How Einstein's E=mc^2 Works (Infographic) How Einstein's E=mc^2 Works (Infographic) By Karl Tate, LiveScience Infographic Artist | May 19, 2014 03:50pm ET MORE Researchers say that soon it will be possible to smash photons together to create matter in the laboratory. Credit: By Karl Tate, Livescience.com infographics artist Updated Tuesday, May 20, at 1:35 p.m. ET Although the idea of a relationship between mass and energy was not new, in the early years of the 20th century, physicist Albert Einstein created a formula that was the first to correctly state that relationship. This practical information led to the creation of nuclear power reactors and atomic bombs. This discovery basically states that the properties of mass and energy are interchangeable, and what people call matter is really just energy in a different form. The idea has some startling implications. For example, if a 2.2-pound (1 kilogram) gold bar absorbs enough energy to heat it up by 18 degrees Fahrenheit (10 degrees Celsius), the mass of the gold bar would actually increase!

But only by a tiny amount: 0.000000000000014 kilograms. Conversely, if the bar radiates heat to cool off by the same amount, its mass will decrease by the same tiny fraction. It is important to note that the total energy of the entire system remains the same; no energy is being created or destroyed. The heat energy is simply changing its form to become mass. A small amount of mass contains an enormous amount of energy, far more than is released in conventional chemical reactions. For example, burning a gallon of gasoline (3.78 liters) produces about 132 million joules of energy, but converting that entire mass directly to energy would liberate 270,000,000,000,000,000 joules, or about 2 billion times as much energy. Nuclear power reactors and nuclear bombs operate on principles of fission or fusion of subatomic particles: splitting atoms apart or smashing them together. These nuclear reactions, however, do not convert the entire mass to energy. Colliding photons, or particles of light, could produce an electron and its antimatter counterpart, a positron.

This would require tremendous energy, such as existed in the early moments of the universe after the Big Bang. In 2014, scientists proposed that a matter-producing collision experiment utilizing only photons could be possible within a year. What is the significance of E = mc2? And what does it mean? - Scientific American Scientific American Advertisement | Report Ad Ronald C. Lasky, director of the Cook Engineering Design Center at Dartmouth College, explains the significance behind this hallowed equation: It is the most famous equation in the world. Many can recite it—and attribute it to Albert Einstein—but few know its significance. It tells us that mass and energy are related, and, in those rare instances where mass is converted totally into energy, how much energy that will be. The elegance with which it ties together three disparate parts of nature—energy, the speed of light and mass—is profound. Here is where the equation of all equations comes from: It was known for some time before Einstein's insights that electromagnetic radiation (light, for example) possessed momentum. This quality of radiation is small in magnitude—after all, you needn't worry about being knocked over by sunlight—but easily measurable.

Applying an understanding of light's momentum within a little thought experiment, it is possible to see how E = mc2 comes about. Consider a cubic hollow box at rest in space with sides of length D and a mass of M. This box is also symmetrical in its mass distribution. One of the faces inside the box is coated with a fluorescing material, and, at a given moment, a photon (i.e., a particle of light) is emitted from that material, perpendicular to its surface. The momentum of this photon causes the box to move in the opposite direction as the photon, and it continues to move until the photon hits the opposite wall. During this time the box moves a very small distance, Δx. Image: RONALD LASKY Newton's laws of mechanics tell us that the center of mass cannot move, because the box has not been acted upon by an outside force. However, in order to keep the center of mass constant, since the box has moved, some mass must have been transferred from the fluorescing side of the box to the absorbing side in the process of generating the photon and its striking the opposite side. Therefore the photon must have a mass, m.

So the photon, which also possesses energy E, is emitted from the fluorescing side of the box. Its momentum, Pphoton, is equal to its energy divided by the speed of light: Pphoton = E / c. The photon will impart this momentum to the box, causing the box to move a small distance, Δx, during the time, t, in which the photon travels to the opposite side of the box. The momentum of the box, Pbox, is also equal to its mass, M, times the velocity, vbox, at which it moves before the photon strikes its target. (Note: The box loses the photon's mass, m, during this process, but this slight loss can be neglected here.) Hence: Pphoton = Pbox = E / c = Mvbox Then vbox = E / cM (1) We can also determine the time it takes for the photon to travel across the box: it is equal to the length, between parallel faces, of the box (which is D), minus the amount the box moved in the opposite direction (Δx), divided by the speed of light, c.

(The target will essentially have moved a slight distance closer, meaning the photon did not have to travel the full distance D.): t = (D - Δx) / c A Fun Way of Understanding E=mc2 - Universe Today Universe Today A Fun Way of Understanding E=mc2 Article Updated: 23 Dec , 2015 by Joshua Carroll Many people fail to realize just how much energy there is locked up in matter. The nucleus of any atom is an oven of intense radiation, and when you open the oven door, that energy spills out; oftentimes violently. However, there is something even more intrinsic to this aspect of matter that escaped scientists for years. It wasn’t until the brilliance of Albert Einstein that we were able to fully grasp this correlation between mass and energy. Enter E=mc2. This seemingly simple algebraic formula represents the correlation of energy to matter (energy equivalence of any given amount of mass). Many have heard of it, but not very many understand what it implies. Many people are unaware of just how much energy is contained within matter. So, for the next few minutes, I will attempt to convey to you the magnitude of your own personal potential energy equivalence. First, we must break down this equation.

What do each of the letters mean? What are their values? Let’s break it down from left to right: Albert Einstein. Image credit: Library of Congress E represents the energy, which we measure in Joules. Joules is an SI measurement for energy and is measured as kilograms x meters squared per seconds squared [kg x m2/s2]. All this essentially means is that a Joule of energy is equal to the force used to move a specific object 1 meter in the same direction as the force. m represents the mass of the specified object. For this equation, we measure mass in Kilograms (or 1000 grams). c represents the speed of light. In a vacuum, light moves at 186,282 miles per second. However in science we utilize the SI (International System of Units), therefore we use measurements of meters and kilometers as opposed to feet and miles. So whenever we do our calculations for light, we use 3.00 × 108m/s, or rather 300,000,000 meters per second.

So essentially what the equation is saying is that for a specific amount of mass (in kilograms), if you multiply it by the speed of light squared (3.00×108)2, you get its energy equivalence (Joules). So, what does this mean? How can I relate to this, and how much energy is in matter? Well, here comes the fun part. We are about to conduct an experiment. This isn’t one that we need fancy equipment for, nor is it one that we need a large laboratory for. All we need is simple math and our imagination. Now before I go on, I would like to point out that I am utilizing this equation in its most basic form. There are many more complex derivatives of this equation that are used for many different applications. It is also worth mentioning that when two atoms fuse (such as Hydrogen fusing into Helium in the core of our star) only about 0.7% of the mass is converted into total energy. For our purposes we needn’t worry about this, as I am simply illustrating the incredible amounts of energy that constitutes your equivalence in mass, not illustrating the fusion of all of your mass turning into energy.

Let’s begin by collecting the data so that we can input it into our equation. I weigh roughly 190 pounds. Again, as we use SI units in science, we need to convert this over from pounds to grams. Here is how we do this: 1 Josh = 190lbs So 190lbs × 453.6g/1 lbs = 86,184g So 1 Josh = 86,184g Since our measurement for E is in Joules, and Joule units of measurement are kilograms x meters squared per seconds squared, I need to convert my mass in grams to my mass in kilograms. We do that this way: 86,184g × 1kg/1000g = 86.18kg. So 1 Josh = 86.18kg.

Now that I’m in the right unit of measure for mass, we can plug the values into the equation and see just what we get: E=mc2 That looks like this: 7,760,000,000,000,000,000 or roughly 7.8 septillion Joules of energy. Artistic rendition of energy released in an explosion. Via Pixabay. This is an incredibly large amount of energy. However, it still seems very vague. What does that number mean? How much energy is that really? Well, let’s continue this experiment and find something that we can measure this against, to help put this amount of energy into perspective for us. First, let’s convert our energy into an equivalent measurement. Something we can relate to. How does TNT sound? First, we must identify a common unit of measurement for TNT. The kiloton. Now we find out just how many kilotons of TNT are in 1 Joule. After doing a little searching I found a conversion ratio that will let us do just this: 1 Joule = 2.39 × 10-13 kilotons of explosives.

Meaning that 1 Joule of energy is equal to .000000000000239 kilotons of TNT. That is a very small number. A better way to understand this relationship is to flip that ratio around to see how many Joules of energy is in 1 kiloton of TNT. 1 kiloton of TNT = 4.18×1012 Joules or rather 4,184,000,000,000 Joules. Now that we have our conversion ratio, let’s do the math. 1 Josh (E) = 7.76 x 1018 J 7.76 x 1018 J x 1 kT TNT/ 4.18 x 1012 J = 1,856,459 kilotons of TNT. Thus, concluding our little mind experiment we find that just one human being is roughly the equivalence of 1.86 MILLION kilotons of TNT worth of energy. Let’s now put that into perspective, just to illuminate the massive amount of power that this equivalence really is.

The bomb that destroyed Nagasaki in Japan during World War II was devastating. It leveled a city in seconds and brought the War in the Pacific to a close. That bomb was approximately 21 kilotons of explosives. So that means that I, 1 human being, have 88,403 times more explosive energy in me than a bomb that destroyed an entire city… and that goes for every human being. So when you hear someone tell you that you’ve got real potential, just reply that they have no idea…. Hydrogen Bomb Blast. Image via Pixabay. Share this: E=mc^2 - An Explanation of the Basics and Units Advertisement What Does the Equation Mean? The equation tells us that energy and mass are, effectively, the same thing, and it also tells us how much energy is contained in a given mass, or vice versa. In other words, mass can be thought of as very tightly packed energy. That energy and mass are equivalent is quite an extraordinary claim and seems to go against two laws that had been established by scientists before Einstein came along: The Law of the Conservation of Mass: As we have seen, mass can be thought of as the quantity of matter in an object.

The law of the conservation of mass states that mass is always conserved. That is, whatever we do with matter in a closed system we will always have the same amount of substance at the end. For example, if we burn a log, the wood gets lighter as the fuel it contains is used up. However, if we gather together the ashes, all of the tiny smoke particles and the water vapour produced by the burning process and then weigh everything we find that the mass is exactly equal to the mass of the log that was burned. Mass is just mass, or so it seems, and while it can be chemically altered, such as burned, the total amount in any system remains the same. The Law of the Conservation of Energy: But what about the energy released in burning the log? The energy released in the burning process is "chemical energy", i.e. the breaking and reforming of chemical bonds between atoms and molecules. Burning the wood released the chemical energy locked up in it. No energy was created in the process and none was destroyed; it was just changed from one sort of energy (chemical bonds) to other forms of energy (heat and light).

In other words the total amount of energy, just like the total amount of mass, remained the same. After many experiments, notably by the scientist for whom the unit of energy is named, James Prescott Joule (1818 - 1889), it was established that the total amount of energy in a closed system always remains the same. This is known as the law of the conservation of energy. What Einstein showed via his now famous equation was that mass and energy are in fact the same thing. Converting one into the other doesn’t therefore violate either of the two conservation laws. Both quantities are conserved, although the state of the mass/energy may have changed. Each atom of a substance can be thought of as a little ball of tightly packed energy that can be released under certain circumstances. Likewise, we can take energy (such as particles of light, called photons) and turn it into matter. This was first achieved in the 1930s.

That light can be turned into matter is perhaps a rather odd idea, but the picture below shows the first successful experiment in which this was done: Cloud chamber photon decay The picture shows the tracks of two matter particles that have been "created" after a high energy photon decayed, i.e. "fell apart", in a cloud chamber. The high energy photon is not in the visible range and has entered the chamber from the bottom of the picture. The Cloud Chamber A cloud chamber is a sealed tank filled with a gas, usually with a magnet to one side of it. When a particle, such as an atom, electron or proton passes through the tank it collides with some of the particles in the gas to produce little clouds that mark its path. For an electrically neutral particle, such as a neutron, the path will be straight. However, for any particle that is not electrically neutral its path will be bent towards or away from the magnet that forms part of the apparatus. The subject of turning matter into energy, through both fusion and fission is dealt with in other pages in this series.

Einstein’s Explanation of his Equation Einstein speaking about the equation E = mc 2 (211kB, .MP3 file) From the soundtrack of the film Atomic Physics Copyright © J. Arthur Rank Organisation, Ltd., 1948. The recording is old, and that, together with Einstein’s accent, sometimes makes it difficult to hear the words properly. This is a transcript of the recording: “It followed from the Special Theory of Relativity that mass and energy are both but different manifestations of the same thing - a somewhat unfamiliar conception for the average mind. Furthermore, the equation E is equal to mc², in which energy is put equal to mass, multiplied with the [by the] square of the velocity of light, showed that very small amounts of mass may be converted into a very large amount of energy and vice versa. The mass and energy were in fact equivalent, according to the formula mentioned before [E = mc²]. This was demonstrated by Cockcroft and Walton in 1932, experimentally." Albert Einstein (1879-1955) Albert Einstein (1879-1955) What do the Letters Stand For?

Each of the letters of E = mc² stands for a particular physical quantity. Writing them out in full we get: Energy = mass x the speed of light squared Introduction A moving steam train Chemical energy - thermal energy - kinetic energy E = Energy c = the Speed of Light Ole Roemer 1644 - 1710 What Does the Equation Mean? The Law of the Conservation of Mass: The Law of the Conservation of Energy: Cloud chamber photon decay The Cloud Chamber A cloud chamber is a sealed tank filled with a gas, usually with a magnet to one side of it. When a particle, such as an atom, electron or proton passes through the tank it collides with some of the particles in the gas to produce little clouds that mark its path. For an electrically neutral particle, such as a neutron, the path will be straight. However, for any particle that is not electrically neutral its path will be bent towards or away from the magnet that forms part of the apparatus. The subject of turning matter into energy, through both fusion and fission is dealt with in other pages in this series.

Einstein’s Explanation of his Equation Einstein speaking about the equation E = mc 2 (211kB, .MP3 file) From the soundtrack of the film Atomic Physics Copyright © J. Arthur Rank Organisation, Ltd., 1948. Albert Einstein (1879-1955) Albert Einstein (1879-1955) What do the Letters Stand For? Without doubt E = mc² is the world’s most famous equation. This page explains what E = mc² means in simple terms and some of its consequences. The equation is derived directly from Einstein’s Special Theory of Relativity and other pages in this series deal with the mathematical and logical derivation. Here though, we will examine the equation as it stands and keep the mathematics to a minimum. Each of the letters of E = mc² stands for a particular physical quantity. Writing them out in full we get: In other words: E = energy (measured in joules , J) m = mass (measured in kilograms , kg) c = the speed of light (measured in metres per second , ms -1 ), but this needs to be "squared".

Note that the case of each letter is important and it would be incorrect to show the equation as, for example, e = MC². This is because physicists use the case of letters as well as the letters themselves to denote particular physical entities, quantities and constants in equations. In order for the equation to be correct we need to "square" the term c (the speed of light), i.e. we multiply the speed of light by itself; hence c² is the same as c times c. This allows us to be write the equation in another, slightly unusual, but equally correct way: E = m x c x c As a matter of interest, and to complete the terms used in the equation, the equals sign was only invented during the 16th century, by the Welsh mathematician Robert Recorde. Apparently fed up having to write out "is equal to" in his work. He could have chosen any number of symbols but chose two parallel lines because, as he himself put it, "noe 2 thynges can be moare equalle". We will now examine each unit (i.e.

letter) in the equation in turn before addressing the question of what the equation means, but if you want to see worked examples of the equations you can do so here . The word "energy" is actually quite new. Its modern use dates from around the middle of the nineteenth century, when it was beginning to be realised that the power that drove many different processes could be explained by the concept of energy being transferred from one system and form to another. For example, the trains of the day were powered by coal. The coal was burned under a water-filled boiler to produce steam, which in turn pushed pistons attached to the wheels of the train, the wheels turned and the train was set in motion. In this example we start with locked up ("latent") chemical energy in the coal. The chemical energy is turned into heat energy (sometimes called "thermal energy") by burning the coal and boiling the water. Finally, the thermal energy is turned into the energy of movement ("kinetic energy") by forcing the steam into pistons to drive the wheels. There are many other forms of energy, such as electrical, gravitational, nuclear, and strain energy, such as that found in springs.

However, as different as all these types of energy seem they can all be measured in the same way and thought of as the same thing. The unit that we use to measure energy, from whatever energy source, is the joule (J). Two ways in which we use this unit in everyday terms are: The total amount of energy in a system: As noted above, one example is a lump of coal, which when burned will release a certain number of joules (J) of energy, mostly in the forms of heat and light. Another, perhaps a more common example, is that it takes about 1 joule to raise an apple by 1 metre. Energy used up over time: Most electrical devices have their power consumption rated in watts (W). A watt is a rate of energy consumption of one joule per second. So, if you have a light bulb in your room that's rated at 100W it's using energy at a rate of 100 joules every second. To go back to the second example in the first bullet point, lifting an apple by 1 metre every second would mean that there is a power output of 1 watt.

For most people this would be quite easy and could be kept up for quite a long time, but now imagine lifting 100 apples a second, i.e. 100W. This, in human terms, is a large power output, but nothing special for many electrical devices. It's not uncommon, for example, for a kettle to be rated at 2000W or more. That's a lot of apples! So, to summarise, energy comes in many forms, and it can be transferred from one system to another. The basic unit of measurement for energy is the joule. Mass is strictly defined as a measure of a body’s inertia, i.e. its resistance to acceleration. Another and simpler way of defining mass is to say that it's the total amount of matter in an object. This latter definition isn’t strictly true, but is good enough for our purposes here. Mass is measured in kilograms (kg). Note that mass isn’t the same as weight, although it's often thought to be.

Weight is actually a measure of the gravitational force (pull) felt by a body and is measured in newtons (N) (note that scientific units that are named after people are almost always in lower case when spelled out fully, hence newtons and not Newtons, watts and not Watts etc). For example, astronauts walking on the surface of the Moon have the same mass as on Earth but only weigh one sixth of what they would do back home. The reason for this is that while the mass of the astronauts hasn’t changed, the pull of the Moon’s gravity is only one sixth of what the Earth’s gravitational pull is. As with energy, the idea that mass is common to all objects is relatively new and again dates back to around the nineteenth century. Before that time, different solids, liquids and gases were all thought to be only loosely connected in conceptual terms. As with energy we now consider that mass is neither created or destroyed, but is merely changed from one form to another, e.g. we can turn water from a solid (ice) into a liquid ("water") and into a gas (steam), but its total mass doesn’t change. We use the letter c to represent the speed of light.

The ‘c’ comes from the Latin word “celeritas”, meaning swift, and it’s a very apt definition - there is nothing faster than light. In a vacuum, such as space, it travels at close to 186,300 miles per second (300,000 km per second ). That’s about seven times around the Earth every second. The speed of light was first accurately estimated by the Danish astronomer Ole Roemer (sometimes written as Rømer) during the 1670s. Up until that time everyone assumed that the speed of light was infinite, i.e. that light arrived at its destination instantly. This isn’t such an unreasonable assumption given that when we look around us light does indeed appear to reach us instantly. During the seventeenth century it was discovered that there was a problem in calculating the orbital time of Io, the innermost moon of Jupiter. It sometimes took "too long" to make an orbit of the planet and at other times was "too quick". It was thought that the problem must be due to a wobble in the orbit of Io, but Roemer took a different, and very radical, view of the matter.

He argued that light, instead of being everywhere instantly, had a finite speed and that this would explain the problem of Io. The Earth was known to travel around the Sun and this meant that sometimes the Earth was closer to Jupiter and sometimes further away. Roemer realised that when the Earth was on the opposite side of the Sun from Jupiter the light from Io would take longer to reach us than when the two bodies were on the same side: This means that the light has to travel further and therefore takes longer, providing, of course, that light has a speed in the first place. During a meeting of the new Academy of Science in Paris in 1676 Roemer demonstrated that the amassed observational data of the astronomer Cassini indicated that Io would next appear at 5.25pm on 9th November of that year. He himself predicted that it wouldn’t appear until 10 minutes and 45 second later, using his theory that light had a finite speed. The day came and virtually every major observatory in Europe was ready to test the prediction. At 5.25pm, the time predicted by Cassini, Io wasn’t visible. Even at 5.35pm Io wasn’t visible.

But at exactly 5.35pm and 45 seconds it appeared, just as Roemer said it would. From this it was possible to make the first accurate measurement of the speed of light and the calculated figure was within one percent of what we know it to be today. You may think that that was the end of the matter and that Roemer was celebrated as a scientific genius, showered with honours and given a secure future. Sadly, that’s far from what happened. He was only 21 when he made his discovery, while Cassini was a well-respected if egotistical elder scientist, who used his powerful friends to back him up to rubbish Roemer’s ideas. Scientists, it seems, are human after all and this wasn’t the first, or sadly, the last time that an ego got in the way of a new discovery. Roemer eventually gave up science completely and later became the director of the port of Copenhagen and then head of the State Council of the Realm. It wasn’t until 50 years later that further experiments convinced the scientific community that Roemer had been right all along.

The equation tells us that energy and mass are, effectively, the same thing, and it also tells us how much energy is contained in a given mass, or vice versa. In other words, mass can be thought of as very tightly packed energy. That energy and mass are equivalent is quite an extraordinary claim and seems to go against two laws that had been established by scientists before Einstein came along: As we have seen, mass can be thought of as the quantity of matter in an object. The law of the conservation of mass states that mass is always conserved. That is, whatever we do with matter in a closed system we will always have the same amount of substance at the end. For example, if we burn a log, the wood gets lighter as the fuel it contains is used up. However, if we gather together the ashes, all of the tiny smoke particles and the water vapour produced by the burning process and then weigh everything we find that the mass is exactly equal to the mass of the log that was burned. Mass is just mass, or so it seems, and while it can be chemically altered, such as burned, the total amount in any system remains the same. But what about the energy released in burning the log?

The energy released in the burning process is "chemical energy", i.e. the breaking and reforming of chemical bonds between atoms and molecules. Burning the wood released the chemical energy locked up in it. No energy was created in the process and none was destroyed; it was just changed from one sort of energy (chemical bonds) to other forms of energy (heat and light). In other words the total amount of energy, just like the total amount of mass, remained the same. After many experiments, notably by the scientist for whom the unit of energy is named, James Prescott Joule (1818 -1889), it was established that the total amount of energy in a closed system always remains the same. This is known as the law of the conservation of energy. What Einstein showed via his now famous equation was that mass and energy are in fact the same thing. Converting one into the other doesn’t therefore violate either of the two conservation laws. Both quantities are conserved, although the state of the mass/energy may have changed. Each atom of a substance can be thought of as a little ball of tightly packed energy that can be released under certain circumstances.

Likewise, we can take energy (such as particles of light, called photons) and turn it into matter. This was first achieved in the 1930s. That light can be turned into matter is perhaps a rather odd idea, but the picture below shows the first successful experiment in which this was done: The picture shows the tracks of two matter particles that have been "created" after a high energy photon decayed, i.e. "fell apart", in a cloud chamber. The high energy photon is not in the visible range and has entered the chamber from the bottom of the picture. Einstein must have spent a great deal of his life explaining his most famous equation. Thankfully, though, someone recorded him explaining it and you can hear it in his own words by downloading the file here: The recording is old, and that, together with Einstein’s accent, sometimes makes it difficult to hear the words properly. This is a transcript of the recording: “It followed from the Special Theory of Relativity that mass and energy are both but different manifestations of the same thing - a somewhat unfamiliar conception for the average mind.

Furthermore, the equation E is equal to mc², in which energy is put equal to mass, multiplied with the [by the] square of the velocity of light, showed that very small amounts of mass may be converted into a very large amount of energy and vice versa. The mass and energy were in fact equivalent, according to the formula mentioned before [E = mc²]. This was demonstrated by Cockcroft and Walton in 1932, experimentally." Q: What does “E=mc2” mean? | Ask a Mathematician / Ask a Physicist Ask a Mathematician / Ask a Physicist Posted on April 7, 2014 by The Physicist Physicist: This famous equation is a little more subtle than it appears. It does provide a relationship between energy and matter, but importantly it does not say that they’re equivalent. First, it’s worth considering what energy actually is. Rather than being an actual “thing” in the universe, energy is best thought of as an abstract (there’s no such thing as pure energy ). Energy takes a heck of a lot of forms: kinetic, chemical, electrical, heat, mechanical, light, sound, nuclear, etc.

Each different form has it’s own equation(s). For example, the energy stored in a (not overly) stretched or compressed spring is and the energy of the heat in an object is . Now, these equations are true insofar as they work (like all true equations in physics). However, neither of them are saying what energy is. Energy is a value that we can calculate by adding up the values for all of the various energy equations (for springs, or heat, or whatever). The useful thing about energy, and the only reason anyone ever even bothered to name it, is that energy is conserved. If you sum up all of the various kinds of energy one moment, then if you check back sometime later you’ll find that you’ll get the same sum. The individual terms may get bigger and smaller, but the total stays the same. For example, the equation used to describe the energy of a swinging the pendulum is where the variables are mass, velocity, gravitational acceleration, and height of the pendulum. These two terms, the kinetic and gravitational-potential energies, are included because they change a lot (speed and height change throughout every swing) and because however much one changes, the other absorbs the difference and keeps E fixed.

There are more terms that can be included, like the heat of the pendulum or its chemical potential, but since those don’t change much and the whole point of energy is to be constant, those other terms can be ignored (as far as the swinging motion is concerned). In fact, it isn’t obvious that all of these different forms of energy are related at all. Joule had to do all kinds of goofy experiments to demonstrate that, for example, the sum of gravitational potential energy and thermal energy stays constant. He had to build a machine that turned the energy of an elevated weight into heat, and then was careful to keep track of exactly how much of the first form of energy was lost and how much of the second was gained. As the weight falls, it turns an agitator that heats the water. Joule’s device couples the gravitational potential of the weight with the thermal energy of the water in a tank. The sum of the two stayed constant. Enter Einstein. He did a few fancy things in 1905, including figuring out a better way of doing mechanics. Newtonian mechanics had some subtle inconsistencies that modern (1900 modern) science was just beginning to notice.

Special relativity helped fixed the heck out of that. Among his other predictions, Einstein suggested (with some solid, consistent-with-experiment, reasoning ) that the kinetic energy of a moving object should be , where the variables here are mass, velocity, and the speed of light (c). This equation has since been tested to hell and back and it works. What’s bizarre about this new equation for kinetic energy is that even when the velocity is zero, the energy is still positive. Up to about 40% of light speed (mach 350,000), is a really good approximation of Einstein’s kinetic energy equation, . The approximation is good enough that ye natural philosophers of olde can be forgiven for not noticing the tiny error terms. They can also be forgiven for not noticing the mc2 term. Despite being huge compared to all of the other terms, mc2 never changed in those old experiments. Like the chemical potential of the pendulum, the mc2 term wasn’t important for describing anything they were seeing. It’s a little like being on a boat at sea; the tiny rises and falls of the surface are obvious, but the huge distance to the bottom is not. So, that was Einstein’s contribution.

Before Einstein, the kinetic energy of a completely stationary rock and a missing rock was the same (zero). After Einstein, the kinetic energy of a stationary rock and a missing rock were extremely different (by mc2 in fact). What this means in terms of energy (which is just the sum of a bunch of different terms that always stays the same) is that “removing an object” now violates the conservation of energy. E=mc2 is very non-specific and at the time it was written: not super helpful. It merely implies that if matter were to disappear, you’d need a certain amount of some other kind of energy to take its place (wound springs, books higher on shelves, warmer tea, some other kind); and in order for new matter to appear, a prescribed amount of energy must also disappear. Not in any profound way, but in a “when the pendulum swings up, it also slows down” sort of way. Einstein also didn’t suggest any method for matter to appear or disappear ( that came later ). So, energy is a sort of strict economy (total never changes) with many different currencies (types of energy).

Einstein showed that matter needed to be included in that “economy”, and that some things in physics are simpler if it is. While it is true that the amount of mass in a nuclear weapon decreases during detonation, that’s also true of every explosive. For that mater, it’s true of everything that releases energy in any form. When you drain a battery it literally weighs a little less because of the loss of chemical energy. The total difference for a good D-battery is about 0.015 picograms , which is tough to notice especially when the battery is ten billion times more massive. About the only folks who regularly worry about the fact that energy and matter can be sometimes be exchanged are high-energy physicists. Cloud chamber tracks like these provided some of the earliest evidence of particle creation and have entertained aged nerds for decades. As far as a particle physicist is concerned, particles don’t have masses; they have equivalent energies. If you happen to corner one at a party (it’s not hard, because they’re meek), ask them the mass of an electron.

They’ll probably say “0.5 mega-electronvolts” which is a unit of energy (the kinetic energy of a single unit of charge accelerated by 500,000 volts). In particle physics, the amount of energy released/sequestered when a particle is annihilated/created is typically more important that the amount that a particle physically weighs (I mean, how hard is it to pick up a particle?). So when particle physicists talk shop, they use energy rather than matter. For those of us unbothered by creation and annihilation , the fact that rest-mass is a term included among many different energy terms is pretty unimportant. Nothing we do or experience day-to-day is affected by the fact that rest-mass has energy. Sure the energy is there, but changing it, getting access to it, or doing anything useful with it is difficult . The cloud chamber picture is from here , and there’s a video of one in action here . February 20, 2016 at 5:23 pm I nitpick your language. E=MC2 does NOT say the two are the same thing. I agree with that.

But instead of “same thing” you chose the word “equivalent”, I think that’s EXACTLY what Einstein is saying. Since one can be changed into the other in a definite predictable way we can say they are equivalent. (Like Einstein’s great principle of General Relativity: Gravity and acceleration can be treated as the same thing. And, he calls it his equivalence principle. In fact he is quoted as once saying that he wished the word “relativity” had never been used. Instead he wanted it to be equivalence or unchanging things. Observers cannot agree about the speed of an object (it’s relative), but they CAN agree about the length of the space time vector being the same for all observers. Thank goodness though that you didn’t say that because the formula included the speed of light that explains why we get SO MUCH energy out of a tiny mass. The problem being that “so much” and “tiny” are arbitrary adjectives with no scientific meaning at all (largER has meaning, largEST does not). Anyway, it’s trivial to create a new SI that defines the speed of light as 1 putting the formula in a much more intuitive form: E=C (though you need to control the dimensions of the result).

Leave a Reply E=mc2 E=mc2 The equation is as famous as the man who wrote it. Click on the image to learn about the equation. In Einstein's first paper about energy and mass, E=mc2 doesn't actually appear anywhere—he originally wrote the formula as m=L/c2. What happened? Einstein was using "L" (for Lagrangian, a general form of energy) instead of "E" for energy. Later, he replaced "L" with "E," rearranged the variables, and the famous form of the equation emerged. The implications of E=mc2 are profound. For centuries, scientists had considered energy and mass to be completely distinct and unrelated to each other. Einstein showed that in fact, energy and mass are different forms of the same thing. Einstein himself was surprised by the finding, calling it "amusing and enticing" and wondered "whether the Lord is laughing at it and has played a trick on me." The Power of a Penny Einstein's equation shows that mass and energy are equivalent—so long as you multiply by the "conversion factor" of c2 (the speed of light multiplied by itself). This factor is huge: 90 billion kilometers2 per second2.

So if you multiply a small amount of mass—say, the mass of a penny—by c2, you'll get a tremendous amount of energy. If a penny could be converted entirely to energy, it would provide enough energy to power the New York City metropolitan area for at least two years. Reality check Converting a penny entirely to energy would require temperatures and pressures much greater than those found inside the Sun. So unfortunately, small coins are not a practical source of energy. E=mc something? Einstein's equation uses just three letters and one number. What do these symbols mean? E = Energy Einsteinlight: Relativity in 5 minutes Why is relativistic kinetic energy different? In Module 4 , we saw that times and distances measured by observers in relative motion are different. So, different observers will also calculate different accelerations, different final speeds and different durations of the accelerations. To say much more than this requires mathematics, which we show in Energy in Newtonian mechanics and in relativity . For this page, where we are keeping equations to a minimum, let's just say that we get a different answer, as the graph shows. However, several important questions remain. One is "what happened to the (½)?

Why does kinetic energy in relativity have mc2 whereas classical kinetic energy has ½mv2?" The short answer to this is that the relativistic expressions involve the expression γ that depends on v. However, one thing that we do know is that Newtonian mechanics works very well at speeds much less than c, so we expect that, at low speeds, Einstein's and Newton's expressions must agree. In Energy in Newtonian mechanics and in relativity , we show explicitly that this is the case. In the graph, the purple line shows the classical kinetic energy, and the red line the relativistic kinetic energy. Another is "how do relativistic and classical mechanics differ in practice?". The short answer is that, at ordinary speeds, the difference is almost zero. However, they become increasingly different as the speed gets closer to c. This is shown both in the graph and in the animation below, which is taken from Module 5 . In this animation, we add energy to the space ship at a constant rate (which is not normal for rockets, by the way). In classical mechanics, the speed is proportional to the square root of the kinetic energy.

But in relativistic mechanics, the kinetic energy is a stronger function of v (it varies more as v changes), so, at high speed, v has to rise only a little as the energy increases. In fact, as v approaches c, the kinetic energy goes to infinity. This means that the rise in v gets smaller as we approach c: no matter how much energy we put in, the speed never gets to c. Where does E = mc2 come from? Remember that, in Module 4 , we saw that clocks run slow and rulers appear short by a factor that depends on speed. That factor is called γ, and we shall write it here as γ(v) to show explicitly that it depends on v. A graph of γ(v) is plotted above. (Incidentally, in module 4, Jasper observed that the light followed the hypotenuse of a triangle, and γ comes from Pythagoras' law, which is why it has a square root. Details here ). We know that, at low speeds, clocks do not run slow and rulers don't shrink, so we know that, for v=0, γ=1. We could write this as γ(0)=1.

When we do the maths , the kinetic energy in relativity turns out to be mc2(γ-1), which we can write like this: Kinetic energy = mc2γ(v) - mc2γ(0)) or, to write it without Greek letters: Kinetic energy = mc2(correction factor for v) - mc2(correction factor for v = 0). Now what do these terms mean? Just from its units, we know that mc2 is an energy. In classical mechanics, ½mv2 was an energy, so a mass multiplied by the square of a speed is an energy. So both terms are energy terms. We are used to seeing proper time and proper length multiplied or divided by this correction factor. Einstein's insight was to see that mc2 was the proper energy of mass m, the energy associated with mass m, independent of its motion. When it had relative speed, its energy was increased from γ(0)mc2 to γ(v)mc2, the difference between them being its kinetic energy. Now you can get back the kinetic energy of a body by slowing it down to zero speed. For instance, you could attach a spring to it and let it stretch the spring until the body came to rest.

In our example of the (ordinary) car, this energy is wasted as heat in the brakes, but in an electric train (or a well designed car) the kinetic energy is turned back into electrical power as the vehicle slows. How would you obtain the mc2 energy? How would you obtain the proper energy of an object that it is already stationary? As this is associated with its mass, you must get it by reducing the mass. Oversimplifying a little, we could say that, if you destroy a mass m you get an energy mc2. For example, when a uranium nucleus undergoes fission, the combined mass of the remnants is very slightly less than that of the original nucleus. So the energy produced in nuclear fission, whether under control in a nuclear power station, or explosive in a nuclear bomb can be related to a slight change in the masses of the nuclear particles involved. The elements of medium atomic mass are the most stable. A large nucleus like uranium or plutonium can break up into less massive components, yielding fission energy. On the other hand, when two very small nuclei fuse together (e.g. two deuterium fusing to form helium), the helium is more stable and less massive.

Again, the loss of mass m is associated with the energy mc2 released. Nuclear fusion may one day be the source of power in nuclear fusion reactors, whose advantages over fission reactors include the fact that helium is an innocuous gas (you can even sell it) and that the deuterium (or heavy hydrogen) comes from sea water, a small fraction of which is deuterated or heavy water. The fact that the helium atom has less mass than that of the two deuterium atoms that fuse to produce it tells us that it takes energy to 'pull' the deuterium nuclei apart. We have to do work against the attractive forces between deuterium nuclei, and that work appears as a greater mass in the unfused nuclei. (For more about such forces, see binding energy .) I am in danger here of giving the impression that this quantification of energy conversion is only important in nuclear reactions. Not true: it is just as applicable to ordinary chemical reactions as well. In chemistry, however, the energies involved are so much smaller that the change in mass is difficult to measure.

In principle, we would expect it to apply wherever work is done: when you do work W on an object by lifting it, one would expect its mass to increase by W/c2. However, because c is so large, this mass would be much smaller than other effects (e.g. the mass of your fingerprints) and would be impossible to measure. To see some values, follow this link . Richard Feynman on explanations with and without mathematics The explanation I have given here may sound less than totally convincing. The more mathematical version is more persuasive, because it uses the reasoning power of mathematics. Richard Feynman was a brilliant physicist. He was also a brilliant lecturer. If I have failed you with these explanations, perhaps he would not. However, when it comes to mathematics, he might have claimed the same extenuating circumstance. In a collection of popular lectures, he said: "it is impossible to explain honestly the beauties of the laws of nature in a way that people can feel, without their having some deep understanding of mathematics. I am sorry, but this seems to be the case. You might say, 'All right, then if there is no explanation of the law, at least tell me what the law is.

Why not tell me in words instead of in symbols? Mathematics is just a language, and I want to be able to translate the language'. In fact I can, with patience, and I think I partly did. I could go a little further and explain in more detail that the equation means that if the distance is twice as far the force is one fourth as much, and so on. I could convert all the symbols into words. In other words I could be kind to the laymen as they all sit hopefully waiting for me to explain something. Different people get diferent reputations for their skill at explaining to the layman in layman's language these difficult and abstruse subjects. The layman searches for book after book in the hope that he will avoid the complexities which ultimately set in, even with the best expositor of this type. He finds as he reads a generally increasing confusion, one complicated statement after another, one difficult-to-understand thing after another, all apparently disconnected from one another. It becomes obscure, and he hopes that maybe in some other book there is some explanation. . . . The author almost made it - maybe another fellow will make it right. But I do not think it is possible, because mathematics is not just another language.

Mathematics is a language plus reasoning; it is like a language plus logic. Mathematics is a tool for reasoning." From: Feynman, R.P. (1965) "The Character of Physical Law" BBC. Reprinted by Penguin Books, 1992. E=MC2 Explained - The Theory of Relativity for Kids The Theory of Relativity for Kids E=MC2 Explained E=Mc2 Explained You may also wonder about the theory E=MC2 , which is often paired with the theory of relativity. This applies to the special theory, and explains how it is impossible to reach the speed of light. The theory’s letters mean: mass (M) going at the constant speed of light (C) equals the amount of energy needed to reach that speed. In other words, it states that the amount of mass you want to reach the speed of light determines the energy needed to do that. The part that says E=M means that energy and mass can be converted into each other. So the amount of mass determines how much energy that object has. In everything, there isn’t enough energy to reach the speed of light, unless you added more energy.

But when you do, you then also have more mass to move, which then needs more energy. As long as you add energy, this will repeat in an endless cycle. But how does light reach this speed? Light is a phenomenon that scientists have yet to understand completely. Light is made up of energy, but has no mass. It is impossible for light to not move at this speed, even though it has no mass. Perhaps by the time you are reading this, scientists will have discovered why, and you can research this on your own. But for now, it remains a mystery. Create a free website What Does E=mc2 mean? @ Super Beefy | Filed Under: Universe 13 Comments E = mc2 is a formula that shows, in mathematical terms, the relationship between energy and mass. In this formula, E is energy, m is mass, and c is the speed of light. The number 2 to the upper right of the c means that c is squared, or multiplied by itself. This formula, first devised by Albert Einstein, shows how much energy would be produced if a quantity of matter could be completely changed into energy.

Suppose that just one gram of matter, or 1/28 of an ounce, were converted into energy. To find out how much energy would be produced, we would multiply one gram times c2. The speed of light is about 30 billion centimeters per second, so the speed of light times itself equals 30 billion times 30 billion, a number that consists of 9 plus 20 zeroes! This is the number of ergs (a very small amount) of energy that would be produced from the one gram of mass. But the number of ergs produced by converting one gram of matter into energy is so large that this amount of energy could power an ordinary light bulb for some 35,000 years! Read More Can you explain it (E=mc2) in a bit more easy to understand way??? That would be great. c means speed of light not a word actually begining with c Anonymous what does the letter “c” stand for? WHAT WORD!!! Anonymous C stands for ‘velocity’ and the constant for velocity is light Anonymous C, it means celeritas, latin for speed Swag_Elite The equation E=mc^2.

E= energy M= mass C^2= speed of light (670,000,000 mph)…only squared so its actually= 448900000000000000 mph. so basically, if you take a small piece of mass..say a baseball, which weighs 5.25oz, and convert that baseball into PURE energy, the amount of joules (energy) it gives off would be equal to the speed of light squared (c^2) multiplied by the weight of the baseball. In this case the product would be 2356725000000000000 joules of energy…which is an enormous amount of energy. annonomous its saying energy= mass times(X) the speed of light squared…. basically if u wanted to convert matter in to energy this is your formula….. knowledge is power Actually, the variable “c” comes from the Latin word “celeritas,” meaning speed or swiftness. BlakesFacts Let me bring it down, as it’s not hard to understand. If you split the Theory up like this, it’s much easier to understand.

E= Energy. C= Speed of light. 2’= Squared. Thus Energy (E) = Amount of Mass (M) times by the Speed of light (C) Squared (2′). J=Awesome I now get it E=MC2 E=energy How to Understand E=mc2: 7 Steps (with Pictures) - wikiHow Understanding the Equation 1 Define the variables of the equation. The first step to understanding any equation is to know what each variable stands for. In this case, E is the energy of an object at rest, m is the object's mass, and c is the speed of light in vacuum. The speed of light, c is constant in all reference frames and is roughly equal to 3.00x108 meters per second. In the context of Einstein's relativity, the c2 functions more as a unit conversion factor than a constant. As such, it is squared as a result of dimensional analysis - energy is measured in joules, or kg m2 s-2, so adding the c2 ensures that the relationship between energy and mass is dimensionally consistent. 2 Understand what is meant by energy.

There are many forms of energy including thermal, electrical, chemical, nuclear and more. [3] Energy is transferred between systems giving power to one system while taking it away from another. Energy can be neither created nor destroyed, it can only take a different form. For example, coal has a lot of potential energy that turns into thermal energy when it is burned. 3 Define what mass means. Mass is generally defined as the amount of matter in an object. [4] There are also a few other definitions of mass. There exists "invariant mass," and "relativistic mass." Invariant mass is mass that remains unchanged no matter what frame of reference you are in. Relativistic mass, on the other hand, depends on the object's velocity. In the equation E = mc2, m refers to the invariant mass. This is very important, because this means that your mass does not grow as you go faster, contrary to popular belief. It’s important to understand that mass and weight are different. Weight is the gravitational force felt by an object, while mass is the amount of matter in that object. Mass can only change if the object is physically altered, while weight changes depending on the gravity of the environment the object is in.

Mass is measured in kilograms (kg) while weight is measured in newtons (N). Like energy, mass can neither be created nor destroyed, but it can also change form. For example, an ice cube can melt into a liquid, but it still has the same mass in both states. 4 Realize that mass and energy are equivalent. [5] The equation states that mass and energy are the same thing and tells you how much energy is contained inside a certain amount of mass. Essentially, the equation explains that a small amount of mass is full of a large amount of energy. [6] Part 2 Applying the Equation in the Real World 1 Understand where usable energy comes from. Most of our consumable energy comes from the burning of coal and natural gas. Burning these substances takes advantage of their valence electrons (unpaired electrons in the outermost shell of an atom) and the bonds they make with other elements. When heat is added, these bonds break and the energy released is used to power our communities. Obtaining energy this way is not very efficient and is costly to the environment. 2 Apply Einstein’s equation to make energy conversion more efficient.

E=mc2 tells us that there is much more energy stored inside the nucleus of an atom than in its valence electrons . [7] The energy released from splitting an atom is much higher than that of breaking electron bonds. Nuclear power is based on this principle. Nuclear reactors cause fission (the splitting of atoms) to occur and capture the massive amount of energy released. 3 Discover the technologies made possible by E=mc2. E=mc2 has enabled the creation of many new and exciting technologies, some of which, we can’t imagine living without: [8] PET scans use radioactivity to see inside the body. The equation allowed for the development of telecommunications with satellites and rovers. Radiocarbon dating uses radioactive decay based on the equation to determine the age of ancient objects. Nuclear energy provides cleaner and more efficient energy sources to our society. Community Q&A You use a melting ice cube as an example of an object changing forms without losing mass. But surely the melted water will occupy less volume than the ice cube? wikiHow Contributor Mass and volume are not the same. You can stretch or compact an object to change its volume, but the amount of matter inside it will stay the same.

In the ice cube example, the molecules in liquid water are closer together, but they're still the same molecules that were in the ice. How is gravity impacted by e=mc2? wikiHow Contributor F=ma and E=mc2 are both encompassed, surpassed, and related by this most fundamental law/truth in all of physics: Inertial resistance is proportional to gravitational force/energy. (Gravity has energy.) This law applies to the Sun and to photons, and it applies to black holes. Balancing gravity and inertia is what is most fundamental and important here. So, force/energy, acceleration, photons/light, gravity and inertia, and larger and smaller space are central considerations for what is impacted by this equation. Can humans travel 1% the speed of light yet? wikiHow Contributor No, not even close. Keep in mind that the speed of light is 3.00×10^8 meters/second.

For us to even go a fraction of that speed, 1% for example, we would have to go 3.0×10^6 meters/second which is approximately 1,864.1 miles/second or 6,710,808.88 miles/hour. We are not even close to that speed yet technologically. I've heard that special relativity is related to time travel. How does that work? wikiHow Contributor There's no such thing as absolute time. Two people moving at different relative speeds can disagree on how much time has passed between two events. However, if you could send a signal faster than light, things get weirder: the two people could disagree over which event came first. This leads to "time travel" paradoxes, such as sending a message to yourself in the past. Most physicists think faster than light signals are impossible, partly for this reason. How does nuclear fission release so much more energy than the break in electrons from burning fossil fuels? wikiHow Contributor Almost all of the mass in an atom is located in the nucleus, where protons and neutrons are bound together very tightly.

Nuclear fission breaks apart these tight bonds and converts some of the nucleus mass into energy. Why can't an object with mass travel at the speed of light? wikiHow Contributor Special relativity explains that accelerating an object with mass takes more and more energy as the speed increases. When you're near the speed of light, this effect is so noticeable that you can only edge closer and closer to light speed, no matter how much energy you put in. You use a melting ice cube as an example of an object changing forms without losing mass. But surely the melted water will occupy less volume than the ice cube? wikiHow Contributor Mass is nothing but the ratio of volume and area. The area of water is more than that of the ice cube and the volume has also changed. As a result, the mass will stay constant. Is there a spiritual aspect to this equation, treating energy as the soul and mass as the body? wikiHow Contributor Physics terms refer to precisely defined, physical phenomena. Burning wood transforms matter into energy, but most religions would not call the result a soul. Einstein himself and many people since have interpreted his theories from a religious perspective, but that's outside the scope of the equations themselves. Why are atoms so small?

wikiHow Contributor Atoms are the building blocks of matter, and they only consist of a certain amount of subatomic particles. They are considered "small" perhaps, since we are so large in comparison, and they are one of the smallest units of creation. Could you simplify this even more, for teaching kids 13 or 14 years old? wikiHow Contributor I would focus on the idea that energy (for instance light and sound) and mass (and physical object) can be converted to each other. The "c squared" part is more difficult to explain, but you could talk about how Einstein figured out that c (the speed of light) is the "speed limit" in the universe. Updated: Views: 812,062 "I loved the simple yet thorough explanation. It's just right for someone who never studied physics but knew of the equation and needed to understand the elements in greater detail."..." more - Vanessa Landau "In layman's terms, I was able to understand the main ideas.

Since I don't have the time to peruse it right now, I will in the near future, and it will be a lot of fun!"..." more - John Leal "I never knew the fact that energy and mass are dependent on one another which I thought both are independent with one another before!"..." more - Venu Gopal "This is really helpful to understand the concept of energy, mass and weight and many more concepts of physics."..." more - Kushal Kumar Soni It's very useful for upcoming students. It's a very valuable equation given to us by Albert Einstein. - Suraj Agartala Amazing. This article really helps. I wish all websites were like this. Thanks to whomever made it! - Bob Cranbrook This is an amazing article. It helped me a lot in understanding Einstein's great theory. - Shama Vishwanthar My mother asked me to do research about this. The article helped me. Thank you. - Ananya Laxmi Banan Scientifically absorbing and fundamentally addictive to read. - Anonymous The explanation of c2 was especially helpful. - Roland Bourret A very good guide for science students. - Sohan Venkatesh Very clear lesson on E=MC2! Thank you.

- Sophia Hamilton Informative, not wordy! Nicely done! - Travis Napoli It is essential to my interest. - Abhishek Umapathy A brief and clear explanation. - Naveen Kumar This is so helpful. - Aayush Gupta

Question: What does 'E' represent in E = MC2?
Answer: Energy