Conservation of Energy

The non-scientist will have heard of conservation, but what is the conservational law of physics? What is being conserved?

Energy pervades all physical systems, even the fabric of the universe is an energy blanket. This is why we say the vacuum is a physical sheet. But energy cannot be lost in this vacuum. Energy does not simply ‘’vanish’’, but only change form. If a bit of energy makes some solid matter, that matter must be just a differential form of conserved energy, so that when the matter is converted back to energy, you end up with the same energy you began. So energy changes, but it never vanishes.

Some countable quality of a system never changes its value, even if its form might change, so the energy the universe began with at some distant point in the history light cone, is the same energy the universe has today (1).

We therefore say, that the conservation of energy is a fundamental law which the universe must always obey. If it didn’t, physical theory would fail as some understandable quality.

The law of conservation, in courses taken at university and college level, take the mathematical form of:

T_e=KE+PE

Which says that the total energy T_e is yielded equivalently as the Kinetic Energy added with the Potential Energy, a form of the equation we saw in the second installation.

Now we will investigate impulse, which is defined as nothing but a change in momentum, which is itself simply the measure of a mass in motion. These terms and buzz-words may be hard to pick up, but read this over again if you find anything hard to digest. Studying Impulse will help us analyze a well-used topic in physics, which is the conservation of momentum.

Impulse

According to Classical Mechanics, (which by definition is a theory of physics which does not take into accordance the Uncertainty Principle (2)), Impulse is calculated as the integral of the force exerted on the system, the integration is with respect to the time:

J=∫ F dt

Where (J) is for impulse, sometimes denoted as (I), F is for force, and dt is the change of infinitesimal time units. Calculating this is relatively easy with a little understanding into calculus,

J=∫ dp/dt (dt)

J=∫ dp

Which then results in

J=Δp

Where impulse is equivalent to a change in the momentum (p). Assuming the mass remains constant, as in non-relativistic speeds, then this can be shown as:

J=FΔt=MΔv=Δp

Since

p=Mv

Back to the Conservation Laws

Now let us imagine you had two snooker balls, and you rolled one to the other ball, one can quickly surmise that they will collide. Traditionally, we call the first ball M_1 and the second simply M_2.

For two objects, just like two snooker balls to collide, their impulses interact; this means that their impulses apply to each other when some physical contact is at work. During such a collision, their impulses are equal in magnitude, but almost certainly in opposite directions, so we can mathematically state this as –

F_1Δt=-F_2Δt

(Here force is also assumed unchanged)

Which by substitution gives

Δp_1=Δ-p_2

So that would allow us to conclude

M_1v’_1-M_1v_1=M_2v’_2-M_2v_2

And if we substitute the right hand side for a change in momentum, we now have

M_1v’_1-M_1v_1=M_2v_2-M_2v’_2

After some mathematical simplification, we find that

p_t=M_1v_1+M_2v_2=0

Where p_t is the total momentum, and these equations state the momenta of the first term is equal to the momenta of the second action, and these state that even the momentum of a body is conserved.

(1) – In fact, how can the universe have a specific measurable energy? For this to be true, there would need to be someone outside the universe to measure it! This is physically true comment, and scientifically correct. It may change ones idea’s on how the universe manifests itself. Today, as there was just a few moments after the big bang (which was neither big, or a bang), there is about 10^80 particles, give or take a few tens. These particles are trapped forms of energy*, and these forms of energy has the exact same value they had before their transformations.

• In fact there is a theory which states that matter is but differential forms of trapped light. The idea is that even though we have many forms of different energy, such as gluon energy, the kind of subatomic energy that binds all of matter, solid matter which can be converted back to energy through antimatter relationships reducing it back to photon energy. So the Luxon Theory of matter (first proposed by Newton), states that high energy conditions (not so much collisions), created all the forms of solid and tangible matter we observe today.

(2) – The Uncertainty Principle was created by Mathematician and Physicist, Heisenberg in 1926, and his principle states that it is physically impossible for some observer to ultimately define complimentary states simultaneously, such as the position and the momentum of a physical system. His law is given as Δx•Δp ≥ h/2, where x is the position, and p is the momentum of the body. Define x with great accuracy, and then p is reduced as even more undefined. In fact, if you could the position x with total certainty, then the system will be made to have an infinite amount of momentum. Likewise, define p with certainty, then it is made to have an infinite amount of positions! You could know for certainty these values, if you are willing to observe the infinite qualities of position of momentum, which for a human observer is impossible.