What is the rigorous quantitative definition of the concept of "Energy"?

[Hamed.Begloo]

Uh, oh... it seems it gone wrong ​

 

First and foremost stop shouting.

 

I never shout anything as I know here is a community of educated people and everyone must talk with each other with respect. I just wanted to show that what my main request is and reveal it distinctively. Anyway if it bothered you I apologize deeply.

 

Edit: I searched the web and I understood it mean shouting. Again apologies.

 

Second I have already given you a correct and complete definition.

 

I read your previous post but I didn't catch your definition. However maybe it's just me who couldn't get the definition and it's my fault.

 

Third this is an exercise in physics not in computer programming so please write the equals sign correctly, instead of using the computer assignment statement.

 

I know it's not common but many places I see people use the "Colon Equal([latex]:=[/latex])" notation for defining new quantities. See here(Link below)

http://mathworld.wolfram.com/Defined.html

It's some how like the equivalent sign([latex]\equiv[/latex])

P.S. I know the "Colon Equal" operator is used for variable assignment in programming.

 

Fourthly definitions do not require an equals or assignment operator.

 

Yes. But they could be defined by an equation(if they are not primitive).

Plus as you see I also stated the language-based definitions of quantities. For example:

 

Velocity: Rate of change of Spatial position (Lingual definition)

or

[latex]\vec{v}:=\frac{d\vec{r}}{dt}[/latex] (Mathematical definition)

 

Fifthly should report your infringement of forum rules in not replying to me?

 

I still don't know How I did an infringement. But as stated early. If I did something wrong I'm so sorry.

Edited October 29, 2016 by Hamed.Begloo

[John Cuthber]

 

...

Let's get started:

"What is energy?"

A High school teacher: Huh it's simple: "The Ability of a system to do work on another system".

Cool. Then "What's work done by a gravitational field?"

Same teacher: It is called "Gravitational potential energy".

Then you mean "Energy" is defined by "Work" and "Work" is defined by "Energy". So it leads to a paradox of "Circular definition".

The teacher: Oo

Work is done when a force moves through a distance.

Energy is the capacity to do work.

Those are the high school physics definitions, and they are not circular.

Your imaginary teacher just wasn't very good; that's not a physics problem.

[sethoflagos]

 

WHAT FINALLY I WANT IS A QUANTITATIVE DEFINITION OF ENERGY. I MEAN SOMETHING LIKE: [latex]E := something[/latex]

 

 

And you will never get one, for the simple reason that it is a universal quantity that exists in a multitude of different forms.

 

And thanks to frames of reference considerations, we cannot even agree on a zero value, so it is only meaningful to discuss changes in energy.

 

Ultimately, you end up with 'That property of a closed system that is conserved as a result of the First Law of Thermodynamics'.

 

Delta E equals zero.

 

How you conceptualise E is purely a matter of personal preference. But it must encompass the universal element - ie a recognition of the quantitative equivalence of heat, work, kinetic energy, gravitational/electrical/chemical potential, rest mass etc etc etc.

 

Personally, I view it as the sum total of all motion or potential to move. Works for me. Others may differ.

[Hamed.Begloo]

 

And you will never get one, for the simple reason that it is a universal quantity that exists in a multitude of different forms.

 

And thanks to frames of reference considerations, we cannot even agree on a zero value, so it is only meaningful to discuss changes in energy.

 

Ultimately, you end up with 'That property of a closed system that is conserved as a result of the First Law of Thermodynamics'.

 

Delta E equals zero.

 

How you conceptualise E is purely a matter of personal preference. But it must encompass the universal element - ie a recognition of the quantitative equivalence of heat, work, kinetic energy, gravitational/electrical/chemical potential, rest mass etc etc etc.

 

Personally, I view it as the sum total of all motion or potential to move. Works for me. Others may differ.

 

But doesn't theories supposed to be designed in an axiomatic way.

 

I know Physics is not math but I know a physical theory is a mathematical framework that fits best with our descriptions of nature. On the other hand mathematics is always constructed in an "Axiom-Theorem" way for the propositions claimed and in a "Primitive notion-Well defined notion" way for the concepts introduced. So it's a real pain when you talk about a so important concept in a theory and have no precise definition of it. Yes I can talk about Work, Heat, Kinetic Energy, Potential Energy, Thermal Energy and so on but I know "Energy" as a whole concept should be defined. For example when we say "The energy of a system is conserved" we are talking about energy itself not its various forms. Maybe physicists are smart enough to conceptualise "Energy" without a rigorous definition but for a noob like me it doesn't work.

[studiot]

 

Hamed begloo

I read your previous post but I didn't catch your definition. However maybe it's just me who couldn't get the definition and it's my fault.

 

So you didn't understand and asked for clarification since it offered all that you asked for?

 

Or did you just carry on demanding an answer to conform to your terms, telling others that they are wrong?

 

 

I know it's not common but many places I see people use the "Colon Equal()" notation for defining new quantities. See here(Link below)

http://mathworld.wol...om/Defined.html

It's some how like the equivalent sign()

P.S. I know the "Colon Equal" operator is used for variable assignment in programming.

 

Again if you don't understand the difference between an identity and an equality, why don't you ask?

 

 

Yes. But they could be defined by an equation(if they are not primitive).

Plus as you see I also stated the language-based definitions of quantities. For example:

Velocity: Rate of change of Spatial position (Lingual definition)

or

(Mathematical definition)

 

 

You can use an equation to define energy, and I did supply one, along with a conventional explanation. But in this case words are better.

 

 

 

I still don't know How I did an infringement. But as stated early. If I did something wrong I'm so sorry.

 

Now that you have got into the habit of replying, perhaps we can carry on the conversation towards understanding?

 

What exactly did you not understand about my definition?

 

What did you make of my comment against the 'force times distance' argument? (note srinam correctly offered force times displacement)

 

You have introduced some vector notation, do you understand that one of the properties of energy is that it is a scalar?

[sethoflagos]

 

But doesn't theories supposed to be designed in an axiomatic way.

 

 

 

No. Not in science.

 

Until someone comes up with a complete and comprehensive description of reality, no one will really be sure which phenomena are primitive and which are derived. In fact, the further we progress, the more abstract everything seems to become.

 

So we make do with consistency, testability and repeatability, with all quantities on more or less an equal footing.

 

It seems to work well enough.

 

So perhaps you should save your idealism for philosophy class.

[imatfaal]

 

No. Not in science.

 

Until someone comes up with a complete and comprehensive description of reality, no one will really be sure which phenomena are primitive and which are derived. In fact, the further we progress, the more abstract everything seems to become.

 

So we make do with consistency, testability and repeatability, with all quantities on more or less an equal footing.

 

It seems to work well enough.

 

So perhaps you should save your idealism for philosophy class.

 

Seth - I think you are being too dogmatic. As an example take a re-read of Einstein's original formulation of his Special Theory of Relativity. He deliberately sets the scene with two postulates and works from there to create conclusions through a series of mathematically and logically consistent reasoning.

 

Science must work on axiomata because - as you correctly point out - the highest level of evidence we have is objective repeatability; this is a good standard but it is not proof. Thus all new scientific work takes as axiomata (intial postulates which are accepted without further evidence) large amounts of work and theory. It then uses mathematics and a logical framework to advance new ideas which can then be tested empirically.

 

That said; Eise's points above still stand and even more importantly does the fact that various levels of definition have been given and all rejected

[studiot]

Development of axiomatic systems was no asked for and is really another discussion.

However the MLT basis actually covers this topic as well.

 

But it all involves starting from the beginning.

[Hamed.Begloo]

So you didn't understand and asked for clarification since it offered all that you asked for?

.

.

.

What exactly did you not understand about my definition?

 

What did you make of my comment against the 'force times distance' argument? (note srinam correctly offered force times displacement)

One of the issues with using Force as a fundamental is the relationship Force x Distance does not always give you energy.

 

My Impression from the above sentence is that you said "Force times Distance" is not necessarily "Energy". So how could I take this as a definition?

 

Or did you just carry on demanding an answer to conform to your terms, telling others that they are wrong?

 

No. Infact The main problem is I have no way to define my terms.

And as I mentioned in my "Post #29" I just think every theory should be formulated in an axiomatic way. For example think of "Classical electromagnetism". With just one primitive notion(Electric Charge) and a set of field equations(Maxwell's Equations) as axioms plus a description of electromagnetic force(Lorentz Force) every phenomena in classical electromagnetism are described. But classical mechanics although dating back to older ages, still seems to be not fully organized and axiomatized.

 

Now that you have got into the habit of replying, perhaps we can carry on the conversation towards understanding?

 

I think now I know why you thought I did an infringement in the forums. But that post was not specifically written for you. I read all the posts before, thought they didn't get what I mean, summed up my words and then posted it for everybody.

 

Listen when it comes to science, I confess I'm the most illiterate one. I'm here to learn something from you all, not to question your knowledge. The challenges that I make are just to (as you said) carry on the conversation. I hope the turbidity is removed.

 

 

 

No. Not in science.

 

Until someone comes up with a complete and comprehensive description of reality, no one will really be sure which phenomena are primitive and which are derived. In fact, the further we progress, the more abstract everything seems to become.

Correct. I agree in science as a whole we couldn't define an axiomatic system. Because the fundamentality of notions are always changing. For example I know in quantum mechanics the notion of "Rotational angular momentum(Spin)" have not the same meaning in the classical mechanics(such that a dot particle without any volume can have a non-zero spin) so we take it as an intrinsic quantity.

But I'm talking about just one single theory(namely classical mechanics) which I expect to work completely in its own scope (not outside its range of validity).

Edited October 29, 2016 by Hamed.Begloo

[sethoflagos]

 

Seth - I think you are being too dogmatic.....

 

Everything you say is true.

 

Ironically, I did consider raising the postulates of thermodynamics as an example of an axiomatic approach to the definition of energy. But then decided that the point would probably be missed.

Edited October 29, 2016 by sethoflagos

[studiot]

 

hamed bigloo

But I'm talking about just one single theory(namely classical mechanics

 

Thank you for finally answering the second question in my first post#19.

 

You have yet to answer my first question there.

 

 

Hamed begloo post#34

 

My Impression from the above sentence is that you said "Force times Distance" is not necessarily "Energy". So how could I take this as a definition?

 

in reply to

 

studiot, on 26 Oct 2016 - 5:41 PM, said:

One of the issues with using Force as a fundamental is the relationship Force x Distance does not always give you energy.

 

Of course I did and repeated it a couple of times.

 

Is this not true?

 

How can it possibly be a definition of energy?

 

It was clearly a reason to not use this definition but employ the one that I actually stated.

 

Are you being funny or what?

 

You have not yet answered my question attached to that statement now thrice repeated.

Edited October 29, 2016 by studiot

[Hamed.Begloo]

I'm sorry but I really didn't get what you mean. Maybe this problems arise because of me not being a native English speaker and not understanding you( or who knows being a total stupid ).

 

You have yet to answer my first question there.

.

.

.

You have not yet answered my question attached to that statement now thrice repeated.

Honestly, I still don't know what question you are talking about. Can you repeat it(by taking my stupidity into account)?

Also:

First you said:

 

One of the issues with using Force as a fundamental is the relationship Force x Distance does not always give you energy.

 

Then you said:

 

(note srinam correctly offered force times displacement)

 

Now again you say:

 

How can it possibly be a definition of energy?

It just seems to me you are negating your own words.

It was clearly a reason to not use this definition but employ the one that I actually stated.

As I already mentioned my stupidity let me review your first post:

I'm sorry but I get the impression you posted this because you just want to cherry pick phrases from everybody and then snipe at them.

 

I didn't mean this but I was in a hurry and answered everybody shortly. However again I accept it was my fault and you are right to make this interpretation.

You posted this in classical physics, but seem to want to discuss quantum mechanics.

 

I don't know What makes you think I want to discuss quantum mechanics.

Classically it is not true to say the 'energy is always distributed or non localised'.

If you are thinking of Heisenberg, this is quantum and the correct pairing is energy and time. For position, the pairing is with momentum.

 

If this is what makes you think so, I can say I was told for example Potential energy of a particle is stored in field lines around that particle. Not in particle itself. Correct me if I'm wrong.

Yes there is more than one way to skin a cat, but you posted this in classical physics where there is an established structure, based on certain fundamental quantities, from which all others are derived.

 

And this is the main reason I'm here: Determining fundamental and derived concepts in classical mechanics which you said is an established structure.

 

So whilst you could develop an alternative set of fundamental quantities and use those, that would loose the advantages already endowed in the conventional set.

These are, minimum set, minimum complexity, maximum coverage, maximum flexibility.

 

What I understood from this line is: We need minimum number of Primitive notions and Axioms therefore the theory is more simple(as all theories seek to be simple) while it covers a wide range of phenomena(which is a very good property for a theory despite its simplicity) and can be easily altered to give some ad-hoc explanations for the phenomena not in its range of validity(like describing Hydrogen with Bohr's atomic model or some non-relativistic cosmological phenomena). Again correct me if I'm wrong.

 

One of the issues with using Force as a fundamental is the relationship Force x Distance does not always give you energy.

 

This is the only quantitative statement you introduced which you yourself don't count as a definition of energy.

 

I gave you a sound quantitative definition of energy in terms of the fundamental quantities of mechanics.

 

What more do you want?

 

Again I didn't find the quantitative statement.

 

[studiot]

OK so let us accept that English is not your first language and put down any misunderstandings to that.

 

Actually I think your written English is pretty good.

 

 

But it is possible you may have more difficulty understanding English written by others.

 

So this could be a double benefit (slang double whammy) for you to improve you understanding of both English and Science here.

 

 

To answer your questions and progress the discussion.

 

 

 

It just seems to me you are negating your own words.

 

Not really.

My words very clearly state that defining energy as force times distance is not a good idea because there are situations when you multiply force times distance and do not obtain an energy.

 

I then asked if you know of such a situation.

I also asked what else you might obtain that is not energy.

 

To save time I will tell you that moment (the americans like to call it torque) is defined as force times distance.

I hope you know the difference between moment and energy.

 

I also asked you the following question

 

 

studiot post#30

 

You have introduced some vector notation, do you understand that one of the properties of energy is that it is a scalar?

 

This is important because Force is (always) a vector and 'distance' in this case is also a vector.

 

Since there are two possible and different ways of multiplying two vectors together,

 

Multiplying force and 'distance' will get you two different answers and two different quantities.

 

Energy is the scalar (or dot) product of the two vectors.

 

Moment is the vector product of the same two vectors.

 

I will stop here for the time being until you can confirm that you have understood what I have said so far.

 

[Hamed.Begloo]

Quite frankly now I'm very happy that you noticed you are talking with someone who have much less knowledge than yourself.

 

I then asked if you know of such a situation.

 

I know that the outcome of the product of "Force" and "Distance/Position/Length" depends highly on either quantities being "Vector" or "Scalar" and also on either the operator acting between them being "Dot product" "Cross product" or simply just a "Multiplication of a vector and a scalar".

 

I also asked what else you might obtain that is not energy.

 

I know the outcome of this product could have the dimension of [Energy] or [Torque] but the outcoming quantity could be either "Difference in Energy", "Work" or "Torque"

 

To save time I will tell you that moment (the americans like to call it torque) is defined as force times distance.

I hope you know the difference between moment and energy.

 

Let me tell you what I know about Moment and Torque then you correct me if I'm wrong.

I know many people use these words interchangeably. But in overall what I saw from most textbooks or on the web usually "Torque" is defined as "Cross product of Position vector and Force vector" while "Moment" usually defined as "Cross product of Position vector and any other quantity" Like:

 

Angular momentum(moment of momentum) [latex]\vec{L}:=\vec{r}\times \vec{p}[/latex]

Torque(moment of force) [latex]\vec{\tau}:=\vec{r}\times \vec{F}[/latex]

etc.

 

And this makes Torque a special case of Moment.

 

This is important because Force is (always) a vector and 'distance' in this case is also a vector.

 

Since there are two possible and different ways of multiplying two vectors together,

 

Multiplying force and 'distance' will get you two different answers and two different quantities.

 

As I mentioned earlier, yes I know there are two possibilities.

 

Energy is the scalar (or dot) product of the two vectors.

 

Moment is the vector product of the same two vectors.

 

I will stop here for the time being until you can confirm that you have understood what I have said so far.

 

 

Now this is my main problem: I agree about Moment/Torque but I know the dot product of "Force" and "Distance" gives you "Work". I know "Work" and "Energy" have the same dimensions but I think they are different quantities. They are other situations where two different quantities have same dimensions. For example "Translational kinetic energy" and "Rotational kinetic energy" have same dimensions but they are not describing one thing. I think If two quantities have same dimensions then not necessarily they describe one thing. Yes "Work" may represent the difference in energy but does not talk about "Energy itself".

 

I hope I delivered my purpose.

[studiot]

I think we have enough to be going on with.

 

Many of the points you make carry some weight, but there is much more to the story.

 

I suggest you postpone extended discussion of turning effects to another thread, it does not belong here. Start another if you wish.

 

I will be out for a few hours now and able carry on in more detail then.

 

[Hamed.Begloo]

I suggest you postpone extended discussion of turning effects to another thread, it does not belong here. Start another if you wish.

 

I'm afraid starting another thread for the same subject being count as another infringement of the forum rules. If you don't mind, I prefer to wait for answers here.

 

Thank you.

[imatfaal]

 

I'm afraid starting another thread for the same subject being count as another infringement of the forum rules. If you don't mind, I prefer to wait for answers here.

 

Thank you.

 

!

Moderator Note

 

No need to worry - they are different subjects and we will always prefer to keep subjects narrow and defined. It is really in Speculations that we prefer to keep every part of a speculative topic quarantined in its own little hermetically sealed reserve and thus we resist multiplication of those threads. This thread is a good example of an explanatory / exploratory thread - and the more of those the better

 

It might be an idea just to pursue one line of enquiry at a time merely for your own sanity - there is clearly a lot of thought going into this thread and I am not sure I for one could maintain that level in two distinct discussions.

 

Thank you for thinking about this. Feel free to PM staff or ask questions in Suggestions Forum.

 

[Sam Batchelar]

Energy in its original state is undefined as anything, it is from this point (its original state) that it may be defined as something such as mass, velocity, a transverse vibration...

[antripathy]

Work can be done when energy flows from high temperature or potential area to lower one even if the quantity of energy is small,say 25 joules.No work can be done when it is in equilibrium, that is uniform temperature and pressure.The atmosphere and oceans contain trillions of joules of energy,brought down from higher temperatures and useless for doing the daily works of the humans.