If you ask what is energy? some people will tell you that energy is an abstract thing. This was how Richard Feynman described it in the Feynman lectures, volume I chapter 4. He used the analogy of children’s blocks. He said these blocks were absolutely indestructible and could not be divided. But then he said there are no blocks. Only then he contradicted himself by saying energy has a number of different forms, such as gravitational energy, kinetic energy, and heat energy:
Image from Assignment point
Then for the cherry on top he said this: “It is important to realize that in physics today, we have no knowledge of what energy is”. Only it isn’t true. Einstein knew what energy was. Now I’ve always been a Feynman fan, and an Einstein fan too. But as I’ve learned more about the physics and the history, I’ve come to appreciate that Feynman was something of a young Turk who did his own thing. One of his close colleagues was Freeman Dyson. In 2007 Dyson told me that way back in the late forties, people like him considered Einstein to be out of touch. So I don’t think Feynman read Einstein’s material. That’s why he didn’t know how gravity works. Or that curved spacetime is not the same thing as curved space. Or that energy is not an abstract thing.
Energy is not just the capacity to do work
Nor is it just the capacity to do work. That’s the answer you usually get: energy is the capacity to do work. But when you then ask what is work? The answer is merely the transfer of energy. That’s circular, and a non-answer pretending to be an answer. That’s unsatisfactory. See for example what Cathal O’Connell said in Cosmos magazine: “Any physics textbook will tell you energy is ‘the capacity to do work’. Then it usually goes on to explain that ‘work’ is the action of moving something against a force. But isn’t this definition kind of unsatisfying?” Yes it is. Energy is not just the capacity to do work, so well said that man. Unfortunately he then said this: “the reason energy is so hard to define is because it’s an abstract notion. In physics, the concept of ‘energy’ is really just a kind of shorthand, a tool to help balance the books”. There’s that energy is an abstract thing again. He also said there is no physical essence of energy, and no such thing as pure energy, and that energy is always carried by something. Only then he contradicted himself by saying energy can be converted into mass. Try pushing a car and you will soon appreciate that mass is not an abstract thing.
Energy is not just the property of a thing
If energy can be converted into mass, and mass is not an abstract thing, that means energy is not an abstract thing either. So it isn’t just some property of a thing. It isn’t like “red”. I can show you a red balloon, a red bus, or a red red ruby. But I can’t remove this red and hold it in the palm of my hand. I can remove the paint or the dye, and I can hold that in the palm of my hand. But I’m still holding a thing that is red. You always need a thing to be red. There is no such thing as pure red. It isn’t like that for energy. If it was, energy couldn’t be converted into mass, and it can. This is why “the mass of a body is a measure of its energy content”. That’s what Einstein said in his 1905 E=mc² paper, and he meant what he said. His paper was entitled does the inertia of a body depend upon its energy-content? and the answer is yes. He used an L for Lagrangian instead of an E for energy, but that doesn’t matter. What matters is that he referred to electron and body on the same line, and he said this: “If a body gives off the energy L in the form of radiation, its mass diminishes by L/c²”. That means when you burn wood in a fire, the total mass of the ash and smoke and gas is less than the original mass of the wood. That’s because a burning log is a body that gives off energy in the form of radiation. Note that according to Einstein, radiation doesn’t have energy, it’s a form of energy. That’s important. Also note that according to Einstein, a body contains energy. According to Einstein, energy is something real, not just some abstract thing, and not just the property of a thing. Let’s play the detective and look into it further.
How do you make that car move? You push it. You put your back into it. You use your muscles. You do work on it. You give it kinetic energy. You add energy to it. How does this work? Via ATP and myosin. See what the Utah Learn Genetics website says: “Adding a third phosphate group (phosphorylation) adds energy, like compressing a spring. Removing the phosphate group (hydrolysis) releases energy, like freeing a spring to uncoil.
Image from the Utah Learn Genetics website
Your muscles employ what can only be described as molecular springs. The atoms in those molecules are held together by bonds, and these bonds rely on electrons and the electromagnetic force. They’re rather like magnets that want to pull together or push apart, only it’s electrostatic attraction and repulsion rather than the magnetic variety. Push two magnets together and hold them there, and you’re storing energy. It’s similar when you compress a coil spring. It’s similar for the energy stored in ATP. In all cases the energy is real. That’s why you can use it to push a car.
It’s the same for chemical energy. See the Wikipedia article on gasoline and note that there’s a section entitled energy content. Gasoline, also known as petrol, contains energy. When you drive your car, petrol is burnt in the engine. That’s like releasing a zillion molecular springs all at once. The petrol and oxygen turn into a hot expanding gas mixture in the cylinders. This pushes the pistons which turn the crankshaft, which turns the propshaft, which turns the wheels. The Wikipedia article says one component of petrol is octane, the combustion of which involves this chemical reaction:
2 C₈H₁₈ + 25 O₂ → 16 CO₂ + 18 H₂O
In essence the octane is behaving like an uncoiling spring, albeit one which is uncoiled using oxygen, and where the component parts are then rerarranged. It’s similar for an explosive. See what Philip Eaton et al said in their 2002 paper Octanitrocubane: A New Nitrocarbon: ”The large bond angle deformations in cubane make it a powerhouse of stored energy. Each strained bond is like the spring in a set mousetrap”. Cubane is strained. It’s under stress. Each strained bond is like the spring in a set mousetrap. When this explosive detonates it’s like releasing a zillion molecular springs all at once. The result is an explosion of devastating force.
It’s similar with nuclear energy, only now we’re talking about the stuff inside the atoms rather than between the atoms, and these springs are stronger. That’s why nuclear bombs are more devastating than high explosive bombs. The most powerful nuclear bomb detonated to date was the Tsar Bomba. It was an H-bomb which weighed about 30 tons and yielded about 50 megatons. However the yield was reduced from a possible 100 megatons to save the aircraft that dropped the bomb, so we’re talking about a power-to-weight ratio that’s circa three million times that of conventional explosives. The mushroom cloud was forty miles high:
Fair use image from the Russian department of Atomic Energy Minatom), see Wikipedia and web.archive.org
Interestingly however the E=mc² matter-to-energy conversion rate was remarkably low. See what “Eli” said on physics stack exchange. Only about 327 kg of hydrogen took part in the proton-proton fusion reaction with the H-bomb. This has an efficiency of 0.712%. So only 2.33 kg of matter was converted into energy. That’s about the same as the bag of potatoes in your shopping trolley.
The efficiency of hydrogen fusion pales into insignificance when compared with matter-antimatter annihilation. When we annihilate an electron with a positron, the matter-to-energy conversion rate is 100%.
Image from Rod Nave’s hyperphysics
If a combined mass of 2.33 kg of matter and antimatter were to annihilate, the result would be a mushroom cloud forty miles high. Everything within a blast radius of forty miles would be totally destroyed. Windows would break five hundred miles away. There’s an awful lot of energy tied up as matter.
Gravitational potential energy
I think that demonstrates how gentle things are in ordinary life. When you compress a spring you do work on it. You add energy to it, so by virtue of E=mc² you increase its mass. The increase is so slight as to be unmeasurable, but nevertheless there is an increase. It’s similar when you lift a brick. You do work on it. You add energy to it, so by virtue of E=mc² you increase its mass. The opposite occurs when you drop a brick. Then gravity converts potential energy into kinetic energy. When the brick hits the ground the kinetic energy is dissipated, and you’re left with a mass deficit. See the Wikipedia binding energy article. Don’t think the potential energy is in the gravitational field or in “the system”, it’s in the brick. When you know how gravity works, you know this. You also know that there is no magical mysterious mechanism by which that kinetic energy somehow streams into the brick as it falls. It was always in the brick, as potential energy, which was mass-energy. You also know that gravity merely converts internal kinetic energy into external kinetic energy. Why? It’s because mass-energy is kinetic energy. You can work this out from Compton scattering and pair production.
In Compton scattering some of the photon kinetic energy is converted into electron kinetic energy. The photon changes direction so it’s decelerated in the vector sense, and its wavelength increases. The electron is deflected in a direction opposite to the photon, and is accelerated in the usual sense:
Image from Rod Nave’s hyperphysics
The point to note is this: if you could do another Compton scatter on this self-same photon, and another and another ad infinitum, in the limit there’s no photon left. That’s because the photon is a singleton soliton electromagnetic wave in space, and it has an E=hf or E=hc/λ wave nature. A wave in the surf has a wave nature too. Note that when you take all the kinetic energy away from a wave in the surf, it just isn’t there any more. So the wave in the surf is energy. It’s the same for a photon. When you take all the kinetic energy away from a wave in space, it just isn’t there any more. So the photon is energy. Perform Compton scattering repeatedly with the self-same photon, and in the end it has been entirely converted into the kinetic energy of electrons.
And yet, and yet: in pair production, you can make an electron and a positron out of photons. So the electron is kinetic energy too. But now this kinetic energy is hidden. We call it mass-energy. Or potential energy. Or field energy. Only there’s angular momentum in this field, and a secret Poynting vector going around and around. See page 26 of Schrödinger’s quantization as a problem of proper values, part II. That’s where he said “let us think of a wave group of the nature described above, which in some way gets into a small closed ‘path’, whose dimensions are of the order of the wave length”. Also see Hans Ohanian’s 1984 paper what is spin? He said “the means for filling the gap have been at hand since 1939, when Belinfante established that the spin could be regarded as due to a circulating flow of energy”. Frederik Belinfante’s paper was on the spin angular momentum of mesons. This circulating flow of energy is why electrons have their dipole magnetic moment, and go round in circles or helixes in a uniform magnetic field. That’s why the electron is a “spinor”. And this circulating flow of energy is there because in gamma-gamma pair production, the photon paths change from a straight linear paths, to closed paths:
Pair production image accredited to McGraw Hill Higher Education, see Google
The opposite happens when you annihilate that electron with a positron. That’s why you see 511 keV photons racing away at the speed of light. From what looked like a standing start, but wasn’t. That’s because in atomic orbitals and everywhere else, electrons exist as standing waves.
Electrons are standing waves
Take a look at the enigmatic electron by Frank Wilczek. He said “the proper quantum mechanical description of electrons involves wave functions, whose oscillation patterns are standing waves”. Standing waves that only look like they’re motionless. Standing waves that are energy, a circulating flow of energy in the guise of a “body” called an electron. A body that doesn’t have a field, it is field. Standing wave, standing field. It isn’t some billiard-ball thing that has charge, it is charge, because it’s a 511keV field-variation wave wrapped and trapped in a twisting turning spin ½ Möbius loop that makes the field variation look like an all-round standing field. The positron is similar, but with the opposite chirality. It has the same mass, because as hinted at by the wave nature of matter and electron spin, mass is just resistance to change-in-motion for a wave going round and round. Annihilation is like unwrapping one standing wave with another, and then both waves aren’t standing any more. Instead they’re off like a shot. It’s similar in low-energy proton-antiproton annihilation. What you see is gamma photons. Energy in the form of radiation:
Image credit: CSIRO Australia Telescope National Facility
Remember what Einstein said: if a body gives off the energy in the form of radiation, its mass diminishes. Only when annihilation occurs, two bodies give off all their energy in the form of radiation and their mass diminishes to zero. The bodies lose all of their mass, and then they’re just not there any more. Because the electron is just a self-trapped 511keV photon in a chiral spin ½ configuration, and so is the positron. Which tells you what happens in Compton scattering: a portion of the photon gets shaved off and applied to the electron. So now the standing wave electron isn’t symmetrical any more. The wave still goes around and around, only it doesn’t end up where it started. As a result the electron moves.
Something similar happens inside the atom. When a hydrogen atom absorbs a low-energy photon, the electron moves, But it’s bound to the proton, so it doesn’t move totally away. Instead it changes orbital. It’s something like a tetherball, only it’s more like a tethered hoop of light. Only it isn’t some thin hoop, it’s a fat torus, so fat that it looks spherical. Only when it changes orbital, it can look different. It can look like a torus, or a dumbbell, or a mixture of both:
CCASA image by Geek3, see Wikipedia
Note that these electron orbitals don’t really have a surface, just as a magnetic field doesn’t have a surface. Also note that these electron orbitals can get more complicated and form bonds. Like I was saying, close your eyes whilst you play repulsion with a couple of magnets, and you can feel the field. The electron is like that field, minus the magnets. Push two magnets towards one another, and it feels like a spring. It would be similar if you could push two electrons together. You are storing energy. Only spring steel springs are made of things like electrons and protons, which are themselves made of energy. So when you store energy in a spring, you are storing energy in energy, because matter really is made of energy. You are too, along with all the matter you can see, and all the light you can see with.
The photon is wave in space
Light is energy because it has a wave nature. It’s comprised of photons, but don’t think of the photon as some billiard-ball particle. Wave-particle duality is a myth. Particles are waves. The photon has a wave nature. See Pascual Jordan’s resolution of the conundrum of the wave-particle duality of light by Anthony Duncan and Michel Janssen dating from 2007. On page 47 they quote Jordan saying this: “The fluctuation effects, which prove the presence of corpuscular light quanta in the radiation field, then arise automatically as consequences of the wave theory. The old and famous problem [of] how one can understand waves and particles in radiation in a unified manner can thus in principle be considered as solved”. As for what sort of wave the photon is, see what Maxwell said when he was talking about displacement current in 1861: “light consists of transverse undulations in the same medium that is the cause of electric and magnetic phenomena”. Also see what Percy Hammond said in the 1999 Compumag: “We conclude that the field describes the curvature that characterizes the electromagnetic interaction. Then think about some other waves. When an ocean wave moves through the sea, the sea waves. When a seismic wave moves through the ground, the ground waves. So, what waves when a light wave moves through space? There can only be one answer, and that answer must be space. Space waves. A photon is just a wave in space. Don’t think of it as an electric wave and an orthogonal magnetic wave. It’s an electromagnetic wave. Or better still, it’s a wave of electromagnetic four-potential. Think of it as a pressure-pulse of space propagating through space.
But don’t think all energy takes the form of light and matter. Yes, you can think of a 511keV photon as a wave in space moving linearly at c, and you can think of an electron as the same thing trapped in its own spatial curvature. But dark matter doesn’t consist of photons and electrons. Nor does gravitational field energy. Einstein said “the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy”. But it isn’t made of particles. It’s spatial energy. Don’t forget that some say the cosmological constant is the “energy density of the vacuum of space”. Or that the modern approach is to treat dark energy as a component of the stress-energy-momentum tensor which “describes the density and flux of energy and momentum in spacetime”:
Public domain image by Maschen, based on an image by Bamse see Wikipedia
The shear stress term on the right tells you we’re dealing with some kind of elastic continuum. The energy-pressure diagonal tells you it’s subject to pressure. For an analogy, imagine you have a block of gin-clear ghostly elastic jelly, with grid lines in. You slide a hypodermic needle into the centre of the block, and inject more jelly. This represents a concentration of energy bound up as the matter of a massive star. It creates a pressure gradient in the surrounding jelly. That might sound novel, but it isn’t. Even Newton knew about this. Léon Rosenfeld talked about it 1969:
Fair use excerpt from Newton’s views on aether and gravitation by Léon Rosenfeld 1969
Stress is directional pressure, the pressure is outwards, and Einstein’s equation Gμν = 8πTμν is modelling the way gin-clear ghostly elastic space is conditioned by the energy you added. But don’t forget that you added jelly to represent energy, and that the jelly also represents space. Space doesn’t just have some kind of innate intrinsic vacuum energy. At some deep fundamental level, space and energy are two sides of the same coin.
Space is aether
Did you notice the reference to aether in Rosenfeld’s paper? Einstein is said to have done away with the aether, but he didn’t. His 1920 Leyden address was on ether and the theory of relativity. He said “according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an ether”. Also see Gustav Mie’s 1913 Foundations of a theory of matter translated by David Delphenich. In chapter 1 section 4, Mie talked about “the so-called ‘four-potential’ that one constructs from the scalar potential j and the vector potential f.” He said “the two potentials, j and f, embody the physical state of the universal ether”. In addition take a look at the Wikipedia aether theories article where you can read Robert Laughlin saying most physicists think space is more like a piece of window glass than ideal Newtonian emptiness.
The contrast between space and matter would fade away
This is important, because in his Leyden Address, Einstein said if we could understand the gravitational and electromagnetic fields “as one unified conformation”, the contrast between ether and matter would fade away. He was saying the contrast between space and matter would fade away. See does matter differ from vacuum? by Christoph Schiller. The answer is no. See Helge Kragh’s preludes to dark energy. He tells how Einstein delivered a lecture in Nottingham in 1930 saying space “remains the sole medium of reality”. What’s a gravitation field? A pressure gradient in space. Why does the universe expand? Because space has an innate pressure. What’s a photon? A pressure-pulse of space propagating through space. It has a polarization, so the pressure is directional, so we call it stress. It doesn’t matter whether you call it pressure or stress, because either way, matter is made from it. That’s why in 1870 William Kingdon Clifford came up with his space theory of matter on Wikipedia.
Energy is a volume of stressed space
There’s nothing more fundamental than space. Space isn’t made of anything else. We can’t examine atoms of space through a microscope or annihilate it to obtain something else. But we know that the dimensionality of energy can be expressed as pressure x volume, and that space always has a volume. If it didn’t, it wouldn’t be space. We also know that space is always stressed, because gravitational fields are everywhere, as is light, and because space expands. So we know that in barest essence, at the deep fundamental level, energy is a volume of stressed space. The greater the volume, the more energy there is. The greater the stress, the more energy there is. Energy isn’t just earth, air, fire, or water. It isn’t just some classical element: “Aristotle added a fifth element, aether; it has been called akasha in India and quintessence in Europe”. Aether is space and space is energy. It’s the quintessence. But in truth it’s the first essence, and the only essence. Because it’s the only thing. The one thing we can neither create nor destroy. The thing from which all other things are made.