How time starts in LQG with onset of Lorentzian phase

[marcus]

In the recent analysis by Mielczarek, Linsefors, and Barrau, the key parameter is ρ_c the highest density achieved in the bounce. The extremes (negative and then positive) of the Hubble rate occur symmetrically at density ρ_c/2

In the contraction preceding bounce, as the density approaches ρ_c/2, lightcones narrow down and the geometry becomes in a sense less Lorentzian. Interaction between neighboring points is suppressed.
Precisely at density ρ_c/2 the geometry FREEZES into a Euclidean phase consisting of a bundle of parallel timelines. Spatial derivatives are suppressed.

However density continues to rise, reaching ρ_c, where it rebounds and declines back down to ρ_c/2. During that Euclidean phase of extreme condensation with interaction turned off, I would say that time does not exist. I cannot imagine how a clock could be constructed under such circumstances, an oscillator or similar cyclical process with a counter recording the cycles. That is the operational meaning of time. If you cannot imagine measuring time, nothing corresponding to that idea exists.

Instead, the excursion of density, from ρ_c/2 up to ρ_c, and back down again, can (if you wish) serve to parametrize the bundle of timelines which spacetime has momentarily become.

The interesting thing, which is the focus of the MLB paper, is the MELTING of this Euclidean timeless phase that occurs after the bounce starting at ρ_c/2 and restores the Lorentzian signature.

MLB call the 3d hypersurface at ρ_c/2 the "silent surface" and they suggest this would be a good place to impose initial conditions and to analyze the power spectrum of quantum fluctuations. Up to that point, interactions have been turned off so neighboring points are "deaf" to each other. I suppose that is the basic reason they speak of it as "silence". This isolation or spatial disconnectedness is reminiscent of the classical 1970 finding by three Russian physicists (B, K, and L) formerly members of Lev Landau's group.
http://arxiv.org/abs/1411.0272v1
Silent initial conditions for cosmological perturbations with a change of space-time signature
Jakub Mielczarek, Linda Linsefors, Aurelien Barrau
(Submitted on 2 Nov 2014)
Recent calculations in loop quantum cosmology suggest that a transition from a Lorentzian to an Euclidean space-time might take place in the very early Universe. The transition point leads to a state of silence, characterized by a vanishing speed of light. This behavior can be interpreted as a decoupling of different space points, similar to the one characterizing the BKL phase.
In this study, we address the issue of imposing initial conditions for the cosmological perturbations at the transition point between the Lorentzian and Euclidean phases. Motivated by the decoupling of space points, initial conditions characterized by a lack of correlations are investigated. We show that the "white noise" initial conditions are supported by the analysis of the vacuum state in the Euclidean regime adjacent to the state of silence...
12 pages, 8 figures

 

[marcus]

The conclusions paragraph, on page 11, puts succinctly what I've been talking about. This is one of the 5 main results:

==quote http://arxiv.org/abs/1411.0272 ==
The main results of the paper are the following:

The state of silence provides a natural way to set initial conditions for the cosmological perturbations. This state is the beginning of the Lorentzian phase, and, in some sense, the beginning of time. This is qualitatively a new feature in cosmology.
...
...
==endquote==

I think in fact that the beginning of the Lorentzian phase is, in a clear sense, quite literally the beginning of time. Where there is no way to measure duration (by counting cycles of some regular repetitive process) one cannot speak of time. There is no means of comparing the duration of that frozen (Euclidean) phase with intervals of known duration in the familiar natural world.

 

[Paulibus]

Mielczarek, Linsefors and Barrau , as far as I can dimly understand, are proposing that the history of the universe includes an 'episode' timelessly called 'a state of silence' in which the time dimension, the fourth in our current Lorentzian ensemble of dimensions, became added to a then-prevailing Euclidean three-space-dimension ensemble. This transition is difficult to write about with a vocabulary coloured by our perception of time, which uses words like 'current', 'became' and 'prevailing' , that imply the passage of time. As confusing as invoking a prior state of 'silence' to describe a state in which the speed of light, rather than that of sound is, zero, perhaps? But even 'ís' so coloured, by a connotation of enduring!

Be this as it may, I'd like to know how one imagines the transition from c = 0, to c = jumbo-sized, as now; a zero to hero transition, if ever there was one!

My imagination boggles at the thought of a change of this magnitude being assumed to 'happen' instantaneously. But I also shrink from imagining a gradual change --- once one deserts the idea of a sudden instantaneous switch of speed, one is led to consider gradual change, and to wondering whether 'gradual' could include a span of say 3.7 billion years. And: if not, why not? Then I begin to ponder if gradual change might not cause the reddening of far away and long ago light; an unthinkable heresy -- this is unshakably assigned to the expansion of space dimensions: but perhaps only relative to the time dimension?

 

[MathematicalPhysicist]

I didn't read the article. But you can't do physics without time and space, there's no kinematics and thus also no dynamics.

 

[marcus]

...
Be this as it may, I'd like to know how one imagines the transition from c = 0, to c = jumbo-sized, as now; a zero to hero transition, if ever there was one!

My imagination boggles at the thought of a change of this magnitude being assumed to 'happen' instantaneously. ...

Hi Paulibus! Good to see you. Take a look at figure 5 on page 8. They are talking about gradual change.

It starts during the expansion phase when the density gets down to ρ_c/2, that is half the critical level.
at that point spatial interaction begins and lightcones begin to open.

I don't see an estimate for "how long" that opening takes. The figure 5 suggests to me that it happens quickly (like the inflation episode that inflation theorists tell us about) but also gradually in the sense of continuously, not as an instantaneous jump (from zero to jumbo as you said). I think of it as a short period during which the Minkowski phase is "waking up", signal propagation is "getting up to speed". If there is some conceivable cyclical physical process whose cycles could be counted (a clock) during that brief episode then I imagine that process as waking up too, more or less in step with the speed of signal propagation.

 

[marcus]

Paulibus, wouldn't you agree that we are really not in the position to tell Nature that she cannot do physics without "time" as we know it? I would advise anyone who is interested enough they want to comment to first look at the paper. If you want the interval from ρ_c to ρ_c/2 to be parametrized so that you can write differential equations and plot curves, then you can use the declining density ρ as a parameter. It will not hurt us not to have "t" for a while. Or invent for ourselves an arbitrary "coordinate time" as in General Relativity, a parameter not corresponding to the reading on any physical clock.
The General Theory of Relativity does not have time as we know it UNTIL the equation is solved and we have a metric---then we can define various observer's timelines. The physics of the GR equation (from which the metric is born) happens without time.

 

[Helios]

Maybe when time is removed, photons crystallize into a Euclidean crystal called "photonium".
Then the Universe could have begun from this primordial infinite crystal, or Cosmic Ice, some state that had a constant density and was incompressible. If the substance exist, it could have had a negative specific latent heat so when it thawed, it gave off heat.

 

[marcus]

Delightful thought! I wonder what photon ice tastes like--I hope it comes in different flavors :w

 

[nikkkom]

I didn't read the article. But you can't do physics without time and space, there's no kinematics and thus also no dynamics.

I am not so sure about it.

Think about analyzing kinematics in Minkowski space, and comparing it to Euclidean space. It is easy to see that in Minkowski space, under "rotations" any object which is moving with velocity |v| = 1 can never, ever escape its light cone - it's just a consequence of how "circle" looks in Minkowski space (it's a hyperbola). That's why Minkowski space has a concept of "future", a place where you will end up no matter how hard you are trying to avoid it.

If you look at the same setup in Euclidean space, by using rotations (changing its direction of travel) object *can eventually reach any point*. Euclidean space has no "future".

But the interesting detail here that while thinking about it, you still allow objects to advance, to move. Thus, *proper time* of a moving object exists (in some vague sense of the word) even in Euclidean space.

This makes me think that a Universe with Euclidean signature *can* evolve, even though it has no coordinate with negative square (a "time" coordinate).

 

[marcus]

That's an interesting way of looking at it. It's different from what I had in mind.

 

[marcus]

I think we first heard about this signature change thing at extreme density (in LQC) from Martin Bojowald in 2011, in any case it has changed over the intervening years. Here is the first mention I know of:
http://arxiv.org/abs/1112.1899
Deformed General Relativity and Effective Actions from Loop Quantum Gravity
Martin Bojowald, George M. Paily
and then again in 2012
http://arxiv.org/abs/1206.2605
Quantum gravity, space-time structure, and cosmology
Martin Bojowald
(Submitted on 12 Jun 2012)
A set of diverse but mutually consistent results obtained in different settings has spawned a new view of loop quantum gravity and its physical implications, based on the interplay of operator calculations and effective theory: Quantum corrections modify, but do not destroy, space-time and the notion of covariance. Potentially observable effects much more promising than those of higher-curvature effective actions result; loop quantum gravity has turned into a falsifiable framework, with interesting ingredients for new cosmic world views. At Planckian densities, space-time disappears and is replaced by 4-dimensional space without evolution.
8 pages, 7 figures, Plenary talk at CosGrav12.
And then there were several more papers by Bojowald and co-authors where the idea came up in various forms. The basic idea of a signature change at Planckian densities persists. And then recently a collaboration with Aurelien Barrau:
http://arxiv.org/abs/1404.1018
Anomaly-free cosmological perturbations in effective canonical quantum gravity
Aurelien Barrau, Martin Bojowald, Gianluca Calcagni, Julien Grain, Mikhail Kagan
(Submitted on 3 Apr 2014)
This article lays out a complete framework for an effective theory of cosmological perturbations with corrections from canonical quantum gravity. Since several examples exist for quantum-gravity effects that change the structure of space-time, the classical perturbative treatment must be rethought carefully. The present discussion provides a unified picture of several previous works, together with new treatments of higher-order perturbations and the specification of initial states.
56 pages
In this Barrau Bojowald et al paper the discussion of signature change starts around page 32.
And after that paper came the "silent initial conditions" paper by Barrau, Linsefors, Mielczarek which I quoted at the beginning of this thread.
this is just a sketch
The signature change idea has not had an easy time being accepted in the LQC research community, I think. Not really sure where it stands now, I'm just a bystander watching from the sidelines. A Euclidean signature episode at high density (seemingly spelled out by the mathematics) may still seem very strange to many of the researchers. And maybe it is a false path. But I am interested in it and want to keep alert to developments. Barrau's research initiatives are almost always interesting anyway.

 

[MathematicalPhysicist]

I am not so sure about it.

Think about analyzing kinematics in Minkowski space, and comparing it to Euclidean space. It is easy to see that in Minkowski space, under "rotations" any object which is moving with velocity |v| = 1 can never, ever escape its light cone - it's just a consequence of how "circle" looks in Minkowski space (it's a hyperbola). That's why Minkowski space has a concept of "future", a place where you will end up no matter how hard you are trying to avoid it.

If you look at the same setup in Euclidean space, by using rotations (changing its direction of travel) object *can eventually reach any point*. Euclidean space has no "future".

But the interesting detail here that while thinking about it, you still allow objects to advance, to move. Thus, *proper time* of a moving object exists (in some vague sense of the word) even in Euclidean space.

This makes me think that a Universe with Euclidean signature *can* evolve, even though it has no coordinate with negative square (a "time" coordinate).

Well, there's the WIck change of phase from Minkowski pseduo metric to Euclidean metric, with the i^2=-1; so theses spaces are in someway interchangeable.

 

[julian]

Paulibus, wouldn't you agree that we are really not in the position to tell Nature that she cannot do physics without "time" as we know it? I would advise anyone who is interested enough they want to comment to first look at the paper. If you want the interval from ρ_c to ρ_c/2 to be parametrized so that you can write differential equations and plot curves, then you can use the declining density ρ as a parameter. It will not hurt us not to have "t" for a while. Or invent for ourselves an arbitrary "coordinate time" as in General Relativity, a parameter not corresponding to the reading on any physical clock.
The General Theory of Relativity does not have time as we know it UNTIL the equation is solved and we have a metric---then we can define various observer's timelines. The physics of the GR equation (from which the metric is born) happens without time.

I just want to clarify something you had said before...A solution of GR is not a particular metric but rather an equivalence class of metrics, each configuration related to each other by an active diffeomorphism. This diffeomorphism invariance washes away any notion physical meaning to space-time coordinates as understood in Newtonian or special relativistic physics. Spatial/temporal location then only has meaning when we have observers that use REAL PHYSICAL measuring devices, clocks, rulers, along with light pulses and such. Only when these real physical objects are included as part of the total physical "configuration", along with the metric, do we obtain a meaning to spatial/temporal localization under active diffeomorphisms.

In general we cannot have spacetime without dynamical entities such as these real measuring devices or other matter fields.