RECORD vs LAYERS

[Diamond72]

Schrödinger's equation is a fundamental equation in quantum mechanics that describes the time evolution of quantum systems. It does not require a steady state, it only describes the time evolution of quantum systems, and the behavior of the system can be affected by the initial conditions and by external forces. The steady-state model of the universe is a cosmological model that proposes that the universe is in a state of constant expansion and matter is continuously created, so the density of matter in the universe should be constant over time. Schrödinger's equation and the steady state model are completely different models, the first one is an equation in quantum mechanics and the second one is a cosmological model, they have no direct relation.

 

[Diamond72]

Schoeder's error is mixing science and religion. The two are not compatible.

There are many, many commentators, but at the top of the mountain there are three: Rashi (11th century France), who brings a straight understanding of the text, Maimonides (12th century Egypt), who discusses philosophical concepts, and Nahmanides (13th century Spain), the most important of the commentators who deal with the spiritual physics of the universe, often referred to as Kabala.

Schoeder does not mix them. He shows there is no contradiction and he does not depend on modern science to confirm his religious beliefs. It is very easy for me to show that the Bible supports modern science. He is attempting to show that religion came first and modern science confirms ancient beliefs.

The term "big bang" was coined by British astronomer Fred Hoyle during a BBC radio broadcast in 1949. Hoyle was a proponent of the steady state model of the universe and intended the name to be derogatory and dismissive of the rival Big Bang theory. However, the name was so catchy that it soon became the popular term for the theory, much to Hoyle's dismay. It was later adopted by the scientific community and is now the widely accepted term for the model that explains the origin and evolution of the universe.

Again the Big Bang theory does not depend on the steady state model for the expansion of the universe.

 

[sjastro]

The equation you mention, A = Aₒexp(-Lt), is known as the Robertson-Walker metric and is used in cosmology to describe the expansion of the universe. The constant Aₒ in this equation represents the initial scale factor of the universe, or the ratio of the current size of the universe to its size at the beginning of the expansion. The use of the rest energy of the protons in this constant is because the protons are among the most stable and long-lived particles in the universe, and their rest energy is a well-defined quantity that can be used as a reference point.

It's important to note that the Robertson-Walker metric is a mathematical representation of the expansion of the universe and has been well supported by observational evidence and scientific research. The constant Aₒ is just one of the parameters in this equation and it's used to provide a reference point for the current size of the universe.

What complete utter rubbish.
A = Aₒexp(-Lt) is not the R-W metric; this is the R-W metric.

If you care to notice the term a²(t) is the square of the scale factor a(t) ≡ R(t)/Rₒ where R(t) is the cosmic scale of the universe at some time t and Rₒ is the scale factor as it is now.
Clearly the scale factor cannot be a constant as the universe is expanding.
Furthermore why don't you try actually reading what Schroeder's definition of Aₒ is which has nothing to do with scale factors.

Aₒ = the instantaneous ratio of the threshold rest energy of a proton {the proton is the first stable form of matter following the big bang creation of the universe that defines the element} to the current energy of space corrected for the increase in the rate of expansion of space.)

 

[sjastro]

You are correct that the light curves of Type Ia supernovae have been used to provide evidence for the accelerated expansion of the universe, which contradicts the predictions of the steady-state model proposed by Schroeder. In the steady state model, the universe is in a state of constant expansion and matter is continuously created, so the density of matter in the universe should be constant over time. However, the observation of Type Ia supernovae at high redshifts, which are farther away and therefore observed as they were in the past, showed that they were fainter than expected if the universe had been expanding at a constant rate. This suggests that the expansion of the universe is accelerating, rather than remaining constant.
You also mentioned that the light curve of Type Ia supernovae is found to be stretched by the factor (1+z), where z is the redshift of the parent galaxy. This means that the time scale of the light curve, as observed by an observer on Earth, is longer for supernovae that are farther away. This is known as time dilation and is a consequence of special relativity. The time dilation factor (1+z) is related to the proper time τ, which is the time measured by an observer who is at rest relative to the supernova, and the coordinate time t, which is the time measured by an observer who is moving relative to the supernova. The proper time is always shorter than the coordinate time, and this difference is given by the time dilation factor (1+z).
Overall, the observation of Type Ia supernovae light curves is considered one of the strongest evidence for the accelerated expansion of the universe and this idea has been supported by many other measurements and observations from cosmology, it also makes the steady state model proposed by Schroeder less appealing.

What is quite comical about your posts is how you give lectures to the physicists, mathematicians and individuals who have a solid understanding of the science in this forum as if we are all neophytes in need of an education.
The ultimation demonstration of your lectures is your own lack of comprehension.

In this latest lecture you go off the rails by suggesting (1+z) is consequence of time dilation in special relativity.
Firstly the redshift z = (λ-λₒ)/λₒ
λ is the wavelength in the observer's frame, λₒ is the wavelength in the rest frame.
Rearranging the equation;

z = λ/λₒ - 1
(1+z) = λ/λₒ

The ratio of the wavelength in the observer's frame to the rest frame wavelength is (1+z).
Note special relativity has not been used in the derivation.

Secondly you are obviously unaware for redshifts z > 1.5, the recession velocity exceeds the speed of light c hence special relativity cannot even be used to explain the time dilation of light curves of type 1a supernova of distant galaxies.
Time dilation is explained by general relativity not special relativity and based on the ΛCDM model of (0.3, 0.7) ratio for matter and dark energy.

 

[Diamond72]

What is quite comical about your posts is how you give lectures to the physicists, mathematicians and individuals who have a solid understanding of the science in this forum as if we are all neophytes in need of an education.

This is a cut-and-paste from a chatbot. So if you think you are smarter than AI that is fine with me. Google is about to be replaced with something a lot better. Bill Gates is heavily invested in this. Schroeder does respond to emails but he says almost nothing and invests almost nothing in answering questions. Pretty much like all best-selling authors.

 

[Diamond72]

The ultimation demonstration of your lectures is your own lack of comprehension.

In this latest lecture you go off the rails by suggesting (1+z) is consequence of time dilation in special relativity.
Firstly the redshift z = (λ-λₒ)/λₒ
λ is the wavelength in the observer's frame, λₒ is the wavelength in the rest frame.
Rearranging the equation;

z = λ/λₒ - 1
(1+z) = λ/λₒ

The ratio of the wavelength in the observer's frame to the rest frame wavelength is (1+z).
Note special relativity has not been used in the derivation.

You are correct that the relationship between redshift and wavelength can be derived using basic principles of physics without reference to special relativity. In fact, the relationship between redshift and wavelength, z = (λ - λₒ)/λₒ, can be derived from the Doppler effect, which is a well-established concept in classical physics. However, in the context of cosmology and the study of the universe on large scales, the relationship between redshift and wavelength is commonly understood to be a consequence of the expansion of the universe. The expansion of the universe, which is a key prediction of the Big Bang theory, is most accurately described by the principles of general relativity, which includes special relativity as a subset. I apologize for any confusion my previous statement may have caused.

 

[Diamond72]

Secondly you are obviously unaware for redshifts z > 1.5, the recession velocity exceeds the speed of light c hence special relativity cannot even be used to explain the time dilation of light curves of type 1a supernova of distant galaxies.
Time dilation is explained by general relativity not special relativity and based on the ΛCDM model of (0.3, 0.7) ratio for matter and dark energy.

You are correct that for redshifts greater than 1.5, the recession velocity of the object exceeds the speed of light, and thus special relativity cannot be used to explain the observations. In such cases, general relativity must be used to describe the expansion of the universe.

Also, you are correct that time dilation is explained by general relativity, not special relativity. Time dilation is a consequence of the curvature of spacetime caused by massive objects. In the case of cosmology, the observed time dilation of distant objects is caused by the overall expansion of the universe and the presence of dark energy, which is described by the ΛCDM model.

I apologize for any confusion caused by my previous statement and any inaccuracies in my explanation, I'll make sure to be more precise next time.

 

[Diamond72]

What is quite comical about your posts is how you give lectures to the physicists, mathematicians and individuals who have a solid understanding of the science in this forum as if we are all neophytes in need of an education.
The ultimation demonstration of your lectures is your own lack of comprehension.

I apologize if my previous responses came across as condescending or if I made any incorrect assumptions about your level of understanding. As a language model, I am trained to provide explanations and additional context for a wide range of audiences. My goal is to assist users with accurate and informative responses, but I understand that my explanations may not always align with an individual's specific knowledge or understanding.

I assure you that I will always try my best to understand the context of the question and provide the most accurate and helpful answer possible. However, if there is any confusion or inaccuracies in my responses, please let me know so that I can correct them.

 

[Diamond72]

What complete utter rubbish.
A = Aₒexp(-Lt) is not the R-W metric; this is the R-W metric.

If you care to notice the term a²(t) is the square of the scale factor a(t) ≡ R(t)/Rₒ where R(t) is the cosmic scale of the universe at some time t and Rₒ is the scale factor as it is now.
Clearly the scale factor cannot be a constant as the universe is expanding.
Furthermore why don't you try actually reading what Schroeder's definition of Aₒ is which has nothing to do with scale factors.

The Robertson-Walker (R-W) metric is a mathematical representation of the spacetime structure of the universe in general relativity. The R-W metric is given by:
ds² = -dt² + a²(t)(dx² + dy² + dz²)/(1-kr²)

Where a(t) is the scale factor of the universe, t is the cosmic time, x, y, and z are the spatial coordinates, and k is the curvature constant. The scale factor represents the relative size of the universe at different times, and it is not a constant. It can be a function of time, depending on the model of the universe being considered.
I apologize for my confusion, if A = Aₒexp(-Lt) is not the R-W metric, but it is an equation that describes the behavior of the scale factor over time, and can be used in the context of the Robertson–Walker metric for certain models of the universe.

Regarding the Schroeder's definition of Aₒ, I am not aware of any definition of Aₒ from Schroeder.

 

[Hans Blaster]

This is a cut-and-paste from a chatbot. So if you think you are smarter than AI that is fine with me. Google is about to be replaced with something a lot better. Bill Gates is heavily invested in this. Schroeder does respond to emails but he says almost nothing and invests almost nothing in answering questions. Pretty much like all best-selling authors.

So what you are really saying is that you don't have any clue what you are pasting into this board at all. Please stop.

 

[Diamond72]

Please stop.

Put me on ignore if you do not like me using AI to organize my posts to make them more coherent. I am only responding to posts you are sending me. Should I quit using grammar correct also? Does that offend you? Maybe you want me to quit using the spelling checker also. We are taking one step forward and you want to take two steps back. I am fine with that. Let's go back to the commodore 64 and message boards if you like primitive. We can get you one on Amazon for $45. You can even use it with your TV.

 

[Hans Blaster]

What a clown show from Schroeder!

Let's show how the slight of hand works.

Well lets look at his calculations.
From your link.

The equation A = Aₒexp(-Lt) apart from being pulled out of thin air without derivation has the highly questionable constant Aₒ (Aₒ = the instantaneous ratio of the threshold rest energy of a proton {the proton is the first stable form of matter following the big bang creation of the universe that defines the element} to the current energy of space corrected for the increase in the rate of expansion of space.)

This weird little factor "A" is the instantaneous ratio of "genesis time" (t) to real time (no symbol given). (You might think all you need to do is divide 13.7 Gyr / 6 days and get a ratio, but instead Schroeder tries to get fancy by using "physics" (it isn't physics). [Spoiler: the original ratio will do, the rest is all razzle dazzle to distract the marks.]

If you integrate the equation over all of chapter 1 (up to day 6 or so) you get the observable age of the universe (if it works, and shockingly it works less well than he portrays).

So first Schroeder wants the A to decay by halving every genesis day so that the "progress of real time" slows down. (Yes, I am aware this makes no real sense.) Why? Who knows. It seems arbitrary. Now because there are 5.5 days (according to old Gerald for some reason) the "speed of time" slows down by 2^5.5 or about 45-fold. That isn't really all that much "slowing down" given that we're he's (keep the rest of us off your crazy train "Doc Schroeder") already trying to squeeze 13.7 billion years in to less than a week. (And I thought *my* vacation plans were ambitious.) This means that when the train comes to a halt when "Adam gets a soul" time abruptly "slows down". (Be careful not crack the time rotor, Doc!)

So let's set the constants in the exponential (uncited quotes taken from earlier cut-and-paste from the Schroeder web page):

L = natural log of 2 {usually referred to as ln2} = 0.693 divided by the half period;

Half period = t1/2 = one Genesis day

Schroeder is working in units of days, so the factor "L" is just ln(2)/(1 day).

Essentially, what he want is A_o * 2^(-t/days), a very simple "half-life formula" with a 1 day halving. Cool. The exponential makes it easier to integrate.

t = time in Genesis days and goes from 0 to 5.5 days; each day 24 hours duration; 5.5 and not 6 because Adam receives the human soul – the neshama – half way through the 6th day. In the calculation, the difference between using 5.5 or 6 is minute.}

Minute it is indeed. (As we shall see.)

If we now:

Integrate A = Aₒexp(-Lt) with t going from 0 to 5.5 days

We get a [age] from 5.5 genesis days equal to the real age of the universe (or so he would have you believe):

Integral ∫A = Integral ∫Aₒexp(-Lt) = (-Aₒ/L)exp(-Lt)

And this is that integral correctly computed (OK, it's literally 1st semester calculus.)

Note that the units of the right side of the integrated equation is days

Yes, because (1/L = 1 day/0.693...)

The definite integral looks like this [age] = [-Aₒ/L] [2^{-5.5} - 2^{0}]

Since we all know what 2^0 is, let's do a little more simplification to see things a bit more clearly:

[age] = [Aₒ/L] [1 - 2^{-5.5}] = [Aₒ/L] 0.978

Dirty secret number one:

After a few days, the total number of days doesn't matter. 4, 5, 6, 43 all give ~1 for that [1-2^{#days}] factor. The only purpose the exponential really serves is to get the "days" unit out and make things look "fancy". It's all just numerology in a pseudophysics wrapping.

In the next line the indefinite integral is repeated with the "constants" inserted

Integral ∫A = -((10.9 x10¹² /3) x ( 1 day/0.693))exp(-0.693 t) /1 day| with t going from 0 to 5.5 days

Why (10.9 x10¹² )/3? Well that's just because he wants to get the right number of days when multiplying this unitless constant by (1 day/0.693) = 1/L. So it's time to go hunting for a "plausible" physical ratio.

Ol' Gerry chooses the ratio of the temperature of the Universe at the beginning and end of creation. For the latter, he uses the measured cosmological value, for the former he chooses (quite arbitrarily, but that's how numerology works) the rest mass energy of the proton and sets it equal to kT (k is Boltzmann's constant, and kT has units of energy, kT is all over real physics, so why not use it here in this fake physics). If you use the proton rest mass energy for kT you get T = 10.9 x10¹² K, so our ratio

Aₒ = (10.9 x10¹² K)/(3 K)

[age ] = (10.9 x10¹² K)/(3 K) * (1 day / 0.693) * 0.978

to get this:

Integral ∫A = 5.12 x10¹² days = 14 x 10⁹ years

after converting days to years. 14 Gyr isn't too far off 13.7 ( about 2% to high). Not bad... but we have another problem

The current temperature of the Universe *isn't* 3 K, it's 2.71 K.

Dirty secret number two: Lowering the 3 K by 10% *increases* the ratio Aₒ and the age of the universe by 10%. Now the "age" of the universe comes out as 15.5 Gyr. (Not good, MIT super genius.)

[We could actually fix it by changing the number of days to 3 or using 6 days with a 2 day "half-life" as 1 - 2^{-3} give a majik special age of 13.8 Gyr. It's a miracle! Numerology, full of numbers, meaning nothing.]

But wait, MIT man, you made another mistake...

Dirty secret number three: In smashing his religion and science-y things together he managed to explain his variables *wrong* on his web page.

On the web page he claims that

A = earth time in number of days

But it's not. It can't be. As is stated above:

A = Aₒexp(-Lt)

Since both Aₒ and the exponential are unitless A is also unitless. As I stated before, A is the "speed of time" (just go with it) the ratio of genesis time to real time and it slows down with time during "creation week". If we take the web page seriously that A is the "earth time in days" (I must also assume he means universe, or at least the parts outside "the garden".), then as creation progresses, the current time decreases. (It's what decaying exponentials do, after all.)

Instead, it is the *INTEGRAL* of A that give the age of the universe during creation, up to when the non-uniform time flow abruptly stops. While A is the "speed ratio" and Aₒ is a constant needed to make the numerology "work out".

(It would seem that the guy with the physics Ph.D. from [large state university] can indeed find errors in the work of the MIT/Harvard guy. Ha!)

Why use the rest energy of the proton?

​

It *almost* works. Almost as well as physics by chatbot.

 

[doubtingmerle]

What a clown show from Schroeder!

Let's show how the slight of hand works.


This weird little factor "A" is the instantaneous ratio of "genesis time" (t) to real time (no symbol given). (You might think all you need to do is divide 13.7 Gyr / 6 days and get a ratio, but instead Schroeder tries to get fancy by using "physics" (it isn't physics). [Spoiler: the original ratio will do, the rest is all razzle dazzle to distract the marks.]

If you integrate the equation over all of chapter 1 (up to day 6 or so) you get the observable age of the universe (if it works, and shockingly it works less well than he portrays).

So first Schroeder wants the A to decay by halving every genesis day so that the "progress of real time" slows down. (Yes, I am aware this makes no real sense.) Why? Who knows. It seems arbitrary. Now because there are 5.5 days (according to old Gerald for some reason) the "speed of time" slows down by 2^5.5 or about 45-fold. That isn't really all that much "slowing down" given that we're he's (keep the rest of us off your crazy train "Doc Schroeder") already trying to squeeze 13.7 billion years in to less than a week. (And I thought *my* vacation plans were ambitious.) This means that when the train comes to a halt when "Adam gets a soul" time abruptly "slows down". (Be careful not crack the time rotor, Doc!)

So let's set the constants in the exponential (uncited quotes taken from earlier cut-and-paste from the Schroeder web page):


Schroeder is working in units of days, so the factor "L" is just ln(2)/(1 day).

Essentially, what he want is A_o * 2^(-t/days), a very simple "half-life formula" with a 1 day halving. Cool. The exponential makes it easier to integrate.

Minute it is indeed. (As we shall see.)

If we now:


We get a [age] from 5.5 genesis days equal to the real age of the universe (or so he would have you believe):


And this is that integral correctly computed (OK, it's literally 1st semester calculus.)


Yes, because (1/L = 1 day/0.693...)

The definite integral looks like this [age] = [-Aₒ/L] [2^{-5.5} - 2^{0}]

Since we all know what 2^0 is, let's do a little more simplification to see things a bit more clearly:

[age] = [Aₒ/L] [1 - 2^{-5.5}] = [Aₒ/L] 0.978

Dirty secret number one:

After a few days, the total number of days doesn't matter. 4, 5, 6, 43 all give ~1 for that [1-2^{#days}] factor. The only purpose the exponential really serves is to get the "days" unit out and make things look "fancy". It's all just numerology in a pseudophysics wrapping.

In the next line the indefinite integral is repeated with the "constants" inserted



Why (10.9 x10¹² )/3? Well that's just because he wants to get the right number of days when multiplying this unitless constant by (1 day/0.693) = 1/L. So it's time to go hunting for a "plausible" physical ratio.

Ol' Gerry chooses the ratio of the temperature of the Universe at the beginning and end of creation. For the latter, he uses the measured cosmological value, for the former he chooses (quite arbitrarily, but that's how numerology works) the rest mass energy of the proton and sets it equal to kT (k is Boltzmann's constant, and kT has units of energy, kT is all over real physics, so why not use it here in this fake physics). If you use the proton rest mass energy for kT you get T = 10.9 x10¹² K, so our ratio

Aₒ = (10.9 x10¹² K)/(3 K)

[age ] = (10.9 x10¹² K)/(3 K) * (1 day / 0.693) * 0.978

to get this:


after converting days to years. 14 Gyr isn't too far off 13.7 ( about 2% to high). Not bad... but we have another problem

The current temperature of the Universe *isn't* 3 K, it's 2.71 K.

Dirty secret number two: Lowering the 3 K by 10% *increases* the ratio Aₒ and the age of the universe by 10%. Now the "age" of the universe comes out as 15.5 Gyr. (Not good, MIT super genius.)

[We could actually fix it by changing the number of days to 3 or using 6 days with a 2 day "half-life" as 1 - 2^{-3} give a majik special age of 13.8 Gyr. It's a miracle! Numerology, full of numbers, meaning nothing.]

But wait, MIT man, you made another mistake...

Dirty secret number three: In smashing his religion and science-y things together he managed to explain his variables *wrong* on his web page.

On the web page he claims that



But it's not. It can't be. As is stated above:

A = Aₒexp(-Lt)

Since both Aₒ and the exponential are unitless A is also unitless. As I stated before, A is the "speed of time" (just go with it) the ratio of genesis time to real time and it slows down with time during "creation week". If we take the web page seriously that A is the "earth time in days" (I must also assume he means universe, or at least the parts outside "the garden".), then as creation progresses, the current time decreases. (It's what decaying exponentials do, after all.)

Instead, it is the *INTEGRAL* of A that give the age of the universe during creation, up to when the non-uniform time flow abruptly stops. While A is the "speed ratio" and Aₒ is a constant needed to make the numerology "work out".

(It would seem that the guy with the physics Ph.D. from [large state university] can indeed find errors in the work of the MIT/Harvard guy. Ha!)

It *almost* works. Almost as well as physics by chatbot.

By golly, I think you're smarter than a chatbox!

 

[Diamond72]

already trying to squeeze 13.7 billion years in to less than a week.

Each day is half the length of the day before. Although there is really only one day, the first day. You can do this with simple 5th-grade math but developing formula is a lot quicker.

This weird little factor "A" is the instantaneous ratio of "genesis time" (t) to real time (no symbol given).

This is to much jibberish for me. I don't know what you are talking about . If Schroeder does not work for you that is fine. But when you have to tear someone so qualified down the way you do it makes me wonder about you.

I told you fifty million billion times. Time is relative. This has to do with the observer effect and your perspective. If you do not understand Einstein's theory you maybe better to find someone else to explain it to you.

In his theory of special relativity, Einstein proposed that the concept of time is relative and not absolute. But you want to insist that Einstein is wrong and time is absolute, not relative. That is fine, do what you want. I have no need to convince anyone of anything.

They say nothing is faster than the speed of light. Yet the universe is expanding faster than the speed of light. That is why we can look and see the light of the universe from 13.7 billion years ago.

We have black holes where the gravity is so strong that light can not escape. But then God said: "Let there be light" and sure enough there was light. Time does not exist for light. You know if you were traveling the speed of light then you would not age. Time would stop for you.

This is why, worm holes are like optical fibers. There is no time because you travel at the speed of light. There was a movie about this. Contact with Jodie Foster. Not that great of a movie but it deal with this stuff.

 

[Diamond72]

By golly, I think you're smarter than a chatbox!

I found a chatbox that gives it's references. If you go to these web sites that is where the problem is. The problem is not the algorithm, the problem is the information on the internet getting fed into the algorithm. Clearly another example of where Bill Gates has failed to get the job done and he clearly is not ready for prime time. This was a chatbot that Musk began the work on, but he quit somewhere along the way.

 

[Hans Blaster]

By golly, I think you're smarter than a chatbox!

Go figure.

 

[sjastro]

This is a cut-and-paste from a chatbot. So if you think you are smarter than AI that is fine with me. Google is about to be replaced with something a lot better. Bill Gates is heavily invested in this. Schroeder does respond to emails but he says almost nothing and invests almost nothing in answering questions. Pretty much like all best-selling authors.

If Google AI comes up with nonsense such as the equation A = Aₒexp(-Lt) being the R-W metric, it has along way to go before it can be considered intelligent let alone coherent.
I note in your follow up posts there is an apologetic tone, is this for real or is it the chatbot?

 

[Diamond72]

I note in your follow up posts there is an apologetic tone, is this for real or is it the chatbot?

That is a part of the chatbot program. I ran your response back into the program so it would correct itself.

If Google AI comes up with nonsense

Chatbots go far beyond google. Some provide their references so you can do your own research.

 

[sjastro]

That is a part of the chatbot program. I ran your response back into the program so it would correct itself.

Well your chatbot might be apologetic but it is still dumb.
Your chatbot response to my comment the equation A = Aₒexp(-Lt) being not the R-W metric;

I apologize for my confusion, if A = Aₒexp(-Lt) is not the R-W metric, but it is an equation that describes the behavior of the scale factor over time, and can be used in the context of the Robertson–Walker metric for certain models of the universe.

A = Aₒexp(-Lt) should be familiar to any high school maths student as an equation for exponential decay.
The common denominator between the chatbot and Schroeder both seem to be unaware of this fact.
A = Aₒ is the initial quantity when t=0 but in Schroeder's definition of Aₒ it is not an initial quantity of 'anything'.

Chatbots go far beyond google. Some provide their references so you can do your own research.

Yes I am aware of the inroads made by AI in science an example of which is provided here.
In this thread however your chatbot is woefully inadequate.

 

[Diamond72]

A = Aₒexp(-Lt) should be familiar to any high school maths student as an equation for exponential decay.

My son is into formulas, I am not. There is a HUGE area

A = Aₒexp(-Lt) should be familiar to any high school maths student as an equation for exponential decay.

Neil Degrass Tyson in his book "Astrophysics for People in a Hurry" talks about how exponential decay applies to the universe and how it works on the cosmological scale, how it explains dark energy, how it shapes the fate of galaxies and how it gives us a glimpse of the ultimate fate of the universe.

Gerald Schroeder does not talk about exponential decay. What point are you trying to make about this? Decay is what makes us finite. God is infinite because there is no decay, and there is no change with God. He is the same yesterday, today, and tomorrow.

The Hasidic teaches that one of the main concepts in Kabbalah is the idea of the "shevirat hakelim" or "breaking of the vessels." This refers to the idea that when God created the world, the vessels that were created to contain the divine light shattered, causing a fragmentation of the divine light into sparks that became trapped in the physical world. This event is said to have caused the spiritual and physical realms to become separate and disconnected, leading to the existence of evil and suffering in the world.

Today we talk about singularities, dark holes and event horizons.