What is Energy at Its Core?

[Dale]

The problem is the assumption that these ideas we use like "energy", "force" and "field" describe real physical things.

The word "energy" is a well-defined term with a clear and unambiguous meaning which has been experimentally measured. Unlike the word "real".

 

[Mueiz]

Energy is the conserved quantity related to time dimension when there is a reaction between two or more systems.
This definition leads to different forms to calculate energy used in different branches of science.

 

[JJBladester]

And? You aren't understanding what I'm saying. Energy will NEVER be something physical, somthing tangible. Why? Because it isn't! This isn't something that we just don't know about yet. Our definition of energy describes how different objects in a system interact with each other. When a weight falls to the ground we can describe precisely what the effects will be at impact because we know how fast it will hit, the properties of the weight and the earth, the acceleration due to gravity, the resistance of air, ETC. Simply saying that the weight has X amount of potential energy is a short way of describing all of that before it happens using known laws.

Drakkith, I'm going to repackage what you're saying to see if I'm getting it.

Energy is a description of the behavior of a system on its own or multiple systems interacting with the behavior being the motion, entropy, charge, or other physical properties.

Am I close?

Energy is the conserved quantity related to time dimension when there is a reaction between two or more systems.
This definition leads to different forms to calculate energy used in different branches of science.

Can you elaborate, Mueiz?

Energy is defined as the source of the gravitational field.

I would believe you, Bill_K, if we had a "Theory of everything" which unified electromagnetism, gravity, and the strong and weak nuclear forces, but we don't have a theory like this. Since gravity hasn't been able to be added to the mix of the other basic physical forces, how can your definition of energy be accurate?

 

[WannabeNewton]

I would believe you, Bill_K, if we had a "Theory of everything" which unified electromagnetism, gravity, and the strong and weak nuclear forces, but we don't have a theory like this. Since gravity hasn't been able to be added to the mix of the other basic physical forces, how can your definition of energy be accurate?

In general relativity or more specifically Einstein's Field Equations, a gravitational field is coupled to both matter AND energy (look up energy - momentum tensor if you want to) because, without going into all the technicalities and rigor, energy and mass are equivalent.

 

[OmCheeto]

I remember answering this question some time back, but it must have been on another science forum.

I believe my response was; "What is red?"

From the OP: E=mc2=hf=(1/2)mv2=mgh=k(q1q2)/r=(1/2)CV2

Energy is merely an attribute assigned to a system.

Wow... Look at that!

mc^2=(1/2)mv^2 --> c^2 = 1/2v^2 --> c=.707v

weird

hmmm... Maybe this isn't a silly question. Where's Integral? I need him to check my math.

 

[Buckleymanor]

Physics is all about breaking physical systems down and understanding the causes and effects. It seems like we don't have a "cause" for energy at this point in physics. That's okay with me. Perhaps we will someday. Then we'll be asking what the cause of that is... and so on, until we meet our Maker.

The trouble with this is that this seems to imply that you believe your maker is the "cause" of all energy somewhere down the line or at the root.
Then again it might be just a figure of speach.
We won't meet a maker and if we did for arguments sake, I will take issue as to what a bad job he did as regards me and you.
Physics generally don't like to rely on god did it what would be the point.

 

[JJBladester]

The trouble with this is that this seems to imply that you believe your maker is the "cause" of all energy somewhere down the line or at the root.
Then again it might be just a figure of speach.
We won't meet a maker and if we did for arguments sake, I will take issue as to what a bad job he did as regards me and you.
Physics generally don't like to rely on god did it what would be the point.

There are numerous great physicists, chemists, biologists, etc who believe in God and have advanced science incredibly. Whether you think there was nothing more than a big bang or you believe in God is besides the point. Let's not turn a physics question into a religious debate.

People do physics because they like physics. I do it because I think it is one of the few noble practices out there. Same with mathematics. (That may be a bit biased, but I have no desire to obtain any kind of "Arts" degree.)

 

[Buckleymanor]

There are numerous great physicists, chemists, biologists, etc who believe in God and have advanced science incredibly. Whether you think there was nothing more than a big bang or you believe in God is besides the point. Let's not turn a physics question into a religious debate.

Exactly, best practice not to invoke the g word else any further debate could develope into something that is not clear.

 

[superg33k]

Energy is a mathematical nicety, that keeps popping up in equations and always seems to be conserved. Given this property everyone has decided that it must have some pretty fundamental meaning, but have had a pretty difficult time deciding what.

Einstein decided in special relativity mass energy and kinetic energy are the same thing just from different observers. He's telling us matter and radiation are two sides of the same coin. And in particle accelerators matter (particles) is created from energy (from giant magnets, i.e. electromagnetic radiation) all the time.

Thermal energy is just movements of matter. Gravitation potential energy is ficticous as general relativity shows gravity aint a force, it just appears like one because of curvy space time. Electrical/magentic potential energy is the energy is in the photons in space around it.

So energy is stuff (photons and matter) and its movements. Pretty much everything except for space and time. Those are the same as momentum, another mathematical niceity.

I just glad no-one has started talking about little bits of string.

 

[JJBladester]

I just glad no-one has started talking about little bits of string.

I read a book two years ago called "The Trouble with Physics" by Lee Smolin. It was about how we haven't made incredible progress in physics since the early 1900s. He talks about how in order to get grant money, physicists often need to be studying something that the scientific community deems important.

He also says that string theory, although mathemtically beautiful, is leading us on a wild goose chase. I'll agree until somebody actually proves experimentally that 10 or 11 dimensions actually have any meaning. At least Einstein's "far-out" ideas were able to be experimentally proven. What's new at CERN, anyway? Did they find the Higgs?

 

[Buckleymanor]

I read a book two years ago called "The Trouble with Physics" by Lee Smolin. It was about how we haven't made incredible progress in physics since the early 1900s. He talks about how in order to get grant money, physicists often need to be studying something that the scientific community deems important.

He also says that string theory, although mathemtically beautiful, is leading us on a wild goose chase. I'll agree until somebody actually proves experimentally that 10 or 11 dimensions actually have any meaning. At least Einstein's "far-out" ideas were able to be experimentally proven. What's new at CERN, anyway? Did they find the Higgs?

No why not have a google and find out Fermilab have some interesting data which seems to steal the march at CERN but there is some doubt.

http://www.wbez.org/story/fermilab/glimpse-new-force-nature-fermilab-84837

 

[TobyC]

My answer to this question would be that energy is simply a quantity, like momentum, which is conserved by the laws of physics. It doesn't necessarily have, or need, any significance beyond that, although in General Relativity it does act as the source of the gravitational field.

Given any mechanical system composed of a set of moving particles (which is ultimately what the universe is) the 'energy' of the system is a function of the relative positions and velocities of the particles which never changes, just because of the way the laws of physics are. In the Lagrangian formulation of mechanics you can get a deeper understanding of this because energy conservation becomes a necessary consequence of the symmetry of laws of physics under translation in time. From this point of view, energy is defined as the conserved quantity associated with time symmetry.

 

[mquirce]

Energy is interaction of mass or massles particles that move in space and the time. During this movement happens that particles change their dimensions (radius), With this they vin or lose energy. After Compton law.

 

[Buckleymanor]

With this they vin or lose energy. After Compton law.

The v is so far away from the w on the keyboard but one looks half as nice as the other.

 

[SpectraCat]

From this point of view, energy is defined as the conserved quantity associated with time symmetry.

I am aware of Noether's theorem, and I understand the derivation of energy conservation based on time symmetry. However, I have always found this hard to rationalize with the second law of thermodynamics, which tells us that time is not symmetric, and that an external observer could tell in which direction time was going by observing the entropy change of the universe. Moreover, I believe that several cosmological theories incorporate time-dependence into the physical constants (Planck's constant, the speed of light, etc.) that are the scaling factors for our physical laws.

So is there an explanation of why these considerations don't affect the assumptions involved in the derivation of energy conservation from time-symmetry in Noether's theorem? Or is it that time-symmetry is only a local (with respect to time) property of the universe, in the sense that Noether's theorem works with generators of infinitesimal translations in time? Are there any ramifications of this for conservation of energy over long (i.e. consmological) time-scales? Or am I just way out in left field (always a possibility)?

 

[TobyC]

I am aware of Noether's theorem, and I understand the derivation of energy conservation based on time symmetry. However, I have always found this hard to rationalize with the second law of thermodynamics, which tells us that time is not symmetric, and that an external observer could tell in which direction time was going by observing the entropy change of the universe. Moreover, I believe that several cosmological theories incorporate time-dependence into the physical constants (Planck's constant, the speed of light, etc.) that are the scaling factors for our physical laws.

So is there an explanation of why these considerations don't affect the assumptions involved in the derivation of energy conservation from time-symmetry in Noether's theorem? Or is it that time-symmetry is only a local (with respect to time) property of the universe, in the sense that Noether's theorem works with generators of infinitesimal translations in time? Are there any ramifications of this for conservation of energy over long (i.e. consmological) time-scales? Or am I just way out in left field (always a possibility)?

Well I'm by no means the best person to answer your questions but I'll give it a go anyway.

Firstly, I don't think the second law of thermodynamics is a fundamental law of the universe in the sense that maxwell's equations are for instance. It is instead a probabilistic law which emerges out of the interactions of many many particles. If you take a video of a glass smashing and play it backwards, what you see is not impossible, it is just exceedingly unlikely. The universe, as it progresses in time, moves from improbable states to probable ones, simply because that's what's more likely, and it is this which gives the universe its apparent time reversal asymmetry, even though the fundamental laws are symmetrical under time reversal.

All that is required to explain the asymmetry in the direction of time is to state that the universe started off in an extremely unlikely state initially (although we don't know why is started off that way) and that is enough to give time a direction, since things will look different depending on whether you are going towards this unlikely initial state or away from it.

However, although I don't know much about quantum theory, I do think it has recently been discovered that certain physical laws (I think maybe the weak force?) are genuinely asymmetric under time reversal at a fundamental level. This still shouldn't make a difference to energy conservation though. This is because in Noether's theorem, energy conservation is a consequence of the fact that the laws of physics are invariant under a translation in time. Whether they are symmetrical under time reversal is a different question, you can have one without the other, and although you are justified in raising these issues about time reversal, I am not aware of any new discoveries which throw time translation symmetry into doubt.

As for energy conservation over cosmological timescales, I think you start getting into weird effects from General Relativity there. Even in Newtonian physics, energy conservation only works if you use an inertial coordinate system, but once you get to General Relativity it is impossible to construct a globally inertial coordinate system, so energy conservation in the traditional sense can only be talked about locally.

I think there are ways of constructing a global definition of energy though, which is conserved, but you can't pin the energy down to a precise location like you can in special relativity for instance.

 

[Dale]

I am aware of Noether's theorem, and I understand the derivation of energy conservation based on time symmetry. However, I have always found this hard to rationalize with the second law of thermodynamics, which tells us that time is not symmetric, and that an external observer could tell in which direction time was going by observing the entropy change of the universe. Moreover, I believe that several cosmological theories incorporate time-dependence into the physical constants (Planck's constant, the speed of light, etc.) that are the scaling factors for our physical laws.

So is there an explanation of why these considerations don't affect the assumptions involved in the derivation of energy conservation from time-symmetry in Noether's theorem?

This is a very good question. Although Noether's theorem is usually broadly stated in terms of symmetry there is actually a little more to it than that. Specifically, there are two important "caviats" that restrict the applicability of Noether's theorem so that it actually doesn't apply in some cases.

First, Noether's theorem only applies to systems which can be described by a Lagrangian. It is the combination of the symmetry and the Euler-Lagrange equations which leads to the conservation law.

Second, Noether's theorem applies only to differentiable symmetries. In other words, symmetries that can be built out of little infinitesimal coordinate transformations. So when we are talking about time symmetry in this context we are talking about time translation symmetry, you can make a big time translation out of a bunch of infinitesimal time translations. Noether's theorem does not apply to discrete symmetries, such as time reversal, which are "all or nothing" symmetries that cannot be built out of little infinitesimal transformations.

 

[James A. Putnam]

Energy is force times distance. It is a sum total. The missing explanation is: What is force? There is no explanation for what force is. The difficulty with explaining force is: We do not know what cause is. Experimental physics is the study of patterns in effects. Theoretical physics is the interpretation of the equations that model the patterns in effects, and, the introduction into those equations of invented properties used to substitute for the unknown cause.

James

 

[harrylin]

I think that this has been brought up by others, but anyway:

1. "energy" started out as a neat calculation aid - it's a human concept, invented by humans (just like "time", which is another important but poorly understood concept).

However:
2. The concept "energy" turned to be increasingly useful and successful, to the point that it became associated with physical reality. That doesn't prove that this concept of ours must directly relate to some unseen physical entity, but the suggestion is there (a variant of "it it looks like a duck and quacks like a duck, it may actually be a duck").

Thus in 1920 Einstein reiterated:

"according to the special theory of relativity, both matter and radiation are but special forms of distributed energy, ponderable mass losing its isolation and appearing as a special form of energy."
- http://www-groups.dcs.st-and.ac.uk/~history/Extras/Einstein_ether.html

That still doesn't tell us exactly what energy is (if it "is" really something), nor how energy works (how do kinetic and potential energy physically differ, and why can they be added?). The question itself isn't unscientific, but apparently the definite scientific answer is for the time being far out of our reach.

Regards,
Harald

 

[Neandethal00]

Energy is defined as the source of the gravitational field.

Sorry, I know that sounds somewhat indirect, overly sophisticated, and removed from common experience. But ultimately that is in fact what energy is. Just as the answer to "what is charge": charge is the source of the electromagnetic field, so energy is anything that acts as the source of gravity. (More precisely, the source is the stress-energy tensor, and energy is the 00 component of that.) The fact that general relativity is invariant under general coordinate transformations requires that its source must be conserved. And the list of things that are commonly known as forms of energy are just those things that produce a gravitational field, and can be turned into each other.

Very interesting topic.
I always had a feeling we don not know (understand) some of the basic 'things' of nature, that is why our 'science' is advancing and 'repairing' itself at a very slow pace. Energy is one such least understood subject, Charge is another, Time is also another.

Sorry, I didn't get to read all 4 pages of posts, someone may have already said what I'm going to say now.

I'm sure you wanted to say 'charge is the source of electric field' , not electromagnetic field. Let's keep the tensors and math out of our experiences. Then one reason you can give credit to energy for creating gravitational field are the total energy of all microscopic particles, in motion or at rest, in a massive object in space. I'm a sucker for any outside the box new ideas.

In that case, a small moving object A (say a fast baseball, which has energy) must pull another object B gravitionally as A passes B. But we observe only time the two objects interact is when A comes in contact with B. If energy is the source of gravity, then A must have its highest interaction with B at their closest distance but not touching it. What is this closest microscopic distance when moving object A will interact with other objects as it passes them without touching? I'm not arguing against you, I am saying it can be experimentally verified no matter how small this pull by gravity is, if correct.

Finally my own thought. Our experience tells us energy, force, motion are related. Motion requires what we call is 'time'. So, the question is 'does energy create time?'.

 

[ZealScience]

In fundamental physics it is defined as the ability to do work, then the problem comes to work itself... Mathematically just the dot product between displacement and forces, I think it is the measurement of what the force have done. Probably it has some new definition by Hamitonian mechanics or quantum (besides E=hf), this is the oldest one.

The equations can be easily derived from W=F·s the definition of work. Actually it is bestly described by an integral, and derived by integrals (except that E=hf is just an relationship for quantum effects). In my opinion, E=mc^2 not only tells that how much energy canbe generated by mass, but it means that mass tells you the presence of energy, because whenever objects gains any types of energy, it gains mass. Lastly, I want to specify that potential energy is betterly described by E=-GMm/R, as mgh is just an approximation...

 

[SpectraCat]

This is a very good question. Although Noether's theorem is usually broadly stated in terms of symmetry there is actually a little more to it than that. Specifically, there are two important "caviats" that restrict the applicability of Noether's theorem so that it actually doesn't apply in some cases.

First, Noether's theorem only applies to systems which can be described by a Lagrangian. It is the combination of the symmetry and the Euler-Lagrange equations which leads to the conservation law.

Second, Noether's theorem applies only to differentiable symmetries. In other words, symmetries that can be built out of little infinitesimal coordinate transformations. So when we are talking about time symmetry in this context we are talking about time translation symmetry, you can make a big time translation out of a bunch of infinitesimal time translations. Noether's theorem does not apply to discrete symmetries, such as time reversal, which are "all or nothing" symmetries that cannot be built out of little infinitesimal transformations.

Thank you! That was quite helpful. I wonder if the second part is related to the fact that the quantum mechanical time evolution operator has to be reformulated when the Hamiltonian's at different times do not commute (i.e. you have to use a Dyson series or its equivalent instead of a simple exponential)? Please note that I am way out of my depth here in terms of the amount of time I have spent in formal study of these topics ... that question just popped into my head when I read your response, and I wanted to write it down before it evaporated. Please feel free to ignore it if it is nonsense ...

 

[johncameron]

Energy is the capacity of a system to do work. Nothing else. There are so many types of energy like mechanical, potential, kinetic, radiant, thermal, chemical, electrical, electromagnetic etc. All you mentioned above its type of energy.

 

[KOSS]

Hope I didn't skim too fast and miss too much of this discussion...

The guts of ENERGY is that it is not a "thing", it is an abstraction. That's partly what folks mean when they say, "it's a useful concept for analysing physical systems that is conserved, etc., etc.". It's also what Feynman might have meant when stating that we cannot say what energy is. That is not a mysterious utterance, it is entirely sensible once we realize that energy is an abstract concept.

Going back to the thread introduced by Mueinz and elaborated by TobyC and SpectraCat, the conservation of total energy is an expression of time translation symmetry for Lagrangian systems. And don't worry about systems that do not have a Lagrangian, since everything classically can be reduced to Lagrangian mechanics. You will want to worry about the implications of general relativity and quantum mechanics, but that is almost a whole other topic which has been touched upon but I won't elaborate on it here, other than to remark that in quantum mechanics not all that much changes, a systems total energy is represented by a Hamiltonian operator which generates time translation, which squares with the classical concept since if the Hamiltonian is constant there will be time symmetry.

If you want to get really philosophical, then everything talked about in physics is an abstraction. We don't really know what mass is, or what charge is, or what space is. All such terms are words we use to describe the world in a semi-objective communicable fashion. However, compared to concepts like mass and charge, energy is on a whole other level of abstraction. This is evident in the way energy can be transformed, KE <-> PE. If a thing can be transformed like this then you know you are not talking about something concrete.

To echo other contributors, this does not mean that energy is ill-defined. On the contrary, the fact that we can track energy, and show that for time symmetric systems the total energy is conserved, means we have a good grasp and definition of the concept.

An appropriate analogy I think is that trying to define what energy is, is like trying to define what money is. You cannot define money as a coin or paper note, since that doesn't cover other forms of payment for goods etc., money is indeed just about as elusive a concept as energy, yet we all know what we mean by money and we use it and try to conserve it everyday without any philosophical qualms about what it really is. It isn't anyone thing, it's a pure abstraction, yet any manifest form of which can be a concrete reality, such as a minted coin, just like any particular form of energy can be concrete, like KE being simply mass and velocity. Caveat: energy is just that bit more subtle than money, since energy is really only a useful concept when referring to changes in energy.

And there, finally, is another clue that you're dealing with a pure abstraction. Changes in energy are the important thing, the particular value of energy itself is meaningless. So once again, energy cannot be any special sort of "thing" since it's value is meaningless. But since changes in energy are extremely meaningful and indeed just about supply a complete way to describe physical motions, you have again the idea that energy is an abstraction, it is a relationship between things, but it is not a thing itself.

That makes me think of other analogies. Is "being taller than a giraffe", or, "being to the left of someone", a thing that you can define and grasp? Yes, of course. But these are not something you can grab a hold of and put in a bottle. They are not things in themselves, but are rather relationships between things. (I think the technical term in philosophy for a concrete "thing" is an "entity", but I don't see much point in worrying about such wording trifles). Such is the way with energy. We need to disabuse ourselves of the notion that when we heat a glass of water we are adding energy like some sort of substance. We are not. We are raising the average kinetic energy of the molecules .

So "Adding heat" = "Raising average KE".

The RHS of this equality of meanings is the correct way to think, the LHS is not quite bogus, but it can be misleading if you interpret it too literally.

So in reality we are not actually adding anything to the glass of water. It is only on some abstract account sheet that we can say we've raised the heat content or "added energy". And that's exactly the point, it's just an accounting ledger system. That's all energy is, however incredibly useful as a unifying concept in physics. Energy is not representing an actual thing we add to the water to make it hotter, it represents instead a change in state of the water that we induce, so it is a relationship between states of a system.

 

[russ_watters]

Energy is the capacity of a system to do work. Nothing else. There are so many types of energy like mechanical, potential, kinetic, radiant, thermal, chemical, electrical, electromagnetic etc. All you mentioned above its type of energy.

My answer to this question would be that energy is simply a quantity, like momentum, which is conserved by the laws of physics. It doesn't necessarily have, or need, any significance beyond that...

In this forum, we get a handful of questions repeated over and over again that perplex me. One is the 'is gravity real?' question, while no one ever asks the same question about any of the other 3 fundamental forces. This question is similar. Energy should be no more mysterious than speed. Like speed, it is just two physical measurements stuck together (or sometimes, one is a derived quanity...such as speed). We have an intuitive grasp of the concept of speed by seeing things move, but at some point, someone had to come up with a way to describe it mathematically. So they figured that a measured displacement and a measured time interval could be used to quantify it. Simple - and everyone accepts it.

Well, the same conceptual process exists for energy. Ever throw a ball? Somehow you learned how to get that ball to go where you wanted it to. You learned projectile motion instinctively/reflexively. Part of that is applying a force to the ball over a distance dictated by the length of your arm to accelerate it to a certain speed. A while back, someone figured that quantifying that would be useful. And then they gave it a name.

What makes the concept of energy broader, but no more complicated or mysterious, is that there are a bunch of different types of energy and all are related. Ever play Angry Birds? Along with the angles part of projectile motion, most of the game is dealing with many of these different types of energy that we already have an intuitive grasp of. You have kinetic, gravitational potential, spring potential, chemical and fracture energy all in one simple little game.

There's no mystery here. Energy is just a useful combination of a few physical measurments that was given a name. Nothing more or less.

 

[Drakkith]

I like your description Koss.

 

[firavia]

Koss I think you found the right conclusion !

 

[guillefix]

I think the definition of energy has been discussed very deeply here already. I personally like the idea of a conserved cuantity, but trying to get a real image of it might be imposible. Physics describes how the universe work in a human language, we try to make laws of how everything we can measure works, but we don't actually know what is the mechanism for it to work, this is one of the ideas that appeared in quantum mechanics. It is also very interesting to take what is called a model dependent reality point of view: just as a fish in a fish bowl could have created all the physical laws, but different because it sees everything deformed, we can't say that his description is less real than ours, because it works. We are probably in some kind of fishbowl as well, but we probably won't ever know. My point is that there are possibly different ways in which we can try to say what is energy, but it would be as real as any other possible way we can explain it, so this kind of destroys the whole reality of the word "real", but it's just as in relativity there is no preferred (and therefore no "realer") frame of reference or point of view. Still we can describe how to our eyes and measurementes, nature works, and that is the model we consider real for convenience, but it's as real as the one which the fish could have made. Richard Feynman, who's videos I really recommend, makes an analogy which I consider the best one to start getting an idea of what physicsts actually did when trying to describe the world with this new thing called "energy":

“There is a fact, or if you wish, a law, governing all natural phenomena that are known to date. There is no known exception to this law—it is exact so far as we know. The law is called the conservation of energy. It states that there is a certain quantity, which we call energy, that does not change in the manifold changes which nature undergoes. That is a most abstract idea, because it is a mathematical principle; it says that there is a numerical quantity which does not change when something happens. It is not a description of a mechanism, or anything concrete; it is just a strange fact that we can calculate some number and when we finish watching nature go through her tricks and calculate the number again, it is the same. (Something like the bishop on a red square, and after a number of moves—details unknown—it is still on some red square. It is a law of this nature.) Since it is an abstract idea, we shall illustrate the meaning of it by an analogy.

Imagine a child, perhaps “Dennis the Menace,” who has blocks which are absolutely indestructible, and cannot be divided into pieces. Each is the same as the other. Let us suppose that he has 28 blocks. His mother puts him with his 28 blocks into a room at the beginning of the day. At the end of the day, being curious, she counts the blocks very carefully, and discovers a phenomenal law— no matter what he does with the blocks, there are always 28 remaining! This continues for a number of days, until one day there are only 27 blocks, but a little investigating shows that there is one under the rug—she must look everywhere to be sure that the number of blocks has not changed. One day, however, the number appears to change—there are only 26 blocks. Careful investigation indicates that the window was open, and upon looking outside, the other two blocks are found. Another day, careful count indicates that there are 30 blocks! This causes considerable consternation, until it is realized that Bruce came to visit, bringing his blocks with him, and he left a few at Dennis’ house. After she has disposed of the extra blocks, she closes the window, does not let Bruce in, and then everything is going along all right, until one time she counts and finds only 25 blocks. However, there is a box in the room, a toy box, and the mother goes to open the toy box, but the boy says “No, do not open my toy box,” and screams. Mother is not allowed to open the toy box. Being extremely curious, and somewhat ingenious, she invents a scheme! She knows that a block weighs three ounces, so she weighs the box at a time when she sees 28 blocks, and it weighs 16 ounces. The next time she wishes to check, she weighs the box again, subtracts sixteen ounces and divides by three. She discovers the following:

(Number of blocks seen)+ [(weight of box) - 16 ounces]/ 3 ounces = constant. (4.1)

There then appear to be some new deviations, but careful study indicates that the dirty water in the bathtub is changing its level. The child is throwing blocks into the water, and she cannot see them because it is so dirty, but she can find out how many blocks are in the water by adding another term to her formula. Since the original height of the water was 6 inches and each block raises the water a quarter of an inch, this new formula would be:

(Number of blocks seen)+ [(weight of box) - 16 ounces]/ 3 ounces + [(height of water) - 6 inches]/(1/4 inch) = constant. (4.2)

In the gradual increase in the complexity of her world, she finds a whole series of terms representing ways of calculating how many blocks are in places where she is not allowed to look. As a result, she finds a complex formula, a quantity which has to be computed, which always stays the same in her situation.

What is the analogy of this to the conservation of energy? The most remarkable aspect that must be abstracted from this picture is that there are no blocks. Take away the first terms in (4.1) and (4.2) and we find ourselves calculating more or less abstract things. The analogy has the following points. First, when we are calculating the energy, sometimes some of it leaves the system and goes away, or sometimes some comes in. In order to verify the conservation of energy, we must be careful that we have not put any in or taken any out. Second, the energy has a large number of different forms, and there is a formula for each one. These are: gravitational energy, kinetic energy, heat energy, elastic energy, electrical energy, chemical energy, radiant energy, nuclear energy, mass energy. If we total up the formulas for each of these contributions, it will not change except for energy going in and out.

It is important to realize that in physics today, we have no knowledge of what energy is. We do not have a picture that energy comes in little blobs of a definite amount. It is not that way. However, there are formulas for calculating some numerical quantity, and when we add it all together it gives “28″—always the same number. It is an abstract thing in that it does not tell us the mechanism or the reasons for the various formulas."

Richard Feynman, The Feynman Lectures on Physics. Chapter 4.

 

[Drakkith]

I think the definition of energy has been discussed very deeply here already. I personally like the idea of a conserved cuantity, but trying to get a real image of it might be imposible. Physics describes how the universe work in a human language, we try to make laws of how everything we can measure works, but we don't actually know what is the mechanism for it to work, this is one of the ideas that appeared in quantum mechanics.

Maybe it's just me, but I don't even think the idea that energy is "something" and that we just don't know what it is, is correct. But that's just my opinion.

 

[superg33k]

We believe nature has some fundamental properties (possibly mass, time etc.). Everything else is secondary definitions (like force, acceleration), defined in terms of these fundamental properties.

Although energy is a mathematical concept, the fact that its always conserved, leads us to equalities in our secondary definitions and in turn our original fundamental properties, indicating that they are not fundamental properties. Particles of matter turning into particles of radiation at CERN, i.e. E=(p^2c^2+m^2c^4)^(1/2)=hf, shows us that momentum, rest mass, and frequency are not independant properties.

The question "What is energy?" is actually "What are the fundamental properties of nature?"


That said, answering this question we must be careful, as always, to take Einstiens relativiy into consideration as he showed that these properties are relative to the observers motion.

Additionally, I think (which I haven't heard lecturers claim, but I have never asked), we should make sure not to think of potential energy as the same as energy. Potential energy is the energy an object WILL receive from energy carrying particles, where the energy of on object is the energy it HAS.

Finally, also remember that gravitational potential energy is, according to general relativity, ficticious.

 

[Dale]

Maybe it's just me, but I don't even think the idea that energy is "something" and that we just don't know what it is, is correct. But that's just my opinion.

I agree, we know exactly what it is since we defined it.

 

[superg33k]

I agree, we know exactly what it is since we defined it.

And what is it defined as, in terms of fundamental properties? I.e. what is the definition of each term that you define energy as?

Many people say "energy is the ability to do work."
But work is force times distance.
And force is mass times acceleration.
And mass is energy.

You cannot define energy in terms of energy!

 

[Dale]

And what is it defined as, in terms of fundamental properties? I.e. what is the definition of each term that you define energy as?

Many people say "energy is the ability to do work."
But work is force times distance.
And force is mass times acceleration.
And mass is energy.

You cannot define energy in terms of energy!

Energy is defined as the ability to do work, and work is defined as force times distance. Force and distance are defined in terms of mass, distance, and time, all of which are defined operationally, i.e. via experimental procedures to measure them. The definitions are not circular.

 

[Drakkith]

Mass is not energy. It has an equivalence to energy, but it in itself is not energy. It is mass.

 

[superg33k]

Mass is not energy. It has an equivalence to energy, but it in itself is not energy. It is mass.

Thats exactly what equivilent means!

Let's continue, mass is energy.
Mass becomes into photons at CERN.
Photons heat water in a steam engine.
A steam engine has the ability to do work.