# why this egality is exact please ?

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Hello joignus

- I think you are making a mistake on the of the notion of sigma arithmetic summation:

look at the help of the French version.

With the formula that I propose we have :

1 mp/2 + 2 mp/2 + 3 mp/2 + 4 mp/2 + 5 mp/2 ...

it reflects the figure 2 of this document quoted before with 1/2 mp by point

I hope this will be enough for you to see where you are making additional mistakes on this point and that not porpotional to tH

1 hour ago, joigus said:

Keep in mind that the expansion parameter, in the FLRW models can have in principle any time-dependence that you want to postulate. It can be accelerated, decelerated, oscillating, etc.

*I'm assuming that by "Hubble mass" you mean the mass of the universe within a Hubble radius. What I'm trying to tell you is that the amount of mass in there is nothing to do with the Hubble "mechanism".

- If I understand you correctly I agree with you on this point. I deal with it in my viXar document unless I am mistaken. I want to come back to it later in this thread

1 hour ago, joigus said:

So, what you're saying amounts to,...

yes except that it is the exact value that can be write tH/2 * c3/G

and that you made a small error : you did mp * tp instead mp / tp

Edited by stephaneww

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It's joigus. Hello.

2 hours ago, stephaneww said:

- I think you are making a mistake on the of the notion of sigma arithmetic summation:

look at the help of the French version.

Sorry, I don't speak French. And I didn't make any mistakes.

2 hours ago, stephaneww said:

1 mp/2 + 2 mp/2 + 3 mp/2 + 4 mp/2 + 5 mp/2 ...

This is a divergent series. =(1+2+...+)mp/2

If you're implying a different summation rule (Borel summation), or re-ordering, you should say so. What summation criterion are you using?

2 hours ago, stephaneww said:

and that you made a small error : you did mp * tp instead mp / tp

No. My expression checks for units of mass. I bothered to check. It it were as you say, it wouldn't. And it does. I didn't write mP*tP anywhere. Check it out.

It's a finite sum, by the way, so it should be no problem. ??

I mean, no ordering criterion or Borel transform should affect it. Are we on the same page?

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It seems that the names and representations are not unified. Moreover I referred to a French site which may be wrong .

It seems that for you it is, if I am not mistaken, this divergent series which stops at tH if I am not mistaken:

(1+2+3+4+5+....+tH) * (1/2 mp/tp)

where mp/tp is the Planck mass flow rate (please look at my 3 sources on this line)

you well did an error because you find hbar/c2 =mp * tp  instead c3/G for Planck mass flow rate =mp / tp

I have finished my edits on this short message, I await a feedback with pleaser. oops I did 2 more edit sorry ☺️

Edited by stephaneww
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9 hours ago, swansont said:

Doesn't want to be quoted?

I am only a passionate and messy amateur who did not wish to abuse his fame. We agreed on that

7 hours ago, joigus said:

*I'm assuming that by "Hubble mass" you mean the mass of the universe within a Hubble radius. What I'm trying to tell you is that the amount of mass in there is nothing to do with the Hubble "mechanism".

good job 😊

...but there are other things to do with in the ΛCDM model next. 😉

Edited by stephaneww
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5 hours ago, joigus said:

It's a finite sum, by the way, so it should be no problem. ??

yes

5 hours ago, joigus said:

I mean, no ordering criterion or Borel transform should affect it.

I don't understand what you mean here but I have an intuition of what it means and especially of the consequence.

5 hours ago, joigus said:

Are we on the same page?

and the consequence is that I think : yes we are

Please note that my english is poor. I realise all my tranlations with DeepL.com so sometime it can be be a problem for understaning

Then, if it's good, we'll go to the next step. 😊

Of course, everyone is welcome to ask questions about this passage if they feel there are things to improve or challenge. (reference figure 1 and 2 of this document arxiv)

11 hours ago, stephaneww said:

Hello

to try to be simple and educational :

- the big bang theory tells us that in Plank's time, the mass of the universe is 1 Planck mass

- the figure 1 starts with two units (two circles). To have 1 Planck mass at the beginning, each sphere should weigh 1/2 Planck mass

... hence the 1/2 in the formula of the summation.

- figure 2 starts with an empty set according to the authors. however following the same logic as above it starts with 1/2 Planck mass.

- the summation adds 1 unit of 1/2 mPl per unit of Planck time to the previous summation. this is a formula that explains how we go from a universe that weighs one Planck mass at the origin to a universe that weighs 10^54 kg today

my pdf says the same thing with mass or energy densities

after my toy cosmological model gives also the explanation of the homogeneity of the universe. but each thing in its time

Edited by stephaneww
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5 hours ago, stephaneww said:

...but there are other things to do with in the ΛCDM model next. 😉

I'm all ears. I don't know how it affects the fact that you can plug in any dependence a(t) for the expansion parameter in Hubble's law, so there is no direct proportionality between the life of the universe and the amount of matter that remains inside the Hubble horizon.

And yes, the sum is finite, but you still have to explain the coefficients. I don't have a lot of time now, but I see you're using dimensionless time in one factor and dimensionful quantities in another. Please, clarify your notations and we may have a meaningful conversation. The expression I derived is correct if you use dimensionful quantities throughout and the sum is understood literally the way you wrote it down. I may be able to give you more details later.

Now it seems like you''re implying something like,

$m_{H}=\sum_{n=1}^{Nt_{H}/t_{P}}n\frac{m_{P}}{2}$

for some discrete index n and some upper limit N, which went unspecified.

If you drop the attitude that you're teasing out bits of cosmological wisdom and piecewise letting them fall on me like clues of a riddle, it will help along the conversation immensely.

Edited by joigus
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Hello joignus. Thank you for your feedback. It's a pleasure to read you again.

9 hours ago, joigus said:

I will try. Excuse me, I'm very brouillo.

9 hours ago, joigus said:

If you drop the attitude that you're teasing out bits of cosmological wisdom and piecewise letting them fall on me like clues of a riddle, it will help along the conversation immensely.

You are not alone and I try to be educational by moving slowly for all novice readers in cosmology .Plus I'm not good when it goes too fast.  😉

so :

Our summations seems well equivalent to each other now (if your n is well egal to tH/tp)

note : tH = 1/H where H is Hubble constant

...and you can check out my viXra pdf to get more complements to get advance more quickly if you want.

In another attempt to be pedagogical and make physical sense of the summation, consider this:

- In Figure 2, your present time tp of your observable universe is the first point in the graphical representation.

But before you lived 2 times tp
and again before 3 times tp etc...

it is the same for your visible universe (=universe at Hubbe radius): it lives its first time tp at the same time as you and started at tH.

To each point of time tp, of the figure 2, of your current universe is associated its mass mp/2 of the summation in the system of Planck's unit. (it still misses some tinkerings but the main idea is there and is verifiable in agreement with our current knowledge and measurements)

This explains how for us the visible universe started with 1 nucleon and counts today about 1080

Is that understandable?

9 hours ago, joigus said:

I may be able to give you more details later.

I will all ears.

Regards

Edited by stephaneww
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47 minutes ago, stephaneww said:

This explains how for us the universe started with 1 nucleon

Pretty sure this is not part of Big Bang cosmology, and is not consistent with your model, either.

A nucleon's energy is around 1 GeV, while the Planck energy is ~10^19 times bigger

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44 minutes ago, swansont said:

Pretty sure this is not part of Big Bang cosmology, and is not consistent with your model, either.

Hello swansont

http://www.mamwad.org/courses/esp/esp-12.pdf, (at the end of the document)

The beginning with 1 nucleon comes from my source at cnrs

37 minutes ago, stephaneww said:

and is not consistent with your model, either.

explain why it isn't consistent for you please

Edited by stephaneww
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35 minutes ago, stephaneww said:

explain why it isn't consistent for you please

if you were born 3 tp ago you are 3 tp old at the time tp no?. is it consistent like this ?

You said you have a 1 mp at t = 1 tand now you say you have 1 nucleon.

As I stated, these are different by ~19 orders of magnitude in energy.

35 minutes ago, stephaneww said:

note that tp is the smallest unit of time in physics.

Well, not really. It's the shortest time we can make sense of in current cosmology theory (i.e. in GR)

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1 hour ago, swansont said:

You said you have a 1 mp at t = 1 tand now you say you have 1 nucleon.

As I stated, these are different by ~19 orders of magnitude in energy.

I don't know why the researcher of the cnrs told me that at the time of the big bang we had a primitive atom (nucleon). I am only an amateur but it is consistent with the primitive atom of the big bang. I think but I am not sure that it is related to the mass of the nucleon and its Planck temperature at the time of the big bang which makes the energy also equal to mPl c2. Is it coherent like that please?

What I am sure of is that my model is consistent with the standard cosmological model: it allows us to find the number of nucleons in the actual visible universe and explains why the energy of the universe (m c2) increases with time in violation of the principle of conservation of energy.

1 hour ago, swansont said:

Well, not really. It's the shortest time we can make sense of in current cosmology theory (i.e. in GR)

another thing: we can advantageously replace the figure 2 quoted above by this diagram which clarifies the model

time tPl ( in seconds) = 1/H

^

|                   o

|              o   o

|          o  o   o

|      o  o  o  o

|  o  o  o  o  o

0 1  2  3  4   5 -----> age in number of tPl

o is the mass mPl/2 associeted to age and grain of time tPl

Edited by stephaneww
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OK, from scratch. You're using the fact that the Hubble time is a certain number of times the Planck time. That much makes sense. So,

$\frac{m_{P}}{2}+\stackrel{\left(T_{H}/t_{P}\textrm{ times}\right)}{\cdots}+\frac{m_{P}}{2}=\frac{T_{H}}{t_{P}}\frac{m_{P}}{2}$

Now, the Planck scale is defined by,

$t_{P}=\sqrt{\frac{c^{5}}{\hbar G}}$

$r_{P}=\sqrt{\frac{\hbar G}{c^{3}}}$

$m_{P}=\sqrt{\frac{\hbar c}{G}}$

Now, you seem to be saying that,

$M_{H}=\frac{m_{P}}{2}+\stackrel{\left(T_{H}/t_{P}\textrm{ times}\right)}{\cdots}+\frac{m_{P}}{2}$

Forget about dimensionless numbers. We're safer here if we do dimensions.

Then,

$M_{H}=\frac{1}{2}\frac{t_{H}}{t_{P}}m_{P}=\frac{1}{2}t_{H}\sqrt{\frac{\hbar c}{G}}\sqrt{\frac{c^{5}}{\hbar G}}=\frac{1}{2}t_{H}\frac{c^{3}}{G}$

Is that it? Is that what you're saying?

Dimensions check now. Sorry I made a mistake last night:

$\frac{1}{2}t_{H}\frac{c^{3}}{G}=T\frac{L^{3}T^{-3}}{LL^{2}T^{-2}M^{-1}}=M$

Now, you may well be saying something else, in which case I would be very interested to know what it is.

PS: I agree with Swansont that saying that the universe at the time of the big bang was the size of an atom is a gross mis-estimation in the light of the current cosmological model.

Edited by joigus
math correction
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Hello joigus, As usual it's a pleasure to read you 😊

57 minutes ago, joigus said:

Then,

MH=12tHtPmP=12tHcGc5G=12tHc3G

Is that it? Is that what you're saying?

yes, you will find exactly the same thing in my pdf virax. it makes sense?

57 minutes ago, joigus said:

Dimensions check now. Sorry I made a mistake last night:

Don't worry, I do a thousand a day, you're excused 🙂

57 minutes ago, joigus said:

Now, you may well be saying something else, in which case I would be very interested to know what it is.

My model/egality explains the homogeneity of the visible universe no? do you agree?

this also explains why we not found the other half of the mass of the visible universe, no?

57 minutes ago, joigus said:

PS: I agree with Swansont that saying that the universe at the time of the big bang was the size of an atom is a gross mis-estimation in the light of the current cosmological model.

Yes, I agree with both of you. Besides, the researcher of the cnrs told me that to speak of mass at the moment of the big bang was improper.

Prefer the notion of energy (mPl c2) for what I express improperly with the Planck mass.

I use the notion of mass for the simplification of the calculations

I think I've finished my edit. You can answer without that its problem for me☺️

Edited by stephaneww
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35 minutes ago, stephaneww said:

My model explains the homogeneity of the visible universe no? do you agree?

No, sorry. I don't see that coming out of your idea. The present universe is not homogeneous. You should aim at explaining the present degree of inhomogeneity --deviations from homogeneity.

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4 minutes ago, joigus said:

No, sorry. I don't see that coming out of your idea. The present universe is not homogeneous.

oops I made an error me too. I wanted to say "Isotropie"

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2 minutes ago, stephaneww said:

oops I made an error me too. I wanted to say "Isotropie"

Three strikes, you're out!

47 minutes ago, stephaneww said:

My model/egality explains the homogeneity of the visible universe no? do you agree?

------

47 minutes ago, stephaneww meant to say:

My model/egality explains the homogeneity isotropy of the visible universe no? do you agree?

-----

No. I don't see that either. How?

3 hours ago, swansont said:

and is not consistent with your model, either.

This is also obvious, may I point out...

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44 minutes ago, joigus said:

Three strikes, you're out! 😉

Ok I don't know the name of the propriety I want describe

Consider this diagram

3 hours ago, stephaneww said:

another thing: we can advantageously replace the figure 2 quoted above by this diagram which clarifies the model

time tPl ( in seconds) = 1/H

^

|                   o

|              o   o

|          o  o   o

|      o  o  o  o

|  o  o  o  o  o

0 1  2  3  4   5 -----> age in number of tPl

o is the mass mPl/2 associeted to age and grain of time tPl

1, 2, 3, 4, 5 are radius of their Hubble sphere

in each direction of the ray (1, 2, 3, 4, 5), wherever you look in the visible universe, they are identical with the same number of masses o

what does this correspond to in the standard cosmological model ? there should be a match in my opinion, normally. there must be one in my opinion normaly

44 minutes ago, joigus said:

his is also obvious, may I point out...

please develop, I don't undertand where there is a problem (formulas + values in J or kg)

bonus: do you agree that my model gives the actual number of nucleon in the visible universe  with 1 nucleon at the beginning of the universe (big bang)?

Edited by stephaneww
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27 minutes ago, stephaneww said:

what does this correspond to in the standard cosmological model ?

Isotropy (sameness in all directions.)

30 minutes ago, stephaneww said:

please develop, I don't undertand where there is a problem (formulas + values in J or kg)

If the universe starts out at Planck scale, that's much, much smaller than atomic scale in time and length, and far, far bigger than atomic mass in energy scale.

Keep in mind that Planck's time and length are ridiculously small, while Planck's mass is more like the size of an amoeba or a neuron, or something like that...

Funny, isn't it? So disparate!

It's kept me wondering for more than 30 years. It still does.

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38 minutes ago, stephaneww said:

what does this correspond to in the standard cosmological model ?

10 minutes ago, joigus said:

Isotropy (sameness in all directions.)

so there is indeed in addition to the mass at Hubble radius an additional correspondence with the ΛCDM model?

Edited by stephaneww
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You should be your number one critic. Isn't your model isotropic just because you assume isotropy from the get go? That's called begging the question, and I think that's what you're doing.

I'm perhaps the wrong person to discuss these matters with. I tend to think almost everything one thinks is wrong. Including myself.

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this is a new area for me. please excuse my delay in answering. i will be back as soon as possible.

Edited by stephaneww
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What does it give you for the #photon/#nuclei ratio? Why is it nearly 1010?

Why are there about 1090 photons in the universe?

Those are the questions you should be asking yourself in the context of your model.

3 minutes ago, joigus said:

Why are there about 1090 photons in the universe?

I meant the visible universe --within the Hubble radius.

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4 hours ago, stephaneww said:

I don't know why the researcher of the cnrs told me that at the time of the big bang we had a primitive atom (nucleon). I am only an amateur but it is consistent with the primitive atom of the big bang. I think but I am not sure that it is related to the mass of the nucleon and its Planck temperature at the time of the big bang which makes the energy also equal to mPl c2. Is it coherent like that please?

The primordial atom was Georges Lemaître‘s idea.

But speaking of temperature, it was too hot to have nucleons until about 10^-6 sec, according to Big Bang theory.

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Thank you swansont.

I think I have transcribed wrongly what the researcher told me. Here is what it looks like with a web translator

"it is inevitable that at Planck time, the temperature (in units k_B T) is equal to the Planck mass (multiplied by the speed of light squared), and that the horizon at that time contains only about a single particle. In other words, this is not a coincidence, it is simply a consequence of the dimensional analysis that can be performed with the quantities c, hbar and G".

was the singularity a "plasma" at Planck temperature as I think with your add? That could help me to correct my mistakes..

Edited by stephaneww
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9 minutes ago, stephaneww said:

was the singularity a plasma at Planck temperature? That could help me to correct my mistakes..

I'm not swansont, but I would suggest the answer to that question, is that we have no idea as yet, what matter/space/time is like at Planck scale.

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