick than a quark).

Feynman and others explained in the 1940s that the Coulomb force between electric charges is mediated by the exchange of (virtual) photons (or "light particles," see below). This theory is called the Quantum Electrodynamics [QED] and remains one of the triumphs of theoretical physics. Likewise, quarks inside the protons and neutrons “interact” with each other by force carriers called gluons. You might think of these gluons as how the quarks let other quarks know they are there. The gluons “carry” the force that keeps the quarks together, the action that also keeps the nucleons together in the nucleus. The quarks inside the neutrons and the protons communicate their force by way of gluon and “stick” together (hence, gluon is like glue). This theory is called Quantum Chromodynamics [QCD].

There are six different kinds, or flavors, of quarks, and physicists have thought of some creative names (maybe these scientists have spent too much time in their offices alone!): up, down, top, bottom, charm, and strange quarks. A proton is made of two up and one down quark. The neutron is made of one up and two down quarks. Just think of the different types of quarks as different types of bricks used to make different things. Quarks also have another property similar to the property of charge that we see with electrons and protons, and physicists call it color. Please note that the color of a quark has nothing to do with colors that we see, it’s just a way of categorizing (they can be red, blue, and green).

Question 8: What are alpha particles and where do we get them?

There are many types of particles, and, in fact, physicists often call all the particles together “the particle zoo.” You already know some of them: electrons, protons, and neutrons. There are lots of other types as well. Scientists predicted some of these particles before they saw evidence of them in experiments because they saw patterns. There are probably more particles that are as yet undiscovered.

An alpha particle is identical to the nucleus of a helium atom. If you look at the Periodic Table of Elements, the Helium atom has two protons and two neutrons (it’s the second element).

At the time of the gold foil experiment, scientists knew a little about the element radium. I’m sure you’ve heard of radium. It probably makes you think about radioactivity, and then you probably think of the Earth science lesson you had involving half-life. Radium is an element that naturally emits alpha particles (or helium ions). So radium “puts off” or emits streams of helium atoms. Geiger and Marsden pointed the radium in the direction of the gold foil, much like you would point a gun, and waited for the radium to naturally emit the alpha particles.

Question 9: What really is radioactivity? Why do some elements emit or “put off” streams of alpha particles? Do any elements emit particles other than alpha particles?

Radioactivity occurs naturally, but can also be triggered. Radium, for example, naturally radiates alpha particles, which is why it was a good element to use for the gold foil experiment.

Recall how the electromagnetic force causes protons to repel one another. Also recall that there are three quarks in each proton and neutron that exert forces on each other by way of the gluon, called the strong force. The more protons there are, the bigger the strong force has to be in order to cancel out the electromagnetic force repelling the protons away from each other. This occurs by way of the neutron, because it adds no extra repulsion force, but does contribute to the strong force holding the quarks of the protons and neutrons together. This means that the more protons there are, the more neutrons are needed in the nucleus in order to balance out the repulsion force between the protons.

Moreover, when you group more than about \begin{align*}83\end{align*} protons together, no matter how many neutrons are included, the nucleus becomes unstable. This is where we get nuclear decay, which causes radioactivity. Instability of the nucleus can also occur if the nucleus has too many neutrons. We call nuclei that have lots of protons and neutrons heavy nuclei, and heavy nuclei are not stable. The atom tries to gain stability through various means.

The three most common means for an atom to gain stability are as follows. The first way is by ejecting alpha particles. The second way is by converting a proton to a neutron or a neutron to a proton (whichever is needed) by ejecting a beta particle. A beta particle is another name for an electron or a positron. A positron is a positively charged particle that has the same mass as an electron, but is positively charged. We have not talked about it yet, but neutrons themselves can convert to protons by releasing an electron (and a tiny particle called an anti-neutrino). When we say that the neutron releases an electron, we don’t mean that the electron is somewhere inside the neutron and the neutron lets it out. Rather, the electron and antineutrino are essentially essentially created out of ``nothing," as strange as this may sound. The third way a nucleus gains stability is by releasing energy via a gamma ray or gamma emission. A gamma ray is just a photon or a bit of light. Sometimes we call this electromagnetic radiation. Gamma rays are on the high-energy, and therefore high-frequency and short wavelength side of the electromagnetic spectrum.

Question 10: What is quantum mechanics and why did it develop? What part of physics was not complete?

“The more success the quantum theory has, the sillier it looks.” (Einstein, “Zangger”)

Quantum mechanics is the study of subatomic particles (particles smaller than the atom), like electrons, protons, neutrons, and light (photons), and how they interact. Anything you see now in the news about nanoscience deals with quantum mechanics. It may help you to know that about \begin{align*}10\end{align*} carbon atoms lined up gives you the size of one nanometer. Nanotechnology is just the manipulation of atoms on the nanoscale.

You may have seen atoms pictured like solar systems. The nucleus is like the Sun and the electrons orbit around the nucleus like the planets orbit our Sun. This is not quite what happens and scientists who study subatomic particles have found some very interesting results in experimentation and philosophical thinking, using logic (Einstein called these logic experiments “thought” experiments, or gedanken experiments).

So what led scientists to think that the atom was like a solar system? And now what leads them to think that the atom is not exactly like a solar system?

Let’s explore the first question by studying Ernest Rutherford who was a scientist around the early 1900s (just after J. J. Thomson discovered clear evidence of the negatively charged electron in the cathode tube). Recall the Geiger-Marsden experiment from earlier. Geiger and Marsden sent alpha particles (created by the natural radioactivity of radium) toward gold foil and they found that a small percentage of the alpha particles bounced back. This caused Rutherford to believe that a dense mass is located in the center of an atom, albeit small. In 1911 Rutherford theoretically placed the electrons zipping around the nucleus for his model of the atom. It was known that the overall charge of the atom was zero and if the electrons were around the outside of the dense center, then the center had to be positively charged to keep the whole atom neutrally charged.

Rutherford explored this scenario and did some calculations, which produced some confusion. According to classical physics, the electron should release electromagnetic radiation while it orbits. In accordance with classical physics, all accelerated charged particles produce radiation, or in other words, release waves of light. The key word here is accelerated. Note that here we are referencing the familiar centripetal (circular) motion.

Recall that any object moving in a circle is constantly changing direction, and for an object to change direction, there must be a force acting on it causing it to change direction. According to Newton’s second law, if there is a force, there is an acceleration \begin{align*}(F_{net} = ma)\end{align*}. The laws of electricity and magnetism then show that the electron must be releasing radiation because it is constantly accelerating (orbiting). As it releases the radiation, it will lose energy, and therefore it should spiral inwards toward the nucleus. According to this theory, all matter is unstable, and the amount of time it would take the electrons to collapse into the nucleus is only \begin{align*}0.00000010 \;\mathrm{s}\end{align*}! There has to be a better theory for the structure of an atom, as this one does not work for two reasons. The first is that the electrons would collapse into the nucleus. The second is that scientists would be able to detect a continuous (smooth) spectrum of radiation emitted by the spiraling electron, and they do not. The reason that the radiation from the electron is continuous is that the radiation emitted by the orbiting electron depends on the radius at which the electron is orbiting, and if the radius of the electron continuously decreases (toward the nucleus), then the frequency of the radiation produced by the orbiting electron must also change continuously, and in fact would increase (Weidner \begin{align*}175\end{align*}).

What scientists do detect is radiation of discrete frequencies, meaning that there are no in-between frequencies emitted. Think of it this way: Electrons may emit a frequency of a or a frequency of \begin{align*}b\end{align*}, but no frequencies in between. Therefore, the electron can’t be spiraling inward, as it would have to emit each frequency associated with each radial distance from the nucleus. (A thorough analysis of the mathematics that govern this logic can be studied in a modern physics course, usually the course taken right after a general physics class in college.)

Niels Bohr came next with an improvement on the picture of the atom around 1913 (he was a student of Rutherford and Thomson). Bohr suggested that the atom had a nucleus of positive charge like before and that the electrons orbit around the nucleus at specific radii, like our solar system (like Rutherford’s model), with some modification. It does not describe the atom quite as accurately as Louis de Broglie does in the 1920s, but it does make some good leaps forward. He involves Einstein’s idea of the photon, which we will discuss later.

What Bohr did was discard the very idea that the orbiting electron would spiral inward (as predicted by classical mechanics), and proceeded from there. He considered the idea that the electron orbited at discrete radii instead. What is meant by this is that the electron can be at a distance of \begin{align*}r\end{align*} or \begin{align*}2\mathrm{r}\end{align*} from the nucleus, but nowhere in between. This would mean that the electron would not spiral inward and would have a certain amount of energy, the amount associated with that radius of orbit. For an electron to increase or decrease its distance from the nucleus, it would have to obtain or release a discrete amount of energy that would place it at the next orbit. In other words, if you don’t give the electron enough extra energy, it won’t jump to the next orbit, and it won’t orbit in between. Perhaps thinking of orbits like a flight of stairs would help. You may stand on the first step or the second step, but you can’t stand in between. You have to use the exact amount of energy needed to get to the next step. Using enough energy to get halfway to the next step will not result in you floating in-between the second step and the first step; that is preposterous! It’s the same, according to Bohr, for the electron. This solves the problems Rutherford’s model had. This means that no energy is lost by orbiting, and therefore the electron does not spiral to the nucleus, and does not emit a continuous spectrum of light as it spirals inward. Bohr doesn’t explain how the light (photon) is created, rather he just makes the connection that as the electron makes a quantum jump to a lower orbit (closer to the nucleus), it emits a photon whose frequency corresponds to the amount of energy lost in moving closer to the nucleus.

So what are the shortcomings of Bohr’s model of the atom? It does not account for the wave-mechanical nature of matter and light (it’s okay if you don’t understand that phrase), nor can it account for atoms with more than one electron, and also it doesn’t really explain why certain radii are allowed. We need a new scientist to take us a little further into understanding the internal structure of an atom.

The next person to make a conjecture for the structure of an atom is the French scientist Louise de Broglie. First, let’s discuss light for a moment. Sometimes we think of light as little traveling packets, called photons. Sometimes we think of light as waves, with a frequency and a wavelength. It turns out that both seem to be good descriptions of light depending on the nature of the experiment we want to understand. We’ll discuss this in a moment using Einstein’s Nobel-winning experiment called the photoelectric effect. Louise de Broglie initially just made the assumption that matter had wave-like properties, and then followed the logic to its end by using mathematics. The idea is strange, but the mathematics produces an accurate model for physics, and corroborates with experimentation results well.

The more we peer into the internal structure of atoms, the stranger things seem to be, and because we can’t see inside directly, we rely on mathematics and indirect methods of analyzing the particles. Sometimes physics is stranger than science fiction! Please note, though, that physics is always logical, just not always intuitive. The natural language of physics is mathematics, and mathematics by its very nature follows logical reasoning. However, its solutions are not always what we expect!

Question 11: What is the photoelectric effect? What does it mean to say that matter has wave-like properties?

Einstein was awarded the Nobel Prize in physics for interpreting the results of this ingenious experiment, first performed by Heinrich Hertz in the late 1800s. The photoelectric effect explores the energy of electrons and the energy carried by light. What Hertz did was shine ultraviolet light on zinc and he found that it became positively charged, which could not be explained at the time. The striking finding is that electrons are observed as soon the light is turned on, rather than the several minutes predicted from classical theory (electricity and magnetism). What Einstein figured out was that electrons can be “knocked” from the metal through the energy from the light shined on the metal, with a few important reservations. First, it depends on the frequency of light that is used. If you use a frequency that is not high enough, the electron will not be affected. The frequency necessary depends on the amount of energy binding the electron to the metal, called the work function. Of course, all light has energy. Prior to the results of this experiment, scientists believed that if you shone light on an object long enough, the energy possessed by the light would build up in that object. What Einstein showed is that energy does not “build up” in the electron. One has to use a frequency of light that has enough energy to provide one swift “kick” (the energy of the light is proportional to its frequency, as predicted by de Broglie) to cause the electron to jump from its orbit.

What are the ramifications of this experiment? For one, we learn that light can be described as a little chunk of energy. For example, suppose your friend is standing on the edge of the deep end of a pool and you want to push him in. Suppose you use a tiny push and he doesn’t fall in, so you push him again with a tiny push. Will he fall in this time? No. It doesn’t matter how many tiny pushes you give him in a row, if the push isn’t large enough, it won’t overcome the friction he has between his feet and the ground and therefore he won’t fall in. It only takes one push that is “just large enough” to make him fall in. It’s the same with an electron. You can “push” on an electron with a bit of light as long as you want, but it won’t be knocked out of its orbit unless the push you give it is sufficiently large. This led Einstein to see light as little particles instead of waves. If light were a wave, one would surmise that the energy would build up over time, but if you think of light as a little packet or ball of energy, you can then see that if the packet doesn’t contain enough energy, it will never cause a change in the electron. You can also think of the light hitting the electron as a collision like you studied in your momentum chapter. The energy from the light-packet (photon) is given to the electron, and if it’s not enough, the electron will not have enough energy to escape its orbit and eject from the atom (any extra energy will go into kinetic energy of the electron). This was a breakthrough for physics.

But physicists have sufficient evidence of the properties of light to also see it as a wave (the way it interferes with other light), so we say that light has wave-particle duality. It is neither an ordinary classical particle, nor an ordinary wave; instead it has properties that are similar to both a particle and a wave at the same time.

The same can actually be said for all matter. The difficulty in seeing evidence of the wavelength of matter results from how very tiny its wavelength is. Light has a long wavelength relative to the wavelength of matter. (Please note that light is not made of matter, rather it’s just a bit of wiggling energy made of electricity and magnetism. It’s a strange concept.)

So what evidence do we have that matter itself is also a wave? If we look at “stuff,” we don’t see it “waving.” Of course, earlier we said that de Broglie just made the assumption mathematically and the theory followed from there to produce accurate mathematical relationships. Experimentally we now have evidence as well (so we don’t have to just rely on an assumption that de Broglie used), and the wavelength for matter is called its de Broglie wavelength.

Now you might ask: How in the world could one test to see if matter, such as an electron, has a wavelength? Let’s consider how we know that light has wave-like properties. We know that light waves interact, or interfere. We know that if two beams of light overlap, i.e., when two crests or two troughs overlap, we get constructive interference (the amplitudes add together) and when a crest and a trough overlap, we get destructive interference (they cancel out for that position). You should recall this from your lessons on light and sound. If we could cause two electrons to interfere like that, we would know that electrons, and therefore matter, behave like waves.

Physicists have been able to do this. (If you would like to view some great pictures or diagrams of this, visit http://en.wikipedia.org/wiki/Double-slit_experiment. Picture two little slits parallel to one another (like two cuts in a thick sheet of paper). Now picture shining a beam of light through these slits. The light would pass through the two slits and form two beams on the other side, but they wouldn’t just be two columns of light. Think about how light shines through a keyhole. On the other side of the keyhole the light spreads out. This result is called diffraction. The light shining through the two slits will diffract and form two beams of light that spread out. Because they spread out, they will overlap and interfere, and if you place a screen for the beams to shine on, you should see the pattern of interference. Where the two beams’ crests overlap, you have a bright place on the screen, and the same for two troughs. Where you have a crest interfering with a trough, the two beams will cancel out, and you will have a dark spot. (You can show this by using a simple, handheld laser pointer and a piece of hair. Simply tape a piece of paper on the wall where the beam will shine and hold a piece of hair in the path of the beam. You will see a series of bright and dark spots formed by the interfering beams. The piece of hair serves as an obstacle around which the laser has to diffract on either side.) Scientists have done the same experiment with electrons, called the double-slit xperiment. They shot electrons through two slits and used a detecting screen to show the pattern they made. If the electrons behave like little balls (picture baseballs being thrown through two slits) one should see two bright spots across from the slits where the electrons hit. If the electrons behave like waves, one should see an interference pattern just like that of the beams of light. What scientists found is that an interference pattern emerged when releasing many electrons one particle at a time. It’s as if each electron “interfered with itself” and formed the pattern, one hit at a time on the screen. It doesn’t make intuitive sense, and wrapping your mind around such a foreign and abstract concept is difficult, however, the mathematics that predicted this behavior for the electron (and all matter) is now supported by this experimental evidence. C. Davisson and L. H. Germer were the first scientists to confirm the wave-nature of electrons in 1927, followed by scientist G. P. Thomson.

Question 12: What is special relativity and why did it develop? What part of physics was not complete?

If you were to ride on a beam of light, what would light look like? This is the question that Einstein asked himself while he was just a teenager. We already discussed that light is a bit of electricity and a bit of magnetism oscillating, or waving, so what would this look like if we could travel with it?

Suppose you are driving on a highway right next to another car and you are both traveling at the same speed. What do you see if you look over at the other car? Does it look like it is moving? To you, the other car may seem like it is at rest and that you are at rest as well (and that the ground is moving behind you). This observation is because there is no difference in your speeds. So what would you see if you could travel next to a beam of light and look over at it just as you did with the other car?

And, better yet, consider this. We know that in order for us to see, light bounces off an object and into our eyes, and our brains interpret the light signal. What if you are traveling at the same speed as light and you hold up a mirror. Would you see your reflection? When you are sitting still the light bounces off your face, then bounces off the mirror to your eyes. If you are traveling at the speed of light, would the light ever be able to go ahead of you, bounce off the mirror, and then travel back to your eyes, or would you see a blank reflection because you are traveling with the light?

These are questions that Einstein spent many years thinking about before he developed any answers, and he built his theories on those of many other physicists that came before him. By the end of the \begin{align*}19^{th}\end{align*} century the speed of light had been tested to a pretty accurate \begin{align*}299,792,458\end{align*} meters per second (that’s about \begin{align*}670,616,629\end{align*} miles per hour!). What Einstein postulated is that light always travels at this speed, which we call \begin{align*}c\end{align*}, no matter how fast you are going. Our experience tells us that if we are going \begin{align*}25\end{align*} miles per hour and another car passes us at \begin{align*}30\end{align*} miles per hour, that other car seems to be going only \begin{align*}5\end{align*} miles per hour, which is called the relative velocity. This approximation works for us, but when you begin thinking at extremes, just adding or subtracting velocities does not work, however strange it may sound. In our experience we know that if we are in a truck going \begin{align*}25\end{align*} miles per hour and throw a ball in the direction we are traveling, the ball will have the velocity of the truck (\begin{align*}25\end{align*} miles per hour) plus the velocity we give it, say \begin{align*}30\end{align*} miles per hour. In the absence of air resistance, an observer on the side of the road would see the ball go \begin{align*}55\end{align*} miles per hour. Along the same thread, suppose you are on a ship going \begin{align*}75\end{align*}% of the speed of light \begin{align*}(0.75\mathrm{c})\end{align*} and you launch a missile at half the speed of light. According to Newton (and our intuition), the missile would have a velocity of \begin{align*}1.25\mathrm{c}\end{align*}, which cannot happen if light is the maximum speed. In reality, according to special relativity, it is incorrect to simply add the velocities. The most important thing to remember is that light travels at a constant speed, and it is the fastest anything can travel. The way to combine velocities is a bit more complicated than that, but results different than Newton would have predicted only become apparent at very fast speeds. This is why here on Earth at a tiny speed of \begin{align*}70\end{align*} miles per hour we don’t have to worry about relativity. Light-speed is the limit for speed. Therefore, if light were coming toward you, and you started to run, it would still approach you at a speed of \begin{align*}c\end{align*}, no matter how fast you run.

If you are in a car going almost the speed of light and you turn on your headlights, the light from your headlights would still appear to travel away from you at the speed of light. If you are watching somebody drive by at nearly the speed of light and they turn on their headlights, you would see the light still travel at the speed of light. The velocity of the car does not add to make the light go faster, as you might suspect. This seems ridiculous, it’s true, but there is experimentation to support this. Let’s look at some of the ramifications.

If we set the speed of light as a constant in all reference frames, whether you are moving or not, and we know that speed is displacement over time, then what must be varying from one observer to another is displacement and time. The variable \begin{align*}v\end{align*} (which is \begin{align*}c\end{align*}) cannot change for light, so the displacement and time must change.

The concept is often explained by considering a flashlight on a moving vehicle. Suppose you are on a vehicle that is traveling at a constant speed. On this vehicle you have a flashlight mounted to the floor and pointed toward the ceiling and you watch as a beam of light travels from the flashlight toward the ceiling where you have placed a mirror. You use a stopwatch (a very fast one) to time how long it takes for the beam of light to travel from the flashlight to the mirror and back again. Because you know that light travels at a constant speed of \begin{align*}c\end{align*}, you can calculate the distance over which the light traveled \begin{align*}(c = \;\mathrm{distance/time})\end{align*}. Now you jump off the vehicle (it’s still moving at a constant speed) and repeat the experiment, but this time you measure from the side of the road. Notice that when you were on the vehicle, the light only had to travel up to the ceiling and then back to the flashlight. When you are on the side of the road, the light has to travel a bit further. Consider the diagrams above to help clarify.

Diagrams of distance traveled by light

Diagrams of Distance Travelled by Light.

Notice in the diagrams that the light as viewed by the observer on the side of the road has to travel farther to reach the mirror and then return back to the flashlight. If the speed of light does not change, how do we reconcile these two observations? Is one of the observers wrong? The explanation given by Einstein and special relativity is that time slows down for observers who are traveling faster. The faster you go as the observer, the more time slows down for you. This is called time dilation. So the passenger on the vehicle taking the time for the light will measure a longer time than a person on the side of the road measuring the same light traveling at the same instance (or same event). The person on the side of the road measures a longer time on their stopwatch (the stopwatch ticks faster, so more time passes). The person on the vehicle measures a shorter time (the stopwatch ticks slower, so less time passes). That is, the stopwatches tick at different speeds. With this remedy we have reconciled the problem with the speed equation: \begin{align*}\;\mathrm{speed} = c = (\;\mathrm{distance})/(\;\mathrm{time})\end{align*}.

  • For the passenger on the vehicle: \begin{align*}c = (\;\mathrm{shorter \ distance})/(\;\mathrm{shorter \ time})\end{align*}
  • For the observer on the side of the road: \begin{align*}c =(\;\mathrm{longer \ distance})/(\;\mathrm{longer \ time})\end{align*}
  • And so the proportions remain intact and the speed of light can remain a constant.

Not only is it true that time depends on the observer, but if we apply the laws of physics with this constant speed limit for light, then an object’s size and mass depend on the relative speeds of observers as well. What Einstein was able to show is that the faster your speed, the slower your time ticks (time dilation), and the faster you go in a straight line, the shorter you become in that direction (Lorentz contraction). It seems the deeper we probe and question, the stranger the explanations become!

But we have also seen this with real experimental evidence. One case in which this phenomena has been observed is with the muon in particle accelerators. A muon is just a particle, like an electron except much heavier. When just sitting, a muon will decay (kind of like radioactive decay) into other particles in about two millionths of a second (very, "very fast"). If accelerated at nearly the speed of light, the muon has been measured to last about ten times longer. Imagine if you lasted ten times longer than you normally would. For example, if you would normally live for 80 years, you’d live for 800 years if you were accelerated at such a rate! A factor of ten is quite significant. However, with the slowing down of your clock comes the slowing down of all your functions, and therefore you would not get “more done.” You would digest slower, think slower, etc. Everything would slow down. Essentially, from the slow person’s perspective, he or she would be living the same amount of life, just slower. It’s just relative. As it turns out, going super-fast to slow down your clock is not the fountain of youth (Greene \begin{align*}42\end{align*}).

We have also seen evidence of special relativity on an airplane. Scientists placed an atomic clock (a clock that works by detecting the back-and-forth movement of electrons by detecting the emitted frequencies) on a plane while measuring the amount of time the plane was in the air according to an observer on the ground. When comparing the time shown on the “stopwatch” from land to the atomic clock on the plane, there was a definitive difference. The atomic clock measured less time, which means its “ticking” must have slowed down, evidence of special relativity (time dilation).

Another important application of special relativity is the global positioning system, or GPS. GPS uses satellites that are orbiting the Earth and traveling very fast, to locate positions, say, of cell phones. Because of their fast speeds, the clocks inside the satellites tick slower. Furthermore, there are the effects of general relativity. General relativity predicts that time ticks faster the further the clock is from a massive object, like Earth. Therefore, according to general relativity, the clocks on the satellites will tick faster. Combining the effects of special relativity (time dilation) and general relativity (distortions in the fabric of space-time due to massive objects), the satellites have a slightly fast clock (slowed by the speed and quickened by the distance from our planet). Because GPS is used in measuring position, and time is a very important ingredient in calculating position, scientists have to take relativity into account to achieve any decent accuracy. Without using calculations considering time dilation the GPS would not work accurately (Pogge “GPS”).

This all may seem hard to swallow and if you are really engaging your brain, it should. If you continue with your physics studies in college and take a modern physics course, you will get a more rigorous treatment of these concepts, and get to use actual mathematics to aid your brain in processing these new, strange theories.

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