# Planck energy is a max, is there a mimimum too?

• hurk4
In summary: Weyl curvature going to zero, in the very late universe.I thought about how if that were to be the case then the universe could be reborn. Crazy, but at least it's something to think about.In summary, Wallace is right. Penrose has a crazy idea, but it's based on sound thermodynamic reasoning. If the Weyl curvature is zero then the universe can be reborn.
hurk4

Hi Hurk!,

I thought your idea in the document file was interesting, so I copied it here. there is a lecture by Penrose in which he considers not energy density going to zero but the Weyl curvature going to zero, in the very late universe.

And he speculates that when the Weyl curvature is (essentially or exactly?) zero then the universe can be reborn. That sounds crazy, and when he gave the talk at Cambridge he admitted it was a crazy idea, but he nevertheless developed it very carefully, with lots of arguements and sketches. he put mathematical thought into it.

So you have a friend and ally in Penrose. curvature and energy density are closely related, and there is at least one other person in the world who thinks that when it gets low enough then something can happen.

I will get back to this later. Have to go out. I will get the link to that Penrose talk, slides and audio.

Planck energy density is a max, is there a minimum too?

Intuition, though sometimes helpful, does not always lead to a good scientific answer.
We now know that where classic theory meets QM we find a maximum for obtainable mass density (Planck density) thus energy density.
Space as we now know can expand (Hubble expansion) at the cost of energy density.
By intuition I have a feeling that it might be a good question to ask whether it is possible to dilute energy density almost to zero. Is it possible from theory (e.g. QT) to expect that there must be an end to such a dilution? IMO it can’t be so that there are voids with absolutely nothing in the space filled with energy. So if energy density, (has a minimum), can not be diluted to whatever low level and if voids, with really nothing, don’t exist then as a consequence expansion of space must come to a halt too?
Do you think my intuition is wrong in this case?

I'm back. Here is the link to slides and audio of the Penrose talk:
www.Newton.cam.ac.uk/webseminars/pg+ws/2005/gmr/gmrw04/1107/penrose/

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In any reasonable current model for dark energy, the energy density will never drop to zero. In the case of vacuum energy, the whole point is that the energy density stays constants in contrast to the matter density that drops with the inverse of the 'volume' of the Universe. So as the Universe expands the relative contribution to the energy density shifts from being matter dominated to being cosmological constant or dark energy dominated.

In the standard model (the one that fits the data!) this has already happened. The 'final' energy density of the Universe will never be much less than it is today. To get what you suggest occurring to happen you have to extrapolate the behavior of dark energy in the future to be much different to what it is today. It must have an equation of state that will increase in the future in a way that is not suggested by the data that we have, or will ever be able to get since we cannot look into the future.

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Hurk, Wallace is right.
In the standard cosmology picture there is the dark energy, to account for accelerated expansion, and it is usually assumed to be constant throughout space and time.

this would correspond to a cosmological constant Lambda, a basic feature of the prevalent LambdaCDM model.

dark energy if you believe in it, is 73 percent of the present total, which means it is about 0.6 joules per cubic kilometer

if you believe in it, and that it is constant, as in the LCDM model, then our universe energy density can never go below 0.6 joules per cubic km.

but there is still something in your idea and you might want to watch Penrose slideshow.
he says that SOMETHING can go to zero, a certain COMPONENT of the energy density one might say. and he argues that this would prepare the possibility for a regeneration or recreation or renewal of some kind.

it can only go to zero if stuff like protons can decay-----leaving nothing but radiation.
If I understand him this renewal could only happen when the universe is very old, so old that it is just empty space with nothing but a dilute radiation in it, and perhaps dark energy.

To me this sounds like a crazy idea, but I respect Penrose so I recommend it.
His explanation of the second law of thermodynamics is very keen. Much of his idea, as he develops it, is based on thermodynamic reasoning.

marcus said:
Hurk, Wallace is right.
In the standard cosmology picture there is the dark energy, to account for accelerated expansion, and it is usually assumed to be constant throughout space and time.

Hi Marcus and Wallace.
Coincidential, last night, after I had posted my last 2 threads, I had dreamy thoughts about the possibility that constant dark energy density could be a solution for my diluting "Emmenthal cheese like" problem.
Lucky enough when I came back home this evening I saw you bringing in the dark energy issue too and I felt it a bit of a happy surprise. I did not notice sofar that dark energy already got the status of belonging to the standard model but I must admit that during the last few years a see it always mentioned as contributing to about 73% of our universe's content. Still I am thinking of my subsequent reaction, but I prevent myselve of beeing too hasty and allow myself one or more dreamy nights to think it over before posting.
At this moment I think that my reaction will probably contain the following 2 constituants:
1) E-M & or gravity energy-density related space expansion and
2) Darkenergy density related constant (not expanding) space.
I will come back soon.
kind regards hurk4.

PS Yesterday a had a problem in bringing directly in a wordfile in the visible frame of PF. So I did it as an attachment file. This might give problems in quoting, correction tools etc. Certainly there must be a solution for that in PF tools?

it may be a little confusing the way I and several other people use the word 'standard' in two contexts
there is the socalled standard model of particle physics (which does not have any explanation for dark energy 73 percent, and only some shaky speculations about dark matter IIRC)

there is also the standard cosmology model, LCDM. It is the one nearly everybody seems to use most of the time, so it is natural to call it standard too
this model has a dark energy with constant energy density (corresponding to Lambda) and a constant ratio of pressure to density, namely w = -1, but it does not say what this should be in terms of laboratory particle physics.

I hope it will continue to be all right with everybody for us to refer to both these two models as standard----one is the prevailing model in cosmology and the other in particle physics.

A standard does not expand. What means constant DED?

marcus said:
it may be a little confusing the way I and several other people use the word 'standard' in two contexts
there is the socalled standard model of particle physics (which does not have any explanation for dark energy 73 percent, and only some shaky speculations about dark matter IIRC)

there is also the standard cosmology model, LCDM. It is the one nearly everybody seems to use most of the time, so it is natural to call it standard too
this model has a dark energy with constant energy density (corresponding to Lambda) and a constant ratio of pressure to density, namely w = -1, but it does not say what this should be in terms of laboratory particle physics.

I hope it will continue to be all right with everybody for us to refer to both these two models as standard----one is the prevailing model in cosmology and the other in particle physics.

Hi Marcus,
As I promissed I now continue.
As you can see I am certainly not a specialist on the topic of dark energy and having a fast look at the thread and posts "Dark energy as a furphy" could not change that position.
But I hope I can learn something and eventually it helps if once an extra paragraph could be added to Lineweavers exellent article about misconceptions about the BB by him or someone else.
I think I still have further questions or remark, but my attachment here might already be too much or even confusing?

Here is my attached file

#### Attachments

• A standard doesn't expand..doc
25.5 KB · Views: 228
hurk4 said:
Hi Marcus,

Here is my attached file
Please correct 0.73J/km to 0.6J/cubic-km.

Kind regards Hurk4

Characteristics of spaces?

hurk4 said:
Hi Marcus,
But I hope I can learn something.
I think I still have further questions or remarks.

Again I put my further questions in an attached file. Maybe it will go as a kind of a non interfering superfluid? By the way I very much appreciate the links with darkenenergy litterature recently supplied by posts in other threads of PF.

Kind regards
Hurk4

#### Attachments

• Characteristics of spaces.doc
24 KB · Views: 208
Hurk4, I just now saw your posts, which have questions to me. I'm sorry to say that I am not prepared to respond! Dark energy is a complete mystery to me. I think you have the accepted estimate for it's density----about 0.6 joules per cubic kilometer. Other than that I don't know anything to say. Also my Mac computer is not reading "doc" files for some reason. It does better with PDF and HTML.

But the file trouble is not the main thing. There have been a number of ingenious ideas proposed to explain why it is this value, or to explain the observed supernovae data without requiring it. I have followed some of these ideas over the course of some months and they don't seem to be going anywhere, at least for the present.

For the time being I regret to say I am a bit discouraged and not a receptive audience for new ideas, but more importantly I'm just not qualified to discuss some of these ideas.

==========================
Ah hah! I got the doc file to open.
Characteristics of spaces.
Hubble space (HS) and dark-energy space (DES) compared.
1) If space is inversely related to its energy density then Hubble space expands when its energy density content only relates to non dark energy. Dark energy related space does not expand because of its constant energy density (roughly 6E-10Jm^3)?
2) DES seems to be of different nature (QM nature?) compared to HS (Classic nature?)?.
3) Locality seems to play its role in HS where non locality might play its role in DES (Quantum nature?)?
4) HS is contained in DES?
5) In HS, DES related energy density increases from roughly zero % at Planck time to about 73% now to maybe 100% where as NDE related density dilutes from about 100% to roughly 0%?
6) In how far as is suggested by 1) to 5) is non dark energy (NDE) related to dark energy (DE)?
7) Is the Casimir effect a manifestation of a relation between CE and NDE?
8) In HS there is no action at distance maybe there is in DES?
===================

I got the other file to open too!
I can see you are calculating how it will be (assuming DE is constant as in the LCDM model) when space expands a lot more so that matter density instead of being 27 percent will be more like zero percent.
Then the total density will be just about 0.6 joules per cubic km.
this will mean that the Hubble paramter goes down from around 71 (what it is now) to around 60.

Have to go. Will try to respond more tomorrow

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marcus said:
Hurk4, I just now saw your posts, which have questions to me. I'm sorry to say that I am not prepared to respond! Dark energy is a complete mystery to me. I think you have the accepted estimate for it's density----about 0.6 joules per cubic kilometer. ==========================
Ah hah! I got the doc file to open.
Characteristics of spaces.
Hubble space (HS) and dark-energy space (DES) compared.
1) If space is inversely related to its energy density then Hubble space expands when its energy density content only relates to non dark energy. Dark energy related space does not expand because of its constant energy density (roughly 6E-10Jm^3)?
2) DES seems to be of different nature (QM nature?) compared to HS (Classic nature?)?.
3) Locality seems to play its role in HS where non locality might play its role in DES (Quantum nature?)?
4) HS is contained in DES?
5) In HS, DES related energy density increases from roughly zero % at Planck time to about 73% now to maybe 100% where as NDE related density dilutes from about 100% to roughly 0%?
6) In how far as is suggested by 1) to 5) is non dark energy (NDE) related to dark energy (DE)?
7) Is the Casimir effect a manifestation of a relation between CE and NDE?
8) In HS there is no action at distance maybe there is in DES?
===================

I got the other file to open too!
I can see you are calculating how it will be (assuming DE is constant as in the LCDM model) when space expands a lot more so that matter density instead of being 27 percent will be more like zero percent.
Then the total density will be just about 0.6 joules per cubic km.
this will mean that the Hubble paramter goes down from around 71 (what it is now) to around 60.

Have to go. Will try to respond more tomorrow

Hi Marcus,
You have a very good collegea and nobelprice winner Gerard 't Hooft who about one or maybe two years ago remarked something like "dark matter is a mystery I (we) don't really understand it yet". So who am I that I dare to even post questions like these? Still I am curious and I am very glad that you are so kind to try to give me a reaction.
In the mean time I tried to correct my questions and even added one more. Again you will find it in an attached file.

Kind regards
Hurk4

#### Attachments

• Characteristics of spaces -II.doc
24.5 KB · Views: 227
So Wallace is saying that energy (that we readily observe) and darkenergy are not quite the same thing and although energy can approach zero, dark energy doesn't? I'm wondering what are the two together?

I'm a retired mathematician who is interested in quantum gravity and cosmology. So I'm not speaking as a professional. Hurk4 you may know better than I what 't Hooft's current views on Dark Energy are.

Personally I am hopeful that it will turn out to be neither a constant Lambda in the law of gravity, nor a type of energy! But for now just plugging in this constant Lambda seems to make the quations fit the data, so we do it. It is better than nothing and one can think of it as a type of energy with constant density.

Amp1 said:
So Wallace is saying that energy (that we readily observe) and darkenergy are not quite the same thing and although energy can approach zero, dark energy doesn't? I'm wondering what are the two together?

Usual energy is associated with matter and radiation. So if you double the volume of space, and the amount of matter and radiation stays the same, then the energy density goes down by half.

The unique thing about dark energy (postulated to explain the cosmological constant Lambda) is that its density is constant. If it is 0.6 Joules per cubic kilometer now, then it will always be that, and it has always been.

So what Wallace says, and you are saying too, is that as a volume of space increases the ordinary energy density goes down (and can approach zero, as you say) but the dark energy density does not. It stays the same!

Hurk4 has pointed to some other physics that might be related to dark energy----to vacuum energy, and the Casimir force. I will let him explain that. It has been discussed quite a bit but if 't Hooft says it is a mystery then I am in full agreement with him
================

At this point I'm in a wait-and-see mode and believe that everybody's ideas about dark energy deserve attention. I will tell you what I think, but I don't want to claim that this has more chance than someone else's.

I just listened to a seminar talk in the ILQGS (international LQG seminar) series by Kirill Krasnov. The slides are very clear but the audio was terrible for the first 35 to 40 percent of the time. You should drag the button 40 percent of the way across and let it start there. Around slide #17 is where the clear audio begins.
http://relativity.phys.lsu.edu/ilqgs/
I don't recommend anyone try to listen to the audio, but one can download the PDF slides and get a rough idea of what the talk is about.

He does not have a constant Lambda and he does not have dark energy. He has a modified law of gravity where what used to be Lambda now depends on the curvature. It is a cosmological function, not a constant. In the past 6 months i have been seeing theories like this coming up more and more often. In effect they involve the "running" of the cosmological constant.

I admit that this makes things even more confusing. for mental economy and simplicity one would fervently hope that there is just a constant Lambda and a constant dark energy density. But I am beginning to suspect that it isn't that simple and that people like Krasnov may be on the right track.

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## 1. What is the Planck energy?

The Planck energy refers to the maximum amount of energy that can exist in a given space and time. It is named after German physicist Max Planck who first proposed the concept in 1900.

## 2. Is there a minimum energy in addition to the maximum Planck energy?

Yes, there is also a minimum energy known as the Planck energy scale. This is the smallest possible unit of energy that can exist in the universe and is approximately 10^19 GeV (gigaelectronvolts).

## 3. Why is there a maximum and minimum energy in the universe?

According to quantum mechanics, energy can only exist in discrete units rather than continuously. The Planck energy serves as the upper limit because at this scale, the laws of physics as we know them break down. The minimum energy, on the other hand, is a fundamental limit that is a result of the uncertainty principle.

## 4. How does the Planck energy relate to other units of energy?

The Planck energy is much larger than any other unit of energy commonly used in physics. For comparison, the energy released in a nuclear explosion is about 10^10 GeV, while the energy of visible light is around 1 eV (electronvolt). The Planck energy is also equivalent to about 10^32 Kelvin.

## 5. Can the Planck energy be observed or measured?

No, the Planck energy is far beyond the capabilities of current technology and is unlikely to ever be observed or measured directly. However, scientists can study its effects through theoretical models and experiments at smaller energy scales.

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