Entropy.

The Effect of Time Dilation on The Second Law of Thermodynamics and Entropy.

Part 1.
Historical Note - 'Pre-Time-Dilation Physics'.

The Second Law of thermodynamics states that in natural circumstances heat always passes from a hot to a cold body and, in so doing, not all the thermal energy transferred is available at the cold body to do work. Another way of expressing this law is through the notion of entropy, which is thought to be an intrinsic inefficiency in the conversion of heat into work, an idea which has been extant for a century and a half, and has been thought to embrace all activity. It can be argued that these fundamental expressions were, like the first law, postulates, for they are interdependent and until now they have relied mainly on observation. They were assumed to be laws, being self evident truths, by virtue of repeated consistent results.

The observation and implicit question that has been the principal puzzle at the centre of thermodynamics is, why doesn't heat energy move from the cooler body to the hot? Various aspects of the question have been addressed by such luminaries as Nicolas Leonard Sadi Carnot 1796-1832; James Prescott Joule, Lord Kelvin, and Rudolf Julius Emmanuel Clausius, who were all born in the period 1818-1824. Their generation thrust thermodynamics to the forefront of scientific thought. In the fullness of time, Ludwig Boltzmann of the next generation of scientists strove to incorporate this branch of physics with others then starting to be developed.

Ludwig Boltzmann was born in 1844. His contribution was to establish a connection between the properties of matter on the large scale, that is to say, between Kelvin's and Clausius's thermodynamics and the separate atoms of matter on the small scale. Kelvin, Clausius, and their contemporaries were able to establish a large number of observational relationships between their many experiments on the transfer of heat and work. However, a comprehensive understanding of these relations has been slow in coming even with the assistance of Boltzmann's mechanistic explanation in terms of atoms. Boltzmann had a keener insight of the structure of matter than most of his contemporaries, bringing to bear new ideas on the deep structure of Temperature change; moreover, it must be remembered that he did this before the existence of atoms was generally accepted. His statistical mechanical theory suggested a relationship between the notional entropy or disorder and the degree of organization of the atoms and molecules of a given system. His ideas were scorned by his contemporaries and thinking his views on the atom would not become accepted and being tragically afflicted by instability and unhappiness, he committed suicide in 1906.

The work of these scientists is of historic importance as their observations and measurements established the laws of thermodynamics, which control every aspect of our day to day existence. However, the physics used to explain their observations was limited in scope being all pre time-dilation physics. In other words, they lived and worked in an age when flat Newtonian time was the order of the day, having no concept of the now well proven phenomenon of time dilation and the effect this has on energy. It left them free to conjecture on the arrow of time, certainly at the atomic or molecular level.

Historically the notion of the reversal of the arrow of time is a human invention. While we have never really expected broken articles to spontaneously put themselves together again, nonetheless, statistically speaking, such an event has been considered not impossible, just extremely unlikely. For instance, the complexity of a broken article would have to transform itself back once more, into the simplicity of the whole article. This event being considered so statistically remote that time is regarded as unidirectional, which is the same as saying that spontaneous processes are irreversible. For spontaneously occurring processes entropy was understood to be continuously increasing with time.

The view was commonly held in the past that at the atomic level, there is no reason for irreversibility; the atoms can take any direction they want. It was thought that at the atomic and molecular level, all processes were able to proceed in all directions. A time arrow could not be discerned at this level, but it made sense to attribute a direction of time to the changing aggregations of atoms and molecules. The debate still lingers among scientists and philosophers as to whether the notion of entropy can indicate an arrow of time. Although Boltzmann's statistical treatment provided a much deeper insight into entropy and irreversibility, many scientists criticized his approach, on the grounds that he used reversible mechanical laws of the movement of atoms or molecules in a gas to infer irreversibility. We shall see how the question of the directional flow of heat, energy and time is now resolved, by the application of time dilation and the Tempo field theory.

Part 2.
The Relevance of 'Time-Dilation-Physics' to Thermodynamics.

Classical thermodynamics does not worry about why energy is conserved or why entropy increases. Thus, these theories have been viewed as theories of principles and not constructive theories, as are gravity and the kinetic gas theory. Consequently, a model hasn't previously been thought necessary to configure the known end results. However, there is now the Tempo field model, which not only explains gravity, but also the first law of thermodynamics that is to say, why energy is conserved and cannot be created or destroyed. In addition, it explains the second law in such a way as to combine for the first time the Clausius and Kelvin statements. They are equivalent statements of experience, being two aspects of a single Second Law. It also unites the principles of thermodynamics with those of inertia.

The Tempo field theory embraces the fact that over the past century it has become well established that time can dilate (go slower) and also contract (go faster). An object's time domain, that is to say, the degree of time dilation or contraction it enjoys, depends on its state such as its temperature, speed and whether it is on or near a massive body. The greater these parameters the more dilated becomes the object's time. No longer can we regard time as being a flat continuum.

I submit that this takes on an important significance in light of the first law of thermodynamics, which states that the energy of a system is always conserved. If energy has to be conserved, while time can vary, then there has to be a way of transferring energy between two of these time domains, which have different time dilations, without breaking this conservation law. It is the consideration of such a mechanism that leads us on to the Second law, and the analysis of why heat always has to pass from a hot to a colder body and never the other way about. Answering this question by means of established physics, will elevate the First law on the conservation of energy and the Second law on the direction of the flow of heat, from postulates to proven laws.

The concept of this mechanism is totally new, being derived from the Tempo field theory, but the physics upon which it is based is common ground, the veracity of which has been established over several decades.

How then can the Tempo field theory explain why it is necessary for energy to be conserved? In that theory it is recognized that the energy of a body is commensurate with its time dilation. Accordingly, it is implicit, that if energy could be destroyed, then we would have the impossible consequence of vast amounts of time also disappearing, taking with it current events and processes. Fortunately such happenings are not a feature of our universe, and we can content ourselves with the knowledge that energy and time are constant features in our world.

The credibility of the Tempo field model is supported by the fact that in addition to explaining the First and Second Laws of thermodynamics, together with entropy, at the quantum energy level, it also, at the macro physical level, explains 'inertial effect', when mechanical energy is transferred between bodies. In so doing it achieves two of the most elusive goals in physics,- it unites the physics of the very small, at the quantum level, with macro physics at the large level, and then leads onto the theory of quantum gravity, (see 'Time- The Hidden Dimensions Of The Missing Physics' by Frank Atkinson).

Part 3.
The Application of Time Dilation.

Let us take for the purpose of illustration, two identical metal weights. If we heat up one of the weights, then we are imparting to it more energy. As a result of increasing its energy we are also dilating its time. This means all measurements that are made from its perspective will be made subject to that dilated time which, for the weight, is its real time. The real time of the weight that hasn't been heated will of course, remain contracted relative to the heated weight.

If, for ease of illustration, we ascribe exaggerated values to these time dilations, we can say that the heated weight's time is dilated to twice that of the cool weight's time. So that in comparative terms, one second for the hot weight, is equal to two seconds for the cold weight. (It must always be remembered, that the weights are not aware of time dilation, it is a comparative effect only, in either case a second is just a second, and is their real time).

We know that in nature energy can only take the course of least resistance, that is to say a body cannot, in natural circumstances, expend more energy in doing work than it has. So applying this axiom, it can be seen that heat energy cannot flow from the cold weight to the hot, because it would take two seconds of effort-energy, from the cold weight, to produce one second of result-energy, in the hot weight. The only direction or route that energy can be moved as heat, without the receiving body receiving more energy per second than the giving body has to give, is for it to flow from one hot-body-second of effort into two cold-body-seconds of result. Because the mechanics of this situation rely solely on established physical laws, it can be claimed that the Second law has moved from a postulate, to being a law in its own right. [It can also be stated that this explanation holds good from the macro level all the way down to the subatomic level, thereby uniting the physics of the large with the very small.]

This is fine from the point of view of the hot weight, but it leaves the cold weight in a no win situation. It cannot move its energy naturally across to the hot weight nor can it use the energy it receives from the hot weight with total 'second for second' efficiency. (This built-in inefficiency is the explanation for Kelvin's statement of the Second law). This brings us on to the question of 'entropy', which was the name Clausius gave to the phenomenon when it was first observed, but the apparent inefficiency was not understood.

We are concerned here only with the classical entropy of Clausius. Efficiencies for engines such as those driven by steam have always been found to be substantially smaller than 100%. To understand the reason for this, we first need to differentiate between classical entropy and the modern general usage of the term 'entropy'. For example, (see The Second Law of Thermodynamics, by Atkins), before we start up a steam engine to generate work, we have an amount of coal and a bucket of cold water. We fill the boiler of the steam engine with the cold water and ignite the coal in the furnace to heat the water. Steam will form and drive the pistons of the steam engine. In addition to the steam formation we also generate a lot of hot gases from burning the coal. After some time all the coal is burned and the steam engine cools down. In the condenser we have collected cold water from the condensation of the steam. Thus at completion of the process we are left with ash, a bucket of cold water and, of course, a certain amount of work we have generated by our steam engine. However, in its general sense, we have created entropy because the entropy of hot gases and ash is higher than the entropy of coal. We can also say that coal is a more ordered substance than the hot gases and ash it is converted into.

All this general entropy is in addition to classical entropy. We know that the First law demands that the amount of energy enclosed in the coal is converted into an amount to generate work and an amount that cannot be accessed to do work. It is this latter amount which is classical entropy. We have long been aware that it is this form of entropy which keeps even a notional frictionless steam engine, to an efficiency of less than 100%. Therefore, a grasp of this classical form, in terms of time dilation, is called for, if we are to fully comprehend it.

Part 4.
The Second Law and Entropy Explained In Terms of Time Dilation.

Over the same historical perspective of a hundred and fifty years it has been noted that when heat energy is transferred across from a hot to a cold body, not all the energy is available to do work. The formal restatement of this observation is known as the Kelvin statement of the Second law. No process is possible in which the sole result is the absorption of heat from a reservoir and its complete conversion into work.

The most important point to pick out of this statement of the Second law is what was regarded, at that time, as the dissymmetry of Nature between the hot and cold bodies, which is in fact the dissymmetry 'of time' that has already been mentioned. The law tells us that it is impossible to convert heat completely into work. So to keep within the law of the conservation of energy, (the First law), they had to bring the missing energy into their calculations under the name of entropy. We can now fathom what the problem is. It is all to do with the time differential as between the hot and the cold bodies. If one second worth of energy is transferred from the hot weight, only half of it can be used in one second of the cold weight's time. The unused half has to carry over to the next contracted cold second. It is therefore, something of a misconception to think of any part of the heat energy as being locked up. It is latent only in the sense that not all the heat energy can be used in the current cold-second, the balance being carried forward to the next second. So if an energy audit is carried out, it can be seen how the law of the conservation of energy is maintained. Energy is always conserved, when the comparative times are taken into account, but the energy can only be made use of relative to the recipient's time.

As we have seen the observation had been noted in the past, but because time dilation was not then known about, Rudolf Clausius had to rely on observation alone, the results of which he called entropy, (meaning to turn or change energy). The energy from the hot weight was referred to as Total energy, and the energy that the cold weight could make use of per second as Free energy, or the energy available to do work. Further observations by several physicists revealed that in spontaneous processes, the product of the temperature and the change in entropy, equals the amount of heat or energy that is in a non-available form and that entropy always increases. We now know that what is really meant by the expression, 'a non-available form', is that the energy flow is not the same per unit of time as between the hot body and the cold. This is due to the indirect effect of the heat energy itself making the units of time, as between the hot and cold weights, to have different comparative values. This work concluded with the misapprehension that energy has two states; free, or available, and bound, or latent, and that free energy always goes from free status to latent status. It appeared as if all energy eventually becomes latent. Indeed this is a significant misconception to put right, as in recent times it has been thought that this state at the cosmologic level, would give rise to a Heat Death as all the universe would eventually reach the same temperature. This state, if it could exist, would prevent all forms of energy transference, thereby precluding any mechanical or biological process taking place. In Part 7 we shall conclude by showing why this is a misconception. In the meantime in Part 5 we shall examine the connection between time dilation and temperature, and in Part 6 we shall examine the connection between the Second law and inertia.

Part 5.
Time Dilation and Temperature.

It is a well observed fact that nature is inclined to convert energy into heat. Electrical, mechanical and chemical energies all convert easily into heat. Consider for instance electrical energy being used in lamps and fires, mechanical energy being turned into heat by friction and chemical energy being released in the form of heat, as in burning. To understand why, we need to look at the nature of heat.

Heat is produced by the movements of atoms and molecules, and these can move in several ways, such as, linear velocity, vibration, and rotation. Temperature determines the intensity of these atomic and molecular movements; the higher the temperature, the greater the speed. In this way matter has been observed to accommodate an increase in energy by raising the temperature. This is why heat has been recognized as playing such a predominant role in the transfer of energy from one location to another: However, that is not the end of the story.

Historically the connection of the motion of the atoms and molecules with the dilation of their time has not been recognized. The connection of heat to the movement of atoms and molecules was discovered well after the First and Second laws were formulated, and it was not until much later, that time dilation was recognized and Twentieth Century scientists began to develop an understanding of it.

Our understanding of time dilation has progressed to the point where it is universally accepted that a body's time dilates when it moves and also when it is heated. The degree of time dilation of the body is specific to its state and consequently is unique to it, being independent of the time field around it, (See 'Time - The Hidden Dimensions Of The Missing Physics', and previous Paper on E=mc²).

I submit that this time dilation phenomenon originates at the atomic and molecular levels. That is to say, that the proportion, by which the atom's time is dilated by the increase in its velocity due to heating, is the same as for the entire body. This is because the body is merely the sum of its atomic or molecular parts. It can be deduced from this that the temperature of a body, which can be measured as the velocity of its atoms, (its atoms kinetic energy), is also a measure of the amount by which the body's time has dilated, (this is the body's own local time that is particular to it, and does not have any influence on the Tempo field).

To clarify this point on the degree of time dilation, there are two levels of dilation that need to be distinguished. The first is a basic level at a notional zero degrees absolute, that the mass of a body would have in the Tempo field, (which we will call Tempo time). This level is a combination of the body's own time field, increased by the strength of the universal Tempo field at its location. The second is the proportion by which this Tempo time is dilated due to the infusion of energy and can be discerned by the kinetic energy of its atoms or molecules, (kinetic time). Where the infusion of energy takes the form of heat we can make the following connection - thermal energy increases the speed of the atoms and molecules, which equates to both an increase in temperature (hotness) and kinetic time dilation. So the amount of hotness and kinetic time dilation parallel each other, and being correlative, are both measured by temperature.

Retrospectively it can be appreciated how the concept of entropy came about, in a 'pre time dilation' era and how it was used to account for certain observed phenomena that were otherwise inexplicable. As we have seen, among the foremost of these, were the questions, raised by Clausius and Kelvin respectively, in their statements on the Second law. The respective questions they raised were of why heat always moves from hot to cold regions, and why is it when heat is transformed into work, a kind of waste occurs as some heat gets trapped into a form of energy that cannot be accessed to generate work? Why this is so, is now solved in a single united explanation offered by the Tempo field theory that takes in both the statements of Clausius and Kelvin. The underlying reason for this perceived inefficiency set out in the Second law, is due to the natural dispersal of thermal energy across the time differential between two regions.

The Second law regards thermal energy as an established concept, and deals with its dispersal. Even though we might not comprehend the nature of energy, it is easy to comprehend what is meant by its dispersal. While we do not know what energy is, we do know why it must be dispersed and not destroyed. If it were not conserved, amounts of time, commensurate with the energy, would go missing from the Universe, taking with it relative events and processes.

As we have seen it is implicit in any dispersal system that it is not reversible. This requirement has been rationalized, over the last century, by the acceptance, that despite the possibility of energy travelling in such a way that, by chance, it ends up in a hotter region, it can be ignored, because the likelihood is so remote. This however, is not good enough as the, albeit, remote possibility of it happening remains. On the other hand, the Tempo field theory which has energy moving along the prescribed line from time dilation to time contraction gives an inviolable system that provides an incontrovertible arrow of time.

We are now equipped with sufficient understanding, to be able to comprehend the relation between the zero degrees absolute for temperature and the absolute zero point of kinetic time dilation, (the latter having formerly been thought to be a property of entropy). The phrase absolute zero when applied to temperature and absolute kinetic time dilation or entropy, reflects the fact that they can be measured with reference to a notional zero value. The Boltzmann's equation for entropy is, in fact, an expression for the absolute entropy which, while being totally counter to the classical entropic theory, is in close harmony with the Tempo field interpretation of time dilation. Boltzmann's equation contrasts with the classical definition that says we can speak only about a difference or change in entropy between one situation and another. Classical thermodynamics defines entropy, solely in terms of changes between states. It can have no exact zero value for a defined entropy.

We are now in a position to explain the difference between Classical and Boltzmann's theories of entropy and take it to a deeper level of understanding. Boltzmann's equation's ability to yield absolute zero is in fact an impossible situation to reach. To understand this we must consider the theorems of both the German physicist W. H. Nernst and Lord Kelvin on the Third Law of Thermodynamics.

Nernst's heat theorem states that at the absolute temperature of zero Kelvin, all atoms will occupy the lowest energy level available. If that were the case, all processes would become adiabatic because heat would no longer be exchanged. This means that for processes to occur at absolute zero, the change in entropy is zero.

That the zero condition cannot be reached is exemplified by Kelvin's Third law of thermodynamics, which states that we cannot bring matter to a temperature of absolute zero in a finite number of steps. Such a state can therefore, only ever be approached but never reached.

The illusory zero state can now be explained by reference to time dilation, for the kinetic time dilation of matter cannot be reduced to a zero amount. Relative to an external observer, it can only be reduced to an infinitesimal amount. The reason for this is, that such greatly contracted time, (or greatly dilated time), is always the real time of the matter. Any change or process, from the matter's perspective, naturally has to be done relative to its real time, which, for it, is as extensive as any other time. This is in complete harmonious symmetry with our understanding of kinetic time dilation for objects with greatly dilated time at the other end of the time scale. It is already well understood that an observer can perceive such objects (having a very high gravitational mass, or moving at a very high speed), to have almost infinitely dilated time.

Part 6.
The Effect of Time Dilation on Mechanical Work and Inertia.

We have seen that when heat is used to do mechanical work, scientists have detected a dissymmetry between the heat energy input and the work output. In the reverse direction however, when mechanical work is done to produce heat, they have not found a similar dissymmetry between the work done and the heat actually produced. This state is allowed for in the Tempo field theory. In that theory, as a consequence of the work producing the heat in the body also dilating the body's time, the heat and the time naturally have a common value and are always synchronized.

There are other cases where there is no time differential involved to create inefficiency. For example, in fuel cells the chemical energy enclosed in fuels is directly converted into electrical energy. Thus no heat conversion is involved at all and, as a result, the efficiency can be much higher than in coal fired power stations.

However, when mechanical work is done on a body otherwise than to produce heat, say motion instead, then there is a time dissymmetry. For example imagine a man pushing a frictionless body, like a hovercraft that is lifted a little off the ground. Ignoring air resistance, it will be the case that the more the hovercraft accelerates, the harder he will find it to transfer more energy to it, by pushing. The reason for this is that the foot that the man is pushing with at any instant, is always stationary on the ground and is therefore in a constant time domain, with relatively contracted time, while his upper body and the hovercraft are constantly having their time dilated the faster they go. If the hovercraft's time is dilated to twice that of the ground, then the man's pushing foot will have to generate two seconds worth of pushing-energy to produce one second worth of accelerating-result-energy at the hovercraft. It is this increasing time differential with acceleration that makes it more and more difficult to push the hovercraft, a circumstance the man recognizes as inertia, (see 'Time,- The Hidden Dimensions Of The Missing Physics' by Frank Atkinson).

So we can now recognize, that it is the case that the principles that govern the transfer of energy by means of heat and give rise to the Second law, are the same as the principles that govern the transfer of energy by mechanical means that give rise to inertia, these phenomena being in accord with the law of the conservation of energy.

Part 7.
How The Universe Avoids The Heat Death.

As we have noted, the abstract concept of entropy was derived from pre-time-dilation-physics. Being unaware of time dilation, naturally meant that those scientists who theorized on the subject of an entropic heat death, formed a picture necessarily different to reality.

In the pursuit of reality the model we can now apply to the transfer of energy between time domains, is the Tempo Field Theory. From that theory we can borrow a thought experiment to help us understand the effect of time on the absorption and conduction of heat.

The benefit of a thought experiment over a real one is that we can, freed from the constraints of trouble and expense, consider an extreme situation; for example, when a massive body is artificially heated to a uniform temperature. We can then consider what happens when the massive body cools down. This will give us a good idea of what will happen in the reverse direction, starting from a natural cool state. We will then have a clear indication as to whether nature could spontaneously attain the extreme entropic state. The following thought experiment illustrates why large scale matter cannot naturally become uniformly heated, by reason of there being a diminishing temperature gradient commensurate with its contracting time gradient.

Expense being no object in our thought experiment, let us borrow a very tall skyscraper to be our large scale matter. Now if we place atomic clocks at the ground, middle and top floors, we will find that they will each run at different rates. It is acknowledged throughout the scientific community, that the clocks will run quicker the higher up the skyscraper we go. So let's give exaggerated values to the three clocks. Let a ground floor second be equal to two middle floor seconds and equal to three top floor seconds.

Now let us by some artificial means, heat the entire skyscraper throughout to the same temperature, which would mimic the state it would have if it could spontaneously undergo total entropy. Because the building is at the same temperature at all levels, all levels must also have the same proportion of dilation to their Tempo times, (the Tempo time reduces the further away we get from the mass of the Earth). If we now turn off the means of heating the skyscraper, so that it is allowed to cool down naturally, we will find that the building will initially not conduct heat through its structure, because it is all at the same temperature. The skyscraper building will however, begin to lose heat to its outside surroundings, which will have the time dilations originally shown on the atomic clocks. So heat will be given out at a faster rate at the top of the skyscraper, where there are three seconds to every one at the bottom, (it is important to remember that each second throughout the building allows the same amount of heat loss, because the building has a uniform temperature throughout). This means that the fabric of the skyscraper will try to maintain an even distribution of temperature, by heat flowing up the structure as the building disproportionally cools. The effect of this will be to allow the temperature to reduce uniformly as it cools.

If we reverse this occurrence, it can be seen that the only way the skyscraper can be made to reach a uniform temperature, is by the artificial method of heating it at increasing rates from the bottom to the top. For example, if one unit of heat energy per second is required at ground level, then two units from the same source are required at the halfway mark where two seconds equal one ground level second and three units at the top level, where three seconds equal one ground level second. It cannot reach a uniform temperature from a single natural heat source, as multiple heat energies are required, delivered at increasing heights.

From all this we can deduce two things. Firstly, a total entropic situation creating a uniform temperature throughout the skyscraper cannot be naturally formed, because it will be the reverse of the cooling situation as seen above. The difference in the basic time as you go up the skyscraper means that it will absorb heat at different rates. This makes it impossible, under natural circumstances, for the skyscraper to attain the same temperature throughout its height. When the skyscraper is heated over its entire height from a single external source, such as the Sun, the bottom of the skyscraper will absorbe heat energy three times faster than the top, which will always cause a line of heat conduction up the building in the direction of contracting time. Secondly, this naturally occurring direction will create what we know as a temperature gradient, with heat always rising into contracted time.

This explanation depends of course, on it being possible for the heat radiation to eventually find its way out into a cold outer space. The next question is therefore, is outer space going to undergo an entropic warming up? Applying the Tempo field theory, we will find that the answer has to be no.

Given only that the universe is uniform on the large scale, with its energy constant and gravitational effect always positive, we find the following scenario when the Tempo field theory is applied. The electromagnetic radiation causing the heating effect from any heavenly body, when setting out across space and negotiating the Tempo field, will initially be gravitationally red shifted. Then as it continues to traverse the Tempo field across space, it will be slightly bent to and fro by the gravitational effect from the different strengths of Tempo field, caused by the presence of other heavenly bodies. Every time it is slightly bent, it will lose energy to the intervening heavenly body whose Tempo field is doing the bending. The loss of energy will be in quantum amounts we call photons. These free photons, while in transit to the intervening heavenly body, form a background radiation which we have detected and call the microwave background radiation. Eventually, the electromagnetic waves will be so diffused and weakened by the gradual loss of photons, as to have zero energy. They will have lost all their energy back to the mass of the universe that created them in the first place. The radiation in outer space is in a closed energy loop, and can never increase beyond the background level it now has. All this will occur in addition to the known falling off of the strength of the radiation at the square of the distance. This scenario holds good for models of the universe that are stationary or expanding. The only way there could be a heat buildup in the universe, is if the universe were to be a finite sealed unit and start to contract in size, so that the radiation within it becomes more intense. However, this would not be an entropic heat death but an energy heat death.

In conclusion, there is a curious anomaly, worthy of note. The modern debate on the possibility of an entropic heat death is precluded by the very principle that unwittingly gave rise to the notion of classical entropy in the first place, that is to say, time dilation.

For further reading on the above, including the authors ideas on a universe that is static on the large scale, see 'Time - The Hidden Dimensions Of The Missing Physics', available for review and purchase together with extensive free summaries on www.tempofieldtheory.co.uk