Dissertation On Time

[Aethelwulf]

A Dissertation

On the Nature of Time

 

 

Albert Einstein (1879–1955):

 

Zeit ist das, was man an der Uhr abliest.

 

''Time is what a clock measures.''

 

Abstract

 

This is effectively an investigation into the nature of time, one which involves a deep analysis of what it means in the quantum and relativistic interpretations which plague physics today; one so being the ''Time Problem'' as it is well-known. We will be establishing that physics is seriously hinting that there may be no such thing as time - that even spacetime itself is not fundamental. What is fundamental is even hard to understand in the context of post Plankian Scales since as I shall show, there is a new discovery linked to the so-called ''Time Problem'' of relativity and quantum mechanics, butone which also involves an inherent problem with energy as well. In fact the latter here is involved in a few solid arguments suggesting that there may not be such a thing as a conservation of energy law for the universe, because timelessness would suggest that you can perform the symmetrical processes of Noether's Theorem to translate the energy since time is a conjugate of energy under this theorem. This would suggest that energy is not conserved in the universe which is supported by current mainstream belief. I will also explain why General Relativity might not even be fundamental, that the attempts to unify it with quantum mechanics will ultimately fail because of a misunderstanding of gravity itself being fundamental.

 

 

 

Part One

The Time Problem in a Nutshell

 

So it is probably best to first explain the ''Time Problem'' which has been speculated upon for many years now, ever since it was discovered that when you quantize Einstein's Field Equations you get back what is called the Wheeler de Witt equation 1). But what makes this equation so damning that it is considered a ''problem?''

Well, the equation itself should come out like that famous wave equation, the Schrodinger equation, but with one exception; it does not have a time derivative. The Wheeler de Witt not having a time derivative is believed to be hinting at this strange prediction for the universe because the wave function is global, meaning that it is the wave function of the universe.

 

1) [math]H|\psi > = 0[/math]

 

Many physicists have attempted to do smart things to solve the problem, like a process called ''reparamaterisation,'' but not every one is satisfied with the situation. There are more problems than just this, the equation is inherently real and not complex. Since the Wheeler de Witt equation describes gravity, this would mean that the field is real (in the mathematical sense) and not complex like the remaining three forces of nature.

 

There is an interesting thing to consider. Fields which are time dependent are always complex. You can check the validity of this statement yourself, by comparing the Time Dependent Schrodinger Equation and it's time independent counterpart. One is complex (the only which depends on time) the other is real. So those who believe that the Wheeler de Witt equation is correct are under the assumption that gravity in the fundamental form is not a complex field. However, this is based on one assumption; that gravity itself is even fundamental.

 

This will be something we will be tackling in this work which will talk more deeply about the Time Problem. This part was really only intended to give you a quick oversight of what the problem actually entails. We will also be studying the work of Julian Barbour, who has, for most of his life, investigated the theory that the universe is essentially timeless.

 

Part Two

 

Several Concepts of Time to Consider

 

Normally on the right hand side of the Wheeler de Witt equation as we have already explained, we would not see the presence of a time derivative. However, this equation should have ended up something like your usual energy Schrodinger equation, but for an entire universe, this does not seem to be possible where one can assign time to it .

 

The fact there is a vanishing time derivative, this had led to the interpretation that the universe, time at least, from a global sense does not exist, that the universe is really about either a static interpretation of time, or one that is completely timeless. This can seem at first like a big of a gee whiz moment, because time being static seems very exotic. However, there maybe still a new way to view this and I will tackle this from Fotini Markoupoulou's stance of time, which we will cover soon and to which I will add new concepts. I don't add them frivolously, this is still a real science.

 

Now, of course, there maybe those still out there shrouded by the veil called time, they cannot see past their own experiences. We do afterall sense time pass, so why should we believe time does not exist? Surely if we experience time, there must be some corresponding physical application to the world at large. Well, over the years of studies I have made, this ''feeling'' of time might just be that: simply a feeling. The psychological arrow of time actually explains really well why we may feel a ''directionality to time''. This directionality of time is the arrow of time many people abuse, thinking it has a real consequence on physical reality. As observers, we experience a local time, but what does it mean when we talk about a ''global time'' or a ''local time''?

 

Global Time

 

A global time, is a time encompassed, or experienced by clocks inside of the universe. It is concerned with many groups of systems and never one alone. If one could sit outside the universe, we would actually view it as a static system. In a way to justify that claim, which Barbour does not do in his paper but does mention this fact, is through the weak measurement physics. In quantum cosmology, Prof. Steven Hawking believes we must view the universe like an atom. So indeed, if we were to view the universe from outside [1] then the energy content would not change. In fact, if we actually could, then we could measure the universes energy. It is well-known that the universe in totality cannot have a very well-defined energy unless someone was to actually measure it; and if no superintelligence exists then perhaps we may assume that the energy cannot be defined.

 

Local Time

 

Local time is the asymptotic time everyone comes to agree on: we all experience time, this cannot be denied. Time seems to be strictly local in this sense, local to bodies like ourselves, including even electrons and perhaps other particles which experience zitter motion. This internal clock was in fact verified according to David Hestenes in an experiment. By this reasoning, many believe, including myself that time is not in fact global, that global time does not exist and if anyone can speak about time, it must be purely local. But I now raise an important question. But even though we believe time exists locally, there are biological reasons we even experience time in the first place.

 

Since we are on the subject of observers, we may as well talk about one special part of the human observer which points to evidence that time is really something we experience and does not exist independent of the human. There is in fact a biological reason for experiencing time as I just explained - there is a gene regulation inside the brain called the Suprachiasmatic Nucleus (This is one of two gene regulators inside of the brain which is responsible for sense of time). This is one prominent reason among the scientific community to why we even sense a time pass. But if we sense time pass, then surely we are simply ''imprinting'' our experience on the outside world as though it was a solid phenomenon of the objective reality?

 

There is while we are on the subject, the idea of an arrow time. I do not believe a true arrow of time exists, however if one can understand what is called the ''Psychological Arrow of Time,'' one can understand why we may think or perceive there being a future and past to events that time itself inextricably moves from one place to another in a linear fashion. This is one of the biggest misconceptions to this day, because time in relativity is in fact geometrical - it is not linear. This was of course realized when Minkowski unified space and time into a single description of the dynamic fabric of the universe.

 

So while we come to experience time in this world of entropy, the human mind appears to have evolution that selected the brain as used by the human was much more valuable to have a sense of time. After all, as Fred Alan Wolf himself once said ''the mind without a sense of past or future, is no mind at all.'' The linear illusion of time is ingrained within our ability to understand cause and effect. In fact, the human brain itself because of this has the capability of extracting knowledge also in a causal manner.

 

Another thing to realize, is that to have a ''true cosmological arrow of time,'' you'd need to have a center to the universe in which you can draw such an arrow. We now know (and have known for a while) there is no such thing as a center to the universe, unless you considered every point in spacetime as the center! So in this sense as well, time does not have an arrow per se. It seems that we are biased simply because our minds would be drowned in insanity if we had no such linear sense of time, the ability to understand ''ordered events.''

 

Geometric Time

 

And thus the question is asked, why does it seem like time exists then? Why should we experience time if it does not exist? What makes us so special?

 

It's not that we are special per se, but we are in an important energy phase of the universe, called the low energy phase. The low energy phase happened late in the universe's history - do not mistake ''late'' as implying a time however. This is where the English language breaks down and we need to use different approaches to explain what we mean. There can be change in Julian Barbour's eye's, but there is no such thing as a time. So can we reconcile change without time?

 

Yes, we can. It may not seem obvious at first, but things like the zeno effect gives us evidence that even if time really did exist, systems don't need to change.

 

Fundamental Time

 

So what is fundamental time? Fotini Markoupoulou created this type of time understanding. However, she takes this fundamental time as real, but I take it as not being real. The reason why I do not agree with Markoupoulou on this one, is because of her own reasoning. Geometry did not appear till very late in the universes history, so we must infer that time did not exist either if indeed Minkowski space is the correct representation for the low energy epoch. Of course, for this reason, fundamental time would be the application of a time dimension when the energies in the universe were very high. But if geometry did not exist, then the universe was born without time. Therefore time is not really fundamental at all. To explain this better, I labelled this as ''induced time''.

 

Induced Time

 

So, if I am saying time did not appear until geometry appeared, am I saying time really exists? The answer to this is ''no'', because induced time is not the same as a real existing time. If you like, the time anything experienced in the low energy epoch is in fact a by-product of slow moving systems; it appears when matter appears. Geometrogenesis is the science of physics and cosmology concerned with the appearance of matter. It wasn't until the phase space of the universe broke symmetries did the original photon fields or other radiation fields gave way to the matter fields which now dominate our portion of the universe. Therefore, geometrogenesis does in fact dictate, not predict, but dictate that time could not exist before the dimensions of space emerged: time is after all a space dimension, it is called the imaginary space dimension - an imaginary leg off the spacetime triangle.

 

Then we must ask, well, if geometry and matter appeared late in the universes history, we ask also then whether time appears from such a geometry? If so, then time is emergent, it is an induced phenomenon which appears alongside the usual suspects: those being space and time. We cannot infer gravity directly because gravity can exist without matter. So curvature can still exist without matter - it just comes in a different guise, a radiation field which don't even have clocks which can tick off real time. (Hopefully everyone knows that photons do not experience time, including any type of radiation.) Relativity cannot deal with time and radiation together in such a way.

 

 

Part Three

 

No Time Must Imply no Energy

 

And so for now, we must understand energy in the context of time. The absence of energy therefor, would imply the absence of time and vice versa; but why is this important?

 

Well, I have a proposal to make. Because Einstein's equations generate a motion in time that is a symmetry of the theory and thus not a true time evolution at all, we seem to be left with a timeless model. The universe would then be timeless.

 

Yet, if this is true and the universe is truly timeless, then surely this would mean that energy is devoid in our universe as well?

 

The counter-intuitive facts just keep on trucking from the soil of Relativity, but this is one fact I must state. The inability of finding a time evolution for the universe would result in a faulty premise concerning whether it has an energy.

Fred Alan Wolf asked the question in his book Parallel Universes

 

''How can the universe have an energy?''

 

He further makes his point clear by saying that for the universe to have a defined energy someone would need to be sitting outside the universe to actually observe the energy. There is a way out of his problem and the paradox of timelessness and energy which I proposed above.

 

The whole universe, can only be observed by two possible ways: that is by someone either sitting outside the universe, or by someone who is sitting in the infinite future. Usually both examples are considered impractical [1] because they seem to purport to unphysical concepts.

 

Usually when we talk about a system not conserving it's energy, we talk about the system not having a symmetry. A symmetry would let a langrangian density be

 

[math]\delta L = 0[/math]

 

That is a conserved energy from symmetry, but if you add something into the equation that break's this symmetry then you no longer have a conserved quantity. So maybe, just maybe Noether's Theorem is not applicable to the universe because it does not retain the symmetry allowed to express the system as a conserved quantity - the only way to do this is if the universe has a time derivative... but if the Wheeler de Witt equation is in fact right and the universe is timeless, then you cannot conserve the universes energy! A very interesting link which must be taken into consideration, because it has been proposed recently in a paper that there is evidence that the universe could be leaking energy. So Global time does not exist, so energy in a Global sense does not exist either!

 

There could be something more sinister to realize perhaps, that maybe the universe is not a conserved case of energy. This statement however just seems to hard to believe ... or does it? The universe is now receding faster than light which seems to indicate that our universe is using energy at a faster rate. In doing so, it might be conjectured that on the crux of things, the universe is not conserving energy like a ground state atom might and thus will quantum leap sometime in the future and give up it's energy. Odd to think of a universe quantum leaping, but this has been the literature in quantum cosmology which attempts to describe the universe like a particle.

 

Part Four

 

''Time is redundant as a fundamental concept.''

 

Julian Barbour

 

 

Not only is time redundant as a fundamental concept, but if we take the Big Bang seriously, then we are forced to think that space itself cannot be fundamental. Wheeler's Geometrogenesis would actually agree with this premise, because in geometrogenesis geometry appears only when the universe begins to sufficiently cool down - it is at this point matter itself appears.

 

Just think about the implications of this. They are quite profound - it would mean that General Relativity is equally redundant in explaining the beginning of the universes origins in terms of geometry. May it be then, of no surprise that all attempts at unifying general relativity with QM has profoundly escaped the grasp of those intrigued with such idea's, perhaps because the application of geometry itself at the beginning of time is totally redundant? As Markopoulou has mentioned in her essay submitted to FQXI, motion arises as a symmetry of the theory in general relativity, it isn't a true time evolution through diffeomorphism invariance within the theory which is like being able to ''shuffle coordinates together'' without bias.

 

Remember, if you don't actually remove geometry, at the very beginning, we find singularities with the incomprehensible and totally unphysical concepts of an infinite curvature in a single point. There cannot be such an infinite curvature if space and time are not fundamental so this does seem to be a breakdown of General Relativity. So we are, perhaps only just beginning to understand why a theory of everything has seemed so evasive.

 

Let's explore what we mean in relativity when we are talking about geometry. We are of course, referring to Einstein's famous field equations. To measure curvature, you require a mathematical equation called the Ricci Curvature Tensor. It uses in the equation, very complicated Christoffel symbols which are by definition, the gravitational field itself. The Christoffel Symbol looks like '' Γ '' and they come in what is called, ''Christoffel symbols of the first kind,'' and those by the ''second kind,'' so as you might imagine, there are many different kinds of them. Of course, many of us have learned that the gravitational field is in fact the same thing as speaking about energy or mass. This comes in the form of the stress energy tensor which makes an appearance in Einstein's famous field equations. They attempt to explain how much curvature is present with a certain quantity of mass, which may depend on size or even density. The denser an object is, just like a Pulsar (a very dense star, about the size of New York) have incredibly strong gravitational fields and therefore posses very strong curvatures. As Markopoulou has mentioned in her essay submitted to FQXI, motion arises as a symmetry of the theory in general relativity, it isn't a true time evolution.

 

Once you have determined how much curvature is present, you can then calculate the motion of particles in the gravitational fields, which follow what are called geodesics. An interesting point to make, is that even though curvature is present, the shortest distance between two points will always be a straight line!

 

Now, one reason to think that General Relativity is not fundamental in it's treatment of gravity is not only because the unification between quantum mechanics has not been fruitful but that General Relativity deals with the world at large not generally the world of the small (quantum). General Relativity is also still a classical theory, meaning that it does not take into consideration the uncertainty principle, a cornerstone of quantum mechanics.

 

And so, with our quick summery of curvature, we can see it is written into the laws of nature as we understand it from General Relativity, but if time and space are truly not fundamental concepts, then relativity in it's usual form must break down - in fact, if we applied the equations to the beginning of time, we reach a point, as I have noted before, a point of infinite density and geometry. This is called the singularity of the Big Bang and for many years, many scientists have seen it as a ''break down'' of the theory on very small scales.

 

Going back now, I explained how no time description for the universe would imply no energy conservation. The two are inseparable fascets of Noether's Theorem. Again, we asked the question before, how can the universe have an energy any way, unless someone was to observe it? Things in QM's cannot have observables like energy until they have been measured. The measurement problem of Big Bang, may not be a problem at all, but rather a hint that things like, space, time and even energy are not fundamental concepts at all. There is in physics also, the Null Energy condition.

 

If all the negative matter cancels out every positive peice of matter, such as the zero-energy universe. In particular interest, it is in fact the Minkowski metric (the four dimensional manifold) which implies zero energy. The reason why the Minkowski metric implies the null energy condition (2) will require only a few steps. We begin with an equation which has been selected because it is a result of the Schwarschild's metric

 

[math]E = Mc^2 - \frac{GM^2}{2R}[/math]

 

If one sets the mass term to zero, all you have left is the metric. This is a very simplified version of the null enery condition but has been a theory in physics for a long time now. At least, in hindsight for this work, we know that mathematics seems to allow the notion that the universe may not only consider energy not being conserved in a universe but that fundamentally it might not even exist.

 

So as bizarre as it all sounds, space, time and energy itself may be things emergent in the universe, they have not always been the fundamental ingredients of the initial ''moment'' of the universes existence. These may very well be considered ''problems'' for the unification of physics. Indeed, singularities are said to posses (in some literature) an infinite amount of negative energy... and an infinite amount geometry (curvature) yet this prediction of relativity is at odds with the counterintuitive fact that there was only point in the very beginning, so general relativity contradicts itself quantum mechanically-speaking.

 

Another existing problem (I did say there was quite a few) is known as the Flatness Problem in cosmology. Basically, in every direction of spacetime we observe, it appears mostly flat. Now, Einsteins equations actually deal with curved spacetime so there seems to be a blatent error in the idea that General Relativity should work on very large scales. Things like Dark Matter may just be a breakdown of relativity on such large scales. General Relativity in other words is only good at approximating local gravitational effects, not global ones. So not only should we consider the impossibility of quantizing Einsteins Field equations into a complete unification but we should also consider that General Relativity only works well locally or at least, not on very very large distances.

 

But the problem is deeper than that unfortunately. As we have established, quantizing the Einstein equations leads to the Wheeler de Witt equation which is supposed to describe gravity in a fundamental sense for the universe. But if the universe is mostly flat, how quantizing equations (involved with the curvature of the universe) be the correct approach? At best, because our universe is mostly flat then it appears it probably would be best to quantize the Newtonian limit for flat spacetime whose energy would satisfy;

 

[math]E = \int_v T_{00}\ dV[/math]

 

The integral is taken over the volume, T(00) is the time-time component of the stress energy tensor and dV is the differential volume. This permits to quasi-static systems, those concerned with very little to almost no gravitational wave influences. Keep in mind, there are of course no evidences for the existence of gravitational waves - they only appear in Einstein's theory with no experimental confirmation. It is a current research program to try and find evidence for these waves, one reason they may appear so allusive is because they may have a bandwidth outside of our detection.

 

When one tries to incorporate flat spacetimes, (or approximately close to it), the metric coefficients are pretty much Minkowskian flat spacetime, where in the realm of weak gravity, the vacuum looks flat in every direction (or in physics language, it looks flat globally).

 

So perhaps this is the equation we should quantize and perhaps equally quantizing the equation might be a more appropriate tool when describing the universe since it is flat globally in a Newtonian-like limit. This is only a suggestion and I haven't taken any time to try and quantize the equation. But it would be interesting to see the results.

 

Without going to deeply into these problems, maybe the idea that the universe has one clock is erroneous. Perhaps time in the Global sense does not really exist but there is motion and change calculating just a sum of all clocks inside that system by locally gauging them? Well, Julian Barbour believes something similar.

 

Julian Barbour has tried to promote the idea that there is no such thing as time itself, but rather all there is, is change. He arrives at an equation which rids any kind of time description ''t'' by using the fact that the speed of a body is not the ratio of it's displacement to an abstract time increment but to one which involves displacements of all the bodies in the system. By doing this, he rids his use of time describing motion; the irony perhaps is that the motion becomes the true definition of time. Most interesting of all, is that his theory predicts that time is no longer measured by particular individual motions, but by a sum of all the motions which is a very relativistic situation. If we use Julian's revelation that equations can describe change without time, then perhaps the universe can be described similarly without a Global time, but perhaps we can retrieve the important dynamics by taking into account all the displacements of the bodies inside the universe?

 

The interesting thing about this proposal is that it cannot work for radiation. I haven't heard Barbour mention this himself, but I am quite sure he is aware of this fact. The reason why is because in special relativity radiation particles move at lightspeed and therefore time does not pass for them due to Lorentz time contraction. In other words, time is stretched for them so much that not a single period of time passes for a photon. A popularized way to imagine this, is that the photon's birth is simultaneously it's death. But again, a breakdown of relativity happens, at least in the counter-intuitive sense. If a photon does not move in time the special relativity must be saying that it does not move in space either, because they appear inseparable. However, the counter-intuitivity lies in the fact that an observer in the lab can watch a photon move from one point in space to another. This contradiction in relativity has never been properly given an answer as far as I am aware.

 

However, matter does experience time. In fact, particles which move at light speed have been classified as ''Luxons'' and slow moving particles, like protons and electrons have been classified as ''Bradyons,'' the root word brady literally means ''slow.'' It is these particles according to relativity which have mass which can act as clocks in the universe. According to geometrogenesis, these clocks of matter did not appear until after the radiation era when the universe cooled down. It was around the same time geometry appeared.

 

Going back to Julian's suggestion that ''time'' does not exist, only change in the universe measured by the displacement of particles I created an equation that would help pave some kind of way to describe this. Before I present the equation, I must remind the reader concerning the concern of the gravitational field not being real (ie. it is not complexified) when quantized. I have tried to point out, that gravity might not be fundamental but instead emergent. Particles with mass, can act like clocks, so my equation needs to take into consideration a few things. One of them being is that it needs to describe the displacement of particles, for a four dimensional case (since it is time dependent now) and is governed by a wave function. The full derivation can be provided if asked for, but for the sake of keeping this dissertation as simple as possible I will present only the equation today in it's full form

 

[math]i\frac{\partial \mathcal{L}}{\partial \dot{q}}(\delta d_i) \nabla^{\mu} \nabla_{\mu} \psi = \dot{m}\psi[/math]

 

Since the universe is approximately flat we may consider this as a flow equation along a surface involving a number (a very large number [math]10^80[/math] particles) which is represented by the displacement ''d''. This flow equation describes a four dimensional case (which can be seen from the use of the d'Alembertian) and the wave function describing the statistical nature of this entropy is global. The small delta symbol attached to the displacement is basically saying we are taking small increments, just as Barbour teaches in his own theory. The equation is also complex, but keep in mind all time-dependent fields are inherently complex. The ''L'' in the equation describes the ''Langrangian'' which is the energy of your system; q' is a generalized coordinate. In fact [math]\frac{\partial \mathcal{L}}{\partial \dot{q}}[/math] comes from describing worldlines which obviously has a lot to do with the history of particles and their displacements relative to each other.

 

You can also write this equation using the quantum action

 

[math]-i \hbar \Box \psi = \dot{m} \psi[/math]

 

[math]\Box = \nabla^{\mu} \nabla_{\mu}[/math]

 

 

Part Four

 

''I am inclined to believe that four-dimensional symmetry is not a fundamental property of the physical world.''

 

Paul Dirac

 

 

All Canonical theories of gravity which have been quantized have to deal with the time problem. I have explained that, if the WDW equation is an equation describing the whole universe, then it is at odd's with how our current theory treats the initial conditions of our universe. Our universe is not fundamentally-concerned with geometry, then neither should a quantized version of the relativistic laws. Time disappears in the Canonical theories of gravity, but the space dimensions are normally retained. That simply cannot have real physical applications when you wind the ''imaginary'' clock of the universe back to the very first instant.

 

Just revisiting very quickly, one problem concerning this area of research is whether the WDW equation should be complexified, and if so, what is the best approach? Should we reconfigure time into the equations? After all, would not such a theory still break down when geometry ceases to exist in a closed universe?

 

Concerning the first part, most physicists would tend to think the equation should be complex. Since we have established from the work of Barbour, that the complex nature is inseparable to time itself, we should note that almost all of the fundamental laws of nature we can write about are in fact time-symmetric. Such as radiation laws, electromagnetism has retarded and advanced solutions, thermodynamics is also a good example of time-symmetric laws, thus the theory of gravity is often thought to have a symmetric case involving time as well.

 

 

What we have is a real and present problem with the dogma of time - it is generally considered that time itself is needed in a quantum mechanical or field theory, but this is not the case. Barbour himself was one of the main proponents to show the world how, our world is governed by change, not by time. He was led on this crusade by Mach, which he himself has often quoted

 

“It is utterly beyond our power to measure the changes of things by time. Quite the contrary, time is an abstraction at which we arrive through the changes of things.”

 

Anyone who is a little versed in the history of relativity are also aware of what a major influence Mach had been to Einstein's train of thought and perhaps, this is one reason why his relativistic theory turned out to be governed by timeless equations. Einstein's GR seriously puts into doubt the idea of time dimension, when you realize that time evolution arises as a symmetry of the theory, it is not like a true time evolution at all.

 

However, the Machian view of time is slightly different to the Einsteinian time found in the special theory. Machian time arises as points which are relative to each other in space, in Einstein's view, you move through time as ''splits'' as you move through space. However, the Machian view does cast doubt in Einstein's relativity and is also at the core of what Barbour believes; that being there is no time, only motion of objects relative to each other.

 

But here is something interesting for the reader to consider. Machian relativity is in fact a wonderful theory when describing how energy can be written into the metric of spacetime. A single particle in relativity cannot have an energy. For it to have an energy, there needs to be something there to compare it too. A little like how you could not tell whether something was spinning if it was the only object in the universe, because there is nothing else to compare with it's frame of reference. As I said, the same goes for energy. Energy appears in the universe as particles emerge relative to each other. The common way to describe this in mathematics is through ''triangulation.'' You may have three particles in spacetime who are relative to each other.

 

In spin dynamics, you can triangulate a kind of geometry on your fibre bundle (which looks like tiny segments on your manifold). Each point of the triangle corresponds to the location of a single particle. Being a completely relativistic thing, energy then is measured by the locations of these objects. One point alone will not have an energy, only another object for instance relative to another object can graph out an energy.

 

A(G) are adjacent vertices and E(G) are the sets of edges found in the configuration space of these particles. To find the energy in our graph, you use the expectation equation

 

[math]E(G) = <\psi |H| \psi>[/math]

 

''H'' is your Hamiltonian, which described the total energy of your system. But just like something forming a triangle, the energy depends on whether they are relative to each other. The Cauchy-Schwartz Inequality theorem describes how there is an uncertainty principle relationship which depends on the lengths of the triangle. Well, I will explain this from a geometrical then a quantum stance. Heisenberg uncertainty is a form of the geometric Cauchy Schwarz inequality law and this might be a clue to how to treat the universe when it first came into existence. The reason why, is because the geometric Cauchy Schwarz inequality states that you can deal with triangles in spacetime on the fundamental level, and their sides reveal an uncertainty relationship - ''a'' must be less than or equal to ''b + c'' , ''b'' less than or equal to ''a + c'', and ''c'' must be less than or equal to ''a + b'' . Attempting to violate this leads to uncertainties in your measurements, just like what you would obtain from Heisenberg's Uncertainty Principle in it's full form.

 

Basically, energy arises as a relativistic principle in this specific configuration space. So what happens when you reach zero size at the initial start-up condition of the universe?

 

All the lengths of your causal triangle go to zero - if there are no lengths between objects, then you cannot have a notion or quantity of energy in a relativistic sense. Note, that this idea ties in very well with our current idea's on how the universe expands - that is, in the beginning, space appeared between the objects, it is space which expands. The geometry made sense when you have this geometry appear in this combinatorial fashion (the triangulation of matter).

 

Therefore, energy was necessarily zero, space is not fundamental and time is an induced property of slow moving systems.

 

Therefore, let us take out mind back to the so-called ''first instant.'' All we had was a point in the beginning of the universe, where all energy was concentrated. There was no such thing as triangulation between particles because space between the particles of energy did not exist. There fore, in the triangulation theory you shouldn't be able to talk about an energy using the graphical tensor notation we used above.

 

This takes us back to the Null Energy condition and hopefully reminds us that energy may not even be fundamental and even if it was, it would be impossible to determine whether energy is conserved in a universe because the path of using the Wheeler de Witt equation will not allow us to investigate this due to the time problem.

 

Final Thoughts

 

It has been a long standing question, just like shadows on Plato's Cave whether reality really is what it seems. For those who have confidence in quantum mechanics, we know fine well life is not what it seems really, that on the fundamental level nothing makes sense. But many of us simply accept it but with good reason I should add.

The idea that... time could be an illusion, that space (the stuff which our universe is made of) may not even be fundamental, the idea that the energy content of the universe is actually zero, even though there are electrons running through the wires powering my computer as I write the ironic words.

I think some exciting papers in the future on pre-planck physics might deliver some answers into the origins of the universe and what actually is fundamental.

 

 

References

 

http://www.fqxi.org/data/essay-contest-files/Markopoulou_SpaceDNE.pdf

 

 

http://platonia.com/nature_of_time_essay.pdf

 

 

http://en.wikipedia.org/wiki/Wheeler%E2%80%93DeWitt_equation

Edited March 29, 2013 by Aethelwulf

[Rade]

A Dissertation On the Nature of Time

Hi, a very nice presentation. I have a few comments, and will give them one at a time.

 

Comment #1. I notice that neither you nor Barbour define 'motion'. I do not understand how he can say time is not a measure of motion when he only looks at one side of the issue...time. Logically he must FIRST define motion before he can make any rational comment about time, because the two go hand-in-hand likes the heads and tails of a coin, one CANNOT exist without the other. Now, Aristotle (Physics Book IV) in his discussion of time first defined motion, then from his logical and rational definition of motion as "fulfillment of what exists potentially", time falls into place, it is nothing more than a NUMBER that is the measurement of this fulfillment of potential! So, if we want to say time is an abstraction, fine, but then so is this , 3.12, an abstraction. When the 'time duration' concept problem is properly viewed as a NUMBER related to a rational definition of motion as done by Aristotle, then we see that Mach errors when he claims:

 

Mach.....“It is utterly beyond our power to measure the changes of things by time. Quite the contrary' date=' time is an abstraction at which we arrive through the changes of things.”[/quote']

 

Mach is incorrect ! We measure "changes of things" using a NUMBER, and [edit] one such potential 'change of things' where there is no change in (x,y,z) dimensions in 'space', we call that concept TIME. The question to ask that Mach fails to answer is, how do we discriminate the MORE or LESS "change of things" when space (x,y,z dimensions) remain constant? It is NOT only by space that we discriminate this change or motion, but also by time. Suppose a can with 10 marbles within the space of the can [define space as the boundary of that which contains the 10 marbles]. We discriminate more or less marbles within the space as "changes of things" when we remove one marble and we say there is 9 NOW (a present moment)instead of 10 (past NOW or past present moment),[edit] and what is intermediate between the two, a measure of more or less 'duration' of the 'changes in thigs'. This 'change of things' is a motion between two NOWs with space unchanged, and thus we measure the more or less 'changes of things' as duration (marbles) using time, which is that which is intermediate between the two moments (the two NOWS).

 

You would have interest in this concerning time and motion for Aristotle:

http://pervegalit.files.wordpress.com/2009/04/0199247900-time-for-aristotle.pdf

 

==

 

I have many comments and I really enjoyed reading your presentation. Perhaps we can discuss my comment #1.

 

Many edits made, please respond to this revision.

Edited March 29, 2013 by Rade

[Aethelwulf]

Hi, a very nice presentation. I have a few comments, and will give them one at a time.

 

Comment #1. I notice that neither you nor Barbour define 'motion'. I do not understand how he can say time is not a measure of motion when he only looks at one side of the issue...time. Logically he must FIRST define motion before he can make any rational comment about time, because the two go hand-in-hand likes the heads and tails of a coin, one CANNOT exist without the other. Now, Aristotle (Physics Book IV) in his discussion of time first defined motion, then from his logical and rational definition of motion as "fulfillment of what exists potentially", time falls into place, it is nothing more than a NUMBER that is the measurement of this fulfillment of potential! So, if we want to say time is an abstraction, fine, but then so is this , 3.12, an abstraction. When the 'time duration' concept problem is properly viewed as a NUMBER related to a rational definition of motion as done by Aristotle, then we see that Mach errors when he claims:

 

 

 

Mach is incorrect ! We measure "changes of things" using a NUMBER, and [edit] one such potential 'change of things' where there is no change in (x,y,z) dimensions in 'space', we call that concept TIME. The question to ask that Mach fails to answer is, how do we discriminate the MORE or LESS "change of things" when space (x,y,z dimensions) remain constant? It is NOT only by space that we discriminate this change or motion, but also by time. Suppose a can with 10 marbles within the space of the can [define space as the boundary of that which contains the 10 marbles]. We discriminate more or less marbles within the space as "changes of things" when we remove one marble and we say there is 9 NOW (a present moment)instead of 10 (past NOW or past present moment). This 'change of things' is a motion between two NOWs with space unchanged, and thus we measure the more or less 'changes of things' (marbles) using time, which is that which is intermediate between the two moments (the two NOWS).

 

You would have interest in this concerning time and motion for Aristotle:

http://pervegalit.files.wordpress.com/2009/04/0199247900-time-for-aristotle.pdf

 

==

 

I have many comments and I really enjoyed reading your presentation. Perhaps we can discuss my comment #1.

 

Many edits made, please respond to this revision.

 

 

Concerning comment 1, motion is defined as the relative displacements. Instead of thinking of a system changing in time, change is a relative situation - what is one system moving relative too? Therefore the motion of individual systems is by definition their relative displacements in Cartesian Coordinates.

[Aethelwulf]

You can actually shuffle coordinates x, y, and z such that you may find no difference which is why ''causal triangulation'' is adopted in this work because as Barbour points out, we may measure change by the ''shapes of the universe'' on small scale interactions. The universe changes in this respect without the need for time. His explanations why we sense time however, is quite different to mine.

 

http://platonia.com/barbour_emergence_of_time.pdf

Edited March 29, 2013 by Aethelwulf

[Rade]

You can actually shuffle coordinates x, y, and z such that you may find no difference which is why ''causal triangulation'' is adopted in this work because as Barbour points out, we may measure change by the ''shapes of the universe'' on small scale interactions. The universe changes in this respect without the need for time. His explanations why we sense time however, is quite different to mine.http://platonia.com/barbour_emergence_of_time.pdf

But, suppose we have this set of changes in "shapes of the universe" { 0 <--> # <--> @ <-->....}. My point is that Barbour cannot say that there is a way to measure this change in shapes without consideration of the <--> = time, in other words, to say one can have change without time is a logical contradiction, just as to say you can have a two-headed coin without having BOTH a head a tail. I hold that since Barbour begins with a logically false definition of motion, he ends with a false understanding of how motion relates to time. Some definitions are 'false definitions' [see Wiki: false premise] and thus to start a presentation with them leads to a false conclusion, which is how I read Barbour and his comments about how motion and time are related. Edit: So, what I am saying is that to say that 'motion is defined as relative displacement' is based on a false premise, a false use of the terms relative and displacement. Example,a growing oak tree is in motion, yet it does have simultaneously have a character that can be measured as 'relative displacement'...thus, Barbour begins with a false definition of motion.

 

Question. Would your "sense of time" match what I present as the <--> ? A yes or no explanation appreciated as it will help me better understand your argument. Thanks

Edited March 29, 2013 by Rade

[Aethelwulf]

Oh I understand Rade, your question now.

 

Julian Barbour has been working on the time problem of the Wheeler de Witt equation for... most of his life. He has investigated it with a number of prominent scientists, such as Wheeler, Motz, Hoyle ect. He doesn't just say that time does not exist, only that our usual idea of time is at tithes of regaining a new definition of time. Basically, Barbour is saying that time can be regained but if one studies the work he has published, it shows us that time is not exactly fundamental which is the whole point.

 

Just taking into consideration the good question you brought to our attention:

 

''My point is that Barbour cannot say that there is a way to measure this change in shapes without consideration of the <--> = time, in other words, to say one can have change without time is a logical contradiction.''

 

It actually appears like an oxymoron, however, this is a misunderstanding of what this theory entails. Time is a subjective phenomenon of the human psyche and this can be proven by analyzing two different gene regulators inside of the human brain. It has been seriously considered in mainstream that this is the origin of the ''sense of time'' itself.

 

If time is completely subjective then what we are, is slaves of our own bias. We ''imprint psychologically'' so to say, our experiences on the world around us. We are biased to the point of belief that the world needs to change because of a concept of ''time.'' In Relativity, ''time is nothing more than what a clock ticks'' but what he really means is that someone needs to be there to measure the ''change.''

 

The objective world is not constrained by a bias that time as a dimension needs to exist because we can even appeal to authority in this case when Paul Dirac himself said that he did not believe that time as a geometrical feature of the universe was actually a fundamental thing. In my own analysis, I have extended this to space, because if in the classical context in a global manifold we would initially find space no longer fundamental.

 

Motion is about relativity but what you need to understand is that relativity does not concern time. Worldlines are static and unchanging. In the local sense, it means that time is like the entropy a human mind can measure, but entropy in the universe does not care for any notions of a past or future. The Universe only cares about an eternal present moment in which only changes appear to happen.

[Aethelwulf]

Also, I kind of answered this question in my essay

 

Geometric Time

 

And thus the question is asked, why does it seem like time exists then? Why should we experience time if it does not exist? What makes us so special?

 

It's not that we are special per se, but we are in an important energy phase of the universe, called the low energy phase. The low energy phase happened late in the universe's history - do not mistake ''late'' as implying a time however. This is where the English language breaks down and we need to use different approaches to explain what we mean. There can be change in Julian Barbour's eye's, but there is no such thing as a time. So can we reconcile change without time?

 

Yes, we can. It may not seem obvious at first, but things like the zeno effect gives us evidence that even if time really did exist, systems don't need to change.

 

 

 

Basically, your 'formula' m <--> t if it is the same thing as saying motion is equivalent to time is wrong. Things on the fundamental level don't need to change in monotonic increase of time in relative respect. Time again is something which we assign on the world we ''think we see.'' The world we really ''see'' is just a hologram produced by the brain in the electrical signals being jumbled about senselessly by your neural transporters.

[Rade]

Basically, your 'formula' m <--> t if it is the same thing as saying motion is equivalent to time is wrong. Things on the fundamental level don't need to change in monotonic increase of time in relative respect.

Yes I agree, and thus it appears I did not explain myself well. I do not have a formula [motion <--> time] such that motion is equivalent to time. Such a formula would be [motion = time]. But for me <--> does not mean =, it means that time cannot be a concept independent of motion because time IS the measure of motion. My problem is that I do not know if this how you view time ? Do you view time as a MEASURE of motion, if yes, OK, then we agree, if not please explain why not. I will stop now and wait for answer because sometimes dialog gets too complex because folks ask too many questions together in one reply.

[Aethelwulf]

Well, time can be a concept independent of motion if motion can exist without time. The only way this can be true is if time is a part of the psychology of the mind, not part of the fundamental physical world. Time appears to exist because of motion, but that shouldn't mean that they are dependent. They only appear to be dependent because the brain makes it so, or we ''collect'' information in other words about the changes about the world and associate it to ''time.'' But that's the fool or even better said, the veil of the mind cast on the world. We are imprinting the need to have time when time objectively may not even exist.

[Aethelwulf]

Also, consider my thought experiment. The Zeno effect is like watching a ''pot that never boils'' as the famous saying goes. If time and motion where dependent, then a system like an atom would always change. But if you watch an atom periodically, the atom will not give up it's energy like you would expect. You are effectively ''halting'' the ''time evolution'' of the system. But time hasn't really stopped because if time really was objective and not a subjective phenomenon, then time really continues to truck on. But evidently, the system you are periodically watching has frozen in time. So it's hard to say that time and motion are synonymous or are somehow dependent.

[Rade]

Well, time can be a concept independent of motion if motion can exist without time. The only way this can be true is if time is a part of the psychology of the mind, not part of the fundamental physical world.

But, why not time is both a psychology of the mind AND how the mind measures the motion as number ? Again, time is NOT objective in-of-itself. Time only gains a veil reality because there is an objective entity in motion. So, I argue that motion cannot exist objectivity UNLESS time exists subjectively.

[Rade]

If time and motion where dependent, then a system like an atom would always change. But if you watch an atom periodically, the atom will not give up it's energy like you would expect.

But, all atoms are constantly in motion as a vibration or resonance and just as we say we cannot put hand into a flowing stream twice and measure the same water, we cannot observe an atom twice and observe the same atom, the motion of vibration has changed the atom between the two measurement events...thus atoms are never frozen in time, only a past moment as a past present is frozen in time, never to be changed. So, I would think that if you want motion without time you would need to observe a past present moment that is in motion with time frozen, but how do we do this, how do we observe a second time the same event as occurred in a past present moment ? I think such is impossible, thus it must hold true that there can never be motion without time as a measure of it in the PRESENT moment.

[Aethelwulf]

Yes, that is very true. Motion is an inherent property of matter. But the release of energy is not, yet, in Noethers Theorem, energy and time are supposed to be conjugates. You effect the time evolution of a system by watching it ''now and again'' you effectively ''stop time itself.'' But you wouldn't really be stopping time per se, only the local effects of change. Motion is fundamental, time is not.

[Aethelwulf]

But, why not time is both a psychology of the mind AND how the mind measures the motion as number ? Again, time is NOT objective in-of-itself. Time only gains a veil reality because there is an objective entity in motion. So, I argue that motion cannot exist objectivity UNLESS time exists subjectively.

 

 

What do you mean friend? Are you asking, why time cannot subjective and objective simultaneously?

[Aethelwulf]

But, all atoms are constantly in motion as a vibration or resonance and just as we say we cannot put hand into a flowing stream twice and measure the same water, we cannot observe an atom twice and observe the same atom, the motion of vibration has changed the atom between the two measurement events...thus atoms are never frozen in time, only a past moment as a past present is frozen in time, never to be changed. So, I would think that if you want motion without time you would need to observe a past present moment that is in motion with time frozen, but how do we do this, how do we observe a second time the same event as occurred in a past present moment ? I think such is impossible, thus it must hold true that there can never be motion without time as a measure of it in the PRESENT moment.

 

 

Again, there is no absolute past moment, nor one which exists in the future. There is only a slur of present moments which are defined by recording intelligent minds capable of dividing time into what I would call... ''slices.''

[Aethelwulf]

There might be an absolute present, but only because it is an eternal present moment. Something which doesn't change externally in the objective world. The subjective world will allow it because our minds are the only way to process such events. Objectively, the world could not care less about a past or a future. It can only be concerned about one moment at a time.

[Rade]

Yes, that is very true. Motion is an inherent property of matter. But the release of energy is not, yet, in Noethers Theorem, energy and time are supposed to be conjugates. You effect the time evolution of a system by watching it ''now and again'' you effectively ''stop time itself.'' But you wouldn't really be stopping time per se, only the local effects of change. Motion is fundamental, time is not.

First, I agree with the statement that motion is fundamental, time is not. But, this does not mean that time cannot be a subjective measure of objective motion, if we allow for two different aspects for time as a measure:(1) a measure of motion as number of the continuous (2) a measure of motion as number of the discontinuous. As you said, we can also allow that the the ability of the mind to use time as a subjective measure of objective reality is regulated by genetics, making such a trait possible for many forms of life, not only humans, and not even requiring a mind, only genes formed by DNA.

 

How can time be a subjective measure of the continuous and discontinuous simultaneously ? Let U be the unitary evolution of the state wavefunction that is a continuous process and let R be the state reduction of the wavefunction during a measurement event. Time measures U as a 'duration interval' between any two R events, such as ...R<---U--->R<---U--->R.... In this picture, each R is a 'now', either a present now, or a present now in the past. Thus one aspect of time is a measure of the motion of U as a "duration or interval". But, time is also a measure of each R event at each present now as what is called 'proper time' (this is what a clock measures). In this view, the objective reality of the wavefunction U is measured by the subjective veiled reality of "time duration", and the state reduction R as "proper time", and both measures occur simultaneously within the subjective mind. I suggest that these two fundamental aspects of time is why I say there can never be motion (either U and/or R) without the possibility that they can be measured by time as a number of the motion.

 

Concerning Noether, would it not be true that the release of energy must occur with the motion at either U or R from above, and given that no other states are possible other than U or R, does this not mean that energy must always be released, since all matter is always (100% of time) in motion. If so, then if time symmetry is valid fact of the universe, then there must be a corresponding law of conservation of energy for science of physics..correct ? Or put another way. If there is energy symmetry in science of physics, then there must be a corresponding time conservation law. So, I do not see any problem with Noether theorems to say that if motion exists so must a corresponding time exist that can be a measure of it, a way to measure the translation symmetry one way or another.

 

Please understand that I reply out of respect for you, not to argue against you, but to argue my point of view on time.

 

Let me ask, how does your dissertation on time change if you allow time to be a simultaneous measure of motion of U and R as I suggest above ?