Exploring the Nature of Energy: A Deeper Understanding

[Cheman]

I feel i need to ask this fundamental question, because everywhere i look i just get a very bland definition with no discussion. So what actually IS energy? Is it just a mathematical thing that we have worked out that just works in a kindo of"number crunching" fashion, or is it more fundimental than that, more like an "entity" of some sort? I don't see how it can just be a number cruching principle, since in relativity, mass is converted to energy and vice versa - is mass if lost then i must become SOMETHING - that something is obviously energy but, but what is energy?

Please feel free to discuss this and elaborate on this as much as possible - I feel that it is a key part of physics to really unddertand properly.

Thanks in advance.

 

[Crosson]

is mass if lost then it must become SOMETHING

The mass becomes light, electromagnetic radiation.

Energy comes in many forms. You surely know about KE = (1/2)mv^2, and this form of energy is motion. It sounds like you are asking about "pure" energy.

Here is your unambiguous answer: Pure energy is the electromagnetic field.

 

[Locrian]

Is it just a mathematical thing that we have worked out that just works in a kindo of"number crunching" fashion, or is it more fundimental than that, more like an "entity" of some sort?

What's the difference?

 

[Andrew Mason]

I feel i need to ask this fundamental question, because everywhere i look i just get a very bland definition with no discussion. So what actually IS energy? Is it just a mathematical thing that we have worked out that just works in a kindo of"number crunching" fashion, or is it more fundimental than that, more like an "entity" of some sort? I don't see how it can just be a number cruching principle, since in relativity, mass is converted to energy and vice versa - is mass if lost then i must become SOMETHING - that something is obviously energy but, but what is energy?

Please feel free to discuss this and elaborate on this as much as possible - I feel that it is a key part of physics to really unddertand properly.

That is a fair question,and one that shows you are thinking.

Energy measures the ability to apply a force over a distance. It was demonstrated by James Joule that the ability to apply a force over a distance is proportional to the ability to generate heat. He found that a slowly descending weight caused a temperature rise in a volume of water that was proportional to the distance the weight descended, (not the time of descent).

The ability to apply a force over a given time is also a useful quantity but not when you are talking about the ability to generate heat, compress a gas, lift a weight, or drag a box.

AM

 

[Cheman]

Everyone please feel free to add as much and go into as much detail as you like on this post - I feel this an important topic to discuss. :-) Further input would be appreciated.

Thanks. :-)

 

[Danger]

There are different definitions of 'energy' depending upon the context. On the absolute fundamental level, everything is energy. Matter is simply energy in a bound state. If you get down far enough, there's nothing physical there. It's all probability wave functions. That's as far as I'm going... let someone who went to school carry on.

 

[PBRMEASAP]

I think Andrew pretty much nailed it. You aren't likely to find a general definition of "energy" in a physics book, because it is sort of an ambiguous notion. This is partly what makes it such a powerful concept, since very general conclusions can be made about energy even before you specify what kind you are dealing with. This is what thermodynamics deals with. A very good explanation of this point of view about energy is given in Understanding Thermodynamics by Van Ness. Dover sells it for about 8 bucks, so it isn't such a bad investment if you aren't able to find it at the library.

However, energy is always associated with the ability (or potential) to do work. An example that still confuses me if I try to think about it too hard is the gravitational field (Newtonian). When you pull two masses apart, you are "putting energy into the field." But where exactly in the field is that energy located? Similarly, if you let two masses fall toward each other, you say "the field has lost energy by doing work on the masses". But where did this energy come from? Neither of these questions really makes much sense. If masses didn't have a natural tendency to pull on each other, then there would be no field and no energy to talk about. The potential energy stored in the field is really a bookkeeping tool to help you calculate how much work the masses do on each other in the course of moving from one place to another. However, that fact that gravitational force can be described in terms of energy differences says something special about the force--the amount of work done on the masses does not depend on the path they take, but only on their initial and final positions. Obviously not all forces are this special. Friction, for example, cannot be associated with a potential energy because if you slide a big rock from A to B, and then back to A, you had to do some work, even though the rock is now in the same place.

 

[pmb_phy]

I feel i need to ask this fundamental question, because everywhere i look i just get a very bland definition with no discussion. So what actually IS energy? Is it just a mathematical thing that we have worked out that just works in a kindo of"number crunching" fashion, or is it more fundimental than that, more like an "entity" of some sort? I don't see how it can just be a number cruching principle, since in relativity, mass is converted to energy and vice versa - is mass if lost then i must become SOMETHING - that something is obviously energy but, but what is energy?

Please feel free to discuss this and elaborate on this as much as possible - I feel that it is a key part of physics to really unddertand properly.

Thanks in advance.

The most precise answer to your question is that nobody knows what energy is. For details on that please see - http://www.geocities.com/physics_world/mech/what_is_energy.htm

Pete

 

[Andrew Mason]

The most precise answer to your question is that nobody knows what energy is. For details on that please see - http://www.geocities.com/physics_world/mech/what_is_energy.htm

That is a bit of an exteme statement. One could say that we don't really know what mass, force, distance or time are. We don't really understand what anything is because at some level we rely on concepts that are fundamental which, by definition, are not explainable in terms of more basic concepts.

Energy is intimately connected with mass - not just because E = mc^2, but because energy is defined in terms of mass (and distance and time): A unit of energy (Joule) is defined as the ability to accelerate a 1 kg mass at 1 m/sec^2 over a distance of 1 m.

None of the conceptual problems in understanding what energy is (which will persist so long as we don't understand what mass 'really' is) prevent us from using the concept.

It is interesting to note that in the 17th Century there was a very heated debate going on between the camps of Liebniz, Descartes, and Newton over whether momentum or energy ("vis viva", as Liebniz referred to it) was the ''essence' of motion.

AM

 

[whozum]

Energy does not physically exist. It is a concept that is created to help understand processes that normally would not be related. You can relate it to electric flux lines, there are not really there, but putting them there brings it all together.

 

[pmb_phy]

A unit of energy (Joule) is defined as the ability to accelerate a 1 kg mass at 1 m/sec^2 over a distance of 1 m.

That is not energy. That is kinetic energy. In conservative systems energy is the sum of kinetic energy and potential energy.

None of the conceptual problems in understanding what energy is (which will persist so long as we don't understand what mass 'really' is) prevent us from using the concept.

mass is a pretty well defined quantity.

Pete

 

[1123581321]

if you really think about e=mc^2, you will notice that you are energy! Infact, you are enough energy to, if fully used, destroy the state of mass. (as in the state as in one of the 50 as in not how much stuff is in you) (that is assuming you are not uberly small or morbidly obese)

Fibonacci

 

[Andrew Mason]

That is not energy. That is kinetic energy. In conservative systems energy is the sum of kinetic energy and potential energy.

It is just energy. An object with kinetic or potential energy of 1 J. has the ability to accelerate a 1 kg. mass 1 m/sec^2 for 1 m. (ie. a 1 kg mass at a height of 1/9.8 m or a 1 kg mass moving at 1.414 m/sec).

mass is a pretty well defined quantity.

Of course. As is energy. But there are great discussions going on about what it is in fundamental terms. My point was that you don't have to resolve all of the philosophical niceties to understand it well enough to make use of it.

AM

 

[pmb_phy]

It is just energy. An object with kinetic or potential energy of 1 J. has the ability to accelerate a 1 kg. mass 1 m/sec^2 for 1 m. (ie. a 1 kg mass at a height of 1/9.8 m or a 1 kg mass moving at 1.414 m/sec).

You can't use a relationship for mass until yopu first define mass. The relationship you speak of is not a definition of energy. It is a relationship between kinetic energy and total energy for a particle when the potential energy is a constant.

Pete

 

[Andrew Mason]

You can't use a relationship for mass until yopu first define mass. The relationship you speak of is not a definition of energy. It is a relationship between kinetic energy and total energy for a particle when the potential energy is a constant.

I don't understand what you are saying. I said that energy is defined in terms of mass, distance and time. That is just a fact. The definition of a Joule is one Newton x one Metre (one kg x one m/sec^2 x one metre). Regardless of what form the energy is in, it can always be expressed in Joules. - ie. in terms of the energy required to accelerate of some mass over some distance - even if you are speaking about electric fields, photons, electric current, pressure, heat, gravitational potential, kinetic, coiled spring, or nuclear binding energy.

AM

 

[Gokul43201]

pmb_phy,

You are providing an extremely misleading view of the subject as well as contradicting yourself.

In one post you say that mass is "pretty well defined" (without actually supplying such a definition), yet you refuse to accept its use in another definition.

 

[pmb_phy]

You are providing an extremely misleading view of the subject as well as contradicting yourself.

I, of course, disagree with that opinion. In no way is what I said misleading.
[/quote]
In one post you say that mass is "pretty well defined" (without actually supplying such a definition), ..[/quote]I have done so ad ignosium in the past. But if you need a refresher for that definition please see

http://www.geocities.com/physics_world/sr/inertial_mass.htm
http://www.geocities.com/physics_world/sr/inertial_energy_vs_mass.htm

..yet you refuse to accept its use in another definition.

I believe that is quite untrue. But to be sure, what are you referring to?
[quoteAndrew_Mason]
I don't understand what you are saying. I said that energy is defined in terms of mass, distance and time.[/quote]What is this definition you speak?

The definition of a Joule is one Newton x one Metre (one kg x one m/sec^2 x one metre).

That is not a definition of energy. It is merely a particular relationship between units. It does not serve as a definition of those quantities.
[qupte]Regardless of what form the energy is in, it can always be expressed in Joules. - ie. in terms of the energy required to accelerate of some mass over some distance - even if you are speaking about electric fields, photons, electric current, pressure, heat, gravitational potential, kinetic, coiled spring, or nuclear binding energy. [/quote]That is also quite untrue.

I recommend that you folks recall Feynman on this. See The Feynman Lectures on Physics, Vol I - III, Feynman, Leighton, and Sands, Addison Wesley, (1963)(1989).

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 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.

Just because you have an example of what a quantity is it does not mean that you know what the definition is. For example, there is no universally accepted definition of life in all of science. However that does not mean that you don't think that you ourself is alive, or your friend, dog, cat, etc.

Pete

 

[Gokul43201]

I was referring to this statement by you :

You can't use a relationship for mass until yopu first define mass.

Why is this necessary if, as you say, mass is already well-defined ?

 

[Gokul43201]

I have done so ad ignosium in the past. But if you need a refresher for that definition please see

http://www.geocities.com/physics_world/sr/inertial_mass.htm
http://www.geocities.com/physics_world/sr/inertial_energy_vs_mass.htm

The OP was asking for a way to "understand" energy by means other than something like "this equation describes the dynamics of the particular system, and this here term is the energy of ...", yet both your refresher links do just that.

Or could you please pick out a statement from either of them that provides an intuitive definition of mass ?

This discussion is getting into what constitutes "understanding" for a physicist, and perhaps that is the question that needs to be answered first. But in my opinion, you understand something by getting familiar with it. When you are familiar with all the quantities that can be called energy, you have understood energy.

Energy looks like X and Y under U and V circumstances. It can do A, B and C if the system is subjected to D, E and F. Describe to me any system, and I'll tell you what its energy is and how it changes with time.

Something of the above nature constitutes, to me, an understanding of energy (or any other physical quantity, for that matter).

 

[Andrew Mason]

I have done so ad ignosium in the past. But if you need a refresher for that definition please see

http://www.geocities.com/physics_world/sr/inertial_mass.htm
http://www.geocities.com/physics_world/sr/inertial_energy_vs_mass.htm

You appear to be disagreeing with E = mc^2. Or am I misunderstanding you?

What is this definition you speak?
That is not a definition of energy. It is merely a particular relationship between units. It does not serve as a definition of those quantities.

Can you provide a definition of energy that does not use mass, distance and time?

That is also quite untrue.

I recommend that you folks recall Feynman on this. See The Feynman Lectures on Physics, Vol I - III, Feynman, Leighton, and Sands, Addison Wesley, (1963)(1989).

That's a large work. Can you provide a page number, volume no. or an actual quote?

Just because you have an example of what a quantity is it does not mean that you know what the definition is. For example, there is no universally accepted definition of life in all of science. However that does not mean that you don't think that you ourself is alive, or your friend, dog, cat, etc.

Well, there may be a gray area in which it is difficult to tell whether something is a life form or not (e.g. virus, prion) but that does not mean that there is not a general consensus on a definition of life.

AM

 

[pmb_phy]

You appear to be disagreeing with E = mc^2. Or am I misunderstanding you?

You misunderstood. E = mc² is an equality between the total inertial mass of a closed system and the total inertial energy of the same system. Some take it as a definition of inertial mass. That is what is incorrect. If you have a non-closed system then the relationship E = mc² does not always hold and thus cannot serve as a definition. I gave a link to an example above.

That's a large work. Can you provide a page number, volume no. or an actual quote?

Vol. I, page 4-2. The section is called "What is Energy."

Well, there may be a gray area in which it is difficult to tell whether something is a life form or not (e.g. virus, prion) but that does not mean that there is not a general consensus on a definition of life.

I'm stating a fact, not an opinion. In science today there is no universaly accepted definition of life. That, of course, does not mean that nobody makes an attempt at such a definition.

Pete

 

[pmb_phy]

The OP was asking for a way to "understand" energy by means other than something like "this equation describes the dynamics of the particular system, and this here term is the energy of ...", yet both your refresher links do just that.

The questioner asked "So what actually IS energy?" and that was what I was addressing.

Pete

 

[pmb_phy]

Can you provide a definition of energy that does not use mass, distance and time?

I already indicated that there is no universally accepted definition of energy so how could I give you a definition of energy?

Pete

Note: If I do not respond to particular comments it is because this subject has been discussed many many times here and I see this discusssion is not one I wish to participate in more than this in open forum to a large extent. Any question will, of course, be addressed in private message.

 

[Andrew Mason]

You misunderstood. E = mc² is an equality between the total inertial mass of a closed system and the total inertial energy of the same system.

E = m₀c² is, where m₀ is the rest mass. But E = mc² is quite correct where m is the relativistic mass ($m = \gamma m_0$).

AM

 

[pmb_phy]

E = m₀c² is, where m₀ is the rest mass. But E = mc² is quite correct where m is the relativistic mass ($m = \gamma m_0$).

AM

E is the inertial energy of a closed system. m is the inertial mass of a closed system. E = mc² for a closed system. It may not be true that, for an open system, that E = mc². It may be true that m does not equal E/c².

If you are unable to see why this is true then see

http://www.geocities.com/physics_world/sr/inertial_energy_vs_mass.htm

It gives a specific example of when E = mc² is not an equality. For this example (box subjected to forces) then the energy is given by

$$E = mc^2 + \gamma\beta^2 {T_0}^{xx} V$$

Obviously E does not equal mc² in this example. It differs by a factor which depends on the force the body is subjected to. Einstein showed something similar to this in 1906.

Rindler's discusses something to this effect in his 1983 intro to SR text.

You have to be careful of what you call "Energy." If you have an electron moving in a static electric field then the total energy = W = Kinetic energy + potential energy + rest energy = K + U + E[sub0[/sub] will not equal inertial energy = kinetic energy + rest energy = K + E[sub0[/sub]. I.e. E will not be conserved. It is W that is conserved in such cases.

I've been searching my physics texts for one which really nails best as far as what "Energy" is. If you have French's text on mechanics see chapter 10 page 367

The above marks do not really define energy. No matter. It is worth recalling once more the opinion that H.A. Krammers expressed: "...the most fruitful concepts are those to which it is impossible to attach a well-defined meaning." The clue to the emmense value of energy as a concept lies in its transformation. It is conserved -- that is the point. Although we may not be able to define energy in general, that does not mean that it is only a vauge, qualitative idea. We have set up quantitative measures of various kinds of energy: gravitational, electrical, magnetic, elastic, kinetic and so on. And whenever a situation has arisen in which it seemed that energy had disappeared, it has always been possible to recognize and define a new form of energy which permits us to save the conservation law.

Its best to read the entire sections of the chapters I've quoted. I've quoted only the relavent parts which I hope to make the entire point clear. I'm far too lazy to type the entire chapters from the texts.

Pete

 

[Andrew Mason]

E is the inertial energy of a closed system. m is the inertial mass of a closed system. E = mc² for a closed system. It may not be true that, for an open system, that E = mc². It may be true that m does not equal E/c².

If you are unable to see why this is true then see

http://www.geocities.com/physics_world/sr/inertial_energy_vs_mass.htm

I read it yesterday. But I could not follow how you got your equations (2) and (5). How are they derived?

AM

 

[pmb_phy]

Note on Eq. (2) in http://www.geocities.com/physics_world/sr/inertial_energy_vs_mass.htm

Notice in Eq. (2) in link above that the ratio of momentum density, g, to mass density [itex]\rho_0[itex] is integrated over entire body to give total mass. Since the stress, T_o^xx in the rest frame is an invariant and as such it will not vanish in any frame. Therefore even in the limit v << c the mass density does not equal rest mass density - quite confusing and I have not yet learned why this is so since it would seem that the mass density should become rest mass density in that limit.

Pete