The Flux Of Time, A Modern Perspective Of Time Physics

[Aethelwulf]

Albert Einstein (1879–1955):

 

Zeit ist das, was man an der Uhr abliest.

 

''Time is what a clock measures.''

 

 

 

How Time Comes About

 

I have found that there are two reasons why a sense of time may come about, a quantum field theory answer and a less fundamental answer lying within biological systems. The first quantum field theory principle which allows time to exist can be thought of the precurser for all systems, even those which have no biology to act as clocks.

 

There are for this discussion over several topics for time - each unique and different to the next, some may exist within the context of science and others which do not. We will quickly investigate all these subjects of time.

 

There are things about time which I won't discuss in great length, but we will be talking about subjects, such as there being no flow to time [1], things like Global Time and timelessness.

 

Global Time

 

Global Time can be thought of the time encompassed by not one system, but the entire collection of systems we associate existing within the universe. It is the time which can be ascribed to the universe as a whole, but there are some problems with the idea of a Global Time, which will be talked about in the Timelessness part.

 

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?

 

As I said, without going to deeply into timelessness, 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 from his paper [2]

 

[math]v_i=\frac{\delta d_i}{\delta t} = \sqrt{\frac{2(E-V)}{\sum_i M_i(\delta d_i)^2}} \delta d_i[/math]

 

and rids any kind of time description 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 which involves displacements of all the bodies in the system. By doing this, he rids his use of time describing motion. 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. If we use Julians 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?

 

Local Time

 

Local Time is like the time you might experience in your zip code, to your neighborhood or to a single particle. According to Lee Smolin, he does not believe there is timelessness, but he does believe that time is strictly local. Local time is not absolute mind you and as distances become large enough, the question of ''what time is it'' becomes obscured in the background of relativity since time has the quality of becoming stretched or distorted. Local Time is good then, as an approximate just like flat space is a good approximation for black holes when you zoom in on their surfaces.

 

Geometric Time

 

Geometric time can be best understood from the context of relativity when Minkowski successfully united space and time as a single entity. It started off as a Galilean relativity led to the ever famous Maxwell's Equations. The Electrodynamic Equations admitted the Poincare Group and the Lorentz subgroup which are directly linked to Special Relativity [3]. Indeed, the Lorentz Tranformations made time not a numerical parameter but something with deeper meaning, one which was helping describe the geometry of space.

 

The Lorentz Tranformations and diffeomorphism invariance allows you to shuffle space and time coordinates freely in such a way that the meaning of the spacetime continuum is that it is timeless, which is a topic so threaded into relavity we will be discussing it soon.

 

The Minkowski metric is a three dimensional space and one imaginary space dimension, where imaginary space is simply time and it is here of course we can speculate the effects of geometry in any universe.

 

Fundamental Time

 

However, Geometric Time and it's formalism into Minkowski spacetime, it does not seem to be fundamental in a quantum field argument. If Geometrodynamics is correct, then geometry didn't appear until the radiation era was over. This means there were no moving clocks since in special relativity, clocks where observers with frames of reference. So, if there were no peices of matter in the universe, and geometry is synonymous with the appearence of matter, then time could not exist in the relativistic sense.

 

This means that there couldn't be a fundamental time because of this reason. If it's not fundamental, what does it mean to be simply geometric in relativity?

 

Real Time and Imaginary Time

 

Real Time is the kind of time where events of real things (actions) take place. Also known as ''Real Time Events'', is the time when measurements are performed in the world. We are included as candidate observers for Real Time Events.

 

Imaginary time is somewhat different. You get imaginary time when you use a Wick Rotation on the real timeline. Imaginary Time move horizontally on the real timeline and it gives the ability for something to move freely in the imaginary time axis. In a somewhat contraversial subject, imaginary time has been applied to the beginning of the universe by Hawking and can use quantum mechanics to rid it of singlarities.

 

Past, Present and Future Time

 

The past, present and future times, are the kind of thing we would associate to an arrow of time. But what if you were told that the past and future where actually illusions?

 

Einstein once said, ''that for those who believe in quantum physics, knows that the distinction of past and future are just stubborn illusions.'' Einstein was aware that when you model particles on wordlines, their evolution is actually static. In fact, General Relativity doesn't actually contain a true time evolution, motion itself arises from a symmetry of the theory.

 

In biology, we experience time because of two gene regulators, which help us have a sense of short-time durations and long-time durations. To many scientists, this could be a reason why we have any ''sense of time'' at all. The Psychological Arrow of time has to do with our perception of events moving from some past and into the future. What is an interesting fact to consider, is that if time is not really linear like this, that space and time have to do with geometry (like we have recently explained), then true arrows of time don't really exist.

 

It's not as if we can draw a line as an arrow and point from one place to another, time is not like this. Time isn't set out linearly like this in the equations, time is a non-linear part of the geometry of SR.

 

It seems, that it is not to incredible to think that the past and future are simply things our genetic evolution has reached to, to keep our minds from a type of insanity. That being, the ability to remember ''events;'' If we could not remember what happened a few moments ago, we would have no sense of mind. So for to make us have the ability to bring order out of the chaos, we required some sense of a past and some kind of future to be expected.

 

Another feature to keep in mind, that really all there is, is a present time. If we could think of time as a sphere that encompasses us (but does not move or flow) then we are always stuck inside this ''present sphere''. The notions of past and future become meaningless because things don't happen in any past or future, everything was always in the present time frame. This is another reason why we may think that our sense of time is not as it seems and perhaps distinction of past and future lead to illusions as well.

 

Timelessness

 

Timelessness has also been called the ''Time Problem of Quantum Mechanics'' and is a well-recognized topic involving the contraints on the equations of relativity. When the Einstein Field Equations are properly quantized, they lead to an equation called the Wheeler deWitt Equation. This equation is like a Schrodinger Equation except it contains no time derivative.

 

[math]\hat{H}|\Psi> = 0[/math]

 

and the wave function is the wave function of the universe which was first suggested by Hugh Everett the III in his dissitation on the statistical nature of the universe which leads to a many worlds interepretation.

 

There are some interesting qualities of the Wheeler-deWitt equation. In it's strongest application, is its importance with quantum gravity in a quantum theory. When this happens, we loose the ''complexity'' in the form of the equation. The Wheeler deWitt therefore could be solved for real solutions. Some physicists think this could be just an unsual factor about gravity, that's it's quantized version is one which cannot be complexified. So perhaps there is some underlying ''unknown'' mystery within the fact that the Hamiltonian and momentum constraints on Einstein's field equations are yielding these mathematical curiosities. The constraints of the Hamiltonian and the momentum could even be modelled on a mini-superspace, a type of special configuration space when you work with a small contrained model.

 

Perhaps the Wheeler deWitt can be interepreted as real [4] could be interepretated to mean that it exists within Real Time Events. Doing so, we can think of time in a Global sense that the interactions inside the universe give rise to a series of Real Time Events. Then by doing so, can we employ Barbour's view then that time is simply the sum of all displacements in the system? If so, would be wrong to think it's then not only all displacements but there is an overall conservation in the energy transferred through interactions?

 

There is one problem with this idea however, current theoretical cosmology seems to suggest that energy is not conserved in universes (another such model, [5]). As the universe expands, more energy is released into the vacuum.

 

Now, it's not that in theory General Relativity cannot have equations which conserve the overall energy for the universe, because GR predicts well-conserved notions of energy for static spacetime solutions. However as most know, our universe does not appear static, it is expanding and a curious feature is that it is now expanding faster than light, which might suggest that the universe is using more and more energy.

 

However, another interesting problem must be noted with the Wheeler-deWitt equation. It does not actually have any physical importance for the universe - General Relativity theory is about the curvature and effects of gravity. When you quantize Einstein's theory, you will quantize for solutions satisfying systems with curvature. This is a problem because the universe is not really all that curved, in fact is mostly flat in every direction we look according to the Wilkinson Microwave Anisotropy Probe. In Cosmology, the name given to this fact of the universe, is the Flatness Problem.

 

So perhaps we are quantizing the wrong kind of solutions, perhaps we need some kind of equations which satisfy the Newtonian Limit. Maybe a semi-classical approach could seem appealing but would still have to deal with the complexification problem of fields with time derivatives.

 

Induced Time

 

And we come to my own concept, the idea that time is in fact Induced - which means brought about as an artifical effect by slow moving matter. Fast moving particles are often called massless particles or some texts might call them Luxons. Slow moving particles are things with rest mass and can either take on the name Tardyons, or Bardyon, the root word ''Brady'' meaning slow. In relativity, you can only deal with moving clocks if they contain a rest mass. Things like photons and gluons ect do not possess rest mass and do not act as relativistic clocks.

 

Interestingly, Geometric Time is closely related to the Induced Time concept and the reason why is because if time is related to moving clocks with rest masses, then according to Geometrogenesis, time as we know it could not have appeared until the universe had sufficiently cooled down after the radiation era. Geometry in the universe did not appear alone, matter appeared alongside it and could be thought of the space and time dimension as sufficiently ordered enough to allow the kind of geometry we veiw every single day.

 

Therefore, the Induced Time is symonymous with the appearance of mass and geometry dealing with low temperatures in the universe. This brings us back to the question whether time is actually fundamental - time as we know it in relativity did not exist in the radiation period and the further you wind the clock back, you get to a point where geometry (the stuff of space and time) would completely cease to exist, the so-called origin of the universe which has thought to have arisen from a single point without dimensions.

 

Conclusions

 

So my conlusions are, that there is a Geometric Time, but it is not fundamental and fundamental time doesn't even really exist. Biological systems have the distinction of past and future but this does not have a physical relevance in the world at large. There is only the present time and the brain fools itself into thinking that the past and future exists by remembering events and by measuring what we call ''entropy''. We may sense time flow, but that sense of time would come about from us creating this view of entropy by remembering past states.

 

I think the Wheeler deWitt equation perhaps has a better solution yet to be found and in this work I showed there being a possible solution in light of quantizing at the Newtonian Limit instead of the Relativistic Limit. Our universe is mostly flat afterall.

 

Perhaps however, time can be retrieved again by taking Barbour's approach suggesting that time is really the displacement of all the bodies in the universe? Then locally gauge special relativity with these positions to unify them? If you can rid other equations of time and define it as the motions of systems instead, surely there should be a way to describe this for a universe?

 

I haven't tackled solutions. I have wondered if we should be thinking of equations like

 

[math]\dot{m} \psi = (\frac{\partial \mathcal{L}}{\partial \dot{q}_i}) d_i \nabla^2 \psi[/math]

 

Where [math]d_i[/math] is our displacement of our particles and [math]\frac{\partial \mathcal{L}}{\partial \dot{q}_i}[/math] is our classical canonical momentum part where [math]q_i[/math] sums over all [math]i-[/math]th particle velocities. This equation then has dimensions of a mass flow rate [6]. The time dependancy arises on the left hand side of the equation, but the right handside has a generalized velocity.

 

So in my case, I want to calculate the energy and positions of particles in the universe at any given slice of time [math]\sum[/math] or even can be seen as a slice of time out of a worldline of a particle. In terms of it calculating the positions of particles, it is very similar to Barbour's approach [2] where he calculates the [math]i-[/math]th particles of all the displacements:

 

[math]T = \sum_i \frac{M_i}{2} (\frac{\delta d_i}{\delta t})^2[/math]

 

This makes up a kinetic energy term. The kinetic energy has relationships with my own equation since the canonical momentum can be given as

 

[math]\frac{\partial}{\partial v} \frac{Mv^2}{2} = P[/math]

 

Which comes from Langrangian Mechanics. You can derive Lagrange's equations as

 

[math]\frac{d}{dt}(\frac{\partial \mathcal{L}}{\partial \dot{q}_j}) = (\frac{\partial \mathcal{L}}{\partial q})[/math]

 

It is important to note that [math]\dot{q}[/math] should not be viewed as a derivative really, but rather as a variable.

 

In terms of a statistical analysis, you can view the flow of mass as a net flow rate as

 

[math]\sum^{k}_{k=1} \dot{M} \hat{S}_k = \nu_i[/math]

 

Where [math]\hat{S}[/math] is the entropy of the system [7]. You could even take a quantum field Langrangian, and fit it into a type of Eular Lagrange equation for a field for a more comfortable quantum field description, but no doubt that could be difficult to calculate.

 

Time in this sense is really all about increments, short beginnings and end's. So for any slice of time, you calculate a small displacement like [math]\delta d_i[/math] like in Barbour's example and the generalized velocity terms [math]\dot{q}_i[/math] is wrapped up in the Canonical Momentum term. Apply this as though the wave function is a global wave function, then you can calculate all the relevant dynamics Barbour wants you to do in his view of timelessness - the idea is that there is no time, there is only change.

 

 

[1] Whilst George Ellis states here that there is no flow to time in our current theoretical models in physics, he argues for a case for the flow of time http://arxiv.org/abs/0812.0240

 

 

[2] http://www.fqxi.org/...71bae814fb4f9e9

 

 

[3] http://en.wikipedia....car/%C3%A9_group

 

[4] http://www.platonia....lex_numbers.pdf/

 

[5] http://blogs.discove...-not-conserved/

 

[6] http://en.wikipedia/..../Mass_flow_rate

 

[7] http://en.wikipedia.org/wiki/Entropy

[0812.0240] On the Flow of Time

arxiv.org

Edited July 16, 2012 by Aethelwulf

[Aethelwulf]

I actually have more to post, but will take a little time. It will involve my equations approach to view time as a discrete variable, not one which actually flows or one which has any continuous meaning outside of consciousness.

Edited July 11, 2012 by Aethelwulf

[Aethelwulf]

So what is a Hamiltonian constraint? One example might have the form of

 

[math]\pi_t + H = 0[/math]

 

Here, [math]\pi_t[/math] is the momentum conjugate to time and [math]H[/math] is the Hamiltonian. If one wanted to quantize this equation, you would replace the momentum constraint with the momentum operator [math]-i\hbar \frac{\partial}{\partial x}[/math], doing so would make it a time-dependant Schrodinger Equation and we will also notice that the equation would be complexified. Standard quantum theory in this sense is inherently complex, which raises the question how a complexification fo the WDW-equation has any significance in quantum theory.

 

Take into consideration my equation equation again

 

[math](\dot{m} - \frac{\partial \mathcal{L}}{\partial \dot{q}_i} d_i \nabla^2)\psi = 0[/math]

 

The equation is manifestly time-dependant since it is a mass-flow rate equation. If we wanted to quantize the momentum part we would end up with an equation fitting the description.

 

Momentum times distance is the same as energy times time, and this is the quantum action [math]\hbar[/math], so what we have is

 

[math](\dot{m} - \hbar \nabla^2)\psi = 0[/math]

 

If time is discrete, then it means that time is not a flow. It does not have an arrow exactly, because of a non-linearity arising from the geometry of General Relativity, but it rather some starts and stops. If this is the case, maybe the entire energy of a system is not measured rather by the system looked at as a ''whole'' from some universal ''time'' in a continuous sense, but rather energy in a universes arises from the positions of all the particles in the universe at a given instant.

Edited July 20, 2012 by Aethelwulf

[Rade]

I use the definition that "time is that which is intermediate between moments". So, this seems to agree with your suggestion that time has "starts and stops" (I would call these two events different moments).

 

So, for a picture [01] <---------> [02], then 01 = start moment, 02 = stop moment, <---> = time as a two sided arrow. Then, as you say, the total energy in universe arises from the positions of all particles at a given instant that includes all possible moments to which time is intermediate (01, 02, ...etc).

 

The position of particles requires that we merge time with space. If space defined as "the inner most boundary of that which contains", then the inner most boundary (inner to time) of the start moment 01 = ]< and the inner most boundary of stop moment 02 = >[, and space-time as relates to particles in the universe is then pictured as ]<------>[

[Aethelwulf]

I use the definition that "time is that which is intermediate between moments". So, this seems to agree with your suggestion that time has "starts and stops" (I would call these two events different moments).

 

So, for a picture [01] <---------> [02], then 01 = start moment, 02 = stop moment, <---> = time as a two sided arrow. Then, as you say, the total energy in universe arises from the positions of all particles at a given instant that includes all possible moments to which time is intermediate (01, 02, ...etc).

 

The position of particles requires that we merge time with space. If space defined as "the inner most boundary of that which contains", then the inner most boundary (inner to time) of the start moment 01 = ]< and the inner most boundary of stop moment 02 = >[, and space-time as relates to particles in the universe is then pictured as ]<------>[

 

Yes, except, I add to these ''frames of time''... ''real moments of energy''. If time is discrete, then so can only be the energy of a universe at large. You can't have an ''entire frame of energy''... only an ''entire succession of moments'' which ''define an energy''. IN a similar sense, distance in my equation appears not lightly. It appears because in the framework of geometry inside a vacuum, particles obey a type of ''triangle inequality''. As the distance between each particle diminished, so does a description of energy, ironically enough. This is the idea perhaps better said, that energy is defined by more than one particle, but in this model it requires three particles obeying the Cauchy-Schwarz Inequality which is a form of the uncertainty principle... best to see it as, a form of a geometrical interpretation of the uncertainty principle.

 

Thus what we have, is what can and has been called, ''A Fotini Graph''. This graph actually measures the energy of ''neighboring'' systems of particles. Because of this, a single particle does not have an energy, only relativistically speaking with other particles can a ''composite system'' of energy arise. The universe in my eyes is similar. It is a complex mega-structure of particles which is only existent at a single given frame of time. In this case, things like the Wheeler de Witt equation fail a complete understanding simply because of the application of our theory. Instead of thinking of the universe in ''whole'' for instance, we should be thinking of it in ''slices'' which ''makes a whole''.

Edited July 12, 2012 by Aethelwulf

[Aethelwulf]

However, the exact positioning of particles are not without consequence, such as the uncertainty principle. Sure, you may define you particles with a certain energy at any given location in spacetime, but you can't know the momentum with exact precision. This would mean perhaps, that certain energy levels in the universe will always be ... uncertain. Whether you measure a slice of particles in the position range or the momentum range. Either way, neither both definitions can be well examined at any slice of time.

Edited July 12, 2012 by Aethelwulf

[Aethelwulf]

Keep in mind the inseparable relationship between energy and time. They are conjugates of each other when considering the ''symmetries'' when involving energy conservation.

[Rade]

Keep in mind the inseparable relationship between energy and time. They are conjugates of each other when considering the ''symmetries'' when involving energy conservation.

This leads me to a few questions I have been thinking about.

 

Let us suppose that Feynman is correct and antimatter (^M), with ^=anti, is that which moves backward in time (<----) while matter (M) is that which moves forward in time (----->).

 

Then, suppose a system where a 3-mass matter unit [MMM] was to interact with a 2-mass antimatter unit [^M^M], thus the interaction {[MMM] + [^M^M]}.

 

My question is, would not conservation of energy and a stable coexistent result from such an interaction due to time translation symmetry, with one mass unit [M] observed as "real" dimension, where the remaining 4 mass units of antimatter and matter {[<----- ^M^M] and [------> MM]} occupy a virtual reality dimension resulting from time translation symmetry (that is, 2-mass units of antimatter moving backward in time simultaneously with 2-mass units of matter moving forward in time) ?

 

If yes, in this way, perhaps matter and antimatter then can coexist with time in the universe with conservation of energy maintained for the total system. That is, 1/5 of the system observed as real [M], with 4/5 of the system {[MM]+[^M^M]} found within a virtual time translation symmetry dimension (what has been called the dark energy)? Is not ~ 4/5 of all the mass in the universe "missing" ? My suggestion is that it is not missing at all, but the natural consequence of time translation symmetry and conservation of energy that results from interaction of matter and antimatter of unequal total mass (3-mass vs 2-mass). That is, the "missing" mass of the universe is present within a virtual reality dimension of that which humans observe to be "real".

[Rade]

However, the exact positioning of particles are not without consequence, such as the uncertainty principle. Sure, you may define you particles with a certain energy at any given location in spacetime, but you can't know the momentum with exact precision. This would mean perhaps, that certain energy levels in the universe will always be ... uncertain. Whether you measure a slice of particles in the position range or the momentum range. Either way, neither both definitions can be well examined at any slice of time.

Yes, but also neither position nor momentum can be measured unless there is a slice of time, that is, there is no uncertainty where time does not exist.

[Aethelwulf]

Yes, but also neither position nor momentum can be measured unless there is a slice of time, that is, there is no uncertainty where time does not exist.

 

A slice of time is different though than saying there is no time at all? It's just an instant of time, a single frame no?

[Moontanman]

A slice of time is different though than saying there is no time at all? It's just an instant of time, a single frame no?

 

 

Good to see you here Aethelwulf, I have often wondered if time is the most fundamental of all concepts and if indeed time is not just real but exists independent of everything else. In other words if there was no time dimension there would not and could not be any other dimensions....

 

I often read of late that somehow gravity or the properties of gravity is how the universe came into being, some sort of symmetry breakage, but I have wondered if time not gravity was the fundamental force that the rest of reality sprang from when time symmetry breakage spontaneously occurred...

[Aethelwulf]

Good to see you here Aethelwulf, I have often wondered if time is the most fundamental of all concepts and if indeed time is not just real but exists independent of everything else. In other words if there was no time dimension there would not and could not be any other dimensions....

 

I often read of late that somehow gravity or the properties of gravity is how the universe came into being, some sort of symmetry breakage, but I have wondered if time not gravity was the fundamental force that the rest of reality sprang from when time symmetry breakage spontaneously occurred...

 

 

Hello Moontanman,

 

Well as my OP attempts to explain, its hard to think of time fundamentally because when you consider the beginning of the universe (there was no geometry involved). So I suppose, Relativity cannot be applied to the beginning of the universe when time is involved. Maybe this has important consequences such as defining some kind of ''order'' to the first instance. If time is not a factor of the Big Bang in a relativistic sense, maybe it does no good for a universe to be said to have a beginning?

[Moontanman]

Hello Moontanman,

 

Well as my OP attempts to explain, its hard to think of time fundamentally because when you consider the beginning of the universe (there was no geometry involved). So I suppose, Relativity cannot be applied to the beginning of the universe when time is involved. Maybe this has important consequences such as defining some kind of ''order'' to the first instance. If time is not a factor of the Big Bang in a relativistic sense, maybe it does no good for a universe to be said to have a beginning?

 

 

My thoughts on this have grown out of the concept that many seem to have that time is an emergent property of the three other dimensions, time is often treated like the redheaded step child and my musings brought me to the idea that what if time is basic and the other three dimensions emerged from time, this would in effect make time the first dimension and not the fourth, of course my thoughts on this are mathematically ignorant...

 

If time only came into existence when the universe did then the universe has always existed and saying it had a beginning in time is nonsensical... but if time is just a measurement of change then the universe can be said to have a beginning i would think.

Edited July 12, 2012 by Moontanman

[Aethelwulf]

My thoughts on this have grown out of the concept that many seem to have that time is an emergent property of the three other dimensions, time is often treated like the redheaded step child and my musings brought me to the idea that what if time is basic and the other three dimensions emerged from time, this would in effect make time the first dimension and not the fourth, of course my thoughts on this are mathematically ignorant...

 

If time only came into existence when the universe did then the universe has always existed and saying it had a beginning in time is nonsensical... but if time is just a measurement of change then the universe can be said to have a beginning i would think.

 

I wasn't actually sure if anyone took the idea of an emergent time (I call it induced time, but same thing) seriously... until I read this post, so I decided to look for other information on the web and I came across this paper I agree with

 

http://arxiv.org/abs/hep-th/0601234

[Aethelwulf]

I think I might be the first ever however to link geometric time with emergent/induced time concepts. It's not quite obvious there inter-related natures until it is pointed out.

[Aethelwulf]

If time only came into existence when the universe did then the universe has always existed and saying it had a beginning in time is nonsensical... but if time is just a measurement of change then the universe can be said to have a beginning i would think.

 

The one greatest problem, is if there is a time ''to the beginning of the universe'' then it would show that space is actually independent of time. That space and time are inseparable is rooted from relativity.

[Moontanman]

The one greatest problem, is if there is a time ''to the beginning of the universe'' then it would show that space is actually independent of time. That space and time are inseparable is rooted from relativity.

 

 

This idea would seem to indicate that time exists outside what we think of as our universe.

 

http://wwwphy.princeton.edu/~steinh/npr/