Saturday, October 31, 2020

What is Energy? Is Energy Conserved?

Why save energy if physics says energy is conserved anyway? Did Einstein really say that energy is not conserved? And what does energy have to do with time? This is what we will talk about today.

I looked up “energy” in the Encyclopedia Britannica and it told me that energy is “the capacity for doing work”. Which brings up the question, what is work? The Encyclopedia says work is “a measure of energy transfer.” That seems a little circular. And as if that wasn’t enough, the Encyclopedia goes on to say, well, actually not all types of energy do work, and also energy is always associated with motion, which actually it is not because E equals m c squared. I hope you are sufficiently confused now to hear how to make sense of this.

A good illustration for energy conservation is a roller-coaster. At the starting point, it has only potential energy, that comes from gravity. As it rolls down, the gravitational potential energy is converted into kinetic energy, meaning that the roller-coaster speeds up. At the lowest point it moves the fastest. And as it climbs up again, it slows down because the kinetic energy is converted back into potential energy. If you neglect friction, energy conservation means the roller-coaster should have just exactly the right total energy to climb back up to the top where it started. In reality of course, friction cannot be neglected. This means the roller-coaster loses some energy into heating the rails or creating wind. But this energy is not destroyed. It is just no longer useful to move the roller coaster.

This simple example tells us two things right away. First, there are different types of energy, and they can be converted into each other. What is conserved is only the total of these energies. Second, some types of energy are more, others less useful to move things around.

But what really is this energy we are talking about? There was indeed a lot of confusion about this among physicists in the 19th century, but it was cleared up beautifully by Emmy Noether in 1915. Noether proved that if you have a system whose equations do no change in time then this system has a conserved quantity. Physicists would say, such a system has time-translation invariance. Energy is then by definition the quantity that is conserved in a system with time-translation invariance.

What does this mean? Time-translation invariance does not mean the system itself does not change in time. Even if the equations do not change in time, the solutions to these equations, which are what describe the system, usually will depend on time. Time-translation invariance just means that the change of the system depends only on the amount of time that passed since you started an experiment, but you could have started it at any moment and gotten the same result. Whether you fall off a roof at noon or a midnight, it will take the same time for you to hit the ground. That’s what “time-translation invariance” means.

So, energy is conserved by definition, and Noether’s theorem gives you a concrete mathematical procedure to derive what energy is. Okay, I admit it is a little more complicated, because if you have some quantity that is conserved, then any function of that quantity is also conserved. The missing ingredient is that energy times time has to have the dimension of Pla()nck’s constant. Basically, it has to have the right units.

I know this sounds rather abstract and mathematical, but the relevant point is just that physicists have a way to define what energy is, and it’s by definition conserved, which means it does not change in time. If you look at a simple system, for example that roller coaster, then the conserved energy is as usual the kinetic energy plus the potential energy. And if you add air molecules and the rails to the system, then their temperature would also add to the total, and so on.

But. If you look at a system with many small constituents, like air, then you will find that not all configurations of such a system are equally good at causing a macroscopic change, even if they have the same energy. A typical example would be setting fire to coal. The chemical bonds of the coal-molecules store a lot of energy. If you set fire to it, this causes a chain reaction between the coal and the oxygen in the air. In this reaction, energy from the chemical bonds is converted into kinetic energy of air molecules. This just means the air is warm, and since it’s warm, it will rise. You can use this rising air to drive a turb(ain), which you can then use to, say, move a vehicle or feed it into the grid to create electricity.

But suppose you don’t do anything with this energy, you just sit there and burn coal. This does not change anything about the total energy in the system, because that is conserved. The chemical energy of the coal is converted into kinetic energy of air molecules which distributes into the atmosphere. Same total energy. But now the energy is useless. You can no longer drive any turbine with it. What’s the difference?

The difference between the two cases is entropy. In the first case, you have the energy packed into the coal and entropy is small. In the latter case, you have the energy distributed in the motion of air molecules, and in this case the entropy is large.

A system that has energy in a state of low entropy is one whose energy you can use to create macroscopic changes, for example driving that turbine. Physicists call this useful energy “free energy” and say it “does work”. If the energy in a system is instead at high entropy, the energy is useless. Physicists then call it “heat” and heat cannot “do work”. The important point is that while energy is conserved, free energy is not conserved.

So, if someone says you should “save energy” by switching off the light, they really mean you should “save free energy”, because if you let the light on when you do not need it you convert useful free energy, from whatever is your source of electricity, into useless heat, that just warms the air in your room.

Okay, so we have seen that the total energy is by definition conserved, but that free energy is not conserved. Now what about the claim that Einstein actually told us energy is not conserved. That is correct. I know this sounds like a contradiction, but it’s not. Here is why.

Remember that energy is defined by Noether’s theorem, which says that energy is that quantity which is conserved if the system has a time-translation invariance, meaning, it does not really matter just at which moment you start an experiment.

But now remember, that Einstein’s theory of general relativity tells us that the universe expands. And if the universe expands, it does matter when you start an experiment. And expanding universe is not time-translation invariant. So, Noether’s theorem does not apply. Now, strictly speaking this does not mean that energy is not conserved in the expanding universe, it means that energy cannot be defined. However, you can take the thing you called energy when you thought the universe did not expand and ask what happens to it now that you know the universe does expand. And the answer is, well, it’s just not conserved.

A good example for this is cosmological redshift. If you have light of a particular wavelength early in the universe, then the wave-length of this light will increase when the universe expands, because it stretches. But the wave-length of light is inversely proportional to the energy of the light. So if the wave-length of light increases with the expansion of the universe, then the energy decreases. Where does the energy go? It goes nowhere, it just is not conserved. No, it really isn’t.

However, this non-conservation of energy in Einstein’s theory of general relativity is a really tiny effect that for all practical purposes plays absolutely no role here on Earth. It is really something that becomes noticeable only if you look at the universe as a whole. So, it is technically correct that energy is not conserved in Einstein’s theory of General Relativity. But this does not affect our earthly affairs.

In summary: The total energy of a system is conserved as long as you can neglect the expansion of the universe. However, the amount of useful energy, which is what physicists call “free energy,” is in general not conserved because of entropy increase.

Thanks for watching, see you next week. And remember to switch off the light.

We have two chats about this video’s topic, one today (Saturday, Oct 31) at noon Eastern Time (5pm CET). And one tomorrow (Sunday, Nov 1) also at noon Eastern Time (6pm CET).


  1. If energy conservation is not guaranteed, then a basic principle is missing in the theoretical concept. That may not matter for earthly conditions, just like the effects of speeds of physical objects in everyday life, in the context of generally applicable theoretical models, a lack of energy conservation is a theory killer. Regarding the cosmological redshift: If space and mass are inherently linked, as I think contrary to standard physics, then the missing energy is in the increasing space. In simple terms: space is a form of energy, like mass. If you consider this aspect, enery is allways conserved.

    1. According to Dr. Alan Guth in his book on his Inflation Theory (for laypeople), which I read long ago, space that is filled with a gravitational field is a negative form of energy. He explained this with the example of a hollow planet. As calculated by Newton, the inside of a hollow sphere has no net gravitational effect due to the shell of the sphere, whose pulls cancel inside the sphere. Now suppose the shell is an elastic material. Each part of the shell does feel a net inward force of gravity due to the rest of the shell, so the shell will compress and shrink somewhat. The shrinkage means there is more space outside the sphere which now feels the gravity of the sphere, whereas when it was inside the sphere it felt none, and also means that the shell has the potential energy of a compressed spring. (Energy which could be released to do work.) Where did that energy come from? In Dr. Guth's explanation, it is balanced by the negative energy of the additional space which now contains the gravitational field of the sphere.

      Since the book was for laypeople, that might have been a short-cut explanation which might not be technically correct, however. I think it was meant to suggest a simple model of how the universe can expand without losing internal energy, as an expanding gas does. In this model, the energy for expansion is released by filling more space with gravity, which acts as negative energy.

    2. Yes, one can try to assign energy to space-time curvature in special cases with the attempt to establish an analogy to school physics. It works to some extent for simple systems, and cosmology is the simplest case after flat space. The problem with these explanations is that they don't work in general and then people get very confused as to what about their logic is going wrong. It's a similar problem as the attempt to explain special relativity by means of rockets and laser clocks and so on. Works to some extent, but if you think too much about it, it's more confusing than helpful.

    3. Hi Sabine, I’m curious about conservation seems like a very general principle for any theory formulated on a phase space. If you specify a Hamiltonian that generates time evolution, then that Hamiltonian is preserved along the flow that it generates. In fact any phase space observable is preserved along the flow it generates in phase space, that’s just a trivial consequence of symplectic geometry. So let’s say we formulate GR in the Hamiltonian way (e.g. using the ADM formalism). Then presumably we have some infinite-dimensional phase space of metric configurations on spatial slices or some such. Then we define a Hamiltonian that generates time evolution, and that Hamiltonian is preserved along its flow in phase space. So how is GR different in this sense than any other theory formulated on phase space?

    4. Julian,

      A very good question. I actually hadn't thought about this before. What you say is true as long as the Hamiltonian does not itself have an explicit time-dependence. I don't normally use the ADM formalism, so I can only guess exactly how that comes in, but I suppose that in GR it is generically not possible to remove the time-dependence from the slices and also keep the lapse orthogonal from it, these are just too many gauge-conditions on the metric. Eg, you can (curiously enough) pick a metric for FRW that is spatially flat, but the penalty is that the slices are no longer orthogonal to the time-coordinate.

  2. Wonderful video, tricky concepts explained with great clarity. However, there is one very unfortunate mistake, or maybe just a misleading way of putting things: In GR, Noether’s Theorem *does* apply. It applies whenever there is a Lagrangian. What does *not* apply is energy conservation, because, as you say, there is no time invariance. But since the Theorem *does* apply to GR, we can use it to calculate what *is* conserved, which is the canonical energy-momentum tensor. So Noether’s Theorem explains why energy is not conserved in GR, and also shows us what is conserved.

    1. Thank you for pointing out that I have expressed this unclearly. I was referring to the particular application of the theorem I was talking about earlier, that the symmetry of time-translation invariance gives you a conserved quantity which is energy. I am well aware that the stress-energy tensor is the conserved Noether current in GR, as you can easily find out if you check my publications.

    2. I wasn’t suggesting that you don’t know this—obviously you do, probably better than I do. Just that the way you state things in the video is incorrect.

    3. The statement that the theorem does not apply is referring to the derivation I talk about earlier in the video, that energy conservation follows from time-translation invariance.

    4. Yes, it’s quite clear what you meant, but that’s because I already know what’s true. But I couldn’t show this to a student, because the misleading remark would lead to confusion.

    5. My apologies. It appeared that the purpose of these videos was mainly to be educational. But if they are just entertainment for other physicists, then my comments are not very relevant,because we know what you mean.

    6. They are not entertainment and they are not for physicists. I do not understand the purpose of your comment here. You clearly do not have a question about my video. You understand perfectly well what I say. I have already apologized for expressing myself imperfectly.

    7. Sorry for belaboring this—we seem to have been talking at cross purporses. Please feel free to ignore my comments if they are not useful to you.

    8. Thanks, this was helpfull in understanding what is conserved in GR and what not and why.

  3. Does the potential energy of the universe increase as it expands?
    When galaxies recede beyond our light cone, i.e. they are receding faster than light as seen by us, what happens to their contribution to the potential energy of the universe as seen by us?
    Love your videos.

    1. 'Energy' becomes an ill-posed concept in the general relativistic setting, so talking about the potential energy of a distant galaxy is a non-starter. (And this sort of 'ill-posed' and 'non-starter' language is important - it's not like it starts by making sense and we lose track of it. There isn't similar notion of energy conservation in curved space, as discussed in the video.)

      It's very appealing to try to redefine the global energy to include gravity, and this even works out OK if you restrict attention to spaces which have certain symmetries (so not a general curved space, but some special metrics. This suits certain cosmologists who tend to only have one or two metrics they care about.)

    2. The kinetic energy of galaxies increases and so the potential energy decreases.

    3. Whether there energy conservation is defined depends upon whether there is a Killing vector that is timelike. For Minkowski spacetime there is K_t = ∂_t and in the Schwarzschild metric K_t = √(g_tt)∂_t = √(1 – 2m/r)∂_t A major property is the Killing vector is not time dependent. there is then no K_r! This means momentum in the radial direction is not defined. We can think of this as due to the inability to solve a 2-body problem in GR. In the Kerr metric there is K_φ that describes the frame dragging of a mass with the rotating black hole.

  4. If the universe is a hologram, then the possibility of obtaining free energy naturally arises in a new type of mechanical gyroscope, the rotor of which rotates around three fixed Cartesian axes per cycle. After the occurrence of a phase transition, it is enough to spend energy on the rotation of the rotor around one axis, around the remaining two axes, the rotor rotates itself. It becomes possible to convert part of the vacuum energy into electrical energy. We can patent the device together and solve a lot of problems for everyone. Thanks.

    1. great, then please go an patent it and become rich, but stop submitting your theories in my comment section, thank you.

  5. Hi Sabine, thanks for this post; I like it a lot because I have had for a long time one (perhaps silly) question.

    The wavelength of a photon increases because space expands; OK, that much I get.
    What about the wavelength of electrons? (atoms, etc..., the Schwarzschild radius of a given BH).


    1. Stays the same, unless they have a really large momentum.

    2. That would be very tiny momentum, where the wavelength λ determines the momentum by p = ħ/λ. If the wavelength is really long so as to be significantly stretched by the dynamics of space then momentum is changed.

      Yeah, it is easy to make little goofy mistakes.

    3. Lawrence,

      A gas of ultrarelativistic electrons will fapp behave like radiation. You are not talking about the wave-length, you are talking about the width of the wave-packet. The latter is fapp irrelevant, unless you want to claim electrons are commonly found with Gpc wavelengths.

    4. Alright I concede your point there. I guess even if the wavelength is very tiny it gets stretched. I was just thinking of a small wavelength as not significant with respect to curvature. But with cosmologies curvature is in R_{tt} for the most part.

    5. I think Sabine's answer to akidbelle is wrong.
      The de Broglie wavelength of a single electron in
      intergalactic space is stretched just like the
      wavelength of a photon is. The reason is that
      the gravitational field of a single electron
      as a wavepacket in intergalactic space
      is much too small to stop the accelerated
      cosmic expansion locally.

      Sabine's answer probably refers to the fact
      that the electron's energy will only decrease
      proportional to the stretching factor if
      the electron is ultrarelativiatic in the CMB rest frame.
      But akidbelle did not ask "does the stretching
      change the electron's energy appreciably?" (to
      which Sabine's answer "only if it is has a really
      large momentum (more precisly: is ultrarelativistic)" is
      correct) but only "Does the electron wavelength stretch?"
      (to which the correct answer is simply "yes").

    6. An electron wavepacket spreads even in flat space. Funny, huh?

    7. And, well, since I suspect you may not understand my answer, let me add. The momentum of a particle is not determined by the width of its wave-packet. The width of the wavepacket determines the uncertainty. Different thing entirely. Your reply is trivially wrong. Also, you can very easily check that the energy density of non-relativistic fermions does indeed fall with the inverse volume in an expanding universe, as I said.

    8. > The momentum of a particle is not determined by the width of its wave-packet.

      Yes, of course. Where did I claim otherwise?

      > Also, you can very easily check that the energy density of non-relativistic fermions does
      > indeed fall with the inverse volume in an expanding universe, as I said.

      Yes, correct. And this is because the energy of non-relativistic fermions
      is dominated by their rest mass which is not influenced by the stretching.
      But akidbelle did _not_ ask "Is the energy of an electron influenced
      by the stretching." Right?

    9. Franzi,

      I have no time for your denial. Please take your "arguments" elsewhere.

  6. According to suggestion of Roger Penrose, after very long time all matter in the universe will turn into Black Holes that in turn will evaporise into light. Then all of these light will turn into what? You said that photon energy is lost due to expansion of universe. I understand that gravitational waves if exist will have same issue, energy will "dissolve" into vacuum of universe. Are there any limits of this sort of process? Like minimum light frequency of single photon?

  7. dear Biene,
    I've been wondering about the physicist's version of the 'circular reasoning' you found in the Encyclopedia : in grade school, energy (and momentum) are introduced in the classical mass-distance-time system of mechanics. But later on, (rest-) mass and energy are shown to be related, even convertible. That leaves the original definition of energy 'hanging by it's bootstraps', no? Maybe your definition based on Noether's theorem is free of this circularity, but I can't tell for sure. Can we define 'Lagrangian' without implicitly using the momentum concept?

  8. The expansion of the universe is presumably being driven by some force. If you add that in would energy then be conserved, or does it fundamentally break down?

    1. We have no reason to think that the expansion of the universe is driven by some force.

    2. How about the acceleration?

    3. Strange - I’ve often heard dark energy described as a force?

      I appreciate its not a force in the normal ways we would describe them, and I know its tricky from a physics perspective as you have to consider ‘something speaking into the universe’, but I’m confused why you wouldn’t call anything that drives any type of acceleration a ‘force’ of some type?

    4. Dark energy is not a force. It isn't an energy either. It's a constant of nature, called the cosmological constant.

    5. Only in the narrow interprrtation of general relativity.

      In complete principle the spacetime or any coordinate system we describe have to be only due to interactions, no background canvas allowed.

      Then if we define energy via currents of all those physical interactions, we'll get the coordinate system where that total energy can be set to zero and conserves.

    6. Also, we see space falling continuously in balance with gravitating energy by curved time. Then potentials are huge per planet, star or any object. In fact, the marginal bias of expanding space could be explained like in entropic gravity theories. But imho, it's already as the part of GR dynamics...

    7. What I have seen "dark energy" described as is not a force but a negative pressure. I'm not sure that is true either, but the units are different. Force is mass times distance over time-squared, and pressure is force divided by distance-squared.

      Normally one thinks of a (positive) pressure as being produced by a lot of microscopic forces but the cosmological constant is just a term in an equation without any underlying model, as far as I know. I guess one could say the universe sucks. (In all directions.)

    8. Hm. Vice versa perhaps. Depends on thinking the spacetime continuum being universe or its content, structures. Let' study basic principles.

      Normal positive pressure makes repulsion between structural particles and the space sucks in particles in time.

      A negative pressure makes attraction between particles and the spacetime expands between them.

      Now, you must forget gravity as an attractive force but consider it as direct motion in space with curved time. When space sucks particles to each other the repulsive force is due to fermions exlusion principle. When space expands, particles can feel attractive force by inertia - but in cosmological expansion the case seems to be different. Otherwise the speculation about dark matter being the consequence of the expansion and dark energy (extra attraction / orbital velocities by continuously changing of inertial frame) would be the solution.

    9. @Eusa: google as I just did "dark energy negative pressure". My first hit is:

      "Dark Energy is a hypothetical form of energy that exerts a negative, repulsive pressure, behaving like the opposite of gravity. It has been hypothesised to account for the observational properties of distant type Ia supernovae, which show the universe going through an accelerated period of expansion."

      So I stand by my statement: the Universe sucks (particles away from each other in all directions). (Note that a gas under positive pressure compresses, and expands as its pressure lessens; and to suck is to create a lower pressure.)

    10. Then you consider only particles being the Universe, not void. Still, it sounds a little weird to use word "sucks" when particles feel attraction, right, but the space expands between them. The space seem to be operator, not matter - but obviously it's up to the both.

      I wouldn't say the Universe sucks or blows but its diversity evolves.

    11. To be added: the concordance opinion is that the Universe doesn't expand to anywhere outside it - so there cannot be any "vacuum pump" that sucks outside to get pressure lessen in the space. Analogue: if you suck vacuum for a sealed chamber, a balloon there will expand.

      Yet another speculation: if positive pressure is due to reflective bounces of interaction signals on matter, is negative pressure due to congestion of signals?

    12. Sabine you say:

      “Dark energy is not a force. It isn't an energy either. It's a constant of nature, called the cosmological constant.”

      But isn’t it a physical process which we have to understand? Recently you have complained that the need of reductionism is overlooked in present physics. I fully agree. But isn’t this, dark energy, a typical application of this requirement? (In the case that we believe this problem at all.)

    13. antooneo,

      Not sure what you think I said about reductionism. What I am sure I have said many times is that a constant of nature is as simple as an explanation can get, and trying to replace it with something more complicated is superfluous, hence unscientific. No, a constant is not a process.

    14. Sabine,

      I think that the goal of physics is to find the cause of a process or of a rule. In former times people have said that the orbital radius of a specific planet is a constant and that’s it. Nowadays we know Newton’s laws and we know the cause of the orbit and of its radius.

      Dark energy is about the topic of the accelerated expansion of the universe. There must be a cause for it. As an example, C. Wetterich assumes a field as a cause which he calls “quintessence”. I do not follow this idea, but I appreciate that he has seen the necessity to find a cause. – That is what I have meant. And that is the way of reductionism.

    15. antooneo,

      "I think that the goal of physics is to find the cause of a process or of a rule."

      Well, then you are simply misunderstanding what science is. Science is about describing observations. The cosmological constant is a constant in the model that best describes observations. If you replace it with something superfluous, that's religion, not science. If you allow unnecessary "explanations" or "causes" you may as well allow the addition "god did it" to the laws of nature.

      "Dark energy is about the topic of the accelerated expansion of the universe. There must be a cause for it.

      No there does not have to be a "cause" for a constant of nature. What you say is just wrong and I have no idea what makes you think so.

    16. You should start a church. Sure sound dogmatic enough. If science were 'decribiting observations' then a pig pointing to truffles would be a scientist.
      Yes, CC is a constant in a model. It says so in the name. And frankly my dear, that means jack shit. Something to use until we figure out somethin better. A flint before we had matches. That's all that our models are. Saying that expansion of the universe; let's for the sake of argument say that it really and it's not just something our limited observational and comprehension abilities tricks us into seeing, is just constant in some set of equation is as dogmatic as one can get. It can be anything, including god farting. Have you put some plausible constraint on it not happening due to divine indigestion? I would think not.
      Science is about figuring out what the hell is going on without any preconception as to where that will lead the scientist.
      Question everything including your questions but at the very least question all the answers.

    17. Sirk,

      You are not following. Of course it would be good to have a "better" explanation. What I am saying is that none of the existing explanation are "better". Instead, they all just make the theory more complicated, but introducing utterly and totally unnecessary fields and potential and relaxation mechanisms. If you introduce unnecessary parts into a hypotheses, then that's no longer scientific. I cannot think of anything that's scientifically a better explanation than a constant of nature.

    18. One a good math of theory describing phenomenon often reveals new physics and then it's possible to observe more deeply. I think that Sabine's point lays here: no reason to rush guessing causes before the effects known sharply enough.

    19. Sabine, you say:

      >> Well, then you are simply misunderstanding what science is. Science is about describing observations. The cosmological constant is a constant in the model that best describes observations. If you replace it with something superfluous, that's religion, not science. If you allow unnecessary "explanations" or "causes" you may as well allow the addition "god did it" to the laws of nature. <<

      Science means only a description of observations? That was Plato’s position who saw the world as defined by structures – not material. One result was the Ptolemaic system. - This was basically changed by Newton where we learned that physical processes can be deduced from a lower level. Like the planetary motion. Is its deduction via Newton’s law religion?

      I think in history the great advances in physics have been made by physicists who asked for causes. Example is the spectroscopy in the beginning of the 20th century. The equations which they found were extremely precise. So no reason to look for an underlying mechanism. The physicists, who nevertheless looked for just this, developed the atomic model. And they developed quantum mechanics. Was that a religious activity? And Hendrik Lorentz asking for a cause for relativistic dilation found the internal oscillation of particles. Which was confirmed 40 years later by Dirac and Schrödinger in an independent way. No point in this?

      About reductionism: Wikipedia says: “Methodological reductionism … is the scientific attempt to provide explanation in terms of ever smaller entities. - Such entities are the ones I have described above.

      >> No there does not have to be a "cause" for a constant of nature. What you say is just wrong and I have no idea what makes you think so. <<

      If we once find a cause for the accelerated expansion, that will be seen as a great progress in physics. And I know about a mechanism which has a quantifiable cause for that; which at the same time explains the cosmological inflation. If this will once be accepted by mainstream, or another underlying cause will be found which is then accepted by mainstream, everyone will surely say that this is a great progress in the understanding of the world. - You don’t think so?

  9. What do you mean, a basic principle is missing? The basic principle is time invariance, and our universe violates that. Also, the energy isn't gone, just … diluted into the fabric of space-time, and therefore no longer accessible because we're part of that spacetime. If you could convince the Universe to stop expanding and to contract back, which was one possible fate until 1970 or so, you'd get that energy back.

    1. All the timelike structures have their proper time - why not the total amount of the space in universe to be balanced with the all proper time in structures - and because proper time can only increase then space expands.

  10. ...."remember to switch off the light".

    Indeed, energy is a scarce, economic good. In this context reading John Kenneth Galbraith on power and money I am inclined to think that energy is what energy does, being nothing more than what is commonly exchanged for mass and velocity.

  11. Sabine,

    In the ecosystem modeling of Howard T. Odum, money moves as a counter-current analog of energy. In system transactions, money moves one way and energy moves the other. Instead of energy translations between kinetic and potential, one could say money varies between currency and capital and, in practice, the more capital you wish to preserve in one place, the greater the physical and procedural barriers you need to prevent its dispersion.

    Analogously with energy, the greater the potential, the more physical structure required to sustain its state as potential rather than kinetic.

    By this circuitous route we come to perhaps a very naive question: Is it basically the electromagnetic field that dynamically resists the collapse of that sustaining physical structure?


  12. Sabine,

    With regard to Einstein’s comments on energy, I remember seeing a film in which a hip, young physics teacher (John Travolta?) informs his high school class that Einstein said energy is always moving, is never still or static. This is not the best sort of factual reference and I have been unable to find any quotation like that attributed to Einstein.

    Would you have any thoughts on this?


    1. E=mc^2 means that energy does not require motion. I have no idea what that movie was about, but it can't have been very good.

    2. Okay, but isn’t mass, at root, an embodied dynamic?

    3. E=mcc means that energy requires amount of mass units of inner interactions at rate c.

      Einstein's quote in my memo:
      - Concerning matter, we have been all wrong. What we have called matter is energy, whose vibration has been so lowered as to be perceptible to the senses. There is no matter.

      He also mentioned that we as matter are all "light beings". It's up to interpretation if light not considered as motion, but isn't it ultimate motion?

    4. nothing is lost nothing is created everything is transformed
      Rien ne se perd, rien ne se crée, tout se transforme

      Portrait d'Antoine Lavoisier.

      Portrait d'Anaxagore de Clazomènes.
      Rien ne se perd, rien ne se crée, tout se transforme est une citation apocryphe d'Antoine Lavoisier sur la conservation des masses lors du changement d'état de la matière.

    5. I have no idea what that's supposed to mean.

    6. E=MC^2 is special relativity, not general relativity. Which means it "works" locally, but not on cosmological scales.

    7. Hm. Are you sure? When we take large cluster of galaxies, why not can we say that all its energy content is gravitating mass as Mcc? How you separate mass and energy in different situations and scales? Well argumented?

      Maybe you have an illusion about flat spacetime geometry applicable in general - no, it's not. Just study Shapiro effect in SR and GR. When Einstein spoke in view of SR, he said that speed of light slow down - but in curved spacetime of GR you can keep speed c global; it can vary only for coordinate-observers. Often this might be confused by forgetting to take account all aspects with time (cosmology).

    8. Sabine: “E=mc^2 means that energy does not require motion. I have no idea what that movie was about, but it can't have been very good.”

      Okay, but isn’t mass, at root, an embodied dynamic?

      Sabine: “I have no idea what that's supposed to mean.”

      Sorry, that happened. I have often had this problem in the past.

      What I am trying to say is that Einstein’s comment (if made) would make sense if matter is simply a constrained dynamic. I read that only a portion of the mass in the universe is due to the Higgs mechanism with the majority being due to the strong force and the energy of the interaction between quarks and gluons. In either case there would be a wave description that implies some sort of ongoing dynamic.

      Is that the way one should look at it?

      My feeling is that the movie was okay, though clearly not memorable for the most part.

  13. To the question: Is energy always conserved?

    A consideration may be the case of exchange particles. Let’s take the case of an electrical charge. An electrical charge applies a force to another electrical charge. The connecting electrical field has an infinite range. This fact itself is independent of the distance, only the force falls of by 1/r^2. The force is mediated by the corresponding exchange particles. If we look at one exchange particle which hits another charge at a distance of, say, one light year, then it applies an impact and so transfers energy, extremely weak but existent. So far no problem. But the originating charge emits a steady flow of those exchange particles into all directions and so carries energy into all directions. Most probably most of them will never meet another charge but have to carry the energy, otherwise in the rare occasion of a hit no transfer would be possible.

    But the emitting charge cannot not loose energy, otherwise it would disappear after some time. What now about the conservation of energy? Is it really fulfilled? And so, can it be a general law?

    Otherwise, if we look into the structure of elementary particles and particularly the mechanism of mass / inertia, we can *deduce* that for such particle as a unit the energy is always conserved – without the necessity of a general law. And that is the conservation which we observe in corresponding experiments and in daily life.

    From this, one could conclude that energy conservation is not a general law but the consequence of the set-up of an elementary particle. And this can been shown quantitatively by the application of an appropriate particle model. - In this way the logical problem shown above would not occur.

    1. If every charge is emitting, every charge is absorbing. If your theory does not conserved energy, it must explain how information is conserved. If your theory doesn't conserved information, your theory is bound by magic... There is a creation of information from nothing. Einstein's first thought was a static Universe.

    2. The existence and functionality of exchange particles is not my theory but part of quantum mechanics. And in my understanding it is a good part of QM as it gives us a lot of explanations. Now, if we assume the existence of exchange particles, the consequences which I have described are logical consequences of this model.

      What is the problem of information? The exchange particle transports the information that there exists a charge and tells the direction of it by its direction of motion. The exchange particles which go to nowhere cannot transport information. Is that a problem? – And where is information created here from nothing?

    3. I am an amateur, but until you get a better answer ...

      Digging deep into my memory of Susskind's online lectures on the 'theoretical minimum', I believe he said that all lines on a Feynman diagram are attached at both ends. In other words, there is no supply of photons disappearing into nothingness and radiating away information.

      Feynman, in his QED thesis, developed with Wheeler the idea of advanced and retarded waves. Advanced waves (apparently) going backwards in time. This is related to minimised action. It is also relevant to superdeterminism as photons are not produced randomly but need to negotiate an ending place before or at the same time that they are emitted from their starting place.

      Feynman aparently needed to account for some kind of instantaneous recoil at the point of emission which he accounted for by an advanced wave from the ending point!

      This is also relevant to finding a minimum path - as how do you know the minimum path unless you know where you are going in advance?

      IMO there are problems with photon emission from a free electron. What causes emission (I do not believe in randomness)? Where does the weak isospin of the electron go (to the higgs fields?)? What is the content of a photon ... energy (I do not believe that particles are made of energy alone)? IMO energy is a catalyst for change rather than being the contents of a particle.

      Austin Fearnley

    4. Antooneo says:

      "But the originating charge emits a steady flow of those exchange particles into all directions and so carries energy into all directions. Most probably most of them will never meet another charge but have to carry the energy, otherwise in the rare occasion of a hit no transfer would be possible."

      This is why I argue that this model cannot be correct.

    5. I don't think anyone thinks it is correct. Particles are a cartoon to help you do calculations with fields.

    6. I hasten to add, a very handy cartoon. No shade.

    7. Greg Feild,

      >> "Antooneo says:

      But the originating charge emits a steady flow of those exchange particles into all directions and so carries energy into all directions. Most probably most of them will never meet another charge but have to carry the energy, otherwise in the rare occasion of a hit no transfer would be possible."<<

      “This is why I argue that this model cannot be correct.”

      This model is one of the cornerstones of quantum mechanics. And it is able to explain a lot. However, the physicists who use it seem to be not aware of this consequence.

      But the model is not only very helpful for the description of fields and forces. It also helps to have an understanding of what the cause of energy conservation is as we know it. - And in general it is always better to have a deduction of a law than to assume the law as a priory. Because that is progress in understanding the world, I think.

  14. If energy is the 'capacity for work' then could not consciousness be reconceptualised as energy?

    Didn't the early quantum physicists, Planck and Schrodinger in particular, explicitly make this connection?

  15. Ha, so there exists an analogy between inflation in economics and cosmological inflation :)

    1. That's facetious. Thoughts are instantiated in action; kinetic energy. Did your fingers type out your reply without engaging your mind? Actually maybe they did.

      Also, disregard my uninformed opinion by all means but Planck and Schrodinger?

  16. Dr. Hossenfelder,

    Your topics never cease to create interesting comments and ideas. For me this is one of the reasons why I find your blog so fascinating. For me, no matter the thought/theory, it is always interesting to read as sometimes they really make me think just like your posts do.

    I am reading one of Dr. S. Carroll's books right now and a few chapters back he talked about QFT and the density of the vacuum energy. If this density is remaining constant as the universe expands there must be energy coming in from some place else so apparently energy is not always conserved. The interesting question is where is this energy coming from and is it being created? Just one quick thought on this, If we are talking about a conserved energy density in a vacuum since the beginning of the universe, and this density has been the same since the beginning of the universe, couldn't this be considered low entropy? Rhetorical questions, just throwing them out there for thought.

  17. If energy of photons "goes nowhere" when universe expands, is it possible that energy will go "from nowhere" when universe collapse?

    1. Basically, yes, but the universe isn't projected to recollapse.

  18. Sabine,
    This is not the best reference, but we read in a 05/12/16 Symmetry article by Diana Kwon:

    “The Higgs field gives mass to fundamental particles—the electrons, quarks and other building blocks that cannot be broken into smaller parts. But these still only account for a tiny proportion of the universe’s mass.
    The rest comes from protons and neutrons, which get almost all their mass from the strong nuclear force. These particles are each made up of three quarks moving at breakneck speeds that are bound together by gluons, the particles that carry the strong force. The energy of this interaction between quarks and gluons is what gives protons and neutrons their mass. Keep in mind Einstein’s famous E=mc2, which equates energy and mass. That makes mass a secret storage facility for energy.”

    Is this sufficiently accurate?


    1. Hi Don,

      It's right that most of the mass of atomic nuclei does not come from the Higgs, I wrote about this (in 2015)
      here. In any case, the explanation you quote leaves out that Einstein's equation actually reads E^2 - p^2c^2 = m^2c^4.

    2. Sabine,
      I read your 2015 post on the origin of mass and your link to the Nambu–Jona-Lasinio model of nucleons and mesons. My only take away is astonishment that nature requires such an intricate weave at its fundamental level. Perhaps, if you are building a universe, such a foundation is a necessity, something akin to earthquake mitigation in building design.

      On a rule-of-thumb level of description is “mass a secret storage facility for energy?” Can we fairly say that majority of mass in the universe arises from energy constrained in its movement to small volumes and is fundamentally dynamical in nature?


    3. Sabine,
      You have declined commenting on my question:

      Can we fairly say that majority of mass in the universe arises from energy constrained in its movement to small volumes and is fundamentally dynamical in nature?

      Is it because the question, as posed, is not properly formed, is simply garbled in some fashion not apparent to me, or you feel like you have already answered it? I appreciate that you have a lot going on -- no real worries.


  19. Hi Sabine, is it required for a property to be quantizable in order to be conserved (like energy, momentum, charge, etc.)? Metaphorically speaking, does the number of possible values for a property needs to be countable so the universe can "keep track" of them?

    1. The interesting clue: it seems to be a rule that if action is quantized, potential is not and vice versa.

      So, the matter is quantized. Why need to try stubbornly quantize gravity?

    2. Actually, mainstream physics is incorrect, energy is not a property of matter at all. Matter only simulates energy. All attributes of matter are measures.

      Matter is positively charging when it is moving centripetally inwards toward its centre of gravity. Gravitation charges bodies with positive electricity. Matter is discharging when it is moving centrifugally outwards away from its centre of gravity. Radiation discharges bodies with negatively discharging electricity.

      The mass that matter consists of is fundamentally crystallized pressure conditions of light.

  20. I was reading a sample of "The discovery of dynamics" by J. Barbour (you're last post gave a hint on his latest book). He's talking about Newton's first law as still being an open question. Considering special relativity, isn't inertia another statement of the conservation of energy?

  21. As I understand it, absence of a time-like Killing field doesn't mean that there's an energy that is not conserved, it means that there is no canonical way to add up energy density, which is locally conserved in GR. The total energy is just not definable in an invariant way.



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