Tag: Albert Einstein

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physics

Say Hello to Maxwell’s Demon

Image Credit: Phys.org

You likely took chemistry and or physics in high school. and some of you make have taken these courses in college as well. One topic that is covered in both classes is thermodynamics. As a refresher thermodynamics at its most basic level is the study of the heat and how it interacts with energy. There are four laws of thermodynamics that describe how thermal energy interacts with matter. Let’s take a closer look at the laws of thermodynamics. You can find these laws in any high school chemistry or physics textbook. I am using the laws of thermodynamics as found at chem.libretexts.org.

The Law of Thermodynamics

Image credit: sciencenotes.org

The Zeroth Law of thermodynamics “states that if two systems are in thermodynamic equilibrium with a third system, the two original systems are in thermal equilibrium with each other. Basically, if system A is in thermal equilibrium with system C and system B is also in thermal equilibrium with system C, system A and system B are in thermal equilibrium with each other.” You may be curious as to why this law is called the zeroth law rather than the first law. The first and second law had already been established before the zeroth law was developed. Scientists believed that the zeroth law was a more fundamental law than the first and second law. They named it the zeroth law so it would appear first in the numeric listing of the laws.

The first Law states that “…energy can be converted from one form to another with the interaction of heat, work and internal energy, but it cannot be created nor destroyed, under any circumstances.” This is basically a restatement of the Law of Conservation of Energy.

The second Law of thermodynamics states that “… the state of entropy of the entire universe, as an isolated system, will always increase over time. The second law also states that the changes in the entropy in the universe can never be negative.” According to chem.libretexts.org “entropy is simply a measure how much the energy of atoms and molecules become more spread out in a process and can be defined in terms of statistical probabilities of a system or in terms of the other thermodynamic quantities.” You can find a much more in depth description of entropy in one of my earlier posts. The second law also describes the direction of the flow of heat. If two objects of differing temperatures are brought together in an isolated system the heat will flow from the warmer object to the cooler object until both objects reach thermal equilibrium which simply means they reach the same temperature. Another point to be made here is that the temperature of an object is a measure of the average kinetic energy of the object’s particles. So the higher the kinetic energy the higher the temperature. Faster moving particles are hotter than slower moving particles. This will be a key factor later in the discussion.

The third law of thermodynamics “… essentially allow us to quantify the absolute amplitude of entropies. It says that when we are considering a totally perfect (100% pure) crystalline structure, at absolute zero (0 Kelvin), it will have no entropy (S). Note that if the structure in question were not totally crystalline, then although it would only have an extremely small disorder (entropy) in space, we could not precisely say it had no entropy. One more thing, we all know that at zero Kelvin, there will still be some atomic motion present, but to continue making sense of this world, we have to assume that at absolute Kelvin there is no entropy whatsoever.

Gedankenexperiment

Physicists often use gedankenexperiment or thought experiments to describe scientific phenomena when testing the idea may not be practical or possible. One example of a thought experiment is one Albert Einstein had of a person trying to chase a beam of light. He tried to imagine what would happen if a person were able to catch up to the wave and ride it like a surfer riding on a water wave. This idea played a pivotal role in the development of his special theory of relativity. Perhaps the most famous thought experiment was one developed by Erwin Schrodinger known as Schrodinger’s cat. According to wtamu.edu ” Schrodinger’s Cat was simply a teaching tool that Schrodinger used to illustrate how some people were misinterpreting quantum theory. Schrodinger constructed his imaginary experiment with the cat to demonstrate that simple misinterpretations of quantum theory can lead to absurd results which do not match the real world.”

Maxwell’s Demon and the Second Law

James Clerk Maxwell was a Scottish scientist who lived from 1831-1879. He developed the theory of electromagnetism which unified light, electricity, and magnetism into one central theory. He derived a set of four equations that describe electromagnetism. Maxwell is generally regarded on equal footing as Isaac Newton and Albert Einstein. His ideas helped in the derivation of Einstein’s theory of special relativity as well as contribute to quantum theory.

Image credit: thunderbolts.info

Now that we have some of the background information out of the way let’s take a look at Maxwell’s demon and how in pertains to the second law of thermodynamics. Maxwell’s demon is a thought experiment created by James Clerk Maxwell in 1871 to see if it would be possible to violate the second law of thermodynamics. In this thought experiment Maxwell envisioned a container separated in half by a partition which has a small door on it. The air is the same temperature on both sides of the container that is to say both sides of the box are in thermal equilibrium with each other. A demon sits on top of the partition and is able to observe the path and velocity of all the individual particles and this demon has the ability to open the door and let particle pass from one side of the container to the other.

In his thought experiment the demon would open the door to allow high speed particles to pass from the right side of the container to the left. The demon would also open the door to allow slow moving particles from the left side to the right. Eventually the left side of the box would contain all the high moving particles while the right side would contain all the slow moving particles. Remember, the particles on the left side of the box are hotter than those on the right because they are moving faster and because temperature is a measure of the average kinetic energy of the particles. The two sides of the container are no longer in thermal equilibrium with one another. At this point the entropy is lower than it was before the demon began separating particles. Recall that the second law of thermodynamics states that the entropy of an isolated system will always increase over time.

So is that the end of the story? Did James Clerk Maxwell determine that the second law of thermodynamics can be violated by a demon capable of separating high speed particles from low speed particles? If so does our current technology have the ability to do the same thing? Scientists and physicists wrestled with this idea for more than a hundred years as the thought experiment was seen as a threat to the second law of thermodynamics.

The Resolution to Maxwell’s Demon and the Preservation of the 2nd Law of Thermodynamics

In 1961 Rolf Landauer came up with an idea to solve the paradox of Maxwell’s demon and the violation of the 2nd law of thermodynamics. Landauer came up with an idea, now called the Landauer principle which states “any logically irreversible manipulation of information, such as the erasure of a bit or the merging of two computation paths, must be accompanied by a corresponding entropy increase in non-information-bearing degrees of freedom of the information-processing apparatus or its environment.” Great, so what does that actually mean and how does that solve this conundrum? Well, the demon must learn about the particles if he is to do his job. There is an inherent randomness to the particles before the demon starts his task. As he separates the particles the randomness of the particles decreases while the randomness of the demon’s memory increases. Be it a demon or a technological device there is a finite amount of memory available. Eventually the memory must be reset in order for the task to continue. According to an article in cacm.acm.org: “physicists resolved the paradox by noting that Maxwell’s demon eventually would need to erase the information it had gleaned about the molecules, and that this erasure would create enough entropy to preserve the Second Law.” The deletion of information creates heat which is radiated into the box or out to the universe ultimately increasing entropy of the system thus preserving the 2nd law of thermodynamics. Here is a good video describing both the thought experiment as well as the resolution: https://youtu.be/8Uilw9t-syQ

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physics

The Photoelectric Effect

Courtesy of scienceabc.com

A Brief History of the Photoelectric Effect

In 1887 scientist Heinrich Hertz discovered the photoelectric effect while experimenting with a device called the spark gap generator which is a precursor to the radio. What Hertz found while using this device was “…sparks generated between two small metal spheres in a transmitter induce sparks that jump between between two different metal spheres in a receiver.” (https://physics.info/photoelectric/) The sparks that were jumping across the gap were, in fact electrons, which were receiving energy from ultraviolet light. In other words “when ultraviolet light shines on two metal electrodes with a voltage applied across them, the light changes the voltage at which sparking takes place.” (https://www.britannica.com/science/photoelectric-effect) This was an important finding because up until this point people where unaware of the relationship between light and electricity.

JJ Thompson, who many remember for his “plum pudding” model of the atom, discovered that the particles that were freed in the photoelectric effect were the same particles observed in the cathode rays he had been working with. His research using the cathode ray tube led to the discovery of corpuscles which we now know as electrons.

A depiction of a cathode ray tube. Courtesy of study.com

In 1902 Philipp Lenard made a shocking discovery. He found that as the frequency of light increased so to did the energy of the electrons. The expected result was that as the intensity or brightness of light increased the energy of the electron would increase. The experimental observation did not match the accepted theory of the time. So what does all this mean and who could make sense of it all? Before we get to that let’s discuss what specifically the photoelectric effect is.

What is the Photoelectric Effect?

So we know a little about the history of the photoelectric effect and we know that it has something to do with electrons and the frequency of light. So what is it exactly? Great question, glad you asked. The photoelectric effect is a phenomenon which occurs when a light of a high enough frequency is shown onto a photo-sensitive metal resulting in the ejection of electrons from that metal. If the threshold frequency is not high enough then no electrons will be ejected. The threshold frequency varies for different metals and is the minimum frequency required for electrons to be ejected.

Increasing the intensity of the light will result in more electrons being ejected provide the frequency is at or above the threshold frequency. A high intensity light at a frequency below the threshold frequency will not result in the ejection of electrons, in other words the photoelectric effect will not be observed. Increasing the frequency of light results in an increase in kinetic energy of the photons. The intensity of light had no impact on the kinetic energy of the photons only on the number of photons being ejected.

Einstein and the Photoelectric Effect

Einstein is of course known for his theory of general and special relativity, his work with quantum mechanics, and his famous equation E=mc^2. What you might not realize is that Albert Einstein was awarded the 1921 Nobel Prize in physics for “for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect.” (https://www.nobelprize.org/prizes/physics/1921/summary/)

As you now know, Einstein was not the first to observe the photoelectric effect, so why is he so often credited and associated with it rather than Hertz, Lenard, or Thompson? He was the first to accurately describe how it occurs and to make the ground-breaking discovery relating waves and particles.

Einstein realized two facts regarding the photoelectric effect: 1) light is made of particles called photons and 2) the metal can only absorb the entire photon and not any other portion of it, think of it as an all or nothing proposition. Some of the energy of the photon that is absorbed is used to free the electron and the rest is converted to kinetic energy of the photon. The energy required to free the electron is called the work function. The strict definition of the work function is “energy (or work) required to withdraw an electron completely from a metal surface.” (https://school.eb.com/levels/high/article/electronic-work-function/32337)

What does all this mean? The results that Einstein observed were not in agreement with the accepted theory of the time. A new model of light was needed to match observation. Einstein had the insight to recognize that sometimes light acted as a wave and sometimes it acted as a particle. This was a stunning revelation that shocked the scientific community. Sir Isaac Newton thought light must be made of particles in order for it to experience reflection and refraction while Robert Hooke had argued that light had wave like behavior. Finally Einstein came along and settled the argument: light acts as both a wave and a particle.

Today we refer to this as the wave-particle duality or the dual nature of light. In general light travels as a wave and interacts with matter as particles called photons. Light is quantized meaning it is packaged in discrete units or particles which are called photons. In 1900 Max Planck, the father of quantum mechanics derived the equation for the energy of electromagnetic radiation, including light. Here is a short video describing Einstein and his contributions to the photoelectric effect: https://youtu.be/0b0axfyJ4oo

Courtesy of socratic.org

If we use the above equation and compare it to the known work function of a specific metal we can determine if the photoelectric effect will occur. The energy of the photon must be greater than the work function in order for the photoelectric effect to be observed. Interestingly enough, the electrons that were ejected from the metal end up falling back into the metal almost immediately.

What Did We Learn from the Photoelectric Effect?

We now know some of the history of the photoelectric effect and what the photoelectric effect is all about. Let’s take a moment and summarize what we learned from this scientifically significant discovery. Most importantly we leaned that classical physics can not accurately predict what happens at the atomic level. Classical physics predicted that increasing the intensity of light should increase the energy of the photons. What actually happened was that increasing the frequency of light resulted in an increase in the energy of a photon while increasing the intensity of light only resulted in an increases in the number of photons being ejected. Einstein was able to determine the energy of a photon by the equation E=hv and that the energy of the photon must be greater than the work function in order to be ejected from the metal. The photoelectric effected demonstrated the dual nature of light, that is it has both wave and particle behavior, in general light travels as a wave and interacts with matter as particles.

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Uncategorized

The Double Slit Experiment

Thomas Young performed his famous “double slit experiment in 1801. The results of this experiment demonstrated the dual nature of light. The term “dual” in the dual nature of light means that light, which is electromagnetic radiation, has both wavelike and particle properties. While the initial experiment was done with light it has since been repeated with electrons, atoms, and even molecules as large as 60 carbon atoms called a Buckyball. All of these experiments show the same dual nature results.

Common terminology

Before we get into the actual experiment and its results lets discuss some of the vocabulary. The first term we should discuss is quantized. If something is quantized then it exists only in discrete continuous amounts. Light is quantized into quanta called photons. Quanta is the fundamental size unit the smallest, indivisible portion of a property. A small packet or chunk of light, for example, which can’t be broken down any further.

Next we need to discuss some terminology about waves. These terms can be used with water waves, light waves, sound waves, basically any type of wave. There are different types of waves, transverse and longitudinal, that both have the same features. The amplitude of a wave is the height of a wave and is directly proportional to the energy of the wave. The higher the wave, the greater the amplitude. Greater amplitude corresponds to a more energetic wave. The top of a wave is called the crest and the low point of a wave is called the trough.

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An image of a transverse wave. Courtesy of study.com

Diffraction is the term used to describe how waves bend around an opening or barrier.

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Note how the pattern changes based on the size of the aperture.
Courtesy of s-cool.co.uk

Wave interference

Waves can interact with other waves or even with itself and this is called interference. There are two basic types of interference. When the peak also called crest of one wave interacts with the crest of another wave then constructive interference occurs. If the trough of one wave interacts with the trough of another wave then the same constructive interference occurs. Constructive interference results in a larger single wave, as if the two parts of the wave that interacted constructed a new single larger wave. If the crest of one wave interacts with the trough of another wave then the waves cancel one another out in a process called destructive interference.

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Examples of constructive and destructive interference. Courtesy of researchgate.net

Wave Function

The wave function in quantum mechanics is an equation that describes all the characteristics of a particle.

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Schrodinger’s wave equation.

The square of a wave function represents the probability of finding a particle at a given time and place. The square of the wave function becomes significant when trying to determine the location of an object during the double slit experiment.

The Experiment

Thomas Young designed and conducted an experiment which had shocking results. He was attempting to show that light behaved as waves rather than the accepted notion that light behaved as individual particles. Young knew that waves created interference patterns when they interacted with each other. To test his hypothesis he shined a light source at a barrier with two slits which were fairly close to one another. The light passed through the slits and shone on a screen behind the barrier. If light was acting as a wave he would expect to see an interference pattern on the screen. If light was acting as a particle he would expect to see an image of the the two slits as the particles passed through the barrier.

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A depiction of Thomas Young’s double slit experiment. Courtesy of curiosity.com

The Results of the experiment

When Young performed his experiment an interference pattern emerged on the screen behind the barrier. This seemed to confirm Young’s idea that light behaved as a wave. In the early part of the 20th century quantum mechanics was born. Scientists like Max Planck, the father of quantum mechanics and Albert Einstein argued that light behaved as both a particle, the photon and a wave. The double slit experiment was done again only this time scientists were able to fire photons one by one at the barrier. In this case one would think that the pattern that emerged would not be an interference pattern but rather a band of light at through each slit. Think of spraying paint though a two slit barrier. Bands would only be present at the site of the slits, similar to a stencil.

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The top image is what would be expected if light behaved as particles with the photons present directly in line of sight of the slits. The bottom image is what would be expected if light behaved as a wave. The square of the wave function predicts most likely location of the photons. Courtesy of medium.com

This experiment has been repeated many times since Young’s experiment. Scientists have even repeated the experiment using electrons which they could fire one at a time to try to determine wave versus particle behavior. Even when the electrons were fired one by one, eventually an interference pattern emerged. When the electrons are fired one at a time they can not be interacting with other electrons to produce an interference pattern. This means the electrons are interacting with themselves to create an interference pattern.

Here is where it gets weird. In order to for an interference pattern to occur the barrier must have two slits. How can a single electron be aware of another slit? One solution to this question is that the electron splits and goes through each of the two slits and interacts with itself. Another alternative is that the electron does not split but goes through both slits at the same time. Both of these scenarios vary greatly from our everyday experiences dealing with Newtonian mechanics.

With advances in technology we can now perform the experiment using either wave or particle detectors to once and for all determine if an electron behaves as a particle or a wave. Quantum weirdness, however, rears it head once again. If we try to use a detector to see which route, that is which slit, the electron went through, then no interference pattern is detected and the result is consistent with particle behavior. The act of observing, in this case by use of a detector, destroys the interference pattern by collapsing the wave function. The implication is that the act of observing which slits the electrons goes through causes the interference pattern to collapse and the particle pattern to be demonstrated. If, however, no detector is used then the wave interference pattern prevails. These results demonstrate the dual nature of many things once thought of as particles and that observation at the quantum level can have a dramatic impact on the very results one is tying to measure.

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astronomy gravitational waves physics special relativity

Gravitational Waves

A brief history of gravitational waves

Albert Einstein predicted the existence of Gravitational waves in his famous 1916 paper describing general relativity. A century after Einstein’s prediction of these mysterious gravitational waves was made, proof of their existence was detected in September 2015. Einstein, as it turns out was not the first scientist to describe or predict gravitational waves but he was the first to accurately describe the phenomena. Einstein wrestled with the idea of gravitational waves for many years after publishing his paper on general relativity which indicated that these waves could, in fact, be a consequence of his theory of general relativity.

A British physicist Oliver Heaviside first proposed gravitational waves in 1893. In 1905 Henri Poincare predicted the existence of gravitational waves in his paper On Electron Dynamics where he states that a consequence of space-time geometry gravitation must produce waves that travel at the speed of light in a fashion close to electromagnetism. While there is some argument as to who first described the concept of gravitational waves it seems clear that Einstein was the first to correctly describe gravitational waves through his theory of general relativity.

What is a gravitational wave and what causes it?

A gravitational, wave according to NASA’s space place website, is “an invisible (yet incredibly fast) ripple in space. These waves travel at the speed of light through space-time which is “incredibly fast” indeed. These ripples in space physically alter the fabric of space-time as they travel. These waves stretch space in one direction and squeezes space in a direction perpendicular to the direction of stretch. These waves travel at the speed of light, in all directions, through space-time away from the source of the gravitational wave.

Gravitational waves are caused by massive objects which are accelerating around each other and may cause this ripple in the fabric of space-time when they eventually collide or merge with each other. Neutron stars or black holes are examples of objects that are massive enough to cause gravitational waves. Events which may be described as cataclysmic, such as the merger of two neutron stars or black holes or a neutron star going supernova likely produce the strongest of these waves.

How are gravitational waves detected?

The first gravitational waves that were verified were detected by LIGO (Laser Inferferometer Gravitational-Wave Observatory) located in Livingston, Louisiana and its twin inferferomter in Hanford, Washington on September 14th, 2015. The event that caused these waves is believed to be the merger of two black holes that occurred 1.3 billion years ago. The black holes reportedly collide at nearly .5c or 1/2 the speed of light to form a single massive black hole. The result is the release of an enormous amount of energy, in this case the amount of energy that was converted was equal to 3 times the mass of the sun. This process occurs in accordance with Einstein’s equation E=mc^2 which states that mass can be converted to energy. The mass that is converted to energy is discharged in the form of gravitational waves. It is these gravitational waves that were detected by the twin LIGO detectors in September of 2015.

Courtesy of Physics.Org: diagram of LIGO Interferometer and gravitational waves

The LIGO equipment consists of two 4 kilometer detector arms in an “L” configuration which can detect the distortion of space by as little as 1/10,000th the diameter of a proton. These distortions are the result of extremely violent events such as the merger of black holes, neutron stars, or a neutron stat going supernova. According to the LIGO Caltech website the 4 kilometer arms were “long enough that the curvature of the Earth was a factor in their construction.”

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An aerial view of LIGO Hanford and LIGO Livingston. Courtesy of LIGO Caltech

The Virgo interferometer is located in Italy which has arms that are 3 kilometers in length and there are plans for two more detectors, one will be located in India and will be a joint operation between LIGO and three research facilities in India. Another detector will be an underground detector called KAGRA located in Japan. Here is a quick link describing how LIGO detects gravitational waves https://www.sciencemag.org/news/2016/02/gravitational-waves-einstein-s-ripples-spacetime-spotted-first-time

Earth based interferometer can detect waves with a frequency of 30-400 hertz (Hz). These ground based detectors have the ability to detect waves that are longer than the 3-4 kilometer arms of the detectors. Space based interferometers which are slated for deployment in the 2030s are projected to be able to detect waves with a frequency of .1-100 milliHz. LISA, or Laser Interferometer Space Antenna consists of three probes that have the ability to detect waves to much lower frequencies than their ground based counterparts. Scientists are attempting to develop methods of detecting subtle variations from pulsars located within the Milky Way using “pulsar arrays” which are located in Europe, Australia, North America, and one being developed in China. These variations may be caused by the propagation of gravitational waves through our home galaxy. The pulsar arrays can detect frequencies from 1-320 nanoHz

Courtesy of NASA

What can we learn from gravitational waves?

So we know Albert Einstein predicted gravitational waves in his paper on general relativity and we know that the technology used to detect these waves is amazing but why should we study these waves? Why should we care about waves that may have been generated millions or billions of years ago?

Gravitational waves are unrelated to electromagnetic radiation and this allows us a fuller picture of events in the universe. Black holes for example are invisible to electromagnetic radiation but can be studied by the gravitational waves they create as they merge or collide with one another. Scientists are hoping to answer some fundamental questions regarding black holes and how they end up pairing and circling one another prior to colliding.

The study of gravitational waves led scientists to the origin of heavy elements in the universe. In 2017 scientists were able to witness two neutron stars merging by detecting the gravitational waves associated with the merger. Scientists were able to detect the heavy element strontium in the aftermath of the neutron star merger and the resulting explosion and burst of gamma rays known as a kilonova. LIGO Caltech defines a kilonova as “a phenomenon by which the material that is left over from the neutron star collision, which glows with light, is blown out of the immediate region and far out into space.” It is from this event that the scientists were able to prove that the heavy element strontium was created in the explosion of a neutron star. The study of gravitational waves may reveal information about the rate of expansion of the universe, the origin of black holes, and the composition of neutron stars.

Categories
physics special relativity

What’s so special about Special Relativity?

In 1905 Albert Einstein wrote a paper titled “On the Electrodynamics of Moving Bodies” which would drastically transform our understanding of the relationship between space and time. This paper introduced the world to the concept of special relativity. What makes this topic “special” is that the behaviors described in the paper apply to objects traveling in an inertial frame of reference. An inertial frame of reference is a frame in which the object being observed is moving at a constant or non accelerated speed. As an example, If I am standing still then I am in an inertial frame of reference. If a passerby is traveling by me in a vehicle at 55 miles per hour they are in a separate inertial frame of reference. Relativity is all about how objects move relative to one another. In order to describe the behavior of bodies moving in an accelerated frame of reference general relativity is needed. One of the major revelations of special relativity is the unification of space and time. Until Einstein published his now famous paper space and time were thought of as two independent coordinates. In 1908 a mathematician named Herman Minkowski developed a mathematical model based on Einstein’s paper and was the first to use the term space-time.

Postulates of Special Relativity

As noted above the effects of special relativity occur only in inertial frames of reference. If an object accelerates or changes direction then special relativity no longer applies and an object is subject to general relativity. There are two postulates of special relativity which provide the foundation for the entire theory. The first postulate is that there are no preferred inertial frames of reference and that all inertial frames of reference are equally valid and useful. This postulate is the basis for the idea that events that are simultaneous for an observer in one inertial frame of reference need not be simultaneous to an observer in another inertial frame of reference. The second postulate states that the speed of light in a vacuum is a constant and invariant quantity. This idea may sound simplistic but is very different than the way other things work in our daily life. If I were riding in a car traveling at 50 miles per hour relative to the ground and were to throw a ball at 10 miles per hour relative to the car than a bystander at rest on the sidewalk would see the ball traveling at 60 miles per hour relative to the ground. Light, on the other hand, travels only at the speed of light. If you were to measure the speed of light from the headlights of my vehicle at rest, you would measure the speed of light to be 670,616,629 miles per second. If you were to measure the speed of light on an object traveling at the speed of a man made satellite, 16,800 miles per hour, you would still measure the speed of light as 670,616,629 miles per hour. The speed would not be added to the speed of the satellites the way the speed of the ball was added to the speed of my vehicle. This fact will become significant in understanding the idea that time is not absolute and can change depending upon one’s frame of reference.

Courtesy of ilectureonline.com

Consequences of special relativity

There are three effects or consequences that occur as a result of special relativity. These effects do not become discernible until an object is traveling at some significant portion of the speed of light. The first effect is that the faster an object moves through space the slower it moves through time. This is called time dilation and has been repeatedly verified experimentally. Tests have been done using atomic clocks, one on the ground and one flown around the world in a plane. When they compare the clocks after the flight there is a slight disagreement between the clocks. This is not merely an issue of the clock not functioning properly, time is moving differently for each of these clocks. There is a simple mathematical equation that can be used to predict the time dilation between an object traveling at some significant portion the speed of light as compared to the time passage of an object in a rest frame of reference.

The above equation describes the degree to which special relativity varies from classical relativity. This equation can be used to determine time dilation, length contraction, and change in mass of an object.

This equation allows you to calculate the difference between special relativity and classical relativity of an object in a rest frame as compared to an object traveling at a high rate of speed. If you were traveling aboard a space ship traveling at say 60% percent the speed of light for one year, you would experience the passage of one year while people back on earth would experience 1.25 years. This means that you would have traveled 3 months into the future! As of now we have no ability to accelerate a space ship anywhere close to that rate of speed.

Effect number two is length contraction. As an object travels at relativistic speeds the object contracts in the direction of its motion. A passenger on the a space ship would not notice nor experience any difference in time or length in his frame of reference. An observer watching the space ship travel would, in fact, notice the length being contracted in the direction of its motion.

Effect number three is an increase in mass of an object as it approaches the speed of light. The faster an object moves the more mass it gains. Consequently, it is impossible for an object to reach the speed of light because it would become infinitely massive and require an infinite amount of energy to travel at that speed.

The World’s most famous equation!

Everyone is familiar with the famous equation E=mc^2 but what does it actually mean and why is it important? The “E” represents energy in this equation while “m” represents the mass of an object and c represents the speed of light squared. The equations states that the amount of energy you can obtain from an object is equal to the mass of the object multiplied by the speed of light squared. Even if the mass is extremely small the amount of energy available will be extremely large due to the large value of the speed of light squared. https://www.youtube.com/watch?v=hW7DW9NIO9M

It sounds simple-we can get large amounts of energy from everyday objects so we should never have to worry about energy ever again. The difficult part is how to obtain this energy from everyday objects. As it turns out we can harvest energy from very small objects in a process called nuclear fission. In nuclear fission a large amount of energy that can be obtained from a small amount of uranium contained in fuel rods. The splitting of the nucleus releases a large amount of energy energy. The release of energy in which is used to heat water and is eventually converted to electricity. Currently 29 nuclear reactors across the United States generate 20 percent of the country’s electricity by taking advantage of Einstein’s famous equation.