## Wednesday, March 24, 2010

### The Laws of Physics In a Nutshell

The laws of physics may be described best as “the basic laws of the universe” – since the total of accumulated evidence (e.g. gravimetric, spectrographic etc) discloses they apply everywhere in the cosmos. Alas, it is not a short list – but grouped according to different aspects: mechanical, thermal, electric-magnetic, etc.

Students have often asked me in the course of lectures: What laws constitute an essential list, say for a text book of physics or science? I reply consistently that the book must reflect or embody the basic laws we know of, else it can’t be described as any book of physics, or science. Are these laws rigorous? Yes, they are – and at the end we will also see by way of examples how and why certain reported “claims” can’t be justified because they violate one or other of these laws.

Let’s begin with the basic laws of mechanics – embodied in Newton’s laws of motion:

1) Any body at rest or in uniform motion remains at rest or in uniform motion unless acted on by an outside force.
2) The acceleration of an object is directly proportional to the resulting force acting on it (F = ma)
3) If 2 bodies interact, the force that body 1 exerts on body 2 is equal and opposite to the force that body 2 exerts on body 1.

Newton’s law of universal gravitation:

Every particle in the universe attracts every other particle with a force directly proportional to the product of the masses, and inversely proportional the square of the distance between them. It may be written:

F = G Mm/ r^2

where G is the universal Gravitational constant, M, m the two interacting masses, and r the distance between them.

NOTE: the behavior of freely falling objects, or what is colloquially called the “law of gravity” is actually a special case of the universal law applied to Earth and employing Newton’s 2nd law, such that:

F = ma = mg = GMm/ (R(E)^2

where M is the mass of the Earth, m an object on it and R(E) the radius of the Earth.

By algebra (m cancels on both sides):

g = GM/ R(E)^2

and if the body is at some height h above the surface (h added to the radius to get R) we know:

R = h + R(e)

so

F = GM m/ R^2

Basic laws of energy, heat – thermal behavior:

Definition of Energy:

Operational : "The ability to do work" - e.g. E = F x d (force acting in a direction x displacement in that direction)

Ideal definition: (Noether's): “Energy is that quantity that’s conserved because of time-displacement symmetry”

The last segment, “time-displacement symmetry” refers to the constancy of physical laws in time. Time goes on, but the laws of physics retain a constancy of their properties within it.

Law of conservation of energy-mass:

The total amount of mass-energy in the universe in a system remains constant.”

This includes as a generalization the first law of thermodynamics, e.g. that internal (heat) energy is conserved, i.e. if two bodies are in thermal contact – and at different temperatures- the cooler body will have heat energy transferred to it, while the hotter will LOSE heat enerhy.

The Second law of thermodynamics (entropy law) is simply stated as:

The entropy (degree of disorder of a system) increases in all natural processes

Thus, for example, gasoline once burnt in your car engine cannot be captured from the exhaust gases and used over again.. Also, any energy process will also have a large part of any energy produced coming off as unusable waste energy. There is no way, or any process that can deliver 100% usable energy.

Side Notes:

1-Energy is relative. It depends on the frame of reference. For example, consider the energy of an object moving at velocity v. But, to the observer O moving in a reference frame with the same velocity, the object appears at rest so its kinetic energy = 0.

In more technical consideration, on the basis of the Lorentz transformation the energy E’ in a new frame will depend on the energy E in an older frame according to:

E’ = y_o(E – v_o p_x)

Where v_o is the velocity and p_x the momentum in direction (x). The factor y_o =

m(o)c^2 / [1 – {v_o/c)^2] and m(o) is the rest mass.

The point is that the energy in the new frame E depends on the momentum in the old frame, p_x. If this momentum is not conserved, then energy won’t be conserved in the new frame.

2- Regarding the “rest energy”: this is typically revealed in processes wherein particles are created then quickly destroyed with energy release. For example, the pi mesons.

The typical pi meson (call it pi) lasts 10^-16 sec then vanishes yielding two gamma ray photons in its wake,viz.

Pi -> gamma + gamma

Thus, rest energy is real energy and is capable of doing work. In the case of the pion above, the total mass 2.4 x 10^-28 kg, is converted to electromagnetic energy.

3- The “total conversion” of mass into energy isn’t feasible since it would violate the conservation of baryon number.

Law of Conservation of Linear Momentum:

In the law of conservation of linear momentum- let two masses m1 and m2 collide with each other with respective velocities v1 and v2, then the total linear momentum before collision must equal the total linear momentum after. Thus:

BEFFORE: m1v1(i) + m2 v2(i)

AFTER: m1v1(f) + m2 v2(f)

Where (i,f) denote initial and final values, so: P12(i) = P(12)f

Note the above law applies whether a collision is elastic or inelastic. The difference is that in the latter case, the mechanical energy (i.e. kinetic) is not conserved because some will be lost as heat due to friction.

Conservation of Angular Momentum:

This law applies to rotational motion. It states that the total angular momentum of a system is constant if the resultant external torque acting on the system is zero:

Thus IF: (SIGMA) d(T)_ext/ dt = dL/dt = 0

Then: Ii(wi) = If (wf )= const.

Where Ii, If are the initial and final moments of inertia, and wi,f denote the angular velocities.

The law (expression) is valid for rotations about a fixed axis or about an axis through the center of mass of the system.

Basic laws of Electricity and Magnetism:

Coulomb’s Law: Any 2 charged particles (e.g. electrons, ions) attract (or repel) each other with a force inversely proportional the square of the distance between them and directly proportional to the product of the charges (Q, q)

F = k Qq/ r^2

where k is a constant, Q, q the charges, and r the separation. Note the similar mathematical form to the universal law of gravitation. The difference is that the latter is ONLY attractive, while the Coulomb interaction may also be repulsive. (E.g. two like charges will always repel)

Gauss’ Law: The net number of electric field lines passing through a surface that encloses a net electric charge is proportional to the charge enclosed within the surface.

Other Electric –magnetic laws:

“There are NO magnetic monopoles. All magnetic field lines must end on one or other of two poles.”

Changes in magnetic flux always produce an induced electric current (Faraday’s law)

Moving electric charges in a closed circuit or loop give rise to a magnetic field (Ampere’s law)

From Maxwell’s E-M equations:

At every instant, the ratio of the electric field magnitude to the magnetic field magnitude equals the speed of light, c”

Generalized law for E_M waves arising from Maxwell’s equations, laws:

“Electro-magnetic waves are generated by accelerating charges and consist of oscillating electric and magnetic fields which are at right angles to each other and also at right angles to the direction of wave propagation.”

Basic laws of quantum mechanics:

Whenever electrons change position (energy levels) in an atom, energy is given off in a discrete packet such that:

E = h f

where h is the Planck constant, and f is the frequency of the emitted light (photon) corresponding to the difference of energies in the levels.

This may also be written: E = hc/ L

where L is the wavelength

Every material particle has associated with it a de Broglie wave with a wavelength

L = h/ mv

where h is Planck’s constant, and m the mass, v the velocity.

All atoms represent systems that can be described in terms of probability waves, such that these waves disclose the probability of where the constituent electrons are at any given time.

Pauli Exclusion Principle:

“No 2 electrons in an atom can ever be in the same quantum state, that is – no two electrons in the same atom can have the same exact set of quantum numbers (n, l, m(s) or ml)”

Einstein’s mass-energy equation: E = mc^2

“In any fusion or fission reaction, the total rest mass of the products is less than the rest mass of the reactants – the change (decrease) in rest mass appearing as energy released in the reaction.”

Thus: Delta E (change in energy) = [m_R - m_p] c^2

where the bracketed quantity on the right side is the difference in rest masses between reactants and products.

Special relativity:

Principle of Relativity: All the laws of physics are the same in all inertial reference frames.

Thus – this implies “the speed of light has the same value in all inertial reference frames

Thus- - in no inertial reference frame can any material object exceed the speed of light.

Time dilation: All moving clocks run slower relative to an identical clock in a stationary frame.

Finally, the “fourth dimension” is NOT a basic law. Rather it arises out of the Principle of Relativity – by virtue of referencing all physical actions, laws in terms of TIME as well as the three dimensions of space (x, y, z).

In fact, in principle, given the four dimensions x, y, z and t ANY ONE could be “the fourth dimension”! (The order of choice is not important, what’s important is that four dimensions are required to specify and follow physical laws between difference reference frames).
Examples of violations of one or more laws:
In the Bible:
i) Jesus' walking on water (violates Newton's laws, and law of gravitation)
ii) Lazarus back from dead (violates the 2nd law of thermodynamics)
iii) Feeding the 5,000 (violates the law of conservation of mass-energy)
iv) Water into wine (violate basic laws of quantum mechanics, including Pauli Principle)
Conclusion: If the Bible illustrates any such violations it cannot be taken literally or in the least as a scientifically informative source. It must therefore be a book of myths and legends. The physical laws as shown are inviolate, and there is no room for compromise unless counter-evidence can be provided or the miracle passages proven.