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1. The Problem of Time leads to a Problem of Energy for the Universe

note, the problem of time in physics ellucidates to the timelessness of relativity. In this post, I will show how if relativity is taken seriously, then we have a problem concerning energy which is a direct consequence of Noether's Theorem. I offer two possible solutions.

Energy is related to Time and Space

Bernoulli's equation is a representation of the law of "the conservation of energy" which is related by Noether's Theorem to the geometry of time - this basically means that it does not matter when you might conduct an experiment, there is a symmetry of a systems action which should imply a conservation law each time.

No Time Must Imply no Energy

And so for now, we must understand energy in the context of time. The absense 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 truely timeless, then surely this would mean that energy is devoid in our universe as well?

The counterintuitive facts just keep on trucking from the soil of Relativity, but this is one fact I must state. The innability 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.

I however, can see merit in the idea that something in our future has defined a total energy for the universe and by doing so, we may be able to recover the present moment; though it will not let us create the past and future, no amount of nip and tuck will rectify the problem that the past and future are simply illusions of the mind.

Enter the Transactional Interpretation (TI). In a seperate post mentioned how the TI could allow for signals to be sent back from the future to our past and shaping the past as we know it. This is not wild speculation but is a corner stone understanding of physics in general, through what is called Wheeler's Delayed Choice Experiment. In this experiment, which for the sake of getting to the point quickly will be oversimplified. The ability to make an observation on a system which may have traversed multiple paths due to the wave function will collapse into a single path - but what we are really doing when we observe the system is we are effectively creating a defined past for that object (mind I am using past as a calculational tool).

So a particle might travel the universe, take every possible path, arrive here on earth to be observed by a scientist to send quantum information backwards (the negative time wave solution of the TI) to the past history of the particle and define attributes which were but a smear of possibilities... Now, before we loose track, I will quickly get to the point. This is perhaps what is happening in our universe and why thinking about an observer in the infinite future is important. You can't have an observer sit outside space, nothing can exist outside of the universe, not even an observer.

Well, it turns out you don't even need an infinite future. To solve this, you need a boundary, or rather a symmetry in time. The very last instant of the universes existence will be were an observer would need to sit to view all the energy of the universe. By doing so, they would define whether the universe began with an energy or not. Who is this observer? Is it a form of intelligence? I don't know, all I know is that there is a problem if timelessness exists and that is that energy automatically ceases to exist, yet to solve this is by saying something intelligent is located in the very last instant of the universe which is sending signals back in time in the form of quantum waves (the kind you find in the transactional interpretation) so that the early universe could have some kind of defined volume of energy and perhaps maybe squeezing in the present time.

I am not completely against the idea of a present time existing outside in the universe defining objects, I just think it should be noted that the past and future certainly do not.

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 receeding 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 and thus will quantum leap sometime in the future. Odd to think of a universe quantum leaping, but this has been the literature in quantum cosmology.

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 $\delta L = 0$. 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.

What do you think, can you think of any other solutions to this problem I raise today?

2. Oops sorry, my citation

[1] http://xxx.lanl.gov/PS_cache/gr-qc/p.../9811053v2.pdf

3. This thread should be posted in the Physics forum, or in Alternative Theories or Pseudoscience. It is not appropriate for General Science and Technology.

4. Moderator note:
Thread moved

5. Originally Posted by Mister
Bernoulli's equation is a representation of the law of "the conservation of energy" which is related by Noether's Theorem to the geometry of time - this basically means that it does not matter when you might conduct an experiment, there is a symmetry of a systems action which should imply a conservation law each time.
What has Bernoulli's equation got to do with the rest of your post?

No Time Must Imply no Energy

And so for now, we must understand energy in the context of time. The absense of energy therefor, would imply the absence of time and vice versa; but why is this important?
You haven't established why an absence of energy would imply an absence of time.

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.
Einstein's equations include a time evolution. What are you talking about? Time is one of the coordinates in Einstein's equations.

Obviously, our universe is not timeless, so Einstein's equations would be useless if they did not include time evolution.

The counterintuitive facts just keep on trucking from the soil of Relativity, but this is one fact I must state.
"Counterintuitive" is not the same as "wrong". That's a mistake that many cranks make.

Fred Alan Wolf asked the question in his book Parallel Universes
Isn't he a crank?

''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.
Did he explain why?

I however, can see merit in the idea that something in our future has defined a total energy for the universe and by doing so, we may be able to recover the present moment; though it will not let us create the past and future, no amount of nip and tuck will rectify the problem that the past and future are simply illusions of the mind.
I'm not sure I understand what you're saying here.

Are you saying that the past of the universe is determined by the future, and not vice-versa?

Also, you seem to be clearly saying that in any case "past" and "future" don't really exist. That leaves only "the present", whatever that is.

How and why does the mind create these illusions of past and future? What of causation? Where does it leave time if there is only now and no before or after?

Enter the Transactional Interpretation (TI). In a seperate post mentioned how the TI could allow for signals to be sent back from the future to our past and shaping the past as we know it.
But this would all be only in the mind, since past and future exist only there. Right?

This is not wild speculation but is a corner stone understanding of physics in general, through what is called Wheeler's Delayed Choice Experiment. In this experiment, which for the sake of getting to the point quickly will be oversimplified. The ability to make an observation on a system which may have traversed multiple paths due to the wave function will collapse into a single path - but what we are really doing when we observe the system is we are effectively creating a defined past for that object (mind I am using past as a calculational tool).
And this tells us about the Transactional Interpretation, does it? What is the Transactional Interpretation, exactly?

The material you have presented above is not a "corner stone" of physics that I am familiar with. Why is it not included in all the standard textbooks?

Well, it turns out you don't even need an infinite future. To solve this, you need a boundary, or rather a symmetry in time. The very last instant of the universes existence will be were an observer would need to sit to view all the energy of the universe.
If the universe is infinite in time, there is no last instant.

I am not completely against the idea of a present time existing outside in the universe defining objects, I just think it should be noted that the past and future certainly do not.
Does that mean your mind is all that exists?

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 receeding faster than light which seems to indicate that our universe is using energy at a faster rate.
My house isn't receding faster than light. And it is part of the universe.

Also, please explain how the universe uses energy in the sense you're talking about.

In doing so, it might be conjectured that on the crux of things, the universe is not conserving energy like a ground state atom and thus will quantum leap sometime in the future. Odd to think of a universe quantum leaping, but this has been the literature in quantum cosmology.
What will it leap to?

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 $\delta L = 0$.
What is a Lagrangian density? Please explain.

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.

What do you think, can you think of any other solutions to this problem I raise today?
I think your idea that past and future are all in the mind fails at the most basic test of common sense.

6. ''What has Bernoulli's equation got to do with the rest of your post?''

You will need to excuse that little snippet mentioning Bernoulli's equation as it was extracted from the book I am writing, what was important about the snippet however was the mention of conservation and Noether's Theorem.

''You haven't established why an absence of energy would imply an absence of time.''

That is simply a title, the reason becomes obvious later when explained.

''Einstein's equations include a time evolution. What are you talking about? Time is one of the coordinates in Einstein's equations.

Obviously, our universe is not timeless, so Einstein's equations would be useless if they did not include time evolution.''

That's Ok James, I will assume you don't know about timelessness, or how it enters Einstein's equations. I was actually discussing this in the ''what is time'' thread. I had been elaborating on the fact that timelessness exists in relativity, among other concepts, to which later Dinoasaur made a post:

''First: If you need a definition for before & after, you are not able to understand time & can forget about this thread.

Einstein once wrote something like the following about time, which I think is very succinct and pretty much describes it.
When an individual ponders his experiences, he can order the events in his life using the criteria of before & after. He can assign a number to each event in such a way that events assigned a lower number occurred before events assigned a higher number.

It is convenient to use a device called a clock to provide a consistent set of numbers for use in ordering events.

In describing the laws of physics using the language of mathematics, it is convenient (if not necessary) to use a continuous variable called time. This variable similarly orders events based on the criteria of before and after.

There is little (if anything) more that can be said relating to time.''

He further addresses some issues of time in relativity:

''BTW: Einstein's remark about past, present, & future was not intended to be taken at face value.

That remark was made in the context of a discussion of World Lines, which model the laws of physics as static geometry.

Most people do not realize that the mathematics of both Special & general relativity treat physics as geometry. A moving particle is viewed as an unchanging curve. The actions of a person is viewed as a collection of related world lines.

Since the model is geometric, there is no motion. There is no past, present or future. Consideration of motion, past, present, & future require translating the geometric model into concepts compatible with the world of our ordinary senses.

Special relativity is a flat space model (plane geometry), while General Relativity is a curved space model (spherical or other non Euclidean geometry). ''

No doubt he has articulated this better than me, I was actually quite impressed by his post. It is true, that timelessness comes out of the theory, just in much the same sense I described it but articulated less well. I even bolded a particular part to show that evolution is to fit our senses, not the physical objective world.

Evolution, true evolution at that does not exist in GR. Motion arises as a symmetry of the theory, not a true time evolution. It is akin to having diffeomorphism invariance on your theory which allows to you shuffle spacetime coordinates without changing the overall structure of your theory.

I hope this explains it more fuller.

''"Counterintuitive" is not the same as "wrong". That's a mistake that many cranks make.''

I agree. Yet, I state that counterintuitive is perhaps an indication of a break down of understanding... using that to your advantage, we search for other possible solutions.

''Isn't he a crank?''

He revolutionized spin. He is very influential. If he is a crank, that is in the eye of the beholder.

''Did he explain why''

No, but he indirectly meant it involved the theory of Observation. It is true that even a particle can be an observer, but a particle cannot measure a universe. So instead, we use the analogy of a human observer. The reason why the universe cannot have an energy is because no one has measured it.

Believe it or not, but this energy problem of the universe can be solved by believing everything was predetermined at the Big Bang, possibly by the Bohmain Interpretation of QM using Pilot Waves. But neglect any deterministic universe then you run back into the same problem.

[b]''I'm not sure I understand what you're saying here.

Are you saying that the past of the universe is determined by the future, and not vice-versa?

Also, you seem to be clearly saying that in any case "past" and "future" don't really exist. That leaves only "the present", whatever that is.

How and why does the mind create these illusions of past and future? What of causation? Where does it leave time if there is only now and no before or after?

''I'm not sure I understand what you're saying here.

Are you saying that the past of the universe is determined by the future, and not vice-versa?

Also, you seem to be clearly saying that in any case "past" and "future" don't really exist. That leaves only "the present", whatever that is.

How and why does the mind create these illusions of past and future? What of causation? Where does it leave time if there is only now and no before or after?''

A lot of questions in there, I fear by the time I have finished this post I will need to log in again

Yes, the future will determine the past of the universe. Note, we cannot think of past and future in the normal sense. You can think of them also existing within the present frame. One way to tackle the difference between two present frames I have determined is by involving Einsteins ''Relativity of Simultaniety.'' In effect, one person veiwing an event in time can be different to another's perspective. The key clue however is that both observers exist in the present. Think of the future then as a massive time delay between events happening here in our frame of reference, both are true and exist within the present time.

But yes, the future will determine the past if it adheres to Wheelers Delayed Choice Experiment. Right... how does mind create the past and future? I have decided from my own studies that some illusory concept of a past and future can only exist when memory is present, and not just memory, but a device capable of ''knowing'' that memory. We are such devices. One moment which passes stores as memory but is not forgotten, so one way the mind is able to make sense of such a phenomenon is by the illusion itself of the past. We have pasts because we have memory of events, in a shorter simpler way of explaining it.

Causation is a [physical] phenomenon which has some serious problems if one takes relativity seriously, see above concerning mine and Dinosaurs post. Finally, where does it leave time if there is no before or after? There is still the now, and there will always be the now, in the form of the present moment, or present sphere as I call it.

''But this would all be only in the mind, since past and future exist only there. Right?''

Yes. The idea of a past and future is in one's mind, we have not yet articulated a way to talk about how quantum information in the form of psi-waves can stretch through the present moments of existence. I haven't yet been able to articulate it without involving past or future as a way to express the dynamics. I am sure there is a unique way to view it and explain it.

''And this tells us about the Transactional Interpretation, does it? What is the Transactional Interpretation, exactly?

The material you have presented above is not a "corner stone" of physics that I am familiar with. Why is it not included in all the standard textbooks?''

The way the transactional interpretation treats the wave function is the idea of a positive time wave and a negative time wave are able to move from the future to the past and from the past to the future. The wave moving forward in time is an advanced and moving back the retarded wave functions; and as you may guess, the waves are solutions of different quantum information packets which upon the absolute square amplitude they will define real existing things.

The emmiter could be an electron, radiating a photon, which is caused by producing a field. The field is time-symmetric under the Wheeler-Feynman description which and as John Cramer describes it ”time-symmetric combination of a retarded field which propagates into the future and an advanced field which propagates into the past.”

He considers a net field which consists of a retarded plane wave form F1

$F_1 = e^{i(kr - \omega t)}$

for t1 ≥ 1. Here, t1 is the instant of emission. The advanced solution G1 is simply

$G_1 = e^{-i(kr - \omega t)}$

for t1 ≤ 1. The idea is that the the absorbing electron responding to the incident of the retarded field F1 in such a way it will gain energy, recoil, and produce a new retarded field F2=-F1 which exactly cancels the incident field F1. The net field after such a transaction is zero.

$F_{net} = (F_1 + F_2) = 0$

Applying this to a universe can be beneficial. It can help explain how the early universe came into existence, because the future implied it through probability. The future of our universe can shape the early universe in such a way that it can define parts of the universe which are smeared by possibilities and out of which only one true history can survive. So there is the chance that the wave function in our universe is sending information back to points in our universes history where the early universe is just being formed.

''If the universe is infinite in time, there is no last instant.''

James, you qouted me saying ''Well, it turns out you don't even need an infinite future.''

So I am very much aware of this. You just haven't read it right.

''Does that mean your mind is all that exists?''

No. I believe the mind is a subsystem of the system we call the universe.

''My house isn't receding faster than light. And it is part of the universe.

Also, please explain how the universe uses energy in the sense you're talking about.''

The observable universe has been measured to be expanding faster than light. It is not matter moving at superluminal speeds, but the space inbetween. As for how this has to do with the energy of the universe, it is with current understanding that as the universe expands, more energy is released into the vacuum. A faster expansion would mean that energy is being released more rapidly.

''What will it leap to?''

I don't know. A safe articulate way of stating this, would be simply that it's quantum leaps into a new configuration, but what that configuration is, is so far, unclear.

''What is a Lagrangian density? Please explain.''

I will need to use some math here.

We may have a Langrangian

$L = \int dx [\frac{\dot{\phi}^2}{2} - \frac{\dot{\phi_{x}}^2}{2}]$

This would be the canonical momentum in respect to $\phi$. An example of breaking the symmetry, is if you had some potential term in there, and usually a simply potential may have the form

$\frac{M^2\phi^2}{2}$

Interested in the conservation, a simple Noether Theorem would include a transformation with a small parameter, or perturbation. A conserved solution would be

$q_i \rightarrow \phi_i + \epsilon f_i (q)$

The way this transforms is

$\sum_i P_i f_i (q)$

The epsilon dissapears (it is such a small quantity) and you are left with a conserved quantity

$\delta L = 0$

If it was a field momentum, $\pi$ then $\sum_i$ is replaced with $\int dx$ and the momentum is replaced with $\pi(x)$ yielding

$\int dx \pi(x) = C$

where C is some constant.

''I think your idea that past and future are all in the mind fails at the most basic test of common sense.''

Just like I said, it is counterintuitive. But one we must take seriously, I argue.

7. Mister,

I'll get back to the rest later, but right now I've only got time to ask some questions about the maths at the end of your last post.

Originally Posted by Mister
$L = \int dx [\frac{\dot{\phi}^2}{2} - \frac{\dot{\phi_{x}}^2}{2}]$
What is $\phi$ and what is $x$?

This would be the canonical momentum in respect to $\phi$.
What is? $L$, or $x$ or the whole integrand, or what? Which one is the canonical momentum?

An example of breaking the symmetry, is if you had some potential term in there, and usually a simply potential may have the form

$\frac{M^2\phi^2}{2}$
What's $M$? And what would I do with this term? Add it to the integrand of the Lagrangian?

What symmetry would it break?

Interested in the conservation, a simple Noether Theorem would include a transformation with a small parameter, or perturbation. A conserved solution would be

$q_i \rightarrow \phi_i + \epsilon f_i (q)$
What is $q_i$? What is $f_i(q)$? Is the $q$ in the $f_i$ the same as $q_i$?

What equation is this a solution to?

What is Noether's theorem, by the way?

The way this transforms is

$\sum_i P_i f_i (q)$
Sorry. I don't understand what is transforming to what, or why it needs to transform. Please explain.

Also, you have only given an expression for something here. I don't see any explanation of a transform. What is $P_i$?

The epsilon dissapears (it is such a small quantity) and you are left with a conserved quantity

$\delta L = 0$
Can you fill in the intermediate steps for me, please? I don't see how this follows.

If it was a field momentum, $\pi$ then $\sum_i$ is replaced with $\int dx$ and the momentum is replaced with $\pi(x)$ yielding

$\int dx \pi(x) = C$

where C is some constant.
What is a field momentum?

And I'm not sure what you're saying. Which sum becomes an integral? Which thing becomes a field momentum?

And none of this seems to answer my original question: what is a Lagrangian density?

8. The Langrangian density is one which is a function of the fields with in my case, the one space derivative (which could have included more dimensions and time) where the integral is over the space of the Langrangian. To increase your dimensions, you must note to change $\int d^3 x$ for three space dimensions.

That is to answer what the Langrangian Density is, I did answer it above in the math, but I probably could have been clearer.

to the rest of your questions... $\phi$ is a field. $x$ is the space dimension. $L$ is the Langrangian, ''L'' for short. $M$ is the mass.

''What symmetry would it break?''

It would break the symmetry when performing a transformation of the type I gave. A symmetry in this language then comes in the form of $(\phi \rightarrow \phi + \epsilon)$. If it is not a conserved quantity, then it is not a symmetry of the theory.

$q_i$ is velocity.

You may come across some quadratic form of the velocity in a Langrangian, such as

$\mathcal{L} = \sum_i \frac{M_i}{2} \dot{q}_{i}^{2} + U(q)$

Where $U(q)$ is the potential. This equation is equal to

$= T - U$

so then it follows that $(T+U)$ is a conserved quantity.

...Yes, $q$ is the same as the $q_i$, except with our summation. $f$ here is just a number, which can be set equal to $1$. $\epsilon$ is $\delta x = \epsilon$.

So, we may see that

$\sum_i P_i f_i (q)$ is a conserved quantity because it is unchanged under these rules, thus it satisfies the conservation of $\delta L = 0$, the $L$ again is just the langrangian.

$P_i$ is just the momentum.

Now, the field momentum is different to ordinary momentum and is given as $\pi = \frac{\partial \mathcal{L}}{\partial \dot{\phi}}$. It isn't Lorentz invariant. But you can replace $P$ ordinary momentum for the field momentum $\pi$.

9. Oh, sorry, you also asked what field momentum is exactly. When a charge interacts with an electric field, the field makes the charge move. That means that the field gives the particle momentum. This is field momentum. You might deal with a langrangian of the kind of charges in a four vector electromagnetic field as

$\mathcal{L} = \frac{M\dot{x}^2}{2} + \bar{e}\vec{A} \cdot v$

for instance. Thus

$\frac{\partial \mathcal{L}}{\partial \dot{x}} = M\dot{x} + \bar{e}\vec{A}_x$

10. Originally Posted by Mister
''What is a Lagrangian density? Please explain.''

I will need to use some math here.

We may have a Langrangian

$L = \int dx [\frac{\dot{\phi}^2}{2} - \frac{\dot{\phi_{x}}^2}{2}]$

This would be the canonical momentum in respect to $\phi$.
No, it wouldn't. The canonical momentum wrt a particular field has a very specific meaning. You just wrote down a Lagrangian, you even call it so yourself!

Are you picking bits of text from a source you don't understand again?

Originally Posted by Mister
An example of breaking the symmetry, is if you had some potential term in there
No, putting in mass doesn't necessarily break a symmetry. It depends what the symmetry is and how you're putting the mass in.

It's little comments like that which hint at the fact you're trying to reword a particular document you're picking from, rather than explaining things in your own words.

Originally Posted by Mister
Interested in the conservation, a simple Noether Theorem would include a transformation with a small parameter, or perturbation. A conserved solution would be

$q_i \rightarrow \phi_i + \epsilon f_i (q)$
That isn't a 'conserved solution' at all. It's a small perturbation.

Originally Posted by Mister
The way this transforms is

$\sum_i P_i f_i (q)$
This is meaningless since you don't define what the first term in the sum is, nor do you say what it is produced from. Different Lagrangians will be altered in different ways by perturbations.

Originally Posted by Mister
The epsilon dissapears (it is such a small quantity) and you are left with a conserved quantity

$\delta L = 0$
Firstly you've skipped out or mangled pretty much the entire derivation. Secondly the epsilon term doesn't disappear because it is small. If you just did that you'd not be perturbing the Lagrangian at all! Terms quadratic in epsilon are discarded. The terms linear in epsilon are kept and are required to vanish for non-zero epsilon. It's from that which you derive the Euler-Lagrange equations from.

Originally Posted by Mister
If it was a field momentum, $\pi$ then $\sum_i$ is replaced with $\int dx$ and the momentum is replaced with $\pi(x)$ yielding

$\int dx \pi(x) = C$
Again, you've skipped a load of stuff because you haven't even defined a momentum or shown anything about its conservation.

This is what happens when you don't understand the material you're parroting and try to cut it down so it isn't blindingly obvious to everyone that you're just copy/editing something. Since you don't understand the material you don't know which bits to remove so you just try your luck and hope no one notices. It's dishonest and it's very very obvious to those of us who understand Lagrangians.

Originally Posted by Mister
That is to answer what the Langrangian Density is, I did answer it above in the math, but I probably could have been clearer.
You didn't answer it and you definitely could have been clearer. By being less wrong.

Originally Posted by Mister
to the rest of your questions... $\phi$ is a field. $x$ is the space dimension.
Spatial coordinate. There's a difference.

Originally Posted by Mister
It would break the symmetry when performing a transformation of the type I gave. A symmetry in this language then comes in the form of $(\phi \rightarrow \phi + \epsilon)$. If it is not a conserved quantity, then it is not a symmetry of the theory.
No, a symmetry is something else which incorporates alterations to the fields. What you've given there is an alteration to the field of a type not used in the actual derivation of Noether's theorem or the E-L equations.

Originally Posted by Mister
$q_i$ is velocity.
No, it isn't. $q_{i}$ is taken to be the position of an object while the velocity is then $\dot{q}_{i}$. If you were to interpret $q_{i}$ as the velocity then M wouldn't be the mass. That really is a massive mistake because the simplest examples of the E-L formalism is to derive Newtonian mechanics from a simple Newtonian Lagrangian, ie the basic kinetic and potential energies of an object.

Originally Posted by Mister
You may come across some quadratic form of the velocity in a Langrangian, such as

$\mathcal{L} = \sum_i \frac{M_i}{2} \dot{q}_{i}^{2} + U(q)$

Where $U(q)$ is the potential.
Now you use it as velocity.

Originally Posted by Mister
This equation is equal to

$= T - U$
Obviously it isn't because you just changed signs on the potential.

Originally Posted by Mister
so then it follows that $(T+U)$ is a conserved quantity.
No, it doesn't. The Lagrangian can be written schematically as T-U. The total energy is T+U. The reason T+U is conserved follows from a particular property of the Lagrangian involves something you haven't made any mention of.

Can you tell me what that is and how you go about showing it?

You aren't explaining anything, you're just throwing out isolated statements which, when they aren't riddled with mistakes, are unsupported and unexplained.

Originally Posted by Mister
...Yes, $q$ is the same as the $q_i$, except with our summation.
No, the i index refers to the fact the equation is talking about multiple objects. If you've considering a single object then you drop the index. Again, something anyone with working familiarity with this stuff would know.

Originally Posted by Mister
$f$ here is just a number, which can be set equal to $1$. $\epsilon$ is $\delta x = \epsilon$.
Which doesn't appear anywhere in that post and doesn't line up properly with anything in your previous posts. Your habit of picking bits and pieces from source is showing again.

Really, its obvious you didn't spontaneously write that in your own words because it has absolutely no coherent flow. You refer back to things you haven't said and make conclusions based on other things you haven't said. You include conlusions of arguments you don't provide. If you really understood this stuff then you'd be able to write something more coherent. Remember how you said you think you're good at explaining stuff? This is evidence that isn't entirely true. Of course to someone utterly illiterate when it comes to physics, such as wlminex, you might be doing good 'OOB thinking' (out of box thinking) or whatever but clearly you aren't. You're trying to pass off as your own explanation material you haven't written yourself but are lifting from somewhere in bits and pieces. I'm in no doubt you'll deny it but the complete lack of coherency and random snippet nature of your 'explanation' makes it obvious.

Originally Posted by Mister
Now, the field momentum is different to ordinary momentum and is given as $\pi = \frac{\partial \mathcal{L}}{\partial \dot{\phi}}$. It isn't Lorentz invariant. But you can replace $P$ ordinary momentum for the field momentum $\pi$.
The definition of canonical momentum for a variable q in Lagrangian density $\mathcal{L}$ is $\frac{\partial \mathcal{L}}{\partial \dot{q}}$. If the Lagrangian is the standard Newtonian one $\mathcal{L} = \frac{1}{2}m\dot{q}^{2} - U(q)$ then we have $p = m\dot{q}$, which is the normal momentum.

As for Lorentz invariance, of course momentum isn't Lorentz invariant, even in special relativity, because its a Lorentz vector, it has a free index. What Lorentz invariance pertains to is the Lagrangian itself, whether it transforms as a scalar or not. Obviously the Newtonian Lagrangian doesn't so it won't give rise to a Lorentz invariant theory. Again, you're not even getting the concepts right here, you don't know what certain statements are referring to.

Originally Posted by Mister
Oh, sorry, you also asked what field momentum is exactly. When a charge interacts with an electric field, the field makes the charge move. That means that the field gives the particle momentum. This is field momentum. You might deal with a langrangian of the kind of charges in a four vector electromagnetic field as

$\mathcal{L} = \frac{M\dot{x}^2}{2} + \bar{e}\vec{A} \cdot v$

for instance. Thus

$\frac{\partial \mathcal{L}}{\partial \dot{x}} = M\dot{x} + \bar{e}\vec{A}_x$
You've screwed it up again. Firstly you've mixed notation, as you should have replaced v with $\dot{x}$ in the first expression.

Secondly you got the meaning of field momentum wrong. Given a Lagrangian density $\mathcal{L}$ with a field $q(x)$ the field momentum will be defined by the equation I just gave. The EM field $A_{\mu}$ has Lagrangian $F^{\mu\nu}F_{\mu\nu}$ and it's momentum would be computed from that. What you've said is that the field momentum of the EM field is what the particle's momentum is. No, the particle has momentum defined from it's kinetic term in the Lagrangian via the equation I gave and the EM field has its own momentum defined in the same way on its kinetic term.
The equation you give, $\mathcal{L} = \frac{M\dot{x}^2}{2} + \bar{e}\vec{A} \cdot v$ , is the electron's momentum but its not a field momentum because in that formulation the electron isn't a field, it's just a point particle. When you do quantum electrodynamics the Dirac spinor field for the electron then has field momentum.

I don't know how many times I've said this in just this post along, but this constant stream of mistakes shows over and over you aren't giving your own understanding, you've just spewing out what snippets you either half remember or possibly even directly copy from sources. Every time you make any attempt to put things into your own words you screw it up and when you give mathematical explanations you just pull bits and pieces from sources but since you don't understand it you don't know which bits to include and which to leave out.

This stuff is 2 or 3 years before university students get to the Dirac equation, which just highlights how huge the gaps in your understanding are and how laughable your claim to understand the Dirac equation in a decent manner is. Likewise with your belief you could perhaps walk the first year of a university course.

Seriously, find something else to do rather than lie to people online.

11. Alphanumeric, shut up, I AM NOT LYING TO ANYONE. This is how I have learned it.

For citation

http://www.youtube.com/watch?v=vvCeOncgSoA

Everything I have said, corresponds exactly to how I have learned about speaking about it from my favourite scientist, Mr. Susskind. Go watch it and you will see every rebuttal you make must be against his teaching!

12. (Sub-i I should have said, by the way instead of summation when speaking about q_i)

13. I knew it wouldn't have been long before you stalked me to this post, like you stalk every post of mine. You know the irony, the mods in the back room where suggesting I was stalking you in that thread about moderation. I laughed and thought, wtf are they talking about? I was talking in that thread long before you even showed face! If anything, its completely the other way round!

14. I just love how you came in blazing as well with ''all sorts'' of accusations... My favourite was this one..

''Since you don't understand the material you don't know which bits to remove so you just try your luck and hope no one notices.''

Yeah... Completely tore apart susskinds lecture haven't I? lol

If anything, the relevent snippets of information here are as full as he explained it. You really need to sort this attitude out alphanumeric, stop stalking me, because I am not the boy you knew five years ago. I do understand this stuff as it is taught to me. As I teach myself. It's the way you came in saying stuff like

''This is what happens when you don't understand the material you're parroting and try to cut it down so it isn't blindingly obvious to everyone that you're just copy/editing something.''

and

''I'm in no doubt you'll deny it but the complete lack of coherency and random snippet nature of your 'explanation' makes it obvious.''

Deny? I have hard visible proof I haven't taken snippets from anywhere and pasted them all together. If anything, I have taken relative information in it's full when susskind speaks about it, nothing to do with skipping bits of information then hoping no one notices.

You're looking quite the fool aren't you?

And this...

''You're trying to pass off as your own explanation material you haven't written yourself but are lifting from somewhere in bits and pieces.''

Wtf do you mean ''pass it off'' as my own????

When did my name become Noether? Was the Langrangian named after me? Where do you think your BS up?

15. Anyway, moving away from the distraction named, AN, I have so far came up with three solutions to the problem. Another one, a fourth solution to the problem of time implying a problem of energy for the universe has strucken the mind.

There is a concept in physics called the zero-energy universe [1]. If indeed there is zero time in the universe, the lack of a global time, were there is only timelessness, then the zero time could also tie in with the concept of a zero energy universe.

It is not so bizarre now to think of a universe with no energy. Especially in reference to the work I have provided so far.

[1] http://arxiv.org/abs/gr-qc/0605063

16. Originally Posted by Mister
Anyway, moving away from the distraction named, AN, I have so far came up with three solutions to the problem. Another one, a fourth solution to the problem of time implying a problem of energy for the universe has strucken the mind.

There is a concept in physics called the zero-energy universe [1]. If indeed there is zero time in the universe, the lack of a global time, were there is only timelessness, then the zero time could also tie in with the concept of a zero energy universe.

It is not so bizarre now to think of a universe with no energy. Especially in reference to the work I have provided so far.

[1] http://arxiv.org/abs/gr-qc/0605063
Zero energy means when you add all of the energy together with the negative energy.. every action has an equal, and opposite reaction. You get zero as the answer. But it still allows for every point in space time to contain energy. It's like breathing, you breath in to breath out.

17. Originally Posted by Pincho Paxton
Zero energy means when you add all of the energy together with the negative energy.. every action has an equal, and opposite reaction. You get zero as the answer. But it still allows for every point in space time to contain energy.
Yes, that would apply locally. But the wave function of the universe which governs the WDW-equation is not a local wave function, it is a global wave function meaning that the vanishing time derivative must be in some sense a global time. If this is the case, then if there are any problems with understanding energy in a universe, it must be thought of as a global situation. So when you think of the global energy content of the universe, you tend to ask the same problematic questions concerned in the OP.

So a zero-energy universe turns out to be very appropriate for a zero-time universe.

18. Originally Posted by Mister
Yes, that would apply locally. But the wave function of the universe which governs the WDW-equation is not a local wave function, it is a global wave function meaning that the vanishing time derivative must be in some sense a global time. If this is the case, the if there are any problems with understanding energy in a universe, it must be thought of as a global situation. So when you think of the global energy content of the universe, you tend to ask the same problematic questions concerned in the OP.

So a zero-energy universe turns out to be very appropriate for a zero-time universe.
So the global version is an average of the local version. An apple is a bunch of atoms. We break things down.

19. Originally Posted by Pincho Paxton
So the global version is an average of the local version. An apple is a bunch of atoms. We break things down.
The ''Global Version'' takes into consideration the entire, or total energy content. The local version would simply care about individual systems which we obviously can measure and define with energy. Hence why in the OP the problem of a universe with no energy first came from my reading of Doctor Wolf who indirectly explained that the observer effect will define the energy properties of systems, but if no one has observed the universe, how can it have an energy?

One might even appeal to God in my finite universe example, were some intelligence is located in the future and has defined the total energy content of the universe. That seems practical since we can't ever go outside of spacetime to attentively watch the universe and measure any energy.

20. Originally Posted by Mister
The ''Global Version'' takes into consideration the entire, or total energy content. The local version would simply care about individual systems which we obviously can measure and define with energy. Hence why in the OP the problem of a universe with no energy first came from my reading of Doctor Wolf who indirectly explained that the observer effect will define the energy properties of systems, but if no one has observed the universe, how can it have an energy?

One might even appeal to God in my finite universe example, were some intelligence is located in the future and has defined the total energy content of the universe. That seems practical since we can't ever go outside of spacetime to attentively watch the universe and measure any energy.
If an action has an equal reaction you have your answer both locally, and globally. There is no difference. The sum is zero.

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