Introducing Laws and Principles
In physics it is usual for the student to be introduced to what are termed 'laws' or 'principles' as these are to be the basis on which one builds an understanding of the physical nature of the world around us and, indeed, what we see as the enveloping universe.
Thus one is introduced to Newton's Law of Gravity, the Law of Conservation of Energy, Coulomb's Law, Newton's Third Law, the First and Second Laws of Thermodynamics, the Principle of Equivalence, the Heisenberg Uncertainty Principle, and so on. We are expected to regard these laws as sacrosanct because we are assured that those who have pioneered to discover the secrets of Nature have never encountered circumstances which run counter to what they prescribe.
Now, I expect you to question what I say in these tutorials, so I wonder if you are astute enough in your study of physics to see a flaw in what I have just stated. It may be that you have heard, though possibly not well understood, that Albert Einstein is renowned for discovering a new law, one formulated as E=Mc2, and for also introducing a new law of gravity to replace that of Isaac Newton. So, you see, as science advances laws can change.
Concerning those 'principles', these grow from tentative hypotheses until they appear almost self-evident as being based on fundamental truth consistent with the logic by which we reason. The Law of Conservation of Energy is often referred to as the Principle of Energy Conservation and otherwise as the First Law of Thermodynamics. It is so firmly established that it has triple foothold in governing how we build our picture of the scientific world. We shall not question its authenticity. Indeed, all you need to accept is that one cannot take energy from nowhere and apply it to our needs, nor, indeed, can Nature create matter out of nothing, given that Nature is governed by her own laws.
What you need then to ask yourself is: "What is energy?" Also, again if you are astute, you might ask the question: "What is nothing?" Is 'nothing' a way of saying 'space devoid of matter'? If so, then you are facing the question of the 'aether' and whether or not it exists, because the word 'aether' or 'ether', as used in this context, is merely a word we use to mean 'space devoid of matter'. Indeed, to quote dictionary definitions, the Concise Oxford Dictionary (a 1934 edition) that I have had since my school days describes the 'ether', in its physics connotation, as being the 'subtle elastic fluid permeating space and filling interstices between particles of air and other matter'. A Chambers Technical Dictionary (a 1958 edition) I have had for over 30 years has the entry 'ether or aether (Phys.): A hypothetical non-material entity supposed to fill all space whether 'empty' or occupied by matter..., but it possesses no properties in common with matter.' By 1992 in its first publication as Chambers Pocket Dictionary one reads: 'ether (also aether): a substance formerly believed to fill all space, and to be responsible for transmtting light'.
Is it not curious that a dictionary which is supposed only to tell you the meaning of specific words can reflect change in scientific opinion. The word still has the same meaning that it had in the 19th century, but between 1934 and 1958 it ceased to be 'a subtle elastic fluid that permeated space' and became 'a hypothetical non-material entity possessing no properties in common with matter'? Furthermore, between 1958 and 1992, it then ceased to be 'supposed to fill all space' and became a 'has been', something that had a fleeting existence in an earlier era when it was supposed to fill all space. That tells us that, whether or not there is an aether is not a question of fact, but a matter of opinion, as scientists tolerate it in their language only so long as they can influence what the word means. As a result the physics students of the 21st century are destined to live in a world of imaginary make-belief by thinking that the aether can have played no part in the creation of matter. Instead, they will learn that the universe emerged from nowhere, meaning from absolutely nothing, in an event billions of years ago which is termed the 'Big Bang'. Those who compile dictionaries can feel relieved at this, because a two-word expression need not have a dictionary definition. Otherwise, the word for that hypothetical event would need defining in terms somewhat akin to the definition of 'aether'!
Now, we will have none of that nonsense in our tutorials, because we will hold firm in taking that word 'aether' as being that something which is non-material but fills all the interstices of space not occupied by matter. We will use 'aether', rather than 'ether', because 'ether' has a different meaning in chemistry and we do not wish to confuse the terminology.
I assume that you, the reader, will bear with me as I advance my case, because I assume that you think, as I do, that it is logical for energy, whatever that is, to be conserved and so, if matter can be created from energy and appear in our experiments as if from nowhere, then there is something in that 'nowhere'. I note that scientists now believe that particles of matter, pairs of electrons and positrons, can appear 'as if from nowhere', though they hide all this in their mathematical equations and refer to the phenomenon as 'vacuum energy fluctuations'.
They still pretend that there is no aether but we, in these tutorials, will take a bold frontal position and challenge the views of those who lead would-be theoretical physicists into their own non-aetherial field of confusion. Our sights are on that 'energy' theme and the fundamental question of whether we can ever ourselves mimic Nature by tapping into that sea of energy from which Nature created the protons and electrons that form the matter we see as the universe.
Energy at Work
Now we come to a little mathematics in this opening lesson. You will know from Newtonian mechanics that the motion of a particle of mass m around a circular orbit involves an acceleration f equal to v2/r directed radially inwards towards the centre of that orbit. You will also have been told that action and reaction are equal and opposite by virtue of Newton's Third Law of Motion and that, by Newton's Second Law of Motion, the change of momentum of a particle is proportional to the impressed force and takes place in the direction in which that force is acting. So the rate of change of mv which, with m constant, becomes mf if this is the force directed towards the centre of that orbit and it has the form mv2/r. This is elementary, but we are in the world of Newton's laws, his first law merely saying that the particle would keep going in a straight line unless compelled to stray owing to the influence of external forces.
Where, you may ask, is that Principle of Conservation of Energy in this very basic physical picture?
To answer this we will now approach this same problem rather differently by making that principle our starting point and all we will do is to assert that there is a force F acting on the particle from a centre about which it moves. Let r denote, as before, the radial distance from that centre. Then F.dr is the negative work done by that force if dr is the small incremental distance by which r increases in a time interval dt. Had r reduced that force would do work but, owing to r increasing, it stores energy instead. Where does that energy come from and how is it stored?
The energy comes from the work done by the force mv2/r developed inertially by the tendency of that particle of mass m in trying to get back to its preferred state of rectilinear motion if it were free from that restraining force F. In creeping towards that state by increasing r the work done is simply m(v2/r)dr, but you may now ask "What about the change of kinetic energy?"
So you have realized that the kinetic energy lost by the motion of the particle m has to equal this quantity just deduced, which in turn supplies that energy F.dr stored as potential energy by the displacement. Note that this energy change is (mv2/r).dr. This reduces the problem to a simple mathematical exercise involving no laws of physics. Write vr=constant and form the differential expression v.dr+r.dv=0. Rearrange this as (r/v)dv=(-dr) and replace dr in the above expression for work done to get mv.dv as the added potential energy. Then from the integral of this, which is d(mv2/2), you will see that we have conserved energy by balancing kinetic energy loss against the potential energy gained.
From this analysis it is evident that, to conserve energy, the assumption
just made that vr is constant has to be an accepted fact.
Now take stock. We have only used mathematical principles based on a definition of acceleration f as dv/dt and combined this with a physical statement that energy is conserved to show that F=mf. We have not really gone beyond the recognition of what we may term the Principle of Inertia and it could be said that we have deduced that principle from the assertion that energy is conserved. Acceleration is, after all, just a mathematical (kinematic) definition based on what we refer to as distance and time. Why then should we be ensnared by the magic of 'the law'? It suffices to accept that energy is conserved and to recognize that there are three dimensions to physics, namely energy, space (as the cube of distance) and time.
The real challenge of physics is to explain everything in terms of three such physical dimensions, M. L, T, that is mass, length and time being those adopted by tradition, but energy, space and time being those I believe that we should adopt in our ultimate quest to understand all that can become known about fundamental physics. I even include here the representation of the polarity of an electric charge in terms of a time dimension because I see positive and negative polarity as in-phase and anti-phase states of a universal oscillation. However, apart from a few comments in Tutorial No. 2, I will not burden you by saying more on that theme in these tutorial lessons.
No one will ever be able to reduce physics to fewer than three such physical dimensions. They are not arbitrary, but are the facts of Nature. Ask yourself "What is energy?" and you can never answer that question, except by ducking the issue and reverting to your own different choice of three fundamental dimensions. Ask yourself " What is distance or space and to where does it extend?" and you will never find an answer. Ask yourself "What is time?" and whatever you try to say about clocks or the rotation of body Earth you will end up with no answer. Note that I am not asking how time is measured eg. "What is a minute?" That you can answer. No, I am asking you to tell me what, in physics, determines the onward flow of what we call time, meaning the universal rhythm of that something inherent in us all that gives us the feeling that time is passing.
Strangely enough we will in these tutorials come to unravel that mystery as to the steady universal rhythm of time, but we will not ever know what time really is other than a progressive change of state that is ever ongoing. You will see that in the quantized motion of the electric charges that constitute a structured system in the aether. Without time there could be no change in that aether. It would be a sterile system frozen in something akin to a solid state. Without space nothing could have form and without energy nothing could exist. Our physics has to build on the mysterious foundations of energy, time and space and express itself in terms of these three quantities, but the only law or principle that we really need build into our analysis could well be that Principle of Energy Conservation. Everything else is open territory for advancing physics and breaking through a few of the arbitrary barriers put there as man-made 'law'.
Now, take further stock of what has been said above and reexamine that statement that vr is a constant, coupled with the need for m itself to be constant. If you have heard that mass increases with speed owing to Einstein's theory of relativity, then you (quite rightly) will have your reservations, but we can readily dispose of that problem. It arises from energy conservation. Add energy to a particle that is free to move without any restraint and it gains in kinetic energy which is carried along with that particle. Once we can show that all energy is that of electric charge in motion and that an electric charge when accelerated will not, under any circumstances, radiate itself, meaning its intrinsic energy, then we can deduce E=Mc2 and the relativistic equation for mass increase with speed follows as a mathematical consequence. If you need convincing then begin by looking up my books or the reference [1976b] in the bibliographic reference section of these Web pages ('Inertia of a Non-Radiating Particle', International Journal of Theoretical Physics, v. 15, pp. 631-633 (1976)). So far as these tutorial lessons are concerned we are dealing essentially with motion that is constrained by forces which restrain freedom and, especially in the aether where that motion of mass is constrained to be simple harmonic in form, we know that mass does not vary with speed.
I can therefore come back to the point that if vr is constant and m is constant for that state of motion of m under the influence of that force F, we know that mvr is constant. It follows that we have deduced the Law of Conservation of Angular Momentum as it applies in Newtonian theory, rather than simply needing to accept it as a basic fact we have had to learn by indoctrination.
This, therefore, has been a lesson about principles and essentially about our scope for questioning physical laws. It is our starting point for addressing in the next tutorial lesson the question of linear momentum conservation and what that means in the context of 'perpetual motion', which keeps us on track in our interest in getting energy from 'nowhere'. However, we will address the task by using physics in a formal way, as the object of the exercise is to learn the scientific truths which govern us and avoid mischievous speculation.