Tag Archive: wavelength


Why is light pure energy?

Is light a particle or a wave? This artistic rendition attempts to encapsulate the duality. Public Domain Image, source: Christopher S. Baird.

Artistic rendition of a photon (not physically accurate). Public Domain Image, source: Christopher S. Baird.

Light is not pure energy. While it is true that light has no mass, this fact does not imply that light is pure energy. Light is composed of fundamental quantum objects called photons which we list alongside other fundamental quantum objects such as electrons and neutrinos. Each object on this list contains several different properties which determine how the object behaves. Mass and kinetic energy are only two of several properties that a fundamental quantum object can carry. Saying that light is “pure energy” would imply that light only carries the property of energy and no other properties, which is simply not true. A single photon, which is the smallest bit of light possible, carries the following properties:

  • Wavelength – This is the spatial distance between the peaks of the photon’s wave.
  • Frequency – This is the number of times that the wave reaches a peak in a unit time at a fixed location. The human perception of the color of light is very closely related to the light’s frequency. Therefore, the word “frequency” can loosely be used interchangeably with the word “color”.
  • Wavevector – This is the photon’s direction of propagation, as well as the number of wave peaks that exist in a unit length.
  • Period – This is the time between two peaks of the photon’s wave at a fixed location.
  • Speed – This is the rate at which the photon travels through space, which is always 299,792, 458 meters per second.
  • Position – This is the physical location of the photon in space. Although the position of an individual photon is not well defined and contains intrinsic uncertainty while it exists, a photons does carry some degree of location information, thus enabling us to record images in a digital camera based on where the photons hit the sensor.
  • Wave Phase – This is the relative location of the wave peaks of two different photons, and is important in properly describing interference effects.
  • Momentum – This is a motional property that describes light’s ability to collide with other objects and get them moving.
  • Spin – This is a quantum property that loosely resembles the type of spinning we see in everyday life. The spin of a photon is also called its polarization state and represents an intrinsic angular momentum. Photons have integer spin, are therefore bosons, and thus do not obey the Pauli exclusion principle. This means that photons can exist in the same state, such as in laser beams.
  • A Quantized Electromagnetic Field – A photon contains electromagnetic fields. More accurately, a photon is a quantized ripple in the overall electromagnetic field. As such, photons are able to interact with electric charge. Particles with electric charge can create photons, destroy photons, and scatter photons. Also, photons can exert forces on charged particles. Furthermore, photons obey the principles and equations of quantum field theory.
  • Kinetic Energy – This is the energy of the light due to its motion. Note that because a photon has no mass, its kinetic energy equals its total energy. The energy of light allows it to create a gravitational field according to General Relativity.

As should be obvious, energy is just one of many properties that photons carry. Photons are much more than “pure energy”. Photons can exist just fine without having mass since they carry many other properties to make them physically real. Note that many of the properties listed above are very closely related to each other. You could even argue that many of the properties listed above are not independent properties, but are simply slightly different ways of defining the other properties. For instance, the energy E of a photon equals its frequency f times a constant, E = hf. Similarly, the momentum p of a photon equals its wavevector k times a constant, p = ħk. Also, the period T is just the inverse of the linear frequency f, T = 1/f, the wavelength λ is just the inverse of the wavevector magnitude k times 2π, λ = 2π/k, and the speed c is just the frequency times the wavelength, c = . Despite the possibility that some of the properties listed above can be seen as redundant, this does not change the fact that photons exhibit many more properties than just their energy.

There are also some properties that photons do not exhibit, simply by their nature of being photons. The following list denotes properties that photons do not have:

  • electric charge
  • lepton number
  • baryon number
  • flavor quantum numbers
  • magnetic moment (although a photon may indirectly have a magnetic moment through pair creation effects)
  • mass

As we see, mass is just one of many properties that a fundamental object may or may not have. As such, the presence of mass does not confer on an object any extra degree of physical reality, even though mass is the property that we are most familiar with in everyday life. Furthermore, the absence of mass does not make an object any more “pure”. We are so familiar with mass in everyday life that we may be tempted to say, “an object with no mass does not really exist.” But this statement is false. The more accurate statement would be, “an object with no physically observable properties does not really exist.” Since there are so many fundamental properties besides mass, we see that objects can exist just fine without it. Again, the lack of mass does not automatically imply that the object is pure energy, since there are so many other properties involved. Note that mass is actually just another form of energy. The total energy of a fundamental object is its mass energy plus its kinetic energy (note that potential energy is held by systems of objects and not by single objects).

Interestingly, if we combine many photons into a beam of light, we can encode information such as images in the pattern of the photons. Each of the photon’s properties listed above can be exploited to carry information. For instance, human eyes, conventional cameras, and traditional space telescopes extract photon position and frequency (color) information from a group of photons in order to form images. Radio antennas vary the frequency (FM) or the photon count (AM) along the length of the radio waves that they create in order to encode information. Interferometers such as used in some space telescopes measure the phase properties of the photons in a beam to extract information about the source that created the beam. A light field camera extracts photon position, frequency, and wavevector directionality from a group of photons in order to capture three-dimensional photographs. If light was just “pure energy”, then human eyes, cameras, radio antennas, and space telescopes would not function.

Why was color invented by humans?

Color was not invented by humans. Color is a fundamental physical property of light that exists independent of humans. How color is perceived by a certain person is of course human dependent. For example, a standard helium-neon laser always emits a specific red color (scientifically, its color is the color with a wavelength of 632.8 nanometers). Whether a person perceives this color as sharp, dull, alarming, vibrant, evocative, romantic, muddy red, brick red, orange-red, or even yellow (if he is color blind) depends entirely on the human perception. But this does not change the fact that helium-neon lasers emit light with the color 632.8 nm red. A machine can measure the color of helium-neon laser light and will find it to be 632.8 nm red every time, no matter which humans are running the machine. In fact, even a blind person that has never experienced sight can be trained to run a machine that measures the color of helium-neon laser light to be 632.8 nm red. The blind person will not a have a personal conception of what red actually looks like, but he should have no great difficulty measuring and scientifically describing red. The same is true of all colors and not just 632.8 nm red. The blind person’s experience is similar to that of a human with sight looking at an  infrared color. None of us can see an infrared color. Therefore, none of us has any concept of what infrared really “looks like” in the human sense of the word. But infrared still exists physically and can be created and detected using machines. An infrared camera helps a human “see” infrared colors by converting the infrared colors to red or green. An infrared camera, therefore, does not really allow you to see infrared colors. It allows you to see red colors that are in the same spatial pattern as the infrared colors. An intelligent alien on a distant planet that has never had sight can still measure the color red using tools in a similar way to how humans measure infrared colors without being able to see them.

Colors exist physically independent of humans. Every spectral color has a certain wavelength that can be measured scientifically. This image shows the wavelength of various spectral colors. Note that this image is an approximation because computer monitors cannot actually produce all spectral colors. Public Domain Image, source:

Colors exist physically independent of humans. Every spectral color has a certain wavelength that can be measured scientifically. This image shows the wavelength of various spectral colors. Note that this image is an approximation because computer monitors cannot actually produce all spectral colors. Public Domain Image, source: Christopher S. Baird.

Physically, there are two kinds of colors: pure spectral colors and mixed colors. A pure spectral color consists of a beam of light that is a simple sine wave with a single wavelength. The wavelength of the light is the color of the light. Light is a waving of the electromagnetic field. The distance in space between the peaks of an electromagnetic wave is its wavelength, and hence its color. When you run a narrow beam of white light through a glass prism, it spreads the light out into its spectral colors. The resulting red, orange, yellow, green, blue, and violet pattern (and all the colors in between) shows the span of possible visible spectral colors. Red has a relatively long wavelength (compared to the other visible colors). On the other end of the visible spectrum, violet has a relatively short wavelength. All of the visible colors have wavelengths that are on the scale of hundreds of nanometers (or tenths of microns).

A mixed color is a combination of spectral colors. Exactly how much of each spectral color is added to the mix determines what the final color is. As before, the exact nature of a mixed color is a physical property that exists independent of humans. How a mixed color is perceived is human-dependent. We can say scientifically that 10 Watts of 700 nm red light added to 5 Watts of 530 nm green light and 5 Watts of 470 nm blue light makes a mixed color that exists physically and is independent of humans. Whether humans call this mixed color “pink”, “fushia”, “peach”, “salmon”, “romantic”, or “George” makes no difference to the fact that it exists scientifically.

Human sight is actually quite limited. Healthy humans have only three color receptors: red, green, and blue. While it’s true that the red receptors can also pick up orange and yellow, all these colors get collapsed down to a single “red” nerve signal. In the same way, the green receptors can detect yellow, green, and blue colors, but they all get collapsed down by the green receptor to a single “green” nerve signal. The same case holds for the blue receptors as well. What this means is that the color that you get when you mix red light and green light looks to a human the same as a pure spectral yellow light, even though pure yellow and red+green  are scientifically different. If a certain explosive chemical can only be ignited by spectral yellow light, then red+green light will never make the stuff explode, even though human eyes can’t tell the difference. This limitation of human eyes is called “metamerism”.

Scientifically speaking, the human eyes are very bad detectors for measuring the true nature of a certain mixed color. A typical mixed color has many different spectral color components, and not just red, green, and blue. We want to therefore use machines and measure all the spectral colors present in a mixed color in order to accurately describe it. Each spectral color can be present in large or small amounts. In order to completely describe a mixed color scientifically, we have to tell the power and wavelength of each spectral component. The resulting plot of a certain mixed color is called its “spectral power distribution”  or just its “spectrum” for short. If you ask a random intelligent human, “What is the color of the sun?”, you will get the inexact answer “white”. But if you ask a solar scientist or a spectrometer machine this same question, the answer will be the solar spectrum.

string

Fundamental modes of vibration on a piano string are determined by the string’s length. Public Domain Image, source: Christopher S. Baird.

The effect is not psychological. It is physical. Notes on a piano that are separated by an octave are very similar physically. To understand why this is so, you have to understand first the basics of sound. Sound is a waving vibration of air that travels as it oscillates. The pattern of the vibrations in the air (the sound’s waveshape) is determined by the vibrating pattern of the object that created it. For a piano, the sound is created by hitting metal strings to get them vibrating. The piano strings then knock into the air and get it  vibrating in the same pattern. The sound is launched from the string, through the air, and into our ears.  If you take a single string of metal and clamp the two ends down, there are only certain ways you can get it vibrating. Let’s take a look at the basic components of a string’s vibration.

The simplest and strongest vibration a string clamped at both ends can experience (the “fundamental” or “first harmonic”) is half of a sine wave (one hump), as demonstrated in the top of the animation. Because the ends are clamped, they cannot move, so the wavelength of the simplest vibration is determined by the distance between the clamps. The next simplest possible vibration is a full sine wave (two humps), shown in the middle of the animation. This vibration has a wavelength equal to half the wavelength of the fundamental vibration. The next simplest possible vibration is one and a half sine waves (three humps), shown in the bottom of the animation. This vibration has a wavelength of one third the fundamental. Hopefully you see the pattern at this point. The next simplest possible vibration (not shown in the animation) would have four humps and so on. All possible simple vibration shapes on a string have a wavelength that is an integer fraction of the wavelength of the fundamental vibration.

When the piano key’s hammer actually hits a string, you don’t get a perfect sine-wave vibration pattern (you would have to hit it with a giant sine-wave-shaped hammer to get this). Rather, you get a vibration pattern that is a combination off all possible vibrations. In other words, you get a vibration pattern that is a mixture of the various integer-fraction-wavelength sine waves we just talked about. For a piano, the mixture is typically a very strong one-hump vibration (the fundamental), plus weaker one-, two-, and three-hump vibrations (the “higher harmonics” or “overtones”). This combination of many sines waves that are all integer multiples of the fundamental is what gives a piano its distinctive sound. If just the fundamental sine wave vibrated when you pressed a key, it would sound like a cheap alarm clock.

When we experience a sound, its pitch is inversely proportional to its wavelength. Shorter-wavelength vibrations constitute higher-pitched sounds. That is why shorter strings make higher sounds.  When you play the middle C key on a piano, the string’s vibration contains a large, pure middle C sine wave sound (the fundamental) plus a smaller sine wave with half the wavelength (which has a pitch of tenor C) plus an even smaller sine wave with one fourth the wavelength (which has a pitch of soprano C), and so on. So when you play middle C, the sound you hear is actually a combination of all higher C notes with middle C dominating. When you play the tenor C key, the sound you hear is a combination of all higher C notes with tenor C dominating. All notes on a piano keyboard separated by octaves make essentially the same sound, just with a different fundamental tone dominating. That is why all notes separated by octaves are labeled with the same letter of the alphabet.  Now, when you play the middle D, the story changes completely. You are vibrating a completely different string with a different length. The middle D string has its own set of harmonics and therefore is physically very similar to all other D notes on the keyboard. In summary, all the notes on a keyboard with the same letter label make sounds that are very similar physically because of the way only integer-fraction and integer-multiple sine wave vibrations can fit on a string.

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