Trading in the Real Space for Real Time

Note for Reader: Real Space is Imaginary Time while Imaginary Space is Real Time.

Trading in the Real Space for Real Time

In this essay, I will attempt to put forward an idea which will describe the universe from two different perspectives involving time, and how both perspectives can work for each other in eliminating the no-time problem of Quantum Mechanics.

There is no Arrow of Time

I have independantly came to the conclusion in the past to myself, that an arrow of time cannot exist. This depends on two things:

A) To define some definate arrow from the past into the future, there needs to be a point in where everything came from to define some direction in space. Direction does not exist in space. Equally there is no center to the universe according to current understanding, every point on the spacetime map would be the center to the universe.

B) Time does not have a flow.

The last concept I found out was used in a strong arguement against the arrow of time:

http://www.motionmountain.net/download.html

"Time is a concept introduced specially to describe the flow of events around us; it does not itself flow, it describes flow. Time does not advance. Time is neither linear nor cyclic. The idea that time flows is as hindering to understanding nature as is the idea that mirrors Page 71 exchange right and left. The misleading use of the expression ‘flow of time’, propagated first by some flawed Ref. 36 Greek thinkers and then again by Newton, continues. Aristotle (384/3–322 bce), careful to think logically, pointed out its misconception, and many did so after him. Nevertheless, expressions such as ‘time reversal’, the ‘irreversibility of time’, and the much-abused ‘time’s arrow’ are still common. Just read a popular science magazine chosen at random.

Without an arrow of time, the view where time rushed unequivocably from past to the future, while we are inexorably stuck in the present. But current view attends the idea that the past doesn't even exist, but only as a record of the present, a view held strongly by Dr Wheeler. In a sense, it exists itself an arguement based on a deep technicality of ''when things exist''. Things, that is, events themselves only ever happen inside the present sphere. The future cones and past cones exist with their own present frames, and notions of an absolute past and an absolute future cease to exist.

The Wheeler de Witt Equation

The problem with covariance in a quantum cosmological look is that gravity is described by diffeomorphism invariance contraint on the equations describing the evolution of the universe as a whole. This quantum cosmological approach has been widely accepted as one of main problems dealing with an approach towards unified theory on gravity.

A way to derive the equation other than quantizing Einsteins equation comes in a derivation. We must first consider a langrangian \(L(q, \dot{q})\) where it is said the time parameter defines a specific frame of reference and one can define [1] a new time as a monotonic function of \(t\), so an action can be given as:

\(I= \int L(q, \dot{q})= \int d\tau L_{\tau}\)

where \(L_{\tau}= q_{0}_{\tau} L(q,q_{\tau}/q_{0}_{\tau})\)

The corresponding momenta can be given when knowing that our new langrangian depends on two coordinates \((q,q_0)\) and the time \(\tau\), and with Eulers theorem, one finds that the Canonical Hamiltonian vanishes:

\(\mathbb{H}= \psi(p_0 q_{0}_{\tau}+p q_{\tau}-L)= 0\)

where the momentum is:

\(p_0= \frac{\partial L}{\partial q_{0}_{\tau}}\)

and

\(p= \frac{\partial L}{\partial q_{\tau}}\)

The quantum cosmological approach will have an equation describing this as:

\(\hat{H}\Psi= (\frac{2\pi G \hbar^2}{3} \frac{\partial^2}{\partial \alpha^2})+\sum_i[-\frac{\hbar^2}{2} \frac{\partial^2}{\partial x_{i}^{2}}+V_i(\alpha,x_i}]) = 0\)

And basically, the zero quantity refers to time, and mathematically it has plagued the minds of physicists, asking exactly how should we deal with this bizarre nature?

From now on, my approach will be to treat the time evolution in the Hamiltonian as a real time coordinate. The importance in desctinguishing this is to assertain two descriptions of time, and in doing so, will allow me to hypothesize an understanding on the real time measurements in the Hamiltonian of the Wheeler de Witt equation and one in understanding a comsological view of the universe concerning the beginning of time using imaginary time coordinates.

All in all, as Einstein similarily said, for those of us who believe in quantum theory, we must believe that the destinction of past and future are only stubborn illusions; either this, or our understanding of the \(\psi\)-function is incomplete, just as all the information in the Hamiltonian is encoded in the wave function of the universe.

There was no Beginning

According to Stephen Hawking the universe can be viewed to not have a beginning [2], if one looks at the universe in terms of purely imaginary time. Real time events would be when the universe could be said to have just began, but in imaginary reality of time, the big bang vanishes to exist. In his idea, real time is only a tool used by us to describe events in the universe. Similar to that idea, the real time evolution in the Hamiltonian of the Wheeler de Witt equation no longer has a measurable quantity because of the problem of diffeormorphism Invariances on the theory, so from this angle, we may actually forget about real time measurements, and trade it for all it's worth.

By keeping the real time description provided by the Wheeler de Witt equation can we preserve Hawking's vision of a universe in imaginary time. Before this realization, Hawking would have had to admit that the big bang was not exactly made to ''disappear'' - he stresses the universe still has a beginning, only that this view becomes distorted under the correct light. Now we can maintain that view, by adopting that there are no real time measurements at all. We are basically trading in the paradox of time, for a new one, one which has serious implications on the bizarre nature of time and of course, the continuing question of whether a big bang truely existed. By allowing imaginary time into the equations, one can use the Wheeler de Witt equation therefore to justify why we should not take real time seriously.

If we remove the singularity and the beginning of time with imaginary time (real space) we can throw out the paradox of real time remaining by introducing the firm belief in the Wheeler de Witt equation - this requires two different kind of times.

Imaginary Time Evolution

Imaginary time evolution is given as \(-\psi_{\alpha}= (\omega + E - H)^2 \psi\)

Real time extends to our (past) and our (future) - imaginary time is vertical or at 90 degrees off the real time. A Wick Rotation allows us to transform real time into imaginary time, so it may be interpreted that we can easily change our coordinate system in terms of \(t \rightarrow i\tau\). The proceedure actually changes the Lorentzian metric \((-+++)\) to an euclidean metric of signature \((++++)\) and is said to be a good way to go down because:

(1) it makes the path integral solvable
(2) the procedure can be used to explain the thermodynamic properties of black holes
(3) it makes it possible to measure gravitational instantons

So even if changing real time into imaginary time is just a mathematical trick, it has logical applications. In order however to take the stance we have in this essay, we must view the Hamiltonian of the Wheeler de Witt equation as a non-physical application on the theory, and begin to view imaginary time as the only true definition of time in our universe. Essentially, real time vanishes, while imaginary prevails.

Doing this solves:

(1) The problem of the beginning of time including the singularity
(2) The arrow of time, because real time is only an illusion
(3) successfully allows us to remove real time for imaginary time (Solving the no-time problem in GR)

The only way to make the idea successful is to find a way to allow the Wheeler de Witt equation to mathematically co-exist with imaginary time, or the no-boundary proposal. So far, the only clear way to do this, is to find a way to describe the universes wave function in terms of two time perspectives, which are fundamentally independant of each other, those being dressed in real time, and those dressed in imaginary time.

reflection

I forwarded the idea to a PhD because I felt it was a promising approach. The doctor replied saying ''it's a very good idea, but I doubt the Wick Rotation will act as a solution for the theory.'' So reflecting on this, I no longer believe the Wick Rotation will act like a solution to Real Time vs Real Space concept.

Conclusions

There is no explicit time description of the Hamiltonian in the Canonical Wheeler de Witt equation. The time evolution being described may very well describe real time events. By treating it as such, it seems other points of view on time can exist, views which themselves seem to solve the problem of whether a beginning of time should be viewed at all.

[1] http://www.ipod.org.uk/reality/reality_wheeler_dewitt.asp

[2] http://arxiv.org/PS_cache/gr-qc/pdf/9812/9812027v1.pdf

Further reading

http://books.google.co.uk/books?id=...esnum=8&ved=0CEoQ6AEwBzgK#v=onepage&q&f=false

''an incomplete wave function could be possible describing the universe''

~ on the wave function http://arxiv.org/PS_cache/gr-qc/pdf/0308/0308029v1.pdf

http://arxiv.org/PS_cache/gr-qc/pdf/0308/0308029v1.pdf

http://en.wikipedia.org/wiki/Imaginary_time

Timelessness in GR - http://www.fqxi.org/community/forum/topic/376

The Flow of Time*
By George F. R. Ellis - http://www.fqxi.org/community/essay/winners/2008.1

 

Log in or Sign up to hide all adverts.

So you admit these posts of yours are 'essays', in contrast to here?

So you've gone from not knowing what covariant means to now writing essays on its place in quantum cosmology? You can't even work out if a few simple vectors are linearly independent, along with not even being able to write down an actual linear combination of vectors(!), and yet you've got some kind of working understanding of diffeomorphism invariance?

I'll don't dwell much on the other things like variational principles, suffice to say similar comments apply. Why are you doing this, do you think anyone is going to say to themselves "Well I'm sure he understands those things", given your track record?

All you've done is quickly touch on a few well known concepts, you haven't done any actual 'reasoning' or derivation of any result. When I got to the "Doing this solves:" part I thought "Do what? You haven't done anything." because you'd not done any work yourself, just given short synopses of basic stuff covered early on in any course on such an area. And that's beside the fact that you don't prove whatever approach you're putting forth solves anything, you'd only given a paragraph or two of just talk, no details.

While the different natures of time and space do plague the minds of physicists what you just said doesn't. The zero quantity doesn't refer to time. Would you care to try again?

And your equation is wrong too. Would you care to try again?

Nice attempt to try to associate yourself with those physicists you just mentioned.

Not true, just because an operator and a state satisfy a particular expression doesn't mean one is 'encoded' in the other.

Not a meaningful statement.

Says who?

The more I read your essay the more it feels like all you've done is just read up on what a Wick rotation is and what the de Witt equation is and you're just writing an essay on those things in the sense a child would write about them for homework, not in the sense of "I'm intimately familiar with these things, having a working understanding, and I see how all this fits together and I'd like to explain".

What idea? All you seem to be proposing is "If we don't worry about it its not a problem". Mathematical concepts like complexifications, Wick rotations analytic continuations used in physics might seem like some kind of horrible things yet to be 'explained' but that isn't the case. The person who have the most issue with it are those who have little or no experience with it. A Wick rotation is a change of variables, nothing more. Its a mathematical trick to make life easier when calculating certain things, such as path integrals on a computer. Its easier to do things on a computer when you're only dealing with real numbers, not complex ones, so Wick rotations are used when solving QFT path integral processes on supercomputers. But that doesn't mean you must do such a rotation, on a computer or when doing a simple case by hand.

I'm not entirely convinced about any of that.

 

Log in or Sign up to hide all adverts.

Actually, the zero does refer to time, I can recite where you can read up on it, if you've never heard of this. Also, it is well-known all that happens is encoded in the wave function in this case, I can recite this if you want too. (In fact, there should be a reference at the bottom, if you care to look).

You ask who says that about the imaginary time evolution, I can cite this too. This does not look good for you.

 

Log in or Sign up to hide all adverts.

Also, you say a Wick Rotation is just a mathematical trick. I don't know if you know this, but I said the same in the essay. I also said in the essay that I showed this work to a PhD who said this was a very good question, buts doubts that a Wick Rotation would solve the problem. I now believe that two unique time references are required, where one of them vanishes because of the WDW-Equation.

 

Oh please, you ignored everything I said. I guess you can't give a decent reason why we should believe you're capable of doing high level quantum mechanics while you can't even write down linear combinations properly. Or how you're talking about covariance when a fortnight ago you didn't even know what it is!

Hell, I said your equation was wrong and you didn't correct it.

You said :
\(\hat{H}\Psi= (\frac{2\pi G \hbar^2}{3} \frac{\partial^2}{\partial \alpha^2})+\sum_i[-\frac{\hbar^2}{2} \frac{\partial^2}{\partial x_{i}^{2}}+V_i(\alpha,x_i}]) = 0\)

The main body of that expression, \( (\frac{2\pi G \hbar^2}{3} \frac{\partial^2}{\partial \alpha^2})+\sum_i[-\frac{\hbar^2}{2} \frac{\partial^2}{\partial x_{i}^{2}}+V_i(\alpha,x_i}])\) is an operator but its not being acted on a state, yet \(\hat{H}\Psi\) is an operator acting on the state.

You claim the 0 is time. No, the 0 is an element of the Hilbert space \(\hat{H}\Psi\) belongs to, because \(\hat{H}\Psi\) is equal to it. The action of the Hamiltonian is often associated with time variance, ie \(H \sim \partial_{t}\), so if \(\hat{H}\Psi = 0\) then it means \(\Psi\) is time invariant.

That is how time comes into it. It isn't that 'time is the 0', its that the zero means the system doesn't change in time.

Doesn't look good for you. I gave you a chance, you failed to even note a simple mistake like not having acted an operator on anything. Your usual complete lack of understanding of Hilbert spaces means you don't understand what the 0 of \(H\Phi = 0\) represents.

Like I said before, you do no actual work, you just parrot back basic things I'm sure you've found on websites but which you don't understand. If you seriously expect us to believe you can do this stuff when you can't even add vectors properly then you're either naive or an idiot. Stop wasting your own time by trying to convince people you understand things you don't. Yes, its not as glamorous to start with the basic stuff but there isn't a single person whose doing the advanced stuff who didn't cover the basic stuff. You're only slowing yourself down by doing this, so if you honestly do want to be able to do high level physics research then you need to be a lot more realistic.

 

I mean the expression \(\hat{H}|\Psi> =0\) - is not so different from the expression above. In fact, they are identical, and the zero does refer to a vanishing time. I will find proof of this somewhere, as it became common-knowledge to me. Question, tell me, if it does not refer to time, then why is time said to vanish?

Secondly, bigshot, I see you have conceded on the rest.

 

I will find where I have read this.

 

I can't find where I read it. But is it of any surprise people would think of it this way? The true nature of zero in the equation is not fully understood. The wave function does not have a time parameter, meaning the description of time must vanish in accordance to the zero quantity. It must refer to time one way or another.

 

Evgen though you never retorted the ''who said what'' part saying I could cite it, here it is anyway in case you decide I was messing you around with that too

http://arxiv.org/PS_cache/cond-mat/pdf/0010/0010100v2.pdf

 

Also, as for the wave function encoding all information about the state of the universe, which you also refuted, here you go:

http://en.wikipedia.org/wiki/Universal_wavefunction

http://planetmath.org/encyclopedia/WaveFunction.html

''Informally, a wave function encodes all the information that can be known about a certain quantum mechanical system (such as a particle).''

http://en.wikipedia.org/wiki/Wave_function_collapse
''If the wave function merely encodes an observer's knowledge of the universe ''

So even the wave function of the universe encodes all the information, the same thing you refuted.

 

Here in

http://arxiv.org/PS_cache/gr-qc/pdf/9812/9812027v1.pdf

It says the wave function in the WDW equation, is analogous to the schrodinger wave function as well, so there is no destinguishing between the two other than in the context of the equations that are used, meaning that the wave function still encodes all the information on the system.

 

I may end up conceding what I said concerning it referring to time absolutely. The case is not as clear:

http://books.google.co.uk/books?id=...esnum=8&ved=0CEoQ6AEwBzgK#v=onepage&q&f=false

It talks of a vanishing energy, but energy and time are conjugates of each other under Noether theorem, so in a sense I was correct.

 

I think you're confusing states and operators. A wave function can give us what we need to know about a system but to extract this information we act on the state with operators, such as the Hamiltonian.

This is different to the statement "just as all the information in the Hamiltonian is encoded in the wave function of the universe." which doesn't make sense.

Also, in reference to your equation "H \psi = ... = 0" (which you still haven't corrected given AN's prompt)
All that this is saying is that

\( H | \psi \rangle = 0 \) \( \Rightarrow \) \( \mathrm{i} \hbar {\partial\over\partial t} \left| \psi (t) \right\rangle = 0 \)

which means the wave function is time independent.

 

I doubt any of us with disagree that the description of \(|\Psi>\) in the equation is nothing more than the wave function. The link also says the wave function of the universe is analogous to the wave function description of the Schrodinger Equation which suggests to me they serve the same purpose, which would mean that they encode the information of the system.

If you can refute this somehow, I am open ears.

 

Do you know what is covariance?

Did you learn quantum theory?
Do you know what is quantum theory?

Did you ever studied cosmology?

Do you know gravity (relativistric or GR)?

Do you know what is a diffeomorphism?
Before you talk about general coordinate system, do you understand what is an Euclidian coordinate system.
What does it means y=const in \(R^3\)?

I guess you meant constraint.
What is a constraint on an equation?

What is a unified theory on gravity?

shouldn't it be \(I= \int L(q, \dot{q}) d(something)\)

Given a Lagrangian \(L(q_{0},q_{\tau})\), the Hamiltonian is given by
\(\mathbb{H}= p_0 q_{0}_{\tau}+p q_{\tau}-L\)
What is this \(\psi\)?

In the last equation: you take the derivative with respect to \(\alpha[/text], what is [tex]\alpha\)?
you also take the derivative wrt \(x_{i}\). What are the \(x_{i}\)'s?

Yes, the index 0 refers to the time index. you know, in relativity you generally say that the coordinates are \(x_{\mu}\) with \(\mu=0,1,2,3\) and \(\mu=0\) refering to the time coordinate.

No it didn't

 

biker guy, you are just making me repeat things I have already said, which is why I will only apply myself to some of these questions you pose. I simply dont have the patience to go through them all.

''What is \(|\Psi>\)?''

It is the wave function like the same wave function that governs the evolution in the Schrodinger equation.

I ''know'' what Covariance is now, with good description, and also diffeomorphisms.

''Did you take the derivative....''

No, if you follow the extracted links, you will follow the logic.

''and yes, the zero refers to the time index''

Tell that to alphanumeric, the know-it-all.

''no it didn't''

yes it did. Fotini Markopoulou a female doctor of this particular phsyics has made it clear that this has been a problem, because the understanding of time among phsyicists has been distorted because of this fact of relativity. Time basically ceases to exist, and I can refernce more than several papers on this fact.

 

Sorry, correction. I never included the psin in the Hamiltian coefficient. That must be a typo.

 

That is a self contradicting statement.

What about the thing I said, which you actually quoted, did you not understand or not agree with?

Since you're the guy who hadn't heard of polar coordinates till about 10 days ago I hardly think you're the best person to know what is or isn't known or understood by the scientific community.

So it is time invariant, ie \(\partial_{t}\psi = 0\) and since the Schrodinger equation says \(\partial_{t}\psi \propto H\psi\) it thus follows that \(H \psi = 0\). Nothing to do with 'time is zero' but that the variation of time has zero effect.

That isn't the case, something you'd understand if you understood linear algebra, Hilbert spaces etc.

\(H\psi = 0\) means that the wavefunction is an eigenfunction/state of the Hamiltonian, with eigenvalue 0. The Hamiltonian has eigenstates with non-zero eigenvalue, which the wave function has no support on and thus you cannot extract information about that part of the Hamiltonian if given the wave function you have.

Decomposing operators into their eigenspaces is standard practice in many mathematical physics areas.

Now both your link and arfa have said as I did, that \(H\Phi = 0\) doesn't mean that 'time is the 0' but that the zero is the amount of time dependency the wave function has, ie zero, which follows by the trivial application of Schrodinger's equation.

You're doing the same mistake Tach made in Eugene's thread, misunderstanding an article or book and then when we correct you you just think "I can't possibly be wrong, this book says so!", when in fact we're saying the same as the book, its you up aren't.

By the Schrodinger equation the 0 relates to time invariance. Time can still vary in the WdW equation, it just has no effect, just as varying t in f(x,t) = sin(x) doesn't change the output.

Perhaps if you hadn't skipped quantum mechanics 101 and had actually done the Schrodinger equation you'd grasp this.

Didn't you learn last time, ie the electro-magnetics thread of yours here in Pseudo, not to say that? I stopped because I couldn't be bothered to carry on, too much crap and obviously you have no intention of accepting the slightest bit of correction, you just want to delude yourself.

Is that your plan, to just spout enough shit for long enough that eventually no one bothers to correct you at all and then you can go around saying "Look, no one said anything so they must think its valid!". I don't go knocking on the doors of churches saying "Your beliefs are unsupported, often laughable and too often a danger and a hindrance!" but that doesn't mean I agree with them.

 

After three of your comments which have nothing to do with the post, I think I have every right not to reply to you.


You have been reported.

 

That is the most unconvincing professional out.