# Relationship between mass, energy, and a force?

I've never truly understood the relationship between mass, energy, and force. I know what each of the three are, I just don't fully understand how they interact with each other.

For example,

1. How do the forces effect energy?

2. How do they effect mass?

3. How are force related to the four fundamental forces?

4. If all the forces in the universe were eliminated completely, would all matter stand still?

5. How does energy move from particle to particle?

• A writer friend tells me he gets interested in this question at this time of year: "How much energy is my mother going to spend trying to force me to go to mass?" Dec 28, 2015 at 20:50

There is so much detail one could go into, but I will try to point out the most important aspects:

1. The concept of force is closely related to energy: force can be seen as something which changes the energy of a system by doing work on the latter. In kinematics, work is defined by a spatial integral over the force acting on an object:

$W=\int\vec{F}\cdot d\vec{x}.$

Force is defined as a change in a particle's momentum. Since this implies a change in velocity, it will also change its kinetic energy. Another example would be thermodynamics, where a force can change the internal energy of a system.

Within quantum field theory (QFT), the energy of a particle depends on its interaction with other particles. Such an interaction is a quantum mechanical generalization of a classical force and albeit the classical and quantum cases share certain features, there are crucial differences. For further explanation, see my answer to question 3.

2. Thanks to the theory of special relativity we know that mass and energy are equivalent and related by the famous formula

$E=mc^2.$

The terms mass and energy are often used synonymously.

3. To describe the four fundamental forces, we have two theories: general relativity, which is a theory of gravitation (GR); and the standard model of particle physics (SM), which is the theory of the electromagnetic, strong and weak interactions. Classical force laws (Coulomb, Newton) arise as low energy limits of these non-classical theories.

In the context of GR, gravitational force arises as an effect of the curvature of spacetime caused by the presence of energy/mass. The force itself can be considered fictionary and a result of the fact that objects follow the shortest paths through spacetime (geodesics).

The SM is formulated in the framework of QFT, and as such one describes particles in terms of fields. The energy of a particle depends on the presence of other fields (in this case, one speaks of "coupling", the theory is said to be interacting). The concept of a force is generalized in such a way that one now talks about particle decay. Particles decay into others according to certain laws with a certain probability that can be calculated (e.g. beta decay).

4. There can be motion without force. By the definition of force as a change of momentum, one can imagine a universe consisting of particles moving at constant velocity with respect to each other.

5. Within QFT, momentum transfer is described in terms of scattering (for which you can calculate amplitudes) and decay (the process of a particle falling apart into other particles has to respect momentum conservation).

Based on our best available theories including the Standard Model, the answers would be:

Ans 1. Forces between particles arise from the exchange of force carrier particles which are bundles or quanta of energy of a particular kind of field.

Ans 2. Higgs boson, the force carrier of the Higgs field gives mass to fundamental particles.

Ans 3. The Standard Model contains the particles, each of which is an excitation of a particular force field. The electromagnetic force can be described by the exchange of photons. The nuclear force binding protons and neutrons can be described by an effective field of which mesons are the excitations. The strong interaction between quarks can be described by the exchange of virtual gluons. Beta decay is an example of an interaction due to the exchange of a W boson, but not an example of a force. Gravity is not a part of the Standard Model, but it is thought that there may be particles called gravitons which are the excitations of gravitational waves.

Ans 4. If all the forces in the universe were eliminated completely, I think we would have any matter, let alone the idea of matter standing still. There would be nothing to hold up elementary particles to form matter.

Ans 5. By movement of force carriers of the respective force field which transfers momentum from one particle to the other.

We all weigh (so many) pounds or kilogram. Weight is one of very many FORCES (F). Force is Mass(M) times acceleration(a). ..... The Earth attracts us to its center using the FORCE of weight via the acceleration called "g". It varies slightly depending on location. Given our weight and the acceleration of the Earth, our body's MASS is found by M=F/a Our bodies have Mass, a computer has Mass, everything that has weight has Mass, To move a Mass a certain distance, like moving a car, we need ENERGY which is contained in the fuel. To do that we need a Force and the distance(d) we moved the Mass for a certain Time(t). Different units are used for energy; electrical energy, for example, is in Kilowatthours (look at your electricity bill). Heat energy is in Calories. There are many sources of Energy.

there is a short answer. there is a long answer. the long answer is to get a degree in physics.

there are also intermediate answers. those depend on the theory you want to look at. most importantly though, nobody on this planet knows the exact answers to your questions. they are research topics in physics.

one short answer could be: mass, energy and forces are synonyms.

how can that be? especially how can a force be energy or mass? well, in modern physics forces are described by interactions. those interactions in turn are described by so called interaction particles and what they do. we can watch them and what they do by letting particles collide in huge machines, such as particle colliders.

then we can do lots of advanced math and engineering to hide the fact, that we don't actually know the answers to those five questions above.