Sir, my understanding goes like...

Force is the -ve gradient of the potential.  Now if we have some potential energy in a system and if the system is not in a local stable equilibrium position we will realize motion of the subsystems and the potential energy will then convert to kinetic energy.  Now on the course of conversion the subsystems will experience force.  For a specific example one can take the motion of a simple pendulum or of falling of an apple etc..  

Now, Force is a vector quantity where energy is a scalar.  So I don't think equivalence relation is possible b/w them.  

In classical mechanics a force is related to the movement of energy from one place to another.  So if an object experiences a force and is accelerated, it must gain energy, as energy is conserved, then somewhere else energy was lost.  Thus, the forces describe the movement of energy, but aren't energy themselves.

This holds true in QM.  What we would macroscopically call a force is simply an average over a large number of more fundamental interactions where bosons take energy from one particle and deposit it in another.

At the beginning of the 20th century, Newton’s second law was corrected considering the limit speed c and the relativistic mass. At that time there has not been a clear understanding of the subatomic particles. Let us take a new look at the relativistic Newton's second law relation F=d(mv)/dt. Force applies on an object/particle by other object (such as collision) or a field (such as falling object in gravitational field).

In collision, energy transfers from an object to other one (or energy transfers between them). It shows force is an invention concept to explain physical phenomenon. When two opposite charged particles absorb each other, virtual photons (bosons) convert to energy.

Dimension view:

• Work: ( W=F.d) equal to the energy consumed

The equivalence is field-energy. For instance, in electromagnetic waves, the energy density of the wave is proportional the the square of the electrical field. Force is like velocity, belongs to a different class of parameters.

In general, there is many evidence that show force and energy are convertible to each other. For instance, when a stone is moving upward in gravitation field of the earth, its kinetic energy converts to force, and when it is moving downward, force converts to energy. In formal physics this phenomena is explainable by energy conservation law.

Theories (classical mechanics, quantum mechanics and special relativity and general relativity) have problems. But each of these theories in its areas works well. So, the purpose of the mentioned problems is in the way to generalize them. As far as this issue is concerned, the relations; F=d(mv)/dt, definition of work, the equivalence of mass and energy and work energy theorem work well. Also, energy and work have the same unit and dimensions.

We'll have to see how they are using to find an equivalence relation between force and energy. Of course this cannot be simple and direct such as the equivalence of mass and energy. 

In Bucherer experiment filed works on electron and electron takes energy, in fact according quantum mechanics bosons converts to energy. So, we should find an equivalence relation between boson and energy.

It is always healthy to revisit the (basic) concepts of physics.  However, with respect, one should not overdo it!  Having said this, please allow me to make the following brief remarks.

In classical physics, there is an intimate relation between mass and energy (for example, kinetic energy, gravitational potential energy, and so forth).  This relation was promoted to 'equivalence' thanks to Special Relativity and the dramatic role occupied in the theory and in Nature itself by the speed of light in vacuum.

There exists an equally intimate relation between force and energy.  A conservative force can invariably be derived from a potential and vice versa.  This is deeply rooted in the concept of work.  Even in nonrelativistic, (relatively) low-energy microscopic physics, one can often express the interaction field between two particles as a binary potential whose gradient gives the force between them.  One could refer to this intimate relation, broadly speaking, as 'equivalence'; but this would be mere semantics!  What would it be for?

Dear Humam

Thank you for kindly respond. If we find a like-equivalence between force and energy, then we can resolve many of physical unanswered problem. In fact like-equivalence force-energy should be able explain how bosons convert to energy and vise versa.

Why I have propounded this question about relationship between force and energy?

About 100 years ago, Einstein propounded relativity. One of its results was the limitation of speed and shows nothing moves faster than light speed. Also in relativity, gravity effect moves with speed of light. Relativistic Newton's second law (F=vdm/dt+mdv/dt) contains two important and considerable results;

1- Mass is variable

2- Nothing moves faster than light speed

Also according relativity and quantum mechanics, massless particles such as photon (real and virtual photons) only move with speed of light.

According to quantum mechanics virtual photon carries electromagnetic force that moves with speed of light. Take a new Look at the Bucherer experiment. Relativistic kinetic energy increases to infinity when approaching the speed of light, thus no massive body can reach this speed. In fact when electromagnetic force applies on the electron, virtual photon (boson) convert to energy and kinetic energy and momentum of it is added to electron's energy and momentum. It is explainable by conservation laws of energy and momentum.

In reality is that in Boucherer experiment, an electron in acceleration gains energy and after exiting from the accelerator tunnel, because of collision with another particle or because of passing through a field that gives it negative acceleration, it loses the energy and in terms of mass it returns back to its former state. One could always use this experiment to prove relativity mass, but could not explain the real interaction between force and mass with relativistic mass. Same process happens for falling object in gravitational field.

The classical definition of energy that defines energy as the ability to do work, could not explain the interaction among the particle in high energies.

Dear Kwei

Please consider that I do not claim force and energy are equivalence (or equal), in description of the this question I have mentioned "Are the forces (according to quantum mechanics bosons) and energy are converted into each other?". In addition, I have defined a quantum of work (as Wq=Fg.Lp) many years ago. Please see; that republished at April 3, 2005 , link below;

http://www.ghandchi.com/394-MonadsCPHEng.htm

Dear Kwei

Thank you for your comprehensive questions.

According E=mc^2, mass and energy are not equal, it shows energy and mass are convertible to each other. Same as E and m, force and energy are not equal, but work and energy have same dimentions and unit.

In last comment, I defined Wq=Fg.Lp, there Wq is least quantum of work and in generaly W=nWq, where n is a natural number.

Where did you see Vc >c?

"Is your concept peel reviewed and published? "

Please see following articles;

Interactions between real and virtual spacetimes

Fundamental Journals

International Journal of Fundamental Physical Sciences (IJFPS)

Sciences (IJFPS) ISSN:2231-8186

IJFPS, Vol 4, No 4, pp 114-121, Dec , 2014

DOI:10.14331/ijfps.2014.330075

http://dx.doi.org/10.14331/ijfps.2014.330075

New Discoveries and the Necessity of Reconsidering the Perspectives on Newton's Second Law

Journal of Nuclear and Particle Physics

p-ISSN: 2167-6895 e-ISSN: 2167-6909

2012; 2(3): 31-35

doi: 10.5923/j.jnpp.20120203.02

Definition of Singularity due to Newton's Second Law Counteracting Gravity

Scientific Journal of Pure and Applied Sciences

Vol 2, No 3 (2013)

It is notable that this is a scientific debate, which of subject or question can be true or false. Any questions or comments should not be expected to be introduced, it has been published. If you are among the hundreds of questions and discussions of a discussion to reach a scientific conclusion, discussions and questions have been inconclusive.

Dear Kwei

Newton's second law of motion pertains to the behavior of objects for which all existing forces are not balanced. So, in relations F=ma and W=Fx, F is net force.

Please take a new look at mass, energy and force. Mass and energy are not equal, as you know E=mc^2 , but what is important is that mass and energy are convertible to each other.

Work and energy are equal (W=Fx or Fdx=- dU, they have same unit and dimensions), I have not said force and energy are equivalence, force and energy are convertible to each other too.

As long as I am sitting on a chair, the forces are balanced.

I stand up and jump up, my energy will be converted to force and momentum of my body is changing. While I go to the top, my kinetic energy is converted to the force of gravity (you say that Kinetic energy turns into potential energy). When my velocity reaches to zero, I fall down and the force of gravity converts into kinetic energy.

Look at the spring and hand, the spring is pushed by hand. During the time that hands were pushing the spring, hand's energy converts to force.

In fact a lot of photons (electromagnetic energy) leave the hand and enters the spring. The momentum of these photons is transferred to the spring. Hands had lost momentum (and energy), and spring gained momentum and energy. Other example is pendulum.

The path of light around a star is another example.

When the light is closing to the star (in this example photon does not fall in stat, it is passing around the star), the force of gravity is converted into energy (like blueshift). When light is moving away from the star, the electromagnetic energy is converting to gravity force (like redshift).

According to quantum mechanics virtual photon carries electromagnetic force that moves with speed of light. Take a new Look at the Bucherer experiment. Relativistic kinetic energy increases to infinity when approaching the speed of light, thus no massive body can reach this speed. In fact when electromagnetic force applies on the electron, virtual photon (boson) convert to energy and kinetic energy and momentum of it is added to electron's energy and momentum. It is explainable by conservation laws of energy and momentum.

In reality is that in Boucherer experiment, an electron in acceleration gains energy and after exiting from the accelerator tunnel, because of collision with another particle or because of passing through a field that gives it negative acceleration, it loses the energy and in terms of mass it returns back to its former state. One could always use this experiment to prove relativity mass, but could not explain the real interaction between force and mass with relativistic mass. Same process happens for falling object in gravitational field.

The classical definition of energy that defines energy as the ability to do work, could not explain the interaction among the particle in high energies.

According relation F=d(mv)/dt, force is able to change the m and v, so what is the effect of m and v of F? In generally, how an object produces force?

How you explain the collision between two objects without considering that energy converts to force and vise versa?

Dear Kwei

Thank you, you have shared important notes about classical mechanics, relativity and quantum mechanics. I do not disagree with you.

There are various theories in physics, but nature is unique. This is not nature's problem that we have various theories; nature obeys simple and unique law. So, we should improve our theories.

Please consider that in last comment I have noted the Newton's second law only, (in fact acceleration, in other word F=d(mv)/dt). Motion is an inherent property of physical being (In the absence of external force).

First of all, what we know about acceleration? And what is the definition of acceleration? In physics, acceleration is the rate at which the velocity of an object changes over time that in classical mechanics is given by Newton's second law with a=F/m. In special relativity an accelerating particle has a world-line which is not straight. This is not difficult to handle. The 4-vector acceleration can be defined as the derivative with respect to proper time of the 4-velocity. It is possible to solve the equations of motion for a particle in electric and magnetic fields, for example. Accelerating reference frames is a different matter. In general relativity the physical equations take the same form in any co-ordinate system. In special relativity they do not but it is still possible to use co-ordinate systems corresponding to accelerating or rotating frames of reference just as it is possible to solve ordinary mechanics problems in curvilinear co-ordinate systems. This is done by introducing a metric tensor.

However, Newton and Einstein define the acceleration regardless of the structure of particles (in classical mechanics and relativity). This definition belongs to Newton era or macroscopic level era. It should be noted that the interaction between large objects (e.g. collision of two bodies) under the action of the quantum layer (in fact sub quantum level) has been done. Thus, according to quantum mechanics and mass–energy equivalence E=mc^2 , we must redefine acceleration. It means we should review the relativistic Newton's second law.

There are a lot unanswered questions and complex concepts in theoretical physics that the standard model and relativity do not have answers for and the physicists believe that it is due to the inability of theories.

Standard model of particle physics describes the fundamental particles, fermions and their interactions with one notable exception graviton. Any imagination of space without gravity effect (or graviton from quantum mechanical perspective), is away from the physical reality.

The vacuum of space is not empty. In fact, quantum theory predicts that it teems with virtual particles flitting in and out of existence. In QED, charged particles can emit and absorb virtual photons. Although these virtual photons can’t be observed directly, but the uncertainty principle overcomes this problem.

By using review of relativistic Newton's second law we can explain zero point energy and vacuum energy directly (without using the uncertainty principle). Also, it is a powerful tool to answer the unanswered questions and complex concepts in theoretical physics. According to the special relativity theory, nothing moves faster than light speed. Also, boundary between visible particle and invisible particles is light speed, where real space-time and virtual spacetime intertwine and interact with other. To do this, the following items are done;

1- Review of quantum vacuum and reconsidering the relativistic Newton's second law.

2- Describing the mechanism of virtual and real photon’s production in a quantum vacuum without using the uncertainty principle. There is much evidence that shows a quantum vacuum produces real photon.

3- Review of physical events from quantum scales to cosmological theories by using reconsideration of relativistic Newton's second law.

4- Describing physical being and time. It shows physical being and time are inseparable. In fact; every physical existence is a clock, some clocks have longer lifetime than others and some clocks are more regular than others.

Dear Kwei

I appreciate of your humbly, you are a honest scientist. I am glad know you.

Let me be honest, I do not know what a theory of everything is or human is able find a theory that it be able explain everything. As I said before, let's take a new look at relativistic Newton's second law. I have done it; maybe it will be interesting for everybody.

With Best Regards

Dear Kwei

It is a good start point. Please see following articles;

New Discoveries and the Necessity of Reconsidering the Perspectives on Newton's Second Law

http://article.sapub.org/10.5923.j.jnpp.20120203.02.html#Ref

Reconsidering relativistic Newton's second law and its results

http://gsjournal.net/Science-Journals/%7B$cat_name%7D/View/5518

Dear Kwei

As you know better than me, the laws of thermodynamics describe the characteristics for the transport of heat and work in thermodynamic processes. In fact, the laws of thermodynamics have become some of the most important laws in all of physics and other branches of science connected to thermodynamics. They are often associated with concepts far beyond what is directly stated in the wording. According review of relativistic Newton's second law, I have described thermodynamic laws and entropy by using the SQE (sub quantum energy) concept. But I it not easy to explain this new look in a comment. So, please see pages 60-62 of following link.

http://gsjournal.net/Science-Journals/%7B$cat_name%7D/View/5977

Dear Kwei

Thank you for your suggestion. You are right about Physical Review.

I have tried. Not recently. But many years ago they rejected my paper and said it ignores the principle of uncertainty.

They were right, because I am explaining physical phenomenon without using the uncertainty.

Dear Kwei

It was not only complaint, English writing was an other complaint. I know it is not easy job. I never used uncertainty principle.

In my opinion many physical phenomenon such as vacuum energy are explainable without using uncertainty principle.

Also, our research and understanding is limited by uncertainty principle and light speed c. Light speed in a vacuum is equal c only in observable physical phenomenon. I sent my personal email address for you, please check you researchgate box.

Dear Kwei

You are right. Let me explain some important notes about my work.

Of the first, I have published my paper in General Science Journal at 2006.

http://gsjournal.net/

Journal of Nuclear and Particle Physics, 2012

http://article.sapub.org/10.5923.j.jnpp.20120203.02.html#Ref

Scientific Journal of Pure and Applied Sciences, 2013

http://www.sjournals.com/index.php/SJPAS/article/view/602/pdf

International Journal of Fundamental Physical Sciences (IJFPS), 2014

http://cph-theory.persiangig.com/e931011-interactionrealandvirtualspacetimes.htm

I am looking forward your advices.

Dear Kwei

Following article is a breif of reconsidering relativistic Newton's second law and its results (also it is attachted to this comment.).

New Discoveries and the Necessity of Reconsidering the Perspectives on Newton's Second Law

Journal of Nuclear and Particle Physics, 2012

http://article.sapub.org/10.5923.j.jnpp.20120203.02.html#Ref

Thank you so much.

Thank you for your mention.

"you put VE/c^2 +0.5 mV^2" . Please mention the number of relation (equation) and page number that I have used. If it is possible for you. 

Dear Kwei

Thank you so much for your attention. May be there is a problem to download. I have looked on the file and Eq 12, there is not any number such as 0.5 in my paper. I sent a picture of Eq 12 with this comment (please see attachment). Also you can download PDF file directly of Journal site, please see following link;

http://article.sapub.org/10.5923.j.jnpp.20120203.02.html#Ref

Also, there is not (mdVdt), it is (m dV / dt), or mx(dv)/dt that it is force.

Dear Kwei

" left hand side is rate of change of mass, right hand side is dmC^2/C^2  =dm"

You are right, but in above of relation Eq 12, I have defined dm/dt=nmSQE, in fact it should be dm/dt=(nmSQE)/dt , but I have chosen dt=1, please consider to "Here one could correlate increased mass to the gain of energy in Newton's second law, i.e.:" (attachment). If it is a problematic concept, we can replace dm/dt=nmSQE by dm/dt=nmSQE/dt.

Dear Kwei

I agree with you, thank you. I have done it. Its results work better than before, especialy conversion force and energy to each other.

Please see attachment.

Dear Kwei

"I cannot see this in your expression." You are right, if we stop in this article and Eq 12. But it is a a new tool to answer the many of unanswered questions and complex concepts in modern physics. For examples; Singularity, quantum vacuum (without using uncertainty principle, review Friedmann equation and... that relativity (both special and general) and quantum mechanics are not able to answer.

Dear Kwei

I have published a few articles about what I mentioned in last comment.

Please consider that I will not avoid uncertainty. In fact uncertainty works at quantum level well. In quantum mechanics, we cannot ignore Probability, Statistics and Uncertainty, but they are not able to explain many physical phenomenon. So, we should pass of quantum level and enter to sub quantum level.

About personal email; I think AOL does not work in my area. Do you have other email address? If yes please send me a test in my personal email.

dear Jawadi and Kwei,

It is a good question. In deed, in reality these terms (energy and force) are very closed. In mechanique for example one classify forces in forces which conserved the mechanical energy of the system and in non energy conserved foces. for the first type it is easy to demonstarte that these forces are derived from the so-called field of force or the potential energy fonction, which is not the case for the other type. 

Dear Marzouk

Thank you for interesting comment.

"... classify forces in forces which conserved the mechanical energy..."

How we can explain it by using the quantum mechanics concept of force (bosons)?

dear sirs,

Currently, I am dealing with subjects which are far away from this question. but, in the past I was formed in the physic solid state. I remember that there are 4 main forces which govern the microscopic and the macroscopic physical systems: the weak interaction, the strong interaction, the electromagnetic force (Lorentz force) and the gravitational force. According to my previous lectures this was the big dream of the eminent researchers of the 20 th century such as M. Planck, Enstein, L. de Broglie, Heizenberg... to build a global theory allowing to study at the same time the microscopic and the macroscopic systems. since few years ago Garet Lezi affirmed that he realized this theory by using the representation theory and precisely by using the Lee groups (number 8 and 9). However, his theory supposed to discover new quarcks (neutrinos). I was very curious on the results of the latest experiment realized in the CERN to see if G. Lezi theory is good or not. But, the only result was the confirmation of the Higz boson.

Dear Marzouk

Modern physics is based on relativity and quantum mechanics. But there are some unanswered questions or complex concepts in modern physics. The questions that modern physics does not have answers for, and the physicists believe that it is due to the inability of theories.

This shows that the quantum mechanics problems is inseparable of relativity.

I tried from a new approach, turn out to merge the fundamental principles of quantum physics, relativity and classical mechanics through a new definition of rest state of particles like photon, and attempts to present the reasons and the possibilities of the existence of the superluminal speeds. So according to this new view some complex concepts and unanswered questions is explained.

Dear Kwei

You are most welcome.

Let me explain in following terms:

1- Reconsidering relativistic Newton's second law, is a development of relativistic Newton's second law. So, it is able to cover special relativity well.

2- It is able to develop Dirac equation, and explain zero point energy, Hawking radiation and virtual photon directly;

http://gsjournal.net/Science-Journals/%7B$cat_name%7D/View/950

3- It is able to explain path of light in gravitational field (curvature of space directly without using Einstein's field equations). It means we can explain curvature of space by using quantum mechanics concepts (attacment).

4- It shows how gravity cancels by Newton's second law and is ignores old definition singularity (zero volume and infinite density).

Definition of Singularity due to Newton's Second Law Counteracting Gravity

http://www.sjournals.com/index.php/SJPAS/article/view/602/pdf

5- It is able to review Friedmann equation

http://gsjournal.net/Science-Journals/Research%20Papers/View/5534

Beyond the Modern Physics and Cosmological Equations

http://gsjournal.net/Science-Journals/%7B$cat_name%7D/View/5651

6- It is able to develop QED by new look at vitual photon

Sub quantum space and interactions properties from photon structure to fermions and bosons

http://sjournals.com/index.php/SJPAS/article/view/678

And there more results that I have mentioned hrer.

However, please consider that I was alone (approximately) in this way. I agreed that they need to develop it.

In the end, you are most welcome to cooperation.

Dear Kwei

I agree with you. What is your opinion about Institute of Physics (www.iop.org)?

I think it is proper.

Together we write this article. please consider that my English is not good.

Dear Kwei

Ok, thank you for your help and advice.

I am trying to find an other co-author. I need time.

I will do soon as soon is possible. Let me count on your help.

Dear Kwei

Thank you for your suggestion. You are right, especialy it is new look at formal concepts.