The Idea of Time and a Possible Solution to the WDW-equation

[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 which was provided from 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 position coordinate.

 

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

Edited July 7, 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 t}[/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

 

[math](\dot{m} + i\hbar\frac{\partial}{\partial x}d_i \nabla^2)\psi = 0[/math]

 

A negative sign would have appeared because of [math]\hat{P} = -i\hbar\frac{\partial}{\partial x}[/math] which explains why we have ended up with a plus sign.

 

But perhaps just a mathematical note, instead of quantizing the equation, you may notice on the right what we have is momentum times displacement. If this is for small increments then it would have the same length as a distance.

 

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]

Edited July 7, 2012 by Aethelwulf

[michel123456]

(...)

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.

(...)

 

How can an evolution be static?

 

Don't you need time for any kind of change to happen?

See dicussion this thread where the conclusion seemed to me that change doesn't exist without time. And "evolution" is a kind of change, isn't it?

Edited July 7, 2012 by michel123456

[Aethelwulf]

How can an evolution be static?

 

Don't you need time for any kind of change to happen?

See dicussion this thread where the conclusion seemed to me that change doesn't exist without time. And "evolution" is a kind of change, isn't it?

 

It's because in physics, we model the evolution of particles on worldlines. Worldlines are actually static and they can't distinguish between a past or future - these are ''static curves'' in a 4D spacetime. Because General Relativity take a similar view on the worldline, it's outcome is similar for our 4D static worldline case. So when an evolution is looked at like this from relativity, concerning the worldlines of particles, it seems to be static.

 

I think there is change in systems, the worldlines for 4D curves is probably not the best example - I think there is no smoothness to time, that time is not a continuous flow. There are only ever ''moments'' and each moment may seem unchanging without looking at all the ''moments'' together.

 

And evolution anyway isn't even a true evolution in GR because motion arises as a symmetry of the theory.

 

And change and time are not synonymous... just a quick thought, noticing how that certain systems don't need to change for time to simply truck on. There is an obvious distinction between things that change and what time is. The two are not equal.

 

Besides, physical events where change is concerned involved physical things we can measure, time is not even an observable.

[Aethelwulf]

I'm curious mods, would I have been able to post this elsewhere than speculations? I do make some speculations but I draw them out and I explain why they are made?

[hypervalent_iodine]

I'm curious mods, would I have been able to post this elsewhere than speculations? I do make some speculations but I draw them out and I explain why they are made?

 

I am far from being a physicist, so I will not comment on specific content here, but I would like to make some more general remarks. The purpose of the Speculations forum isn't to punish OP's and having a thread here doesn't necessarily mean that the content is wrong. It is simply for speculation and for positing ideas that are not always in line with currently accepted science. If you think that you have written a thread containing your own scientific speculations or hypotheses, then this is certainly the place to put it. If you can explain them and back them up, all the better.

 

Happy posting.

[Aethelwulf]

I am far from being a physicist, so I will not comment on specific content here, but I would like to make some more general remarks. The purpose of the Speculations forum isn't to punish OP's and having a thread here doesn't necessarily mean that the content is wrong. It is simply for speculation and for positing ideas that are not always in line with currently accepted science. If you think that you have written a thread containing your own scientific speculations or hypotheses, then this is certainly the place to put it. If you can explain them and back them up, all the better.

 

Happy posting.

 

I think the biggest speculation is the Induced Time theory. Ok, my own creation but it is rooted from hard scientific disciplines involving moving clocks in relativity which possess a frame of reference... I don't know.When is a speculation a speculation?

 

Is a speculation backed by evidence a reason to say it can be mainstream?

[md65536]

I think the biggest speculation is the Induced Time theory. Ok, my own creation but it is rooted from hard scientific disciplines involving moving clocks in relativity which possess a frame of reference... I don't know.When is a speculation a speculation?

 

Is a speculation backed by evidence a reason to say it can be mainstream?

 

How is the idea of "induced time" different from the idea of "emergent time"?

 

Edit: I first came across the topic here: On the Origin of Gravity and the Laws of Newton

http://arxiv.org/pdf/1001.0785v1

It might be off topic but it speaks of the idea of emergent spacetime and expressing things in terms of entropy... there's probably a better introduction to the idea elsewhere.

 

 

It might be due to my own inexperience but I get the feeling that some of your terms are not scientifically meaningful??? Does "artificial" have an unambiguous meaning that I don't know? Are you saying that it's a man-made concept, not natural, or that there is an unreal or illusory aspect to it?

 

Are all of your references "accepted" mainstream science? If so, and if you are arguing that your ideas are a logical consequence of them, then I personally (not speaking for either scientists or the forum admin) would consider that a discussion of mainstream ideas. If not, I think you'd first have to prove that references correspond to mainstream science or something??? Probably better accomplished through writing papers. I don't think that internet forum consensus counts for much.

 

 

Anyway, some interesting ideas and discussion of previous works I've never heard of... some of it "sounds wrong" but again it might be due to my lack of understanding of the topic and references.

Edited July 9, 2012 by md65536

[smithy]

Brilliant Thread.

 

I am a scientist, been graduated from physics for 13 years now. For once I have been able to see someone bring archaic idea's into the modern framework like this, then run it through by logical axioms.

 

Thank you for this, a good read indeed!

[Phi for All]

Brilliant Thread.

 

I am a scientist, been graduated from physics for 13 years now. For once I have been able to see someone bring archaic idea's into the modern framework like this, then run it through by logical axioms.

 

Thank you for this, a good read indeed!

It's great that you're so supportive of Aethelwulf. You both have a lot in common, including the same ISP. I'll bet you even wear the same size socks!

[ecoli]

Is a speculation backed by evidence a reason to say it can be mainstream?

 

Publishing in a peer-reviewed journal would be a good start. That way the scientists who produce mainstream work can evaluate it. Most users here aren't qualified to evaluate modern physics.

[smithy]

It's great that you're so supportive of Aethelwulf. You both have a lot in common, including the same ISP. I'll bet you even wear the same size socks!

 

I hope I haven't complicated anything for them. I just wished to express my own opinion.

[zapatos]

It's great that you're so supportive of Aethelwulf. You both have a lot in common, including the same ISP. I'll bet you even wear the same size socks!

Yep. You got him. Well done!

[Aethelwulf]

It's great that you're so supportive of Aethelwulf. You both have a lot in common, including the same ISP. I'll bet you even wear the same size socks!

 

I actually don't know who this is. But I have a few idea's who it could be. I have over 600 friends on facebook and I even posted a link to my thread on my page. I can assure you this wasn't me. I've not been able to access this page in over a week.

 

Yep. You got him. Well done!

 

Well you'd be very wrong. Not the first time though, so I'll let you off.

 

So, in my absence, I have been doing more thinking into my theory but it involves math. Not may of you ever comment on math so I don't know if it is a waste of time.

 

 

First of all it seems best to explain why the term [math]\frac{\partial \mathcal{L}}{\partial \dot{q}}[/math] is important when describing world lines.

 

Consisder a simple spacetime interval as:

 

[math]d\tau^2 = dt^2 - d\vec{x}^2[/math]

 

Where we have set [math]c=1[/math] in this case. You actually calculate the length of a worldline by taking into consideration the integral

 

[math]L(W) = \int_W d\tau[/math]

 

You can, it was shown to me a while ago now, that worldines can be written in terms of time by the chain rule. Doing so, you can rewrite the time derivatives as dots on your variables and can end up with

 

[math]L(W) = \int_{t_0}^{t_1} \sqrt{1 - ||\dot{x}||^2}\ dt[/math]

 

From here, you would calculate the Langrangian by simply multiplying mass into the equation, so we would have

 

[math]\mathcal{L} = -M\sqrt{1 - ||\dot{x}||^2}[/math]

 

Now in my equation, we have been using the generalized velocity, and can be freely exchanged now to make the above equation into

 

[math]\mathcal{L}(\dot{q}\dot{q}) = -M\sqrt{1 - \dot{q}\dot{q}}[/math]

 

Now, the canonical momentum part in my equation can be written as

 

[math]\frac{\partial \mathcal{L}}{\partial \dot{q}} = \frac{M\dot{q}}{\sqrt{1 - \dot{q}\dot{q}}}[/math]

 

This is relativistic and is incomporated as one can see, into the idea of worldlines. Now, in my equation, I decided to multiply the momentum with distance. Of course, this was just the quantum action [math]\hbar[/math], but ignoring that fact for now, we wish to calculate the distance really as a displacement of all the particles in the universe [math]d_i[/math] using Barbour's approach. Doing so, will require an integral.

 

Taking the integral of the equation, which ''cuts up'' or ''slices'' a worldline for a particle, then the distance will be small [math]\delta d[/math] for a particle which is the way elluded to in the OP for how to calculate displacement of particles instead of distance exactly.

 

Remembering that

 

[math]\frac{\partial \mathcal{L}}{\partial \dot{q}} = \frac{M\dot{q}}{\sqrt{1 - \dot{q}\dot{q}}}[/math]

 

then my equation

 

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

 

Can actually be rewritten (including the integral this time) as

 

[math]\int \dot{m}\psi\ dt = \int (\frac{M\dot{q}}{\sqrt{1 - \dot{q}\dot{q}}}) \delta d_i \nabla^2\psi\ dt[/math]

 

So as you can see, the integral not only ''cuts'' up the worldline of a particle appropriately, but making the interval short enough will ensure that your distance is really just a very small displacement on a system of particles.

 

 

So, if the final equation is taken seriously, we actually have a type of relativistic mass flow equation which can describe the wordlines of each particle as a flow of mass in the universe. There is of course, not just one matter field in the universe, there are a few so one might change the mass sign for a matter field sign we can give as

 

[math]\int \dot{\Xi}\psi\ dt = \int (\frac{\Xi \dot{q}}{\sqrt{1 - \dot{q}\dot{q}}}) \delta d_i \nabla^2\psi\ dt[/math]

 

Each slice of a worldline has something to say about this thing we might call ''the arrow of time.'' As explained in the OP, my investigations have led me to believe there is no such thing as an arrow of time, that time itself is not a continuous thing but rather momentary fleeting flashes of existence of beginnings and ends. This nature is expressed in it's fullest when you consider that the sliced worldline view has basically tried to sum up very small displacements of particles in any given instant of time. If you want to measure the entire worldline, you need to piece these instances together like a jigsaw puzzle. Again, the nature of quantum mechanics would begin to take place if you wanted to know more than simply the momentum of these particles, say if you tried to measure their positions as well, the uncertainty principle is bound to take effect.

 

 

Now assuming my approach has been ok, how would one describe the energy then of a single particle in context of the previous equation? The energy of a single particle can be thought of as

 

[math]E\psi = c^2 \int \dot{m} \psi\ dt[/math]

 

And perhaps even then, a simple Langrangian might have the form

 

[math]\mathcal{L} = (\frac{1}{2}\dot{r} \cdot \dot{r}\int \dot{m}\ dt - V)\psi[/math]

 

Now I am working on a covariant form for these equations. This will take some time but I am on my way to completing them.

[zapatos]

Welcome back!

[Aethelwulf]

Welcome back!

 

An estranged welcoming from someone who I thought disliked me.

[juanrga]

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.

 

The first quantum field theory principle? And who said you that biology has been reduced to quantum field theory?

 

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

 

But you have not cited even one simple problem.

 

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?

 

Barbour has not eliminated time t from physics, he has only eliminated dt from some simple equations. The above equation continue depending upon time t, although it is not explicitly written.

 

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 does not have to be confused with global time. Physicists use different symbols when both are to met in the same equation.

 

It started off as a Galilean relativity which was provided from the ever famous Maxwell's Equations.

 

Maxwell equations are not Galilean relativistic 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,

 

Time was never a "numerical parameter" in Newtonian theory.

 

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.

 

Special relativity does not shuffle space and time but maintain both physically different. Neither it says that spacetime is 'timeless'.

 

The Minkowski metric is a three dimensional space and one imaginary space dimension

 

A metric is not a space. Neither time is "one imaginary space dimension". The trick to use "iT" instead "t" was an earlier trick to made that some formulae look more symmetrical in a 4D formalism. It is unneeded and pretty abandoned today in classical relativity.

 

Fundamental Time

 

However, Geometric Time and it's formalism into Minkowski spacetime, it does not seem to be fundamental in a quantum field argument.

 

Quantum field theory is build over a quantum Minkowski spacetime.

 

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.

 

The timeline of the cosmological evolution of universe predicted by relativity has been tested in the radiation era.

 

Real Time and Imaginary Time

 

Real Time is the kind of time where events of real things (actions) take place.

 

Spacetime events do not take place in time but in spacetime.

 

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

 

He tried, but he has not advanced in that program.

 

Einstein once said, ''that for those who believe in quantum physics, knows that the distinction of past and future are just stubborn illusions.''

 

You have invented this quote. He never said what you put within "".

 

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.

 

General relativity contains true time evolution and this fact is emphasized in the 3+1 formalism designed to deal with dynamical situations.

 

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.

 

The term "arrow of time" used in physics has a radically different meaning than you pretend. It of course does not mean that time looks as an arrow.

 

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.

 

When the field equations are properly quantized we obtain something similar to what string theory obtains.

 

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.

 

The analogy with the Schrodinger equation is only based in visual analogies because people uses symbols that other people uses. [math]|\Psi>[/math] is not a wavefunction, not even close. The classical limit does not give general relativity. And Everett Many Worlds is nonsense, as has been shown.

 

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.

 

The no conservation of energy in GR has nothing to do with cosmological expansion.

Edited July 16, 2012 by juanrga

[Aethelwulf]

The first quantum field theory principle? And who said you that biology has been reduced to quantum field theory?

 

 

 

But you have not cited even one simple problem.

 

 

 

Barbour has not eliminated time t from physics, he has only eliminated dt from some simple equations. The above equation continue depending upon time t, although it is not explicitly written.

 

 

 

Local time does not have to be confused with global time. Physicists use different symbols when both are to met in the same equation.

 

 

 

Maxwell equations are not Galilean relativistic equations.

 

 

 

Time was never a "numerical parameter" in Newtonian theory.

 

 

 

Special relativity does not shuffle space and time but maintain both physically different. Neither it says that spacetime is 'timeless'.

 

 

 

A metric is not a space. Neither time is "one imaginary space dimension". The trick to use "iT" instead "t" was an earlier trick to made that some formulae look more symmetrical in a 4D formalism. It is unneeded and pretty abandoned today in classical relativity.

 

 

 

Quantum field theory is build over a quantum Minkowski spacetime.

 

 

 

The timeline of the cosmological evolution of universe predicted by relativity has been tested in the radiation era.

 

 

 

Spacetime events do not take place in time but in spacetime.

 

 

 

He tried, but he has not advanced in that program.

 

 

 

You have invented this quote. He never said what you put within "".

 

 

 

General relativity contains true time evolution and this fact is emphasized in the 3+1 formalism designed to deal with dynamical situations.

 

 

 

The term "arrow of time" used in physics has a radically different meaning than you pretend. It of course does not mean that time looks as an arrow.

 

 

 

When the field equations are properly quantized we obtain something similar to what string theory obtains.

 

 

 

The analogy with the Schrodinger equation is only based in visual analogies because people uses symbols that other people uses. [math]|\Psi>[/math] is not a wavefunction, not even close. The classical limit does not give general relativity. And Everett Many Worlds is nonsense, as has been shown.

 

 

 

The no conservation of energy in GR has nothing to do with cosmological expansion.

 

Oh Juan... do you really wanna do this...

 

... as you wish. Hold on.

 

''Local time does not have to be confused with global time. Physicists use different symbols when both are to met in the same equation.''

 

Who says it is? I am going through over several different concepts of time, I explained this from the very beginning.

 

Is this not you reading again?

 

''Maxwell equations are not Galilean relativistic equations.''

 

I never said that. I said it started off with Galilean relativistic equations... am I suprised to say, you have read me backwards? Maybe this is your problem you generally read things backwards maybe?

 

''Time was never a "numerical parameter" in Newtonian theory.''

 

Yes it was. Time was always a numerical parameter.. It still is today with some theories.

 

''Special relativity does not shuffle space and time but maintain both physically different. Neither it says that spacetime is 'timeless'.''

 

General Relativity does. When have you ever heard of diffeomorphism invariance within the context of special relativity?

 

And yes, special relativity does not say the universe is timeless. I can't help but feel you are trolling, I have already explained in my OP that the GR EFE equations when quantized lead to the WDW equation .you KNOW this, we have explained this many times now.

 

''A metric is not a space. Neither time is "one imaginary space dimension". The trick to use "iT" instead "t" was an earlier trick to made that some formulae look more symmetrical in a 4D formalism. It is unneeded and pretty abandoned today in classical relativity.''

 

I said, the Minkowski metric is a four dimensional spacetime. What is your problem with this statement exactly?

 

''Quantum field theory is build over a quantum Minkowski spacetime.''

 

I don't see your point. All I said was that time is not fundamental in a quantum field argument. This is true in the context of high energy physics and the beginning of big bang - the region we hope to unify physics.

 

''The timeline of the cosmological evolution of universe predicted by relativity has been tested in the radiation era.''

 

There is no timeline, not in the sense of moving clocks. Well done, you have managed to show me you understand nothing of what I am saying, not that I am really all that surprised.

 

''Spacetime events do not take place in time but in spacetime.''

 

Absolute utter jibberish.

 

''You have invented this quote. He never said what you put within "".

 

Just because you haven't seen it, I make it up yes?

 

http://www.quotesdaddy.com/quote/1184698/albert-einstein/the-distinction-between-past-present-and-future-is

 

Your logic doesn't surprise me.

 

''General relativity contains true time evolution and this fact is emphasized in the 3+1 formalism designed to deal with dynamical situations.''

 

Wrong

 

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

 

Read the abstract.

 

''The term "arrow of time" used in physics has a radically different meaning than you pretend. It of course does not mean that time looks as an arrow.''

 

Actually, the definition is some direction in time. There is no such direction since time geometrical.

 

''When the field equations are properly quantized we obtain something similar to what string theory obtains''

 

You just like to sound smart I think. String theory obtains practically anything it wishes. It would, I hope, obtain the same quantization rules as Einsteins equations, or it would be bunk as a mathematical theory.

 

''The analogy with the Schrodinger equation is only based in visual analogies because people uses symbols that other people uses. is not a wavefunction, not even close. The classical limit does not give general relativity. And Everett Many Worlds is nonsense, as has been shown.''

 

Of course it is a wave function. This is why many worlds was created. A generic wave function ahs a infinite amount of possible solutions. However the wave function can have at least one minimum and may have several maxima or minima. This is what a parallel universe is, a complicated potential with many solutions to your wave function. If there are people treating it not as a wave function, then it surely isn't parallel universe theory.

 

''The no conservation of energy in GR has nothing to do with cosmological expansion.''

 

That's my theory. I made that up. It's my pet belief of a possible theory.

 

 

 

So well done. I am not impressed one bit.

 

Oh and Juan, if you do reply to this, and I don't reply. Keep in mind that I have actually asked for the mods to disable my account here.

 

Ok?

[juanrga]

''Local time does not have to be confused with global time. Physicists use different symbols when both are to met in the same equation.''

 

Who says it is?

 

From your post "time is strictly local." Once again local time is not global time.

 

''Maxwell equations are not Galilean relativistic equations.''

 

I never said that. I said it started off with Galilean relativistic equations...

 

Your words: "Galilean relativity which was provided from the ever famous Maxwell's Equations."

 

''Time was never a "numerical parameter" in Newtonian theory.''

 

Yes it was. Time was always a numerical parameter.. It still is today with some theories.

 

Time is not a numerical parameter but a physical quantity.

 

''Special relativity does not shuffle space and time but maintain both physically different. Neither it says that spacetime is 'timeless'.''

 

General Relativity does.

 

Your words: "The Lorentz Tranformations and [...] allow you to shuffle space and time coordinates freely in such a way that the meaning of the spacetime continuum is that it is timeless".

 

''A metric is not a space. Neither time is "one imaginary space dimension". The trick to use "iT" instead "t" was an earlier trick to made that some formulae look more symmetrical in a 4D formalism. It is unneeded and pretty abandoned today in classical relativity.''

 

I said, the Minkowski metric is a four dimensional spacetime. What is your problem with this statement exactly?

 

Your words: "The Minkowski metric is a three dimensional space and one imaginary space dimension".

 

And your new claim is also wrong. A metric is not a spacetime.

 

''Quantum field theory is build over a quantum Minkowski spacetime.''

 

I don't see your point. All I said was that time is not fundamental in a quantum field argument.

 

You said more: "and its formalism into Minkowski spacetime, it does not seem to be fundamental in a quantum field argument."

 

''The timeline of the cosmological evolution of universe predicted by relativity has been tested in the radiation era.''

 

There is no timeline

 

Contrary to your claims there is a timeline before the 70000 years

 

http://en.wikipedia....of_the_Big_Bang

 

''You have invented this quote. He never said what you put within "".

 

Just because you haven't seen it, I make it up yes?

 

http://www.quotesdad...t-and-future-is

 

Your logic doesn't surprise me.

 

Your exact words were: Einstein once said, ''that for those who believe in quantum physics, knows that the distinction of past and future are just stubborn illusions.''

 

You invented the first part of the quote. Einstein never said that you put within the "".

 

''General relativity contains true time evolution and this fact is emphasized in the 3+1 formalism designed to deal with dynamical situations.''

 

Wrong

 

http://fqxi.org/data...ou_SpaceDNE.pdf

 

Read the abstract.

 

It says: "It is often said that in general relativity time does not exist." But even if we accept the it "is often said", this is unrelated to my writing above.

 

''The term "arrow of time" used in physics has a radically different meaning than you pretend. It of course does not mean that time looks as an arrow.''

 

Actually, the definition is some direction in time. There is no such direction since time geometrical.

 

The definition is not that.

 

''When the field equations are properly quantized we obtain something similar to what string theory obtains''

 

You just like to sound smart I think. String theory obtains practically anything it wishes.

 

Even critics of string theory accept the derivation of quantum field equations.

 

''The analogy with the Schrodinger equation is only based in visual analogies because people uses symbols that other people uses. is not a wavefunction, not even close. The classical limit does not give general relativity. And Everett Many Worlds is nonsense, as has been shown.''

 

Of course it is a wave function.

 

Calling it a wave function and using a similar symbol does not mean it was a wave function.

 

''The no conservation of energy in GR has nothing to do with cosmological expansion.''

 

That's my theory. I made that up. It's my pet belief of a possible theory.

 

GR is not your theory.

Edited July 16, 2012 by juanrga