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OK,
What is energy, and how does it manifest around us?
- Tue
First, let me preface this answer by saying that energy is a vast subject, not to mention the details of its manifestations, and entire books could be devoted to it. Obviously, there is not the scope here in this forum to expatiate to the point of delivering a book – or even a tiny pamphlet. Thus, my answer will be more in the category of an outline or sketch – with emphasis on some of the more esoteric or less known aspects, i.e. you’re not likely to find in standard textbooks. What I am hoping is that you can use this outline to then google a lot of the content and learn much more using that.
 will be such that the least time is taken.'))
Probably the best definition of energy possible is one provided by Noether’s Principle:
“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.
In ordinary texts, energy is usually defined in a limited way as “the ability to do work” but this operational definition depends in no small part on the fact that the total amount of energy in the universe can neither increase nor decrease – in other words, mass-energy is conserved. (Since, as an aside here, mass and energy display equivalence via the well known Einstein equation: E= mc^2) Again, this is the embodiment of Noether’s principle.
The manifestations of energy run the gamut:
Chemical, potential, nuclear, electrical, gravitational, kinetic, sound and heat – which is actually internal kinetic (i.e. heat arises from the internal kinetic energy of molecules or atoms within a system. The greater their velocity, the grater their collisions, and the more “heat” given off).
Energy transformations, say of one form into another, always act so that energy balance is preserved. Thus, the chemical energy in petrol is converted into kinetic or mechanical energy with heat given off. The original potential) energy latent in say 1 liter of petrol must not be different from the energy expended in kinetic, sound, heat,
A critical aspect of heat is that once energy transforms to that then it’s much more difficult to recycle it back to more useful forms. For most energy conversions, in fact, heat is the ultimate energy dead end. The recognition of this lies at the root of what’s called the ‘Second Law of Thermodynamics” (entropy law) but the point here is that this isn’t a genuine law. (Since technically, microscopically reversible laws governing the motions of molecules in a gas or system can’t lead to a law of irreversibility)
Other interesting and unusual aspects of energy:
1-Energy is relative. It depends on the frame of reference. For example, consider the energy of an object 'x' moving at velocity v in the simple diagram below:
--------v >(x)---------------
!
!
!
! Observer O
!--------------!-------------------> v
But, to the observer O moving in a reference frame with the same velocity, x appears at rest so its kinetic energy = 0.
In more technical consideration, on the basis of the Lorentz transformation (google!) 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. (E.g. Basically, the total number of protons plus neutrons in the universe has to remain constant. One can change into another, but none can just “disappear” as is the case for pions)
What about matter and anti-matter? Given an anti-proton (baryon number of -1) and proton (1) brought together, yields baryon number (0). So nothing prevents the combined masses from disappearing with conversion to energy. This is mutual annihilation. However, there is no feasible way we have to make much larger masses do this (say 1 kg masses) to enable a new form of energy.
4- Principles of Least Action and Least Time:
This is more an addendum which you can google the details of:
Fermat’s Principle of Least Time states that given multiple possible paths that a light ray can take, it will always take the one enabling least time for traversal.
Related to this is the Principle of Least Action:
The Action is defined as shown in the formula given in the uploaded image (along with the motion of a particle-body moving in the Earth's gravity). Thus, it takes the integral between times t1 and t2 for the difference between the kinetic energy (first term) and the potential (second) in the system. Technically, this difference (T- V) is called the "Lagrangian" (google!)
The result for all dynamical systems is that the correct particle path (among an infinite number of possible ones) will always be such that the least time is taken. If the least time is taken then S is minimized, hence also “least action”)
If you have further questions or need clarifications, feel free to ask.
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Philip A. Stahl
Expertise
I specialize in stellar and solar astrophysics. Can answer any questions pertaining to these areas, the spectroscopic analysis of stars – as well as the magneto-hydrodynamics of sunspots and solar flares. Sorry – No homework problems done or research projects! I will provide hints on solutions.
Experience
Have published papers on the relationship between sunspot morphology and solar flares; discovery of SID flares related to this, constructed computerized stellar models; MHD research.
Organizations
American Astronomical Society (Solar physics and Dynamical astronomy divisions), American Geophysical Union, American Mathematical Society, Intertel.
Publications
Solar Physics, Journal of the Royal Astronomical Society of Canada, Journal of the Barbados Astronomical Society, Meudon Solar Flare Proceedings (Meudon, France). Books: 'Selected Analyses in Solar Flare Plasma Dynamics', 'Physics Notes for Advanced Level'.
Education/Credentials
B.A. degree in Astronomy; M.Phil. degree in Physics - specializing in solar physics.
Awards and Honors
Postgraduate research award- Barbados government; Studentship Award in Solar Physics - American Astronomical Society
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