What Is the True Nature of Energy?

[Schrodinator]

I understand that. It is a matter of exchanging words for words. Still the question remains as to what is energy? The question remains because the capacity to do work fits everything except possibly zero point energy. The point is that when one asks what is force or what is energy, one is asking what is cause? Capacity is another trade off word for cause. So, what is capacity?

James

Capacity is not a trade of, it is a measure of volume or an amount, it means what it means. In this example it means the quantity with which an entity is bestowed which enables work to be done.

This definition fits zero point energy to btw.

And what you are asking is unknown, the laws of nature are only reducible so far. Might as well say God done it though if you are looking for a why instead of how question that goes further than the smallest iota. God is the only first cause without a cause ok, happy.

Why does F=ma?

I don't know it just seems to be the way it works.

Why?

I don't know?

Why?

I don't know.

Ad nauseum.

 

[Dale]

Energy is force times distance.

No it isn't. Provide a credible reference or stop saying something that you know is wrong.

You have been provided the definition of energy many times with several credible references. It is becoming obvious that you have a hidden agenda and are not interested in anything else.

 

[Schrodinator]

Much as I hate using the W word. I did say what W was earlier. Wor, er woor oh you know what I mean,it's that W word not energy that equals force x distance.

W = \int_C \mathbf{F} \cdot \mathrm{d} \mathbf{s}

This integral has a limit of the speed of light.

In physics, mechanical work is the amount of energy transferred by a force acting through a distance in the direction of the force. Like energy, it is a scalar quantity, with SI units of joules.

Like being the operative word, work and energy not being the same thing exactly.

Energy = mass x speed of light^2
E=mc^2

Is what energy is in maths jargon.

or e=hf if you are quantumizing it up.

 

[superg33k]

If a body gives off the energy L in the form of radiation, its mass diminishes by L/c².

Einstiens paper
http://www.fourmilab.ch/etexts/einstein/E_mc2/www/

And the mass diminished in this quote is equal to the relativistic mass of the photons. The conservation of relativistic mass is the conservation of evergy (of course the conservation of rest mass isn't true).

Everytime you increase an objects energy (possibly giving it kinetic energy), you increase its mass. Everytime you increase its mass, you increase its energy. To measure its mass, you are measuring its energy. They are equivilent, they are the same thing: Energy is mass.

BTW, when someone disagree's with me please let me know which bits you disagree with.

And I'd evem go further into quantum mechanics to say that energy is mass is frequency. But it'd probably be simpler to argue me on the E=mc2 front.

Don't you wish this forum has a thumbs up/thumbs down thing like you tube so we could see what everyone agree'd with?

 

[Dale]

And the mass diminished in this quote is equal to the relativistic mass of the photons. The conservation of relativistic mass is the conservation of evergy ...

Everytime you increase an objects energy (possibly giving it kinetic energy), you increase its mass. Everytime you increase its mass, you increase its energy. To measure its mass, you are measuring its energy. They are equivilent, they are the same thing: Energy is mass.

In the first paragraph, you correctly used the term "relativistic mass". The second paragraph would be correct if you also continued to use the term "relativistic mass".

Usually in modern physics, the unqualified term "mass" refers to the invariant mass rather than the relativistic mass. The reason is what you have identified here, that the relativistic mass is equivalent to total energy, so there isn't a need for a separate name.

So, if we use the usual approach that "mass" refers to invariant mass then it is true that anything with mass has energy, but it is not true that anything with energy has mass. Therefore, energy is not mass, at least not in modern usage.

 

[superg33k]

In the first paragraph, you correctly used the term "relativistic mass". The second paragraph would be correct if you also continued to use the term "relativistic mass".

Usually in modern physics, the unqualified term "mass" refers to the invariant mass rather than the relativistic mass. The reason is what you have identified here, that the relativistic mass is equivalent to total energy, so there isn't a need for a separate name.

So, if we use the usual approach that "mass" refers to invariant mass then it is true that anything with mass has energy, but it is not true that anything with energy has mass. Therefore, energy is not mass, at least not in modern usage.

Thanks Dale. In lectures we always use mass as rest mass but after reading that conservation of mass is equivalent to conservation of energy I figured everyone else must use mass as relativistic mass. Anyway, I will use mass as rest mass from now on. Therefore (rest) mass is not always conserved.

From my prevo Einstein quote rest mass can be converted into photons.

Would you agree that (rest) mass is a form of potential energy?

 

[Dale]

Would you agree that (rest) mass is a form of potential energy?

Yes.

 

[SpectraCat]

"IMO, if you want an answer that cannot be directly expressed mathematically you are asking for something that cannot be given by physics."

Energy is expressed mathematically as fxd.

No it is not. Energy is a path independent state function of a system. Work is a path-dependent quantity, and in fact is only defined in terms of *changes* in energy between two systems. That's why we define energy as a measure of the capacity of a system to do work.

What's more, the work done moving a mass from point a to point b is NOT a fixed quantity. The difference in energy between that mass when it is at point a and when it is at point b *is* a fixed quantity .. that is why we call it a state function.

 

[JJBladester]

@DaleSpam, @SpectraCat, @Drakkith, et al.

I haven't chimed in much since originally posting the question "What is energy?" I have read all posts (all 10 pages thus far) and am developing a much closer idea of it than before.

Energy describes the state of a system or the state of two or more interacting systems. Energy is a quantity that tells us what is happening (in terms of movement) or what could happen if things change. When I say "things change" I am referring to the position of certain masses with respect to other masses or a change in the velocity of one or more masses.

You can touch mass but you cannot touch energy. You can feel the effects of energy but not energy itself.

Back to my original post... You eat food which gives your body and muscles a capacity to do work (*energy). The work you perform is defined by how you push the door (which has rest mass). You may press straight-on or press the door at an angle; you may press the door near the top or bottom, too. You may also vary the magnitude of your pressing of the door.

*(The door has energy just by the fact that it has rest mass but I'm not talking about that here.)

I like to think of rest mass as something you can touch. If it's not rest mass, it cannot be touched. Relativistic mass is energy that acts as mass but is not mass and cannot be physically touched.

When I say "acts as mass," I am referring to the inertial property of mass (that mass resists a change in acceleration due to an outside force).

With a statement like "this system has energy," one would be stating that the system can "do stuff," namely, the system, or some of its parts, can speed up, slow down, or change directions.

 

[Dale]

You can touch matter, and matter has mass, but I am not sure you can touch mass.

There are many other properties of matter, such as volume, color, charge, etc., would you also say that you can touch volume, color, charge, etc.? If so, then why would you single out energy as being the one untouchable property, and if not, then why would you single out mass as being the one touchable property?

 

[superg33k]

Personally I am still having difficulty with the whole circular thing:

Energy is ability to work
Work if forces times distance
Force is mass times acceleration
Mass is potential energy
And I guess potential energy can become energy

It makes me thing that all these terms cannot be independant.

As well as I am having difficulties making crystal clear the differences between energy and potential energy.

If anyone thinks they can give a nice clear explenation to me that would be awesome. Otherwise if I'll have to think how to formulate a clear question.

 

[JJBladester]

You can touch matter, and matter has mass, but I am not sure you can touch mass.

There are many other properties of matter, such as volume, color, charge, etc., would you also say that you can touch volume, color, charge, etc.? If so, then why would you single out energy as being the one untouchable property, and if not, then why would you single out mass as being the one touchable property?

Matter is anything that has mass and takes up space. Mass is "how much matter something has". Mass is simply a quantity telling us how much matter is present.

I made a bunch of really good points and you jumped to a very minor detail which I hope to have made clear above. Anyway, what about the rest of my post?

With the statement I've made above, you could just use the word "matter" where I had used "rest mass" in my previous post and I think what I had said would be correct from there...

 

[Dale]

I made a bunch of really good points and you jumped to a very minor detail which I hope to have made clear above. Anyway, what about the rest of my post?

I thought the rest was fine. The part about energy describing the state of a system is good. And you specifically mentioned the definition of energy in the eating food bit. And replacing mass by matter when referring to touching makes it all good IMO.

 

[Dale]

Personally I am still having difficulty with the whole circular thing:

Energy is ability to work
Work if forces times distance
Force is mass times acceleration
Mass is potential energy
And I guess potential energy can become energy

It makes me thing that all these terms cannot be independant.

There is an enormous difference between independent and circular. These terms are clearly not independent as you can write mathematical expressions relating each of them to the others. However, just because they are all related (not independent) does not in any way imply that their definitions are circular.

Mass and energy are equivalent as discussed above, but they are defined differently. I won't repeat the definition of energy yet again, but mass is defined operationally. I.e. there is a specific physical experiment (balance scale) which can be performed which will yield a number, and that number is called mass.

When you go through all of the chain of definitions for any physical quantity you find that they are all eventually defined in terms of a series of one or more experiments which can be performed to determine the quantity. In the end this is what prevents physics definitions from being circular.

 

[James A. Putnam]

"No it isn't. Provide a credible reference or stop saying something that you know is wrong.

You have been provided the definition of energy many times with several credible references. It is becoming obvious that you have a hidden agenda and are not interested in anything else."

Weidner, Sells, Elementary Modern physics, 1960, Allyn and Bacon, pages 69-70; "We next ask, 'What is the relativistic kinetic energy K?' To find this, we define, as in classical physics, the kinetic K to be the total work done in bringing a particle from rest to the final speed v under a constant force F."

They go on to derive Einstein's energy equation beginning with the integral of force times distance.

Robert Resnick, Introduction to Special Realtivity, 1968, Wiley, Pages 120-121 "In Newtonian physics we defined kinetic energy, K of a particle to be equal to the work done by an external force in increasing the speed of the particle from zero to some value u. That is, (He goes on to derive Einsteins energy equation beginning with the integral of force times distance) were F*dl is the work done by the force F in displacing the particle through dL."

Energy is force times distance. After it is calculated its sume total can be equated to other quantities and qualities such as 1/2mv^2.

I have no hidden agenda. The question of "What is energy" is not answered by saying it is the capacity to do work. It is answered by saying that it is the sum total of force times distance. The answer ends there because there is no answer for what force is. There is nothing wrong with running out of answers. There is something wrong with not pursuing meanings that exchange words for other words. Real meaning should be pursued until scientific explanations run out. Then we know where to search for extending our knowledge of the fundamentals.

James

 

[superg33k]

There is an enormous difference between independent and circular. These terms are clearly not independent as you can write mathematical expressions relating each of them to the others. However, just because they are all related (not independent) does not in any way imply that their definitions are circular.

Mass and energy are equivalent as discussed above, but they are defined differently. I won't repeat the definition of energy yet again, but mass is defined operationally. I.e. there is a specific physical experiment (balance scale) which can be performed which will yield a number, and that number is called mass.

When you go through all of the chain of definitions for any physical quantity you find that they are all eventually defined in terms of a series of one or more experiments which can be performed to determine the quantity. In the end this is what prevents physics definitions from being circular.

Thanks Dale. I don't know if it was your explination or my baked beans for dinner but I think I get it...

There is a bunch of stuff we measure directly, like mass, position, time. Theres a bunch of stuff we measure indirectly like momentum (by measuring its mass and speed) and energy (mass and speed again). Some of these are always conserved, like energy and momentum. Obviously not all of these are independant.

When I think about the world, I like to think there is some 'real' indepandant quantities, and some other made up useless ones (or for simplifying maths). But which are the 'real' ones, the ones we measure directly, or the ones which are conserved? A question left for the philosphizing.

Annoyingly this is the way I've always thought about it before wondering why. Now I have wondered why and nothing has changed.

I still can't decide if rest mass is energy or potential energy. I think its energy. All energy internal to the object in discussion I think is energy, all energy from its position in space (i.e. external to the object) is potential energy.

Why am I so stupid?

 

[Dale]

Weidner, Sells, Elementary Modern physics, 1960, Allyn and Bacon, pages 69-70; "We next ask, 'What is the relativistic kinetic energy K?' To find this, we define, as in classical physics, the kinetic K to be the total work done in bringing a particle from rest to the final speed v under a constant force F."
...
Robert Resnick, Introduction to Special Realtivity, 1968, Wiley, Pages 120-121 "In Newtonian physics we defined kinetic energy, K of a particle to be equal to the work done by an external force in increasing the speed of the particle from zero to some value u."

These are different from the usual "energy is the capacity to do work" definition, but they are clearly not "energy is force times distance" either. These definitions are in fact the time-reverse of the usual "capacity to do work" definition, and since Newtons laws and SR are time-reverse symmetric they are equivalent in those contexts. Furthermore, they only apply to kinetic energy, and not to any other form of energy.

This certainly doesn't support your case at all, try yet again.

 

[Drakkith]

I have no hidden agenda. The question of "What is energy" is not answered by saying it is the capacity to do work. It is answered by saying that it is the sum total of force times distance. The answer ends there because there is no answer for what force is. There is nothing wrong with running out of answers. There is something wrong with not pursuing meanings that exchange words for other words. Real meaning should be pursued until scientific explanations run out. Then we know where to search for extending our knowledge of the fundamentals.

I've already given you the definition of force. Again, this comes back to you not accepting the definition we have given it. You can argue that it doesn't explain it all you want, in the end science has defined it as such. If you want to continue to disagree, then you should re-read the rules to the forums you agreed to when signing up.

 

[James A. Putnam]

These are different from the usual "energy is the capacity to do work" definition, but they are not "energy is force times distance" either. These definitions are the time-reverse of the usual "capacity to do work" definition, and since Newtons laws and SR are time-reverse symmetric they are equivalent in those contexts.

This certainly doesn't support your case at all, try yet again.

I don't have to try again to get it right. I just need to try again to communicate that the word work is a stand in for change of energy. If the force is a constant, it can be taken out of the integral and K=fxd. Here it can be plainly seen that kinetic energy is force times distance. The word work can be substituted, but it adds no clarity to explaining "What is energy?" I will grant you that the use of the word work is wide spread in texts. Energy is presented as, what I also have referred to, the sum total of force times distance. That sum can be evaluated for a variable force at any instant of time and it will be recognized as energy. The energy is changing. The word work refers to the change in energy. If this is unacceptable to you, then, from my point of view, nothing is lost by rephrasing the original question to: What is work? The change in words still leaves us with explaining what force is or admitting that we do not know how to explain the existence of either work, presumably an abstract way of referring to the fact that change of position is ocurring, or energy, another abstract way of referring to the fact that change of position has occurred. Since energy can be calculated at any point along the way, energy is another abstract way of referring to the fact that change of position is ocurring.

With regard to your 'hidden agenda' remark: My point has to do with the unknown nature of force or cause. All empirical evidence involves patterns in changes of velocity resulting from the action of force or cause. We know about the patterns. We know about effects. We do not know about cause. Presumably there is a cause for the existence of energy. That cause is unknown. Whatever it is that is convertible between energy and mass, it is not a sum total. It is a transferrence of that unknown cause. If you see this as a hidden agenda, so be it. I leave it in your hands. My answers exist elsewhere. I just thought this was an important question to clarify that we do not know what energy is any more than we know what work is or that we know what force is. We only know the effects of force. The resulting effects can have whatever names we wish to give them, but, the introduction of those names do not answer our questions. Best wishes to you.

James

 

[James A. Putnam]

I've already given you the definition of force. Again, this comes back to you not accepting the definition we have given it. You can argue that it doesn't explain it all you want, in the end science has defined it as such. If you want to continue to disagree, then you should re-read the rules to the forums you agreed to when signing up.

What is the definition of force? You posted this: "In physics, a force is any influence that causes a free body to undergo a change in speed, a change in direction, or a change in shape." What is an influence? These questions have to do with physics, not language. Trading words for words explains nothing. When I ask: What is force? I am asking what property of the universe is responsible for change of velocity? It is ok to not yet know that property. It is not ok to pretend that changing the word force for influence is a physics answer.

James

 

[Drakkith]

What is the definition of force? You posted this: "In physics, a force is any influence that causes a free body to undergo a change in speed, a change in direction, or a change in shape." What is an influence? These questions have to do with physics, not language. Trading words for words explains nothing. When I ask: What is force? I am asking what property of the universe is responsible for change of velocity? It is ok to not yet know that property. It is not ok to pretend that changing the word force for influence is a physics answer.

James

It is a physics answer. It is THE physics answer. It is NOT ok to pretend that science doesn't know what it's talking about just because you disagree with how we define something. What property of the universe is responsible for the change in velocity? That IS force.

 

[James A. Putnam]

It is a physics answer. It is THE physics answer. It is NOT ok to pretend that science doesn't know what it's talking about just because you disagree with how we define something. What property of the universe is responsible for the change in velocity? That IS force.

Exchanging words for words is not doing physics. No one knows what force is including you. You only know about effects. Yes we know that force exists. In other words, we know that cause exists because effects exist. We do not know what cause is. All of our knowledge consists of observing patterns in changes of velocity. We do not know what those patterns exist.

James

 

[Drakkith]

Exchanging words for words is not doing physics. No one knows what force is including you. You only know about effects. Yes we know that force exists. In other words, we know that cause exists because effects exist. We do not know what cause is. All of our knowledge consists of observing patterns in changes of velocity. We do not know what those patterns exist.

James

I know exactly what force is as it is defined by physics. That is what you don't understand. I'm not arguing that some mystical unknown "thing" is or isn't force, which is what you seem to be implying. THAT is not doing science, that is something else entirely.

 

[James A. Putnam]

I know exactly what force is as it is defined by physics. That is what you don't understand. I'm not arguing that some mystical unknown "thing" is or isn't force, which is what you seem to be implying. THAT is not doing science, that is something else entirely.

You do not know what force is. What you know is a wordy definition that passes the real answer further down the line. Cause is not mystical. Cause is real. If that which remains unknown but is clearly proven to exist is to be referred to as mystical, then what is physics? Is physics restricted to only that which is currently taught. Certainly that is not true. Physics is about learning the nature of the universe. The nature of the universe is still out there waiting for us to discover it.

 

[Drakkith]

You do not know what force is. What you know is a wordy definition that passes the real answer further down the line. Cause is not mystical. Cause is real. If that which remains unknown but is clearly proven to exist is to be referred to as mystical, then what is physics? Is physics restricted to only that which is currently taught. Certainly that is not true. Physics is about learning the nature of the universe. The nature of the universe is still out there waiting for us to discover it.

This has devolved into a pointless argument and I will take no further part in it. If you want to continue to believe that we don't know what force and energy is, then go ahead. You have simply missed the point entirely. Good day to you sir.

 

[KOSS]

In reply to Putnam's post #85, and most of the following discussion since,
I likened energy to money as an abstraction. JamesA.Putnam did not like it...

JamesA.Putnam said:

"Energy is like money? I read the earlier messages. Money is real. It can be held. It can be contained and tested for its physical effects. It is physical effects that concerns physics. Do we know what energy is or do we not know what it is? Likenesses, meaning analogies, do not count."

You missed the point James! Firstly, the analogy with money is only to aid understanding, most analogies are never intended to be exact correspondences, if so we wouldn't call them analogies. Besides that, JaredJames picked up the essence of the analogy well when he noted that "money doesn't exist"...you cannot say coins and dollars define money because while it's true they are forms of money, that doesn't cover many, many other forms of money, as JaredJames pointed out. This is again analogous with the confusion so many people have, when they think they have a definition of energy as a concrete reality, someone comes along and easily disabuses them of the notion because it cannot cover all forms of what we refer to as energy in physics. The work=energy definition is an example. It is not a sufficient definition. Just like coins are not a sufficient definition of money.

So, in short, the money analogy was never intended to "count" as a definition. The definitions of energy pertaining to relative states of systems and time translation symmetry are probably the best you are ever going to get, since, I submit, they cover everything that is considered "energy" in modern physics. It agrees with the use of the Hamiltonian in QM as the generator of time evolution. Furthermore, the relational definition is precisely what you are looking for when you say you are concerned only about the physical effects. It is indeed the relationships that count, and pretty much only relationships that ever count, all else is unnecessary add-ons (I claim, I'm not saying I'm an oracle who knows all ;-)

Aside: there are even recent attempts to place the foundations of quantum mechanics and quantum gravity on a purely relational basis (eg., http://arxiv.org/abs/quant-ph/9609002). That's not addressing the "what is energy?" question directly, but if the ideas have merit and become mainstream it would do a lot to ease future physics student's qualms about the question 'what is energy?'.I'll reiterate a bit more:
It's dopey to say energy is force times distance or capacity to do work, since that doesn't cover many forms of energy like heat energy with zero free energy and so forth. My plea is to realize how we use energy in physics. You should soon convince yourself that it is a relationship between states of a system, so it's purely an abstract concept, which BTW explains why there is all the confusion when folks think about trying to grasp and touch the stuff, or try to define it in concrete terms, you can't! Or if you do, you will find that you've only got a partial definition that doesn't cover other forms of energy.

 

[James A. Putnam]

In reply to Putnam's post #85, and most of the following discussion since,
I likened energy to money as an abstraction. JamesA.Putnam did not like it... ...(Putnam's dots to show that I deleted much of the quote.)...

I'll reiterate a bit more:
It's dopey to say energy is force times distance or capacity to do work, since that doesn't cover many forms of energy like heat energy with zero free energy and so forth. My plea is to realize how we use energy in physics. You should soon convince yourself that it is a relationship between states of a system, so it's purely an abstract concept, which BTW explains why there is all the confusion when folks think about trying to grasp and touch the stuff, or try to define it in concrete terms, you can't! Or if you do, you will find that you've only got a partial definition that doesn't cover other forms of energy.

I don't have strong feelings about the money analogy. I do prefer more direct answers, but, analogies can certainly be useful, so, for me, yours stands for what you explained it to be. I could do without the 'dopey' description. I would have stated it as "...energy is force times distance or capacity to do work... is a mathematical description. We don't have a physical description outside of patterns of effects. Heat is energy intransit, so I am not clear on your point of separating types of energy. I could use a little friendly further explanation of your point with regard to the zero free energy reference. I am willing to learn because I am driven to learn. It is just that I don't need to learn new words for expressing the same thing. I am not saying that you do this. I am only requesting that explanations delve into the actions of physical properties at least to the extent that they are presently known.

 

[SpectraCat]

I don't have strong feelings about the money analogy. I do prefer more direct answers, but, analogies can certainly be useful, so, for me, yours stands for what you explained it to be. I could do without the 'dopey' description. I would have stated it as "...energy is force times distance or capacity to do work... is a mathematical description. We don't have a physical description outside of patterns of effects. Heat is energy intransit, so I am not clear on your point of separating types of energy. I could use a little friendly further explanation of your point with regard to the zero free energy reference. I am willing to learn because I am driven to learn. It is just that I don't need to learn new words for expressing the same thing. I am not saying that you do this. I am only requesting that explanations delve into the actions of physical properties at least to the extent that they are presently known.

James,

You never responded to my post #158 ... would you care to?

 

[James A. Putnam]

No it is not. Energy is a path independent state function of a system. Work is a path-dependent quantity, and in fact is only defined in terms of *changes* in energy between two systems. That's why we define energy as a measure of the capacity of a system to do work.

What's more, the work done moving a mass from point a to point b is NOT a fixed quantity. The difference in energy between that mass when it is at point a and when it is at point b *is* a fixed quantity .. that is why we call it a state function.

SpectraCat, I missed this one: Energy is not path independent. It is true that the final calculation of the sum total of force times distance is path independent. However, all along the path followed by force times distance, the calculation can be made instantaneously and that sum total will be energy. So the change in energy follows the path of force times distance. It is only the use of two different words that makes energy as the final sum total path independent while its word susbstitute work is acknowledged to be path dependent. In any ncase, you used the word capacity. What is capacity that it should clarify the cause of change of velocity?

Your second point, I think, is clarified by my same answer. So long as vector type changes of direction are taken into account, work can vary wildly and so can energy. It does remain the case that final results are independent of the path taken on a generalized work diagram. If, I make instantaneous calculations of sum totals continuously during the path traveled, I might even say, a generalized energy diagram. However, formally speaking, keeping to separate terminologies, your point is well taken. I am not so interested in the debate about whether the word work or the word energy is more textbook appropriate for a given circumstance as I am interested in the cause of changes of either. That cause must exist but no one knows what cause is. Until cause can be explained, we are only speaking about effects. If energy is only another word for specific effects, then, I find the position that effects can be convertible into matter to be incomplete. Perhaps this point is viewed here as a separate subject. Thank you for your message. Any corrections you have to offer to my opinion are welcome.

 

[SpectraCat]

SpectraCat, I missed this one: Energy is not path independent.

Yes, it is. It is a state function. The amount of kinetic (or potential) energy a body has is determined only by its state at the time of measurement ... the past history of the body is irrelevant to its energy. As you can see, the integral of "force times distance" is most assuredly NOT independent of past history .. it is *defined* by past history. The quantity represented by the integral of "force times distance" is called work in physics. Work is a *change* in energy of a system. In order for a system to do work on its surroundings, it must end up with less energy than it started with. This is why we say that energy is a measure of the capacity to do work.

It is true that the final calculation of the sum total of force times distance is path independent. However, all along the path followed by force times distance, the calculation can be made instantaneously and that sum total will be energy. So the change in energy follows the path of force times distance.

Now you are perhaps getting the idea .. that last statement is close to correct ... work is the *PATH-DEPENDENT CHANGE* in energy as a force is applied to a system over a particular path. If you have two well defined states of a system, the energy difference between those two states will also be a well-defined quantity. However the work required to move the system between those two points is NOT well-defined until you have specified a path (i.e. a trajectory where the position and force vectors are specified at every point).

It is only the use of two different words that makes energy as the final sum total path independent while its word susbstitute work is acknowledged to be path dependent. In any ncase, you used the word capacity. What is capacity that it should clarify the cause of change of velocity?

You seem to think this is all just semantics ... it is not. Energy and work have the same units, but they are not interchangable concepts for the reasons I gave above.