SPACE, AN UNSUNG PARTICIPANT IN THE UNIVERSE?
"I wish we could derive the rest of the phenomena of nature by the same kind of reasoning from mechanical principles; for I am induced by many reasons to suspect that they may all depend upon certain forces by which the particles of bodies, by some causes hitherto unknown, are either mutually impelled towards each other, and cohere in regular figures, or are repelled and recede from each other; which forces being unknown, philosophers have hitherto attempted the search of nature in vain; but I hope the principles here laid down will afford some light either to that or some truer method of philosophy" - Sir Isaac Newton.
It is human to acclaim only participants that are noisy or shiny or have a good or bad smell. But only near super-humans like Newton know that the most important participants may not fall into this category, which is why he says in the quote above that these participants can only be apprehended by the inner senses using the power of reason.
It is true that space has no taste, it has no smell, it has no colour and makes no noise. But can its participation in the drama unfolding in the universe be discerned using the same kind of reasoning from mechanical principles? The view that space is not a nothing comes broadly under the label 'substantivalism'. There are sub-groups, some of which include General relativitists, for whom the substance is then 'space-time', and not just space. Newton, himself in many respects was the arch-priest of this view. In his Scholium and the Principia, he put forward his views using causes, effects and properties for argument, section 5.
I have a substantivalist tendency and with good scientific reasons of my own. This thread is for cosmological topics, but as it has been alluded here that space is nothing, I think it necessary to make some counter presentation to the rational and lucid but IMHO misleading arguments claiming space is nothing. Not to repeat Newton's arguments, I present here evidence from what we can see and evaluate with our eyes - evidence from gravitational orbits, which if interpreted dispassionately indicate the possible roles space may be playing, aside the cosmological roles ascribed to it.
1. THE SHAPE OF ORBITS
Motion according to Newton's first law can continue perpetually unless a frictional force acts to bring the body to rest. Orbital motion was desired to be analogous to the linear motion of Newton's first law of motion in a straight line and would consequently be circular in shape (the form that preserves an equi-potential orbit) and continue perpetually without being driven (a sort of perpetuum mobile?). Alas, orbits are not circular but elliptical in shape. Kepler also desired a circle, but Mother Nature presented us with the ellipse. Perhaps, there is a puzzle in this elliptical gift?
Reasoning from mechanical principles implies such a shape of orbital motion is not according to Newton's first law. The motion is under action of a force or of forces.
2. CENTRIPETAL/ CENTRIFUGAL FORCES
In gravitational orbits, Newton mathematically showed that a centripetal force equal in magnitude to mrω2 was operational, where m is the mass of the orbiter, r its radius from the hub and ω its angular velocity. A centripetal force, like all forces has direction, which is radially inwards to the centre of the circle.
From the laws for circular motion in which a centripetal force is present, there must necessarily be a centrifugal force which will be equal and opposite in effect to the centripetal force so that no resultant force is acting and the body can keep moving with uniform motion equivalent to a state of rest. Switching off the centripetal force makes the orbiting body spiral away and switching off the centrifugal force makes the orbiting body spiral inwards under its momentum collapsing ultimately into the hub.
Unfortunately, in gravitational orbits this centrifugal force that prevents collapse of the circular motion is ghostly and not easily discernible.
Newton seemed to also realize the compelling need for this centrifugal force to balance the effect of gravity and maintain the planets in their circular paths. Seeing no other source, he suggested that the centrifugal force must be arising directly from the motion of the planets themselves. The difficulty and illogicality of this however becomes apparent on three grounds. Firstly, since the centrifugal force must be acting on the body to oppose the centripetal action of gravity which also acts on it, it would appear unusual for the generator of the force, i.e. the orbiting body, to be the subject of the force as well. The idea from Newton's third law is that an object experiences force because it is interacting with some other body or agency and not with itself. Therefore a body cannot give rise to an action force which also serves as a reaction on it. Secondly, a force arising directly from a circularly moving body must be in a tangential direction to the orbit, being a vector like velocity. To balance and be equal and opposite to the centripetal force however, we see that the centrifugal force or its component must act radially outwards on the orbiting body, while the centripetal force acts radially inwards on it. Whatever momentum or force arising from the orbiting body's motion can therefore not be the source of the centrifugal force since it would be acting tangentially at right angles to the orbital radius and cannot have any component in a radial direction to oppose the centripetal force, in the way the centrifugal force would be required to do. Thirdly, a body moving in accordance with Newton's first law of motion as planets are deemed by some to move, while it can be subject to forces whose resultant on it must then be zero, cannot generate force from its own motion or state of rest which would be contributory to the same resultant state of rest or uniform motion. Conclusion: The motion of the planets is not the source of the centrifugal force, whose source must then lie elsewhere.
3. THE MOON KEEPS FALLING BUT DOES NOT REACH THE GROUND!
Newton got deserved acclaim by showing that the acceleration with which objects fall under gravity at the earth's surface was related to the centripetal acceleration towards the earth of the moon in orbit, taking the inverse square law into account. In other words, like objects here on earth the moon is also falling under the influence of the same force of gravity.
Assuming the inverse square law and therefore an acceleration due to gravity on the moon due to the earth to be approximately 0.0027ms-2 instead of the terrestrial value of 9.8 ms-2, we will expect from the most optimistic view of a constant and non-inverse squarely increasing acceleration of 0.0027 ms-2 and using s = ut + ½ gt2 that the moon will fall and reach the ground in about 6 days, if it is indeed falling under the earth's gravity as Newton demonstrated, given that the moon is about 3.8 x 108 metres away and is being acted on by gravity alone and no other force. Unlike the historical apple however, it is long overdue for the moon to fall on our heads, yet something prevents it from doing so. Who or what is this benevolent agent preventing this?
4. MORE CONTRAVENTIONS TO NEWTON'S SECOND LAW OF MOTION
Newton's second law of motion states categorically that acceleration due to force A must take place in the direction of that force. This implies that observed deceleration of an accelerating body acted on by a force A must be due to another force B acting in the opposite direction and cannot be due to the continuing action or stoppage of action of force A. Furthermore, Newton's law of gravitation stresses that although gravitational force can vary in magnitude according to the inverse square law, it has a constant direction of attraction which cannot change. Therefore any change in the direction such as observed repulsion between masses must be due to the presence of another force.
In gravitational orbits, the sun-earth for example, we see the satellite respond to gravity and move closer to the hub as it approaches perihelion. However instead of continuing in that direction, moving closer to the hub, what we see is a kind of repelling action at perihelion. It is as if the direction of gravity has changed. Instead of attraction, we get repulsion.
To simplify and illustrate, we can use the simple pendulum with a visible bob but an invisible string as an example. We expect things to proceed in an orderly manner and for the pendulum to swing from side to side, which is what happens. However, an observer oblivious of the string because it is invisible must be baffled by the ordinary course of events. This observer knowing about gravity is not surprised by the downswing but he must indeed be alarmed if on reaching its lowest point, instead of continuing downwards in the direction of gravity, he sees the bob swing upwards. He must therefore question, whether gravity can reverse its direction, thereby repelling the bob upwards. As the bob accelerates downwards, increasing in velocity, by what means does it stop accelerating and instead start reducing in velocity and decelerating to gravity? The observer cannot be blamed for suspecting a ghost at work. It must however be an orderly ghost, since the pendulum has a period which remains regular. A less superstitious person would however acknowledge that a force yet to be identified but whose characteristics we can discern from our observations is at work and acts on the pendulum bob in a manner opposite to gravitational action thus preventing what will amount to a contravention of Newton's second law and his proposal of a universally attractive nature for gravity.
Analogously, reasoning with these mechanical principles we can suspect that a force opposed to gravity is at work in orbits. It is this force that will prevent contraventions to Newton's laws that will occur and explain the mysterious deceleration to gravity at perihelion. The observed deceleration to gravity will represent a contravention of Newton's second law and his law of universal gravitation if no force is deemed responsible. Newton's second law therefore, compels the presence of another force in addition to gravity to serve as one of the return forces operating the orbit as with oscillations of the simple pendulum.
5. ANGULAR MOMENTUM CONSERVATION DOES NOT WORK AS AN ALIBI
Although using considerations involving angular momentum conservation, angular velocity can increase when the radius of the orbit reduces, it cannot be used to contravene Newton's second law and convert angular acceleration to angular deceleration without the intervention of a force.
A further reason for the non-attractiveness of angular momentum conservation as an explanation for the seeming contraventions of Newton's second law and the universally attractive nature of gravity is somewhat of a mathematical nature.
Angular momentum is given by mr2ω, where m is the mass of the orbiter, r is the radius of orbit and ω is the angular velocity. If the angular momentum is exactly conserved and mass is constant, r2ω will be a constant and ω will be inversely proportional to r2. This will result in disharmony with the inverse square law and Kepler's third law, both of which have the relationship between angular velocity, ω and radius,r as
ω2 = k /r3, where k is a constant.
If angular momentum conservation is to be used in explaining the reduction in angular velocity with increasing radius and the sequential increase in angular velocity with reducing radius, then (1) Kepler's third law will be invalid and T2 will be directly proportional to r4 instead of r3, where T is the period of oscillation and (2) the inverse-square law will be invalid and instead will be an inverse-cube law, with gravitational force proportional to 1/r3.
There is also nothing in the laws of momentum conservation compelling momentum conservation in the direction of deceleration at perihelion as it can be equally conserved in the direction of continuous acceleration and continuous reduction of orbital radius as the orbiter spirals inwards. The angular deceleration seen at perihelion must therefore be the outcome of an orderly force.
Kepler's first and second laws, imply that what we observe in the motions of planets is governed by law and cannot be attributed to random perturbations. That is, even in the absence of perturbation, Kepler's first and second laws with the alternating increase and decrease in angular velocity and the alternating acceleration and deceleration of planets to the sun's gravity will hold. Conservation of angular momentum features prominently in the quantum scenario, but as we cannot observe directly what is occurring, we refrain from using it for argument.
6. CONTRAVENTIONS TO THE LAWS OF ENERGY CONSERVATION - ANY FREE LUNCH?
When the radius of orbit of a satellite reduces, the kinetic energy (K.E.) increases while the potential energy (P.E.) reduces as P.E. is converted to K.E. and the satellite is speeded up.
However because P.E. decreases by twice as much as the K.E. increases by applications of the known dynamical equations below, there is on the whole, a loss of energy when the orbital radius of a satellite reduces.
Assuming the zero of potential energy in the gravitational field of the hub is at infinity by convention,
P.E. of mass in orbit = - GMm/r
while
K.E. of satellite in orbit = GMm/2r
where G is the gravitational constant, M is the mass of the hub, m is mass of the satellite and r is the radius of the orbit.
Einstein's General relativity similar to Maxwell's electromagnetic theory (for charges) says that acceleration of masses in gravitational orbits leads to loss of energy which is radiated away as gravitational waves.
The consequence of the above is that when the satellite accelerates to gravity, it should spiral and the gravitational orbit progressively collapses. Contrary to what physics predicts, orbiting bodies alternately gain and lose energy, with energy and potential being lost as perihelion is approached and energy and potential being regained after perihelion and as aphelion is approached. Ordinarily we could explain away what we see in orbits as conversion of potential energy to kinetic energy and back but for inability to account for the energy loss and the force that makes the orbiter rise to the same height in aphelion as in previous orbital cycles.
The loss of energy and potential due to the effect of gravitational force is comprehensible. What is not accounted for is the source of the energy that makes the orbiter to regain the same potential since the initial energy lost must have radiated away as heat or gravitational waves and is not available for re-conversion to potential energy after perihelion.
Also generally speaking, inter-conversion between potential energy and kinetic energy requires a force to effect the conversion. The simple pendulum once again is a good example that illustrates this inter-conversion. While gravitational force effects conversion of the potential energy of the bob to kinetic energy as it downswings from one end, a different force will be needed to convert the kinetic energy at its lowest point back to potential energy in the upswing. This is provided by the tension force in the string. In gravitational orbits, the force that converts the maximum kinetic energy at perihelion to the maximum potential energy at aphelion is mysterious but it must exist. If we could identity the force then all would be well and if there is no force, then at least we must identify the source of the energy replenishing the orbit.
Putting this quantitatively, from equations for P.E. and K.E. above,
Total energy of a satellite in orbit in joules (J) is given by
P.E. + K.E. = - GMm/2r
Using the sun-earth system as an example and given the mass of the sun as 2x1030kg, mass of the earth as 6x1024kg, the earth's perihelion distance as 147x109m and aphelion at 152x109m, we have:
Total energy of earth in orbit at aphelion (P.E.and K.E.)= - 2.63x1033J
Total energy of earth in orbit at perihelion (P.E. and K.E.)= - 2.72x1033J
Therefore, total energy at perihelion is less than at aphelion by 8.94x1031J as expected from orbital dynamics. This is energy lost per cycle between aphelion and perihelion which represents 3.4% of initial energy at aphelion. If no new energy is added, the next aphelion will occur at a distance of 147x109m instead of the previous 152x109m.
Also although the rate of energy lost is likely to increase more rapidly, if we optimistically assume a steady loss, the orbit is expected to collapse after 29.4 cycles (100/ 3.4 ), that is after about 30 years, but this has not happened billions of years, since the earth formed and started orbiting the sun. Rather what we see is that approximately the same quantity of energy lost is replenished and the aphelion distance is fairly maintained at least for more than thirty cycles. Who is the replenisher and provider of this free lunch?
7. SOME POSSIBLE CHARACTERISTICS OF THE UNKNOWN AGENT PRESERVING THE ORBIT
i. Must be invisible
This is obvious as we cannot visualize the agent responsible for maintaining the orbit. It is certainly not matter, but may be anything else.
ii. Must possess force that can oppose gravity.
The agent must provide force capable of opposing centripetal force of gravity and give the balancing centrifugal force. It must therefore tend to oppose gravity and instead promote spreading tendencies for gravitational masses in space.
iii. Must be able to supply energy
The agent must be capable of supplying energy to replenish the orbit and prevent collapse. In doing this, it must at a stage in the orbital cycle intervene to prevent collapse by causing deceleration of the orbiter to gravity and increasing its potential.
iv. Must be omnipresent in time and place
The agent must always be available to carry out its functions. Since all the orbital cycles are prevented from immediate collapse, the agent must not be a temporary one but present all the time, for all the cycles and as well throughout the visible universe wherever orbits either of stars, planets and galaxies occur.
8. PARTICIPANT IN MOTION IN DIGITAL OR SIMULATED UNIVERSES
In Simulated Universes, the space between objects can be represented, e.g. by pixels on the computer screen for example. When we observe objects move on the screen, the pixels representing the object change to the character of those representing space, while the pixels representing space in the direction of motion, change to the character of pixels representing the moving object. In other words, the cooperation of the pixels representing space is required for motion to take place. It is my opinion that something similar happens in a real digital universe, with slight difference.
This is responsible for my frequent reference to Zeno's Dichotomy Argument and his Arrow paradox, both of which try to show that in some sense motion cannot occur without the fullest cooperation and participation of that which we call space. The Dichotomy paradox suggests motion cannot commence without the cooperation of the first pixel, nor will it end without the cooperation of the last. While the Arrow paradox says something similar, that the Arrow would not even leave the pixels constituting it in the first place unless our concept of motion undergoes a revolutionary review.
Akinbo
(This post are mainly excerpts from an old unpublishable paper of mine in response to John Prytz insistence that Space is Not-thing).
