Testing Creation

[Mordred]

Fair enough, one often sees different claims of our universe being in a BH or WH. The aforementioned difficulty in having a homogeneous and isotropic universe is one piece of evidence against the possibility.

[joigus]

1 hour ago, Genady said:

I tend to agree, but there might be a subtlety in the question, tested by whom? Take the idea of a universe in a black hole, for example. In principle, it can be tested by an observer falling into the BH, and it can't be tested by an observer outside the BH, if I am not mistaken.

That's a fair point, although the words "in principle" are essential here. Garden-variety BHs would destroy in-falling observers with their terrible tidal forces, accretion disks, etc.

Also, I see as an essential part of science, particularly when it comes to testing, the possibility of reporting your results to other scientists. It remains possible, for example, that there is an afterlife, and that most people that ever existed know about it already. This kind of discourse, while logically tenable, does not constitute experimental science IMO.

There are very good questions that are not scientific questions. They belong to what I like to call the world of the tantalising.

[Genady]

1 hour ago, joigus said:

 I see as an essential part of science, particularly when it comes to testing, the possibility of reporting your results to other scientists. It remains possible, for example, that there is an afterlife, and that most people that ever existed know about it already.

Unlike the BH case, necromancy still has a chance 😉

Edited May 7, 2023 by Genady

[MJ kihara]

9 hours ago, Phi for All said:

In each case though, "nothing" means "a complete absence of things", and it's been pointed out that in some instances "nothing" may not be possible. 

A complete absence of things...I concur with you...now here is another issue with it, since we have a word about it and we communicate about it, we are aware that..there can be a complete absence of things, isn't it?

4 hours ago, Mordred said:

However there is an interesting side note. The Hubble parameter is higher in the past than today hence I rarely call it Hubble constant. Now if this formula is used to calculate the energy density of Lambda this would then imply a far higher energy density at the pre-inflation period just after the initial moment of the BB. If this is true then it is the equation of state for Lambda that is constant and not the energy density itself

Energy density of the whole universe remain to be the same ...since it's expanding the energy density per local volume within the universe keep reducing...a higher Hubble constant in the past than today....we are using local volume within the universe to measure hubble constant...in this case local is variable...this make sense so as to maintain energy conservation laws.

When the measurements get too much local we get...

8 hours ago, Mordred said:

This referred to as zero point energy ZPE for short

https://en.m.wikipedia.org/wiki/Zero-point_energy

These energy get too much large ...when nuclear fusion and fission is carried out we don't get out these energy...yet it's there...then..

On 5/6/2023 at 4:41 AM, Mordred said:

Now energy is simply the ability to perform work.

The definition of energy I think should be modified or adjusted to take into account all mentioned factors.

2 hours ago, joigus said:

There are very good questions that are not scientific questions. They belong to what I like to call the world of the tantalising.

An all encompassing scientific argument should be ready to tackle/answer any questions thrown at it,if not it should acknowledge it's limited to that extend.

[Mordred]

56 minutes ago, MJ kihara said:

 

Energy density of the whole universe remain to be the same ...since it's expanding the energy density per local volume within the universe keep reducing...a higher Hubble constant in the past than today....we are using local volume within the universe to 

 

I believe you mean total energy remains the same. As the volume increases the energy density would as well. However consider this detail. Does total energy remain the same if the cosmological constant is constant?

56 minutes ago, MJ kihara said:

 

These energy get too much large ...when nuclear fusion and fission is carried out we don't get out these energy...yet it's there...then..

 

Indeed the energy gets incredibly high along with the temperature which will correspond to the inverse of the scale factor.

As to whether the conservation of mass energy applies to the universe as a whole. Well there are arguments in both corners.

If your curious here is a useful formula to calculate the Hubble parameter at a given cosmological redshift

\[H_z=H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}}\]

Here is an example argument stating why energy conservation wouldn't apply

https://bigthink.com/starts-with-a-bang/expanding-universe-conserve-energy/

However one can easily find counter arguments that energy conservation does apply. For example I've read a recent paper from Allen Guth that it does apply.

Needless to say its still debatable

Edited May 7, 2023 by Mordred

[MJ kihara]

1 hour ago, Mordred said:

I believe you mean total energy remains the same. As the volume increases the energy density would as well. However consider this detail. Does total energy remain the same if the cosmological constant is constant?

Hz=HoΩm(1+z)3+Ωrad(1+z)4+ΩΛ−−−−−−

I think Total energy in this case equals energy density at universal level...but total energy at a local volume within the universe keep changing as zero point energy through quantum fluctuations lead to creation of measurable energy...hubble constant becomes constant at specific time zones during the evolution of the universe.

[Mordred]

That doesn't work sorry to say if a volume changes but the total energy remains constant then accordingly the energy density decreases. The only way energy density would remain constant is if energy is added to the system as the volume increases 

[joigus]

3 hours ago, MJ kihara said:

An all encompassing scientific argument should be ready to tackle/answer any questions thrown at it,if not it should acknowledge it's limited to that extend.

There is no such thing as an all-encompassing scientific argument.

4 hours ago, Genady said:

Unlike the BH case, necromancy still has a chance 😉

Sure. I think many of us here are familiar with the fact that some extremely unscientific disciplines are very difficult to dismiss completely.

[MJ kihara]

1 hour ago, Mordred said:

That doesn't work sorry to say if a volume changes but the total energy remains constant then accordingly the energy density decreases. The only way energy density would remain constant is if energy is added to the system as the volume increase

There two total energy...one that is universal and the other which is local.

The universal total energy is constant ... that include normal matter-energy and dark matter-energy,talking of universal volume...you need to know about the universal displacement in this case the universe is expanding into 'nothing'.Therefore,it's energy density remain constant...I think at such a situation energy and volume reaches unity.

Local Total energy is the one that is changing since it involves local volume-that is,we're not using any known edges of the universe to measure it,using only things within it(within the universe) to determine its volume.in this case energy density keep changing.

1 hour ago, joigus said:

Sure. I think many of us here are familiar with the fact that some extremely unscientific disciplines are very difficult to dismiss completely.

Introducing universal concepts like energy conservation laws...for them to hold they should be obeyed at the beginning and at the end,that is if there is any beginning or end... failure to do that, there should be well convincing reasons for that...that is what science is.

[joigus]

10 minutes ago, MJ kihara said:

Introducing universal concepts like energy conservation laws...for them to hold they should be obeyed at the beginning and at the end,that is if there is any beginning or end... failure to do that, there should be well convincing reasons for that...that is what science is.

Energy conservation is not universal. Energy conservation only holds if 1) The system can be described by a Lagrangian; and 2) The system has time-translation symmetry. This means that the Lagrangian changes only by a surface term when we apply a time translation. As another member has pointed out before:

On 5/6/2023 at 4:25 AM, MigL said:

If I may ...
It makes no sense to talk about energies needed to create a universe at the beginning of time.

Noether's theorem states that 'every differentiable symmetry of the action of a physical system  with conservative forces has a corresponding conservation law'.
If a process exhibits the  same outcomes regardless of time. then its Lagrangian is symmetric under continuous translations in time, and as per Noether's theorem, this symmetry accounts for thelaw of energy conservation of this system.
( paraphrased from Wiki )

As the beginning of time is decidedly non-symmetric, the energy conservation law is not constrained to hold, and the quantum fluctuation would not be constrained in the amount of energy it could introduce to the system.
Maybe enough to create a universe.

 

Also, I see no reason why a universe that's just popping up into existence --from a purely physical POV-- should be time-translation symmetric.

Conservation of energy for mechanical systems can help you solve the equations of motion.

Conservation of energy in GR, OTOH, comes from some kind of tautological consistency condition. You can call it a conservation law, if you want, but it doesn't play by the same rules. This "energy" no longer is our trusty old mechanical energy, but a related construct that includes dynamical, geometric, and vacuum terms. All the terms must add up to zero by definition. Not sure it can be used as any kind of predictive tool.

[MJ kihara]

Hi

2 hours ago, joigus said:

Also, I see no reason why a universe that's just popping up into existence --from a purely physical POV-- should be time-translation symmetric.

Time factor is coming from big bang onwards.

2 hours ago, joigus said:

This "energy" no longer is our trusty old mechanical energy, but a related construct that includes dynamical, geometric, and vacuum terms. All the terms must add up to zero by definition. Not sure it can be used as any kind of predictive tool.

You mean this ''energy'' is just a mathematical artefact...not real energy? 
When the terms are positive and negative to add up to zero...do you mean this "energy" can be positive energy or negative energy?

Can we classify energy as mechanical energy or quantum energy?

[Genady]

47 minutes ago, MJ kihara said:

When the terms are positive and negative to add up to zero...do you mean this "energy" can be positive energy or negative energy?

It can be. Take a look at these slides from Alan Guth's lecture in MIT:

[joigus]

1 hour ago, MJ kihara said:

You mean this ''energy'' is just a mathematical artefact...not real energy? 

I don't know about "real" or "artificial."

I do know that in classical dynamics or quantum mechanics, energy is a parameter that gets fixed by the initial conditions. You take, eg, one pendulum of a given mass and length. That's your system. You chose the magnitude of either an initial kick, displacement, or combination of kick and displacement. That determines the history.

The situation of the parametrics in GR is completely different. You don't fix one energy and get a subsequent evolution. The theory tells you that the energy --the Hamiltonian, as we call it if we hold any hope that the theory will be made consistent with quantum mechanics-- must be identically zero.

This is a common feature of all theories that are "insensitive to deformations of the coordinates," otherwise known as "diffeomorphism invariant." It's kinda puzzling, I know. 

I encourage you to look up: "diffeomorphism invariant theories have zero hamiltonian" on Google search.

And there you go:

https://arnold-neumaier.at/physfaq/topics/diff.html

Quote

Diffeomorphism invariant classical mechanics

Quote

[...] As a consequence, the Noether energy (the formal Hamiltonian constructed in the transition from a Lagrangian to a Hamiltonian formulation) vanishes identically and has no physical content.

 

[Mordred]

2 hours ago, MJ kihara said:

 

You mean this ''energy'' is just a mathematical artefact...not real energy? 
When the terms are positive and negative to add up to zero...do you mean this "energy" can be positive energy or negative energy?

Can we classify energy as mechanical energy or quantum energy?

The two main energy categories used in the Langrangian including Noether is potential energy and kinetic energy. This covers mechanical and quantum energy types. Keep in mind naming energy types is simply convenient labels. 

 The most convenient and near universal labels one can apply being the two I just named as they are used in the Lanqrangians of every gauge group of the Standard model as well as the Langrangian forms describing spacetime. 

This may help if we were to model the universe using the FLRW metric we tend to set the universe as a perfect fluid with adiabatic expansion. With those settings we further assume a closed system where energy is conserved.

FLRW Metric equations

\[d{s^2}=-{c^2}d{t^2}+a({t^2})[d{r^2}+{S,k}{(r)^2}d\Omega^2]\]

\[S\kappa(r)= \begin{cases} R sin(r/R &(k=+1)\\ r &(k=0)\\ R sin(r/R) &(k=-1) \end {cases}\]

\[\rho_{crit} = \frac{3c^2H^2}{8\pi G}\]

\[H^2=(\frac{\dot{a}}{a})^2=\frac{8 \pi G}{3}\rho+\frac{\Lambda}{3}-\frac{k}{a^2}\]

The following setting describes the energy conservation statement

\[T^{\mu\nu}_\nu=0\] gives the energy stress mometum tensor as 

\[T^{\mu\nu}=pg^{\mu\nu}+(p=\rho)U^\mu U^\nu)\]

\[T^{\mu\nu}_\nu\sim\frac{d}{dt}(\rho a^3)+p(\frac{d}{dt}(a^3)=0\]

which describes the conservation of energy of a perfect fluid in commoving coordinates describes by the scale factor a with curvature term K=0.

the related GR solution the the above will be the Newton approximation.

\[G_{\mu\nu}=\eta_{\mu\nu}+H_{\mu\nu}=\eta_{\mu\nu}dx^{\mu}dx^{\nu}\]

Thermodynamics

Tds=DU+pDV Adiabatic and isentropic fluid (closed system)

equation of state

\[w=\frac{\rho}{p}\sim p=\omega\rho\]

\[\frac{d}{d}(\rho a^3)=-p\frac{d}{dt}(a^3)=-3H\omega(\rho a^3)\]

as radiation equation of state is

\[p_R=\rho_R/3\equiv \omega=1/3 \]

radiation density in thermal equilibrium is therefore

\[\rho_R=\frac{\pi^2}{30}{g_{*S}=\sum_{i=bosons}gi(\frac{T_i}{T})^3+\frac{7}{8}\sum_{i=fermions}gi(\frac{T_i}{T})}^3 \]

\[S=\frac{2\pi^2}{45}g_{*s}(at)^3=constant\]

temperature scales inversely to the scale factor giving

\[T=T_O(1+z)\]

with the density evolution of radiation, matter and Lambda given as a function of z

\[H_z=H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}}\]

Now prior to electroweak symmetry breaking everything is in thermal equilibrium so we can describe this period as a scalar field. As I already have the workup for Higgs inflation handy from another thread I will add it here as an example. The subsequent equation does in fact work the same for chaotic inflation so its essentially identical though the derivatives to arrive to the equation of state does vary slightly.

Higgs Inflation Single scalar field Modelling.

\[S=\int d^4x\sqrt{-g}\mathcal{L}(\Phi^i\nabla_\mu \Phi^i)\]

g is determinant

Einstein Hilbert action in the absence of matter.

\[S_H=\frac{M_{pl}^2}{2}\int d^4 x\sqrt{-g\mathbb{R}}\]

set spin zero inflaton as

\[\varphi\]

minimally coupled Langrangian as per General Covariance in canonical form. (kinetic term)

\[\mathcal{L_\varphi}=-\frac{1}{2}g^{\mu\nu}\nabla_\mu \varphi \nabla_\nu \varphi-V(\varphi)\]

where \[V(\varphi)\] is the potential term

integrate the two actions of the previous two equations for minimal scalar field gravitational couplings

\[S=\int d^4 x\sqrt{-g}[\frac{M_{pl}^2}{2}\mathbb{R}-\frac{1}{2}g^{\mu\nu}\nabla_\mu\varphi \nabla_\nu \varphi-V(\varphi)]\]

variations yield the Euler_Langrene

\[\frac{\partial \mathcal{L}}{\partial \Phi^i}-\nabla_\mu(\frac{\partial \mathcal{L}}{\partial[\nabla_\mu \Phi^i]})=0\]

using Euclidean commoving metric

\[ds^2-dt^2+a^2(t)(dx^2+dy^2=dz^2)\]

this becomes

\[\ddot{\varphi}+3\dot{\varphi}+V_\varphi=0\]

\[S=\int d^4 x\sqrt{-g}[\frac{M_{pl}^2}{2}\mathbb{R}-\frac{1}{2}g^{\mu\nu}\nabla_\mu\varphi \nabla_\nu \varphi-V(\varphi)]\]

and 

\[G_{\mu\nu}-\frac{1}{M_{pl}}T_{\mu\nu}\]

with flat commoving geometry of a perfect fluid gives the energy momentum for inflation as 

\[T^\mu_\nu=g^{\mu\lambda}\varphi_\lambda \varphi_\nu -\delta^\mu_\nu \frac{1}{2}g^{\rho \sigma} \varphi_\rho \varphi_\sigma V(\varphi)]\]

 

\[\rho=T^0_0=\frac{1}{2}\dot{\varphi}^2+V\]

\[p=T^i_i (diag)=\frac{1}{2}\dot{\varphi}^2-V\]

\[w=\frac{p}{\rho}\]

\[w=\frac{1-2 V/\dot{\varphi^2}}{1+2V/\dot{\varphi^2}}\]

This last equation is the equation of state for a scalar field for both Higgs inflation as well as chaotic inflation. The result gives w=-1 most of us are familiar with. With w=-1 this tells us Lambda (DE) is constant. In thermodynamics it also represents an incompressable fluid.

If we're dealing with quintessence then we would have a value greater or lesser than w=-1. In this case DE would vary over time.

Anyways what the above shows us is that in cosmology we model our universe under the following assumptions. A perfect fluid with adiabatic and isentropic process where the system is closed (causality via the speed limit of information exchange c further ensures this.) With the further assumption that due to being a closed system we can apply energy conversation. Any conserved quantity must be in a closed system that's one of the golden rules when it comes to any conservation law

[Phi for All]

11 hours ago, MJ kihara said:

A complete absence of things...I concur with you...now here is another issue with it, since we have a word about it and we communicate about it, we are aware that..there can be a complete absence of things, isn't it?

I concur that words are very important in the quality of our communication, and I'm sure that you can appreciate that there can only be a "complete absence of things" in certain contexts, and that they aren't always the same as "nothing". 

[Genady]

12 hours ago, MJ kihara said:

we are aware that..there can be a complete absence of things, isn't it?

I am not aware of it. What is "a complete absence of things"? I don't understand it.

Do you mean, in math? An empty set?

[MJ kihara]

4 hours ago, Genady said:

It can be. Take a look at these slides from Alan Guth's lecture in MIT:

The issue of gravitational field having negative energy to me it's difficult to comprehend and not being realistic... since gravitational field pervades the whole of the universe and could have annihilated matter...we could not be existing.

Am of the opinion that energy should be redefined to take into consideration information,dark energy,dark matter e.t.c so that energy=0 could be comprehendable for people like me.

2 hours ago, Mordred said:

Any conserved quantity must be in a closed system that's one of the golden rules when it comes to any conservation law

Thanks for the enlightment...sometimes math is scary 🤯.

Anyway i think if the universe is enclosed within nothing...the outer of the universe being nothing...then the universe is a closed system then conservation law hold...unless we are in a universe within another universe.

1 hour ago, Genady said:

I am not aware of it. What is "a complete absence of things"? I don't understand it.

Do you mean, in math? An empty set?

Zero,void,nothingness,empty.....empty set  are you aware of it?..am lacking words, in other words..is it there?

[Genady]

1 hour ago, MJ kihara said:

Zero,void,nothingness,empty.....empty set  are you aware of it?..am lacking words, in other words..is it there?

Sorry, but I still don't get it. Even the case of empty set is not "a complete absence of things", because there has to be a set for it to be empty, and this set is present rather than absent.

[Phi for All]

2 hours ago, MJ kihara said:

Anyway i think if the universe is enclosed within nothing...the outer of the universe being nothing...

It's a mistake thinking this way. The universe is everything. It can't be "enclosed". There is no point where the universe ends and "nothing" begins.

If you're describing the universe, there's nothing outside of it. If you were describing a nightclub you visited, there's no part of the nightclub that is outside the nightclub, by its very definition. 

[joigus]

3 hours ago, MJ kihara said:

Zero,void,nothingness,empty.....empty set  are you aware of it?..am lacking words, in other words..is it there?

You should avoid identifying common notions like "emptiness" with mathematical ones ("zero") too glibly.

You would think, eg, that "nothing" or "emptiness" (the vacuum perhaps?) corresponds to the zero state vector in quantum mechanics, when what the theory tells you is that the zero vector is non-physical. All physical states have measure one.

[MigL]

3 hours ago, MJ kihara said:

The issue of gravitational field having negative energy to me it's difficult to comprehend and not being realistic... since gravitational field pervades the whole of the universe and could have annihilated matter...we could not be existing.

It is very difficult to think of an analogy for negative gravitational pressure.

Think of it as a coiled spring.
Gravity, in GR, acts on all forms of energy, and if gravity were to compress this spring slightly, its gravity would further increase because of the added energy of compression.
This would be an example of positive gravitational pressure, and gravity acts like we expect it to.

Now, for the negative pressure example, the best I can come up with is a stretched spring, under tension, but it's not gravity  that's pulling it apart ( no such thing as repulsive gravity ) rather, it is the universe itself through the gravity field, or Cosmological Constant, aka Dark Energy, that is doing the stretching.

This CC or Dark Energy is a scalar term that does not vary with distance, whereas the rest of the gravitational terms do, and so we have gravity dominating at close distances.
But when gravity decreases with the square of the distance, it is a given that at a certain distance the gravitational terms will be less than the CC or Dark Energy term, resulting in expansion.

Sorry if I could not be clearer.

[geordief]

3 hours ago, Phi for All said:

It's a mistake thinking this way. The universe is everything. It can't be "enclosed". There is no point where the universe ends and "nothing" begins.

If you're describing the universe, there's nothing outside of it. If you were describing a nightclub you visited, there's no part of the nightclub that is outside the nightclub, by its very definition. 

Can I think of the place and time where I happen to be now  as the boundary of the universe   in the same way as I heard it explained  that the Big Bang took place at every point?

[Genady]

59 minutes ago, geordief said:

in the same way as I heard it explained  that the Big Bang took place at every point

Curious. I didn't know it needs explanation and more so, there is a way to explain it.

[geordief]

2 minutes ago, Genady said:

Curious. I didn't know it needs explanation and more so, there is a way to explain it.

You  haven't heard this said?

Along the lines of (eg in a tv documentary)"Where did the Big Bang take place?It happened everywhere 

It took place where you are sitting. It took place on the Moon 

It took place everywhere  .There is no one place where it occurred"

 

I have heard this said many times.Perhaps "explanation" is the wrong description.How else to describe it?

 

It is not wrong  is it?

[Genady]

Just now, geordief said:

You  haven't heard this said?

Along the lines of (eg in a tv documentary)"Where did the Big Bang take place?It happened everywhere 

It took place where you are sitting. It took place on the Moon 

It took place everywhere  .There is no one place where it occurred"

 

I have heard this said many times.Perhaps "explanation" is the wrong description.How else to describe it?

 

It is not wrong  is it?

No, of course it is not wrong. Every place in the universe you pick, was inside that hot dense stuff that was the universe content at the time of Big Bang.