dark energy, Unruh effect , Hawking radiation

[stephaneww]

Hello

I would like to know if the relations below are known?

T Hawking the radius of CMB t1 / T Hawking the radius of CMB t0 = (M = total mass of dark energy included)

unruh acceleration with T Hawking with the radius of the CMB t1 / unruh acceleration with T Hawking with the radius of the CMB t0 =

for simplicity:

M t1 * (CMB radius t0) ^ 2 * G / (M t0 * (CMB radius t1) ^ 2 * G ) (1) =

Omega lambda t0 * radius of the CMB t1 / (Omega lambda t1 * radius t0 of the CMB) (2)



equalities (1) and (2) are thus simplify:

Omega lambda t0 * (CMB radius t1 ) * M ^ 3 t0 / (omega lambda t1 * (CMB radius t0) ^ 3 * M t1) = 1

that it simplifies

Omega lambda t0 * H0 ^ 2 / (Omega lambda t1 * H1^ 2) = 1

we have

value of the cosmological constant = 3 / c² * Omega lambda t0 * H0 ^ 2

there is therefore

cste t0 / cste t1 = 1



Additional questions:

- Can we consider the universe as a quantum black hole with Hawking radiation at cmb radius ? (edit)

- Is this the theoretical demonstration (by expansion and experimental) of the validity of the unrhu effect?

- Is it a link between quantum mechanics and acceleration of the universe?

thank you in advance

 

sorry for the text in french : it was translate by google chrome when I modifed the message...

stéphane

Edited September 9, 2015 by stephaneww

[Mordred]

Unruh radiation and Hawking radiation deals with specific system states.

 

Unruh radiation can be applied at the cosmic event horizon or at the EH of a blackhole. However Hawking radiation is specifically at the BH event horizon.

 

That being said an older model of virtual particle production that was once suggested for expansion was Parker radiation. This fell out of use as the process generated too much energy.

 

There is countless virtual particle production variations. For example a couple of suggested forms is the inflaton (inflation) and the curvaton. The last one hasn't been in literature for years though.

 

The Cosmological constant aka dark energy is tricky to explain why it is so close to zero, and why it remains constant.

 

Pretty much any model of explaining it via one form of virtual particle production or another, fell out of use. Mainly because such processes lead to 120 orders of magnitude too much energy.

(Unfortunately the math you posted is extremely difficult to translate the way you wrote it). If you can latex the formulas it would help.

 

Here is a thread on how to latex.

 

http://www.scienceforums.net/topic/3751-quick-latex-tutorial/page-5#entry207217

 

Now onto quantum virtual particle production.

 

One form that was once used to explain expansion was based upon the Heisenberg uncertainty principle via the quantum harmonic oscillator.

A reference for this is zero point energy. Which is QMs lowest possible energy state.

 

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

[latex]E=\frac{\hbar w}{2}[/latex]

 

Even this lowest energy state, without additional particle production leads to 120 orders of magnitude too much energy to explain the cosmological constant

 

[latex]\Lambda[/latex], this is often considered quantum mechanics "biggest mistake"

 

 

It took a bit of digging to find some references on Leanard Parker radiation in regards to CMB anistropies.

https://uwm.edu/physics/people/parker-leonard/

 

https://www.google.ca/url?sa=t&source=web&cd=2&rct=j&q=Leonard%20Parker%20radiation%20pdf&ved=0CCAQFjABahUKEwi_o8GvhunHAhXHSogKHf4ND5A&url=http%3A%2F%2Farxiv.org%2Fpdf%2Fgr-qc%2F9506010&usg=AFQjCNEHw3Tq7jx6JPtPcD21u2IuUSyxKQ&sig2=rUoAsSuqHtUqGQUfxwSBBw

 

 

https://www.google.ca/url?sa=t&source=web&cd=6&rct=j&q=Leonard%20Parker%20radiation%20pdf&ved=0CC4QFjAFahUKEwi_o8GvhunHAhXHSogKHf4ND5A&url=http%3A%2F%2Fwww.uv.es%2Folalgon%2Fpublico%2Fpapers%2FPhysRevD_77_104034(2008).pdf&usg=AFQjCNEh3jdaulAPoNyusQWqhppKLOIAsw&sig2=JYItzL2TrnBr6uEqmAfh7A

 

http://www.oa.uj.edu.pl/user/lasota/Astronomy_News/Parker.pdf

 

The last article is by Parker himself though Parker is a coauthor of the second paper. He has others some behind pay walls.

(You may note the dates of publication, some of his papers precede Allen Guths inflation.) As well as LCDM. So care must be taken in the involved metrics. For example he uses a conformal universe metric as opposed to commoving distances. He also doesn't refer to the cosmological constant. The last paper is based on pre WMAP findings. Dark energy was still debatable, so was universe curvature.

( for that matter Parker radiation precedes Hawking radiation.)

Edited September 9, 2015 by Mordred

[MigL]

Nice Mordred, thanks.

I'd never heard of Parker radiation.

[stephaneww]

Hello

The idea to calculate the temperature hawking at cmb and deduce an unruh acceleration related dark energy is not new:

http://arxiv.org/pdf/1002.4278.pdf

However, despite my research I have not found my equalities and their demonstration

 

Edited October 3, 2015 by stephaneww

[stephaneww]

another link between unruh temperature and the acceleration of the universe in the m-theory:

 

http://arxiv.org/pdf/0908.1001v1.pdf

[stephaneww]

Hello

 

can you help me ?

 

do you think this article confirm my proposition ?

 

http://arxiv.org/abs/1511.05450

 

thank you in advance

 

edit 1

 

i calculate that the relation is right for hubble radius, in fact it's exact for any radius

 

edit 2

 

It's even better than I thought, they make assumptions to arrive at the relation (4) at the temperature of hawking with gravity surface, it starts to feel good for me

 

edit 3

 

However, with the exact values for the relation (10) I don't find the exact value of the cosmological constant with a factor 10

edit 4

oups correction

...

equalities (1) and (2) are thus simplify:

Omega lambda t0 * (CMB radius t1 )^3 * M t0 / (omega lambda t1 * (CMB radius t0) ^ 3 * M t1) = 1

that it simplifies...

Edited November 29, 2015 by stephaneww

[stephaneww]

Hi


I checked and it's ok only for comoving radial distance of the observable universe and with several assumptions. That is why I asked that it be moved to "speculation". I tried to publied a paper about it.It was denied with theses comments :

In this straight paper, the author suppose that the Universe has a Hawking temperature at comoving radial distance. Then, the author claims to have found a relation between Hawking temperature and dark energy. That idea is not new. But, in cosmological context, the hawking temperature is associated not with the radial comoving distance, but with the future horizon distance. The author says that dark energy was discovered, which is wrong. Dark energy is a hypothesis, along with many others, to explain the discovery of cosmic acceleration. The naive assumptions made by the author leads to a cycle, and the alleged relation between Hawking temperature and Dark energy, culminates with the demonstration that the cosmological constant is a constant as assumed in eq. (3). Therefore, the author does not show that dark energy is related with the Hawking temperature as he claim. Also, Hawking temperature dependes of the observer. So, if the Universe has a Hawking temperature should exists privileged observers. But in a homogeneous and isotropic Universe, there is no such observer and Hawking radiation at comoving radial distance should vanishes.

 

I tried to modify my paper based on comments. The new paper is the pdf file attach.I also attached a copy screen of a spreadsheet ods that shows that calculations are accurate. I should have yours opinions, and if theses calculations may have a physical sense ???

 

 

thank you in advance.if you are interested in the ODS or XLT, send me a private message with your email

forum_final.pdf

have a good day

[stephaneww]

hello

 

another relation with hawking temperature in planck units which can be interresting :

 

T_Hawking, with surface gravity= G m_p/l_p² (the same relation which is in the paper) = Planck Temperature / (2*PI)

 

I have no idea about it's sense, thank you if you can also find an explanation to this last relation.

 

Stéphane

Edited August 23, 2016 by stephaneww

[imatfaal]

hello

 

another relation with hawking temperature in planck units which can be interresting :

 

T_Hawking, with surface gravity= G m_p/l_p² (the same relation which is in the paper) = Planck Temperature / (2*PI)

 

I have no idea about it's sense, thank you if you can also find an explanation to this last relation.

 

Stéphane

 

 

I think that is definitional rather than interesting - but I am not totally sure. If i recall correctly - and a quick mess with the basic planck units seem to bear this out - the planck mass is the mass of a black hole with a schwartchild radius (or diameter?) equal to a planck length . The planck temperature is intimately connected with the wavelength of the radiation it would give off - which is what we are talking about with hawking temperature

[stephaneww]

 

 

I think that is definitional rather than interesting - but I am not totally sure. If i recall correctly - and a quick mess with the basic planck units seem to bear this out - the planck mass is the mass of a black hole with a schwartchild radius (or diameter?) equal to a planck length . The planck temperature is intimately connected with the wavelength of the radiation it would give off - which is what we are talking about with hawking temperature

hello imatfaall

 

thank you.

 

we can find G with this definition :

 

T_Hawking, with surface gravity= G m_p/l_p² (the same relation which is in the paper) = Planck Temperature / (2*PI)

 

 

it's

 

[latex]G=\frac{Temp_p*k_B*l_p^2*c}{\hbar*m_p}[/latex]

 

is that this may be the beginning of a definition of quantum gravity ?

 

Thank you for your answers.

 

stéphane

Edited September 2, 2016 by stephaneww

[imatfaal]

hello imatfaall

 

thank you.

 

we can find G with this definition :

 

 

it's

 

[latex]G=\frac{Temp_p*k_B*l_p^2*c}{\hbar*m_p}[/latex]

 

is that this may be the beginning of a definition of quantum gravity ?

 

Thank you for your answers.

 

stéphane

 

Again - I think this is an artefact of the planck units rather than anything profound . All planck units are interelated and the only constants required are the speed of light, newton's graviational, permitivity of free space, boltzmann's, planck's and the value of pi. You can manipulate the dimensions of any of the planck units or combinations of same to punch out these constants - but they are there because that is how the unit system was designed. If you could tie in any of the universal dimensionless constants (like alpha the coupling constant 1/137) with the planck units then you would start getting somewhere.

 

The planck temperature is the temperature at which photons of planck energy would be emitted, it is also the temperature at which emitted radiation would have the same wavelength (factor of 2pi) as the compton wavelength - these would both lead to us assuming that both gravity and quantum effects would need to be taken into account for any calculations at the planck scale or lower. So yes - this is kind of where quantum gravity starts; but I dont think that was what you meant. I don't think your rearranged equation provides any illumination into the question other than by showing how the planck system of units was devoloped

[stephaneww]

ok. thank you imatfaal; i have understand this time

 

have a goode day.

ooops...

 

on a french forum somebody give me an explaination : if there is 2 Pi somewhere, this is because something turn and in the case of Hawking temperature he says it's the time. A story of signature of -+++ and ++++ to simplifie calculation. I'm not able to translate all of his long post; sorry.

 

have a good day

Edited September 2, 2016 by stephaneww

[stephaneww]

Hi

 

 

I checked and it's ok only for comoving radial distance of the observable universe and with several assumptions. That is why I asked that it be moved to "speculation". I tried to publied a paper about it.It was denied with theses comments :

 

I tried to modify my paper based on comments. The new paper is the pdf file attach.I also attached a copy screen of a spreadsheet ods that shows that calculations are accurate. I should have yours opinions, and if theses calculations may have a physical sense ???

 

 

thank you in advance.if you are interested in the ODS or XLT, send me a private message with your email :

(the bad PDF)

dark_energy.png

have a good day

Hello

 

Sorry I just saw that I have made a small mistake in the PDF file on the gravity surface : it needs a square.

 

Joint here the good PDF :

 

forum_final2.pdf

 

I think it's perhaps interresting because it's a link between the LambdaMCD model and the quantum mechanics

Edited December 27, 2016 by stephaneww

[stephaneww]

ooops

 

in forum_final2.pdf there is a small error

 

in (V) : inverse M_t0 and M_t1 please

 

Happy new year

[Mordred]

Several problems that come to mind.

 

1) Hawking radiation only occurs when the BH blackbody temperature is higher than the blackbody temp of the surrounding universe. This hasn't occurred yet for any BH except possibly micro blackholes.

 

2) the Particle production of Hawking radiation will not have a homogeneous and isotropic distribution. The universal speed limit still applies.

 

3) there is evidence the cosmological constant was in effect immediately after inflation. Though just not dominant during the radiation/matter dominant eras.

 

This includes time periods prior to blackholes being able to form in the first place. Including eras where the average temperature was too high for even atoms to form with stability. Let alone Stars/Bh's.

 

Finally if you calculate the average energy density per cubic metre of the cosmological constant. You would find the energy density to be far greater than is producable by all the baryonic matter in the universe. Which is 3% the mass budget. This includes blackholes.

 

Even if every BH was emitting Hawking radiation which we haven't found a single example that is. Every blackhole would have radiate their entire mass and still not produce enough energy to account for the total energy of the cosmological constant.

 

 

The biggest killer though is no known BH has a blackbody temperature higher than the surrounding universe. None are emitting Hawking radiation as the universe is still too hot. Temperature always goes from hot to cold. Every BH is still absorbing the higher universe temperature.

 

This would require blackholes to have less mass than that of our moon to have a blackbody temperature greater than that of our universe for Hawking radiation to start. It is precisely this reason we can neither prove or disprove Hawking radiation. No BH we have found has the right conditions to emit Hawking radiation.

 

The above doesn't mean blackholes don't assist expansion. In fact they do, but they do so by a different mechanism.

 

As matter collapses into structures, the global mass value decreases as matter is being condensed into anistropy regions. As the global mass density decreases the global ability of gravity to cause collapse also decreases. A matter only universe can still expand.

Edited January 8, 2017 by Mordred

[stephaneww]

Hello Mordred

Indeed, there seem to be many serious obstacles to this simplistic calculation.

I observe, however, that the temperature which I obtain increases in the course of time. Moreover, the fact that the thermal agitation increases seems to go together with the increase of the entropy (cf the new theory of E. Verlinde ???).

I am not qualified enough to discuss the theoretical aspects further.

Thank you for your contribution, I felt a little alone.

 

I hold essentially this:

 

No BH we have found has the right conditions to emit Hawking radiation.

 

 

Edit :

 

Uh, however, I have a question: Ratios (II) and (III) only concern the Unruh acceleration, which can also be calculated on the basis of relativistic data. This is close to the value of the acceleration of the expansion of the universe. How do you see the question from this point of view please?

Edited January 8, 2017 by stephaneww

[Mordred]

Unruh radiation only occurs on cosmological horizons such as our event horizon. In essence its to account for the detail that once a particle drops from our observable portion this has implications for the energy budget.

 

This still however leaves the problem that no particle exceeds c, Unruh radiation cannot maintain the homogeneous and isotropic distribution we see today.

 

This would require a mechanism that is present at roughly the same dynamic at every point in our universe.

 

Virtual particles cannot travel far enough from a cosmological horizon to account for a homogeneous and isotropic distribution. In point of detail the mean free path of a virtual particle is incredibly short compared to the real particle of the same type. A virtual particles lifetime being shorter than the real particle restricts this.

 

The only way virtual particles can account for the cosmological constant is via some form of process occurring everywhere at once. Not at specific locations such as horizons.

 

The speed of information exchange being c limits this possibility.

 

The Heisenburg uncertianty would certainly qualify as occuring everywhere but led to a result of 120 orders of magnitude too much energy produced. Today one of the leading possibilities has to fo with the Higgs field and its metastability.

 

This is as far as I know the leading possibilities for the cosmological constant. Though its still under research.

 

 

The main difficulties in the cosmological constant is its homogeneous and isotropic distribution and its constancy. Thermodynamic processes simply are not constant enough to account for its constancy and distribution.

 

Lol side note I spent 5 years trying to find a thermodynamic process that could maintain a constant homogeneous and isotropic distribution.

 

Never did succeed. The ideal gas laws and speed of information exchange defeated every attempt I made. Yes I tried various various forms of radiation. Hawkings,Unruh and Parker. Even the inflaton which is used for inflation but once the universe reached a certain volume even the inflaton wouldn't work. During inflation the universe was small enough for the inflaton to be effective. Our universe today is simply to immense for this to be true. Using the inflaton today would require bubble horizons that propogate outward acvordingly to the speed of information exchange limit.

 

Both Unruh and Hawking are localized to their respective systems. The mean free path and speed of information exchange is too restrictive to maintain a homogeneous and isotropic distribution that stays constant as the volume increases. Not on the scale of our universe's sheer volume.

 

Here is a simplified analogy. Ignoring information exchange. Take a volume that is increasing. You have a constant source of energy adding to that volume. However the density will still decrease as the volume increases unless the added energy also increases to maintain a constant density. This system I just described is however inhomogeneous and anistropic not homogenous and isotropic. Matter would move outward from the source.

 

Both Unruh and Hawking would follow this inhomogeneous and anistropic flow from their respective horizons.

Edited January 8, 2017 by Mordred

[stephaneww]

...

 

This still however leaves the problem that no particle exceeds c, Unruh radiation cannot maintain the homogeneous and isotropic distribution we see today.

 

Does the flow of the expansion don't drive the particles and space beyond c at a certain distance ?

 

This would require a mechanism that is present at roughly the same dynamic at every point in our universe....

The only way virtual particles can account for the cosmological constant is via some form of process occurring everywhere at once. Not at specific locations such as horizons.

I do not understand: it has nothing to do with the fact that we can conceive that every point can be seen as the center of the universe. (I think I have to mix everything up)

 

The Heisenburg uncertianty would certainly qualify as occuring everywhere but led to a result of 120 orders of magnitude too much energy produced. Today one of the leading possibilities has to fo with the Higgs field and its metastability.

This is as far as I know the leading possibilities for the cosmological constant. Though it's still under research.

This is another problem I tried to understand... If you take only the joule value in Planck's units (and let the volume of Planck to calculate the density) * energy density of the cosmological constant in joules/m³ you find something around 1 with ([LaTex]\Omega_\Lambda=1,111*10^{-52}m^{-2}, H_0=67,74[/LaTex]). edit: i have perhaps forget a factor 3/pi The problem become the units : Joules²/m³

 

Lol side note I spent 5 years trying to find a thermodynamic process that could maintain a constant homogeneous and isotropic distribution.

 

Never did succeed. The ideal gas laws and speed of information exchange defeated every attempt I made. Yes I tried various various forms of radiation. Hawkings,Unruh and Parker. Even the inflaton which is used for inflation but once the universe reached a certain volume even the inflaton wouldn't work. During inflation the universe was small enough for the inflaton to be effective. Our universe today is simply to immense for this to be true. Using the inflaton today would require bubble horizons that propogate outward acvordingly to the speed of information exchange limit.

 

Lol note, me too : If you have not succeeded, I do not see how I could

 

Edit :

Here is a simplified analogy. Ignoring information exchange. Take a volume that is increasing. You have a constant source of energy adding to that volume. However the density will still decrease as the volume increases unless the added energy also increases to maintain a constant density. This system I just described is however inhomogeneous and anistropic not homogenous and isotropic. Matter would move outward from the source.

 

 

It resembles the stationary universe abandoned since a long time because of cmb this? no ?

Edited January 8, 2017 by stephaneww

[Mordred]

Your value should be roughly 7.2 ×10^-10 joules/metre^3.

 

No expansion doesn't drive particles at greater than c. Per cubic metre the rate of expansion today is roughly 70 km/s/Mpc.

 

The greater than c expansion term is a misnomer of seperation distance itself. Its a mathematical consequence of the formula v=Hd. This article describes it well.

 

http://tangentspace.info/docs/horizon.pdf :Inflation and the Cosmological Horizon by Brian Powell

 

A way to think of the difference between Higgs treatment to say Unruh is to understand what conditions cause particle production.

 

All particles are merely excitations of a field. They are simply localized anistropies within a tight volume of a field. This includes quantum fluctuations such as virtual particles. Whenever you have potential differences in a field particles are produced.

 

In Hawkings and Unruh these potential differences is localized to the event horizons. In a global field such as our universe, treating the universe as a field, we get quantum fluctuations which can be inherent ie Heisenburg uncertainty principle or phase change symmetry breaking.

 

The Electroweak symmetry break that led to inflation being a prime example. Its no coincidence inflation occurs at roughly the same time that the electro-weak symmetry break occurs. New particles drop out of thermal equilibrium which further affects temperature contributions.

 

In all cases the average field strength is effectively zero on a global scale with the exception of the Higgs field itself. This is the basis for Higgs being a possibility for the cosmological constant.

 

Here these articles better describe it.

 

http://arxiv.org/abs/1402.3738

http://arxiv.org/abs/0710.3755

http://arxiv.org/abs/1006.2801

 

The research leads to a possible explanation for both inflation and the cosmological constant. In point of detail part of the same process for both. Without introducing any particle outside the standard model such as the inflaton.

Edited January 8, 2017 by Mordred

[stephaneww]

Your value should be roughly 7.2 ×10^-10 joules/metre^3.

 

No expansion doesn't drive particles at greater than c. Per cubic metre the rate of expansion today is roughly 70 km/s/Mpc.

 

The greater than c expansion term is a misnomer of seperation distance itself. Its a mathematical consequence of the formula v=Hd. This article describes it well.

 

http://tangentspace.info/docs/horizon.pdf :Inflation and the Cosmological Horizon by Brian Powell

my values are with the most recent values of Mission Planck

 

I find 5,3*10^-10 joules/m^3 for the cosmological constant. I on the pdf now nd ready to read it

[Mordred]

Thats within acceptable degree of accuracy

my values are with the most recent values of Mission Planck

 

I find 5,3*10^-10 joules/m^3 for the cosmological constant. I on the pdf now nd ready to read it

Just keep in mind that value will change everytime we use a different Hubble constant. As its a calc from the critical density formula

Edited January 8, 2017 by Mordred

[stephaneww]

ooops after a quick reading,I think there is perhaps a big confusion :

 

have a look on the image here :

 

http://www.scienceforums.net/topic/91064-dark-energy-unruh-effect-hawking-radiation/ post 7

the horizon I consider in the "paper" is 4,3*10^26 meters, I think that you consider the event horizon (i.e. Hubble radius), but it's not what i talk about.

Just keep in mind that value will change everytime we use a different Hubble constant. As its a calc from the critical density formula

 

I use the formula which is on wikipedia. Edit : and I know that ,)

Edited January 8, 2017 by stephaneww

[Mordred]

no I'm not getting the Hubble horizon confused with either the particle horizon nor the event horizon. When you get down to it all these horizons are apparent horizons based on observer location. Then again so is the BH event horizon lol.

ooops after a quick reading,I think there is perhaps a big confusion :

 

have a look on the image here :

 

http://www.scienceforums.net/topic/91064-dark-energy-unruh-effect-hawking-radiation/

 

the horizon I consider in the "paper" is 4,3*10^26 meters, I think that you consider the event horizon (i.e. Hubble radius), but it's not what i talk about.

 

 

I use the formula which is on wikipedia.

If its the same page I'm thinking of its using the critical density formula. The reason we can use that formula for this purpose is that we know our universe is extremely close to critical density. Edited January 8, 2017 by Mordred

[stephaneww]

ok I think I understand indeed my problem : I consider our universe is a black hole.for calculate a termperature but its horizon is beyond so the calculation have no sense

Edited January 8, 2017 by stephaneww

[Mordred]

That and a horizon is an anistropic and inhomogeneous structure. We need a process that is homogeneous and isotropic throughout its entire volume.

 

By the way glad to see you pay attention to the actual physics instead of clinging to your model idea being correct. Its nice to see in Speculations +1.

 

Couple of hints, in expansion there is no pressure/temperature gradient. There is no net flow.

 

thermodynamically this is an adiabatic and isentropic expansion. Adiabatic meaning no net inflow/outflow of energy.

Edited January 8, 2017 by Mordred