Our Mathematical Universe - by Max Tegmark 2014 - Book review

This document contains comments about the book "Our Mathematical Universe" - by Max.Tegmark 2014.
The sub title is: My Quest for the Ultimate Nature of Reality
• Scientific American May 2003 - Parallel Universes. Not just a staple of science fiction, other universes are a direct implication of cosmological observations. By Max Tegmark
• Scientific American January 2010 - Life in the Multiverse. Could the strange physics of other worlds breed life ? By Alejandro Jenkins and Gilad Perez.
• Scientific American February 2017 - page 28. POP goes the universe by Anna Ijjas, Paul J. Steinhardt and Abrahom Loeb. The latest astrophysical measurements combined with theoretical problems cast doubt on the long-cherished inflationary theory of the early cosmos.
• The Inflationary Universe - by Alan H. Guth Book review
This book review is often mentioned in this book review
For usenet discussions: For more about the Cosmological Parameters Omega(Lambda) etc read this: Friedmann's equation - Question 13

To Measure and To Calculate

One of the words used often in the book is the word Measuring
For example in sentences like:
• At page 78:"1 We measured the dark-energy fraction in two different ways and the answers agreed"
• At page 78:"2 We measured the ordinary-matter (baryonic) fraction in two different ways and the answers disagreed"
The problem is when you make a measurement you perform one observation directly of a physical parameter. You can measure a temperature by using a thermometer.
In certain cases you can also measure a range of parameters. For example by using Gas Chromatography you can establish a range of compounds.

When two measurements are involved the situation is different. In that case the final parameter is calculated
If you want to measure the speed of a train at least four measurements are involved:
• The position r(t1) at a moment t1.
• The position r(t2) at a moment t2.
The speed is than calculated by performing the following equation: v = (r(t2)-r(t1))/(t2-t1)

IMO in the above two cases the word calculated should be used. The issue is what exactly is measured and which calcultions are performed to the two fractions.

IMO in many cases in the book more often the word calculation should have been used.
This puzzle became known as the measurement problem (in physics measurement and observation are synonyms)
Observations tend to have human implications. Like in the sentence: We observe the wild life.
Measurements should be performed independently of any human involvement.
In this case the word measurement is used correct.

To Predict

One of the words used often in the book is the word prediction
For example in sentences like:
• At page 46:"Interesting, Georges Lemaitre has shown in his ignored 1927 paper that the expanding universe solution predicted Hubble's Law: etc"
• At page 106: "Like many succesful scientific theories, inflation got off to a rough start. Its first firm prediction, that space was flat etc."
A theory is a more mathematical description of the physical reality. Using a theory you can make predictions. An example is Newton's Law. In order to make predictions you perform the following steps:
1. This example is based on three objects.
2. First you measure the positions of the three objects at three moments t0,t1 and t2
3. Secondly you calculate the velocities and accelerations for each of the three objects.
4. Next you calculate the mass of each of the three objects using Newton's Law.
5. Next you predict the position of the three objects at a different moment t3.
6. Finally you compare the predicted position with the actual position at t3. The positions should match.
In general when you perform any prediction you should describe a sequence of steps:
• 1. Strating point is a description about a set of facts we all agree upon. These facts can include mathematical equations.
• 2. Next you describe a sequence of actions which include: experiments, new tools and physical reactions that can happen or are possible based on these agreed upon facts.
• 3. Finally you should describe a clear observation, that is currently not possible but can be performed based on what is described above.
• Step 2 can include assumptions (parameters) but than each of these assumptions should be demonstrated by different observations

1. What is reality - page 3

1.2 What's the Ultimate Question? - page 7

But if reality isn't what we thought it is what then what is it? What's the realation between the internal reality of our mind and the external reality?
The most important task of human mankind is describe the reality in as much detail as possible independent of any human involvement.

1.2 The Journey Begins - page 10

We'll begin by arguing that our failure to understand consciousness doesn't stand in the way of a complete understanding of the external physical reality.
I think that the idea that we will ever completely understand the physical reality is a misnomer.
Our understanding of our consiousness has nothing to do with this.
It is even stronger: Our understanding of the physical reality should be based completely independent of any human involvement, our consiousness or our point of view.
page 199 (Quantum Censorship), page 254 (External Reality Hypothesis) and page 363 (The Case for a Greater Reality)

2. Our Place in Space - page 17

2.2 How Big is space - page 30

I find inspiring: we've repeatedly underestimated not only the size of our cosmos, but also the power or our human mind to understand it.
The second part is not true.
There is the danger that some people think that they understand it, but in reality they have it wrong. This is highly possible for certain concepts explained in this book

2.8 What is space - page 30

Imagine drawing a triangle on each of the 2D surfaces of the 3-D shapes in Figure 2.7
In a flat 2D surface the 4 angles of a square add up to 360 degrees. When the surface is not flat this does not work any more. There is no time issue. See "Flatness Problem" page 99
To most people this mathematically discovery of non-Euclidean spaces probably seemed like little more than esoteric mathematical abstraction of no practical relevance to our physical world. But than Einstein came along. Einstein's theory allows our 3-D space to be curved etc.
But than the author has to explain what curved space really means compared to non-curved space.
To let ants walk on the surface of a sphere does not demonstrate/explain curved space. Curved space I expect is more complex.
So the question of what kind of space we inhabit can't be settled from pure logic alone, as some Euclid fans had hoped.
Why is this a problem in the first place?
It can only be resolved by performing measurements - such as making a huge triangle in space (with light rays as edges say) and checking whether the angles add up to 180 degrees.
Using light rays is tricky. Mass bends lightrays.
I shall tell you about how my colleagues and I have fun doing precisely this.
The answer turns out to be about 180 degrees for universe-sized triangles, but significantly more than 180 degrees if a black hole fills up much of the triangle.
And how have you performed this in detail.....
If you want to do astronomy measurements you should use a grid with fixed clocks. Only when you do that you can measure that light is bended by mass.
To mathematicians, studying space is the same as studying geometry, and geometry is is just part of mathematics. One could indeed argue that space is a mathematical object, in the sense that its only intrinsic properties are mathematical properties - properties such as dimsionality, curvature and topology.
Space, the area surrounding us, is not a mathematical object. Space is physics and in order to describe you can use mathematics.

3 Our Place in Time - page 34

3.2 Where Did the Galaxies Come From? - page 35

At page 36:
Through his telescopes, Galileo saw etc. That the moon wasn't a perfect sphere but what looked like a place, complete with mountains and giant craters So why didn't it fall down?
This last question is wrong. It should have been:
So why did it move around the Earth?
Next:
Isaac Newton finally answered this question by exploring an idea that was as simple as it was radical: that heavenly objects obey the same laws as objects here on Earth.
I expect that Isaac Newton would agree more with this text:
That the movement of all heavenly bodies can be described by the same Law

3.2.4 Making Sense of an Expanding Universe - page 46

First of all, are galaxies really moving away from us or is space just expanding?
A more unbiased sentence would be:
are galaxies moving away or is space expanding?
Maybe it is both. It is a physical question.
What does space expansion mean? Does this implies that intergalatic density decreases?
When it is both locally the galaxies do not move.
If our Universe is only 14 billion years old, how can we objects that are 30 billion light-years away. etc
Here the answer is that we're not seeing these distant galaxies where they are now, but where they were when they emitted the light that reaches us now.
The important issue is that we observe these galaxies when the universe maybe was 1 billion years old. This raises a different question: how is it possible that mature galaxies evolved so quickly?
Page 49 tries to answer this question:
when we gaze out into our Universe with our best telescopes, we see something similar: nearby are lots of large and mature galaxies like our own, but very far away we see mostly small baby galaxies that don't yet look fully developed.

4. Our Universe by numbers - page 68

4.1 Wanted: Precision Cosmology - page 69

However, we now understand a great deal about what happened during the 14 billion years since then: expansion and clustering.
The issue is to describe both concepts as detailed as possible.
These two basic process both controlled by gravity have transformed etc.
I doubt if this is correct. The expansion is something happening with the universe at large. Clustering is something happening at small scale. The word controlled is wrong. See next.
How exactly did gravity do this?
Gravity is an attraction force and can only be used to explain the clustering phenomena.
Next
If you stop your bike at a red light you quickly realize that gravity can be destabilizing.
When you reduce your speed and stop your bike in order to stabilize you have to supply a counter force to keep the bike in balance.
The same happens how galaxies form. First you have a clustering phase in which gas collapses. Next you have a rotation phase which is described by an expansion force. When the two forces are equal the galaxy becomes stable.
In the cosmic example, the farther our Universe gets from perfect uniformity the more forcefully gravity amplifies its clumpiness.
First, you cannot make this comparison between a bike and the Universe at large.
Secondly Our Universe is not perfect uniform and this non uniformity changes all the time. Gravity describes these changes but does not amplify this non uniformity or clumpiness.
that we had no clue what 96% of our Universe was made of.
This gives the impression that 4% is baryonic and 96% is of unknown signature.
More detail would be nice.
The mysterious stuff is known as dark matter, which is really little more than a name for our ignorance. The name invisible matter would be more apt.
There are two issues here:
• dark matter is supposed to be non-baryonic matter, while the sun and the earth are made from baryonic matter. This issue is not discussed in this book.
• Secondly to use words like invisible is also wrong, because it is related to our human point of view ie constraints. Words like hot and cold implying that light is emitted (or not) are better.

4.2 Precision Microwave Background Fluctuations - page 71

What's so great about the power spectrum is that not only can we measure it, but we also can predict it: for any mathematically defined model of how our Universe expanded and clustered we can calculate what the power spectrum should be.
A power spectrum in this context is typical something that is calculated in two ways: first based on observations ie the cosmic microwave background radiation and secondly based on a certain equation. What is required are the details of what is observed and how the power spectrum is calculated in both ways.
A typical model is the Friedmann model which is described by Friedmann's equation. Friedmann's equation involves a set of parameters and in principle you could calculate a power spectrum for each set of parameters. Here the details are very important.

Figure 4.2 at page 72

The text near Figure 4.2 reads:
Precision measurements agree beautifully with the curve predicted by the current standard model. You can appreciate the most remarkable aspect of modern cosmology here without worrying about the details: highly accurate measurements now exists and they agree with theoretical prediction.
Its the details that count. See also Reflection part 2 The issue is not so much the standard model but the physical derivation (interpretation) of the Friedmann equation and the parameters involved.
Also at page 72:
The predicted shape of the power spectrum depends in complicated ways on all the things that affect cosmic clustering, so if we can adjust our assumptions about all these things so that the predictions matches what we measure then we have measured these important physical quantities. (density of darkmatter, density of dark energy, etc)
IMO the picture drawn is too simple. More detail is required what is involved.

4.2.2 Gold in the Hills - page 74

To me one of the most beautiful ideas in Einstein's gravity theory is that geometry isn't just mathematics: it's also physics.
The SR theory and the GR theory are both (mathematical) descriptions of the physical realiuty.
Specifically Einstein's equations show that the more matter space contains, the more curved space gets?
How is this curved space measured? IMO you need a grid with straight lines.
This curvature of space causes things to move not in straight lines but in a motion that curves toward massive objects
Newton's Law also describes that objects do not move in a straight line. So what is new?
IMO accordingly to Newton the cause are in the objects
This opens up a totally new way of weighing our Universe: just measure the first peak in the cosmic microwave-backround power spectrum! If its position shows that space is flat, then Einstein's equation tell us that our average cosmic density is about 6 hydrogen atoms per cubic meter. etc.
That maybe true but how do you demonstrate that the relation "its position shows that space is flat" is correct. All this I expect is more complicated and prune to errors.

4.2.3 Dark Energy page 76

As you can see in Figure 4.3 we know the size of the total budget (1) from the first peak position, but we also know the density of ordinary matter (2) and of of dark matter (3) from measuring its gravitational effects on cosmic clustering.
How do we know that the first peak position is a function of the total matter budget? How is the total matter budget (1) calculated from the first peak position?
How is the total amount of baryonic matter (2) calculated?
How is the total amount of non-baryonic matter (3) calculated?

4.4 The Ultimate Map of Our Universe - page 87

We have measured the density of darkmatter (and dark energy), but what is each?
It is important to remark that you have not measured the density but calculated using a certain equation. In principle that is correct. The problem is that if you do not fully understand the equation how do you know that the equation is a correct description of a physical process.
At page 88 Figure 4.7 we read:
The fraction of our observable Universe (left) that has been mapped (center) is tiny, covering less than 0.1% of the volume. (leaving 99.9% of the volume unexplored) We have mapped a thin strip around the perimeter while most of the interior remains unexplored.
In the middle panel the circular region is the CMB radiation which comes from the thin gray edge and the tiny structure near the center is the largest 3D galaxy map from the Sloan Digital Sky Survey
 This picture is misleading. The CMB radiation we observe now comes from a relative tidy sphere ,filled with plasma, in space. This sphere has be grown in size with a radius of roughly 42 billion light years at present. The plasma has evolved in the stars and galaxies we can observe now, not in the way they were just after the Big Bang nor how they are at present, but at different moments in the evolution of the stars and galaxies as a function of the parameter z (red shift) or distance.

4.5 Where Did Our Big Bang Come From - page 93

In this chapter we have explored and we have measured the age of our Universe to 1% accuracy.
It better word is not measured but calculated (based on certain measurements)
To me one of the most striking lesons from precision cosmology is that simple mathematical laws govern our Universe all the way back to its fiery origins.
I think this sentence is rather misleading. The issue is that part of the evolution of the Universe can be described by mathematics. A huge part of the evolution depends on complex chemical processes which sequence can not be described by the same mathematical equations (which are to general).
Anyway to use the word govern is wrong.
For example the equations of general relativity theory govern the gravitational force etc. And not just crudely but with stunning precision as illustrated by Figure 4.2.
Figure 4.2. shows the power spectrum of CMB radiation and power spectrum calculated using the Friedmann equation.
To get this result the parameters of the Friedmann equation are calculated such that there is a match.
So precision cosmology highlights the mysterious utility of mathematics for understanding our world.
Understanding our world implies understanding the physical processes involved in as much detail as possible. This understanding implies to find similarities ie physical laws. Part of these laws can be described by mathematics. But the fact that this is possible has nothing to do with the processes involved.
Newton's Law is a tool to describe the movement of galaxies, stars and planets but this movement is not governed or controlled by this law.

5. Our Cosmic Origins - page 95

5.1 What's Wrong with Our Big Bang? - page 95

Page 96:
Let's go back in time to near the frontier of our knowledge,
That, in particular, there was a beginning of sorts one third of a second earlier, when the density of our Universe was infinite, and everything was flying away from everything else with infinite speed.
Density and speeds are always finite.
Q: What caused our Big Bang?
A: There is no explanation - the equations simply assume it happened.
IMO the best answer is: We do not know what happened before the Big Bang.
Equations are a tool to describe a physical reality. Friedmann's equation describes what happened after the Big Bang.
Q: Did our Big Bang happen at a single point?
A: No
What is a single point? If you do not know you cannot answer this question.
Q: Where in space did our Big Bang explosion happen?
A: It happened everywhere at an infinite number of points all at once
And what does that mean? In fact the answer does not answer the question.
IMO the best answer is: The Question is not clear.
Q: How could (our Big Bang) create an infite space in a finite time?
A: There's no explanation - the equations simply assume that as soon as there was any space at all it was infinite in size.
What is the definition of finite and infinite. There must be a difference. If the difference is not clear than the question is not clear.
Equations are mathematical descriptions of the physical reality designed by humans. The issue that you can use inprinciple equations to formulate an answer has nothing to do with the question.

5.1.1 The Horizon Problem - page 97

The section starts with the remark that the CMB radiation almost identical is in different directions in the sky. Next we read:
If our Big Bang explosion had happened significantly earlier in some regions than in others then etc and the temperature in our observed CMB maps would vary from place to place not by 0.002% but by closer to 100%
This discussion is in a certain sense not very scientific because what does one mean with temperature. How is this temperature measured or calculated.
But couldn't some physical process have made the temperature equal long after the Big Bang?
Maybe what we call temperature(?) was always in some sort of equilibrium.
The catch is that this mixing process takes time: you need to wait long enough for milk and etc to mix.
These mixing processes will happen continuous.
In contrast the distant parts of our Universe that we can see haven't had time for such mixing.
the regions A and B that we see in opposite directions of the sky haven't had time to interact at all.
The author should remark that the positions of two regions, at the moments light was emitted that we observe now, were very close.
This means that Friedmann's Big Bang model offers no explanation whatsoever for why A and B have the same temperatures.
Friedmann's model assumes that the universe is uniform which implies that the universe at large at any moment is identical.
At the bottom part of page 98 we read:
This is exactly what Alan Guth concluded: it couldn't just have been a crazy fluke coincidence that infinitly many seperate regions of space underwent Big Bang explosions all at once - some physical mechanism must have caused both the exploding and the synchronizing.
 In his book "The inflationary universe" by Alan H Guth at page 182/183 the horizon problem is discussed. The concept of Big Bang explosions and synchronization is not discussed. Instead Alan Guth writes: At 300000 years after the big-bang the horizon distance was about 900000 light years This distance is correct assuming the standard cosmological parameters as shown in Table 4.1 at page 86. Next we read: If we consider two photons arriving today from opposite directions in the sky, then we can use the mathematics of the Big Bang Theory to trace back the trajectories to 300000 years after the Big Bang. The calculation which takes into account the expansion of the Universe shows that the photons were emitted from two points about 90 million years apart as illustrated in Figure 10.5 That means 90 millions divided by 900000 = 100 times the horizon distance. This argumentation is misleading. The distance of the two points 300000 after the Big Bang was 2 * 900000 light years. The distance of the two points now is 2 * 42 billion light years. For a better understanding select: Friedmann's equation - The path of a light ray
Next we read at page 99.
One unexplained Big Bang is bad enough: an infinite number of unexplained Big Bangs in perfect synchronization strains credulity
Alan Guth in his book does not discuss synchronization between Big Bangs.
 In his book "The inflationary universe" by Alan H Guth at page 89 writes: Although we do not necessarily understand why the early universe was so uniform, the cosmic background radiation provides direct evidence that it was. (one of the great successes of the inflationary theory is a possible explanation for this simplicity.) For most purposes one can approximate the early universe as being exactly uniform, greatly simplifying the calculation of its evolution. This means the issue is not synchronization between Big Bangs. The issue is that the universe is considered uniform. The issue is why did the sequence of actions involved in the Big-bang nucleosynthesis process happened so synchronised?

5.1.2 The Flatness Problem - page 99

In this ultimately collapsing universe space gets curved so that triangle angles add up to much more than 180 degrees.
In contrast the top curve describes a universe getting curved so that these angles add up to much less than 180 degrees
It should be remarked that this behaviour descibes curving in time which is different than what is explained above (See "What is Space" page 30) where time is no issue.
So why is our Universe so flat? If you change the twenty-four digits in Figure 5.3 to random values and resolve Friedmann's equation the probability that you'll get a universe remaining flat for 14 billion years is smaller than the probability that a dart randomly fired into space from Mars would hit the bull's-eye on a dartboard on Earth.
My question to the author: And Max what is this last chance? If you do not than please do not write it.
The bottom part of page 99 contains the following note:
*We haven't even measured the strength of gravity accurately enough to know what more than the first four of these digits need to be, so the last twenty digits are my guess for illustration
The three values are:
• 447142152489876524709397 g/cm^3 Big Chill
• 447142152489876524709398 g/cm^3 Borderline
• 447142152489876524709399 g/cm^3 Big Crunch
The three numbers are almost identical. The first 23 digits are the same. The difference is in the last digit!!!

5.2.2 Problems Solved - page 103

In this way, inflation solves the "Bang problem" explaining what caused our Big Bang: it was caused by this repeated doubling process.
Doubling process of what?
The problem is that the author explains the Big Bang in the way baby's grow. This is done by cell division. The problem is that our Universe (all that what expanded) does not contain cells or something similar. so you cannot claim that there is some sort of doubling taken place.

You can also raise a different question: What caused this doubling process?

Alan Guth realized that inflation also solves the horizon problem. The distant regions A and B in Figure 5.2 were extremely close together during the early stages of inflation, so they had time to interact back them
Inflation means that during a small period the size of the universe increased exponential. i.e. a small period.
Of course it is easy to write that we are speaking about small period. But how do we know that this is true or not true. Specific what caused this very special period.
A difficult question to answer is what happened before this small period. Again it is easy to postulate that the universe was uniform but difficult to prove.
 Alan Guth in his book at page 184 writes: Nevertheless, it is clear, that before inflation the observed universe was incredibly small. This is the same if you do not accept the inflation theory. The biggest problem is why does he use observed universe in stead of the universe or our universe ? Next Alan Guth writes: There was plenty of time for such a small region come to a uniform temperature. Next he compares this with the cooling of a cup of coffee, a process we all agree upon. Why does he use the word temperature, which is a human based process. You should describe this with terminolgy relevant for the processes involved. What we are discussing is the time extremely shortly after the big bang, the state of which is purely speculation. Most probably many different processes happened simultaneous. It is very difficult to assume that all the changes which happened, happened everywhere synchroneous, simulataneous in harmony. Next: Then, once the uniformity was established in this ver small region, the process of inflation stretched it to become large enough to encompass the entire observed universe. Thus the uniformity in temperature thhroughout the observed universe is a natural consequence of inflation. This is easy to write, but the details are lacking. With details I mean, the description of the physical processes that took place. Anyway the use of the word: Observed Universe is very misleading. Inflation, when its happens, has nothing to do with the observed universe. It should describe the evolution all that happens (Our Universe) after the Big Bang (Our).

5.3 The Gift That Keeps on Giving - page 106

As we saw in the last chapter Einstein's Gravity Theory says that space can only be flat if the cosmic density equals a particular critical value.
The issue is what is this critical value, what is the cosmic density and how are both calculated. When the two values are "considered" equal this difficult problem is solved!!!
so quatum effects could have been important. And indeed they were: as we'll see in Chapter 7, the so-called Heisenberg uncertainty principle of quantum mechanics prevents any substance, including the inflating material, from being completely uniform.
To assume that something is completely identical in all three dimensions at all scales is a very "strange" assumption. Only completely empty space is completely uniform.
The reverse also has no practical value.
If you try to make it uniform, quantum effects force it to start wiggling around, spoiling the uniformity.
That is a wish, and completely outside reality.
When inflation stretched a subatomic region into what became our entire observable Universe the density fluctuations that quantum mechanics had imprinted were stretched as well, to sizes of galaxies and beyond.
The word "Inflation" is a description of a process during the evolution of the universe, but is not a true explanation of this physical process. The same with the word "quantum mechanics". The word "gravity" also explains nothing.
As we saw in the last chapter, gravitational instability took care of the rest, amplifying these fluctuations etc into the spectacular galaxies, galaxy clusters etc that now adorn our night sky.
This sentence explains nothing. Next:
The best part is that this isn't just qualitative blah blah, but a rigorous quantitative story where everything can be accurately calculated.
You can not accurately calculate the CMB radiation.
The power spectrum curve I've plotted in Figure 4.2 is a theoretical prediction for one of the very simplest inflation models and I find it remarkable how well it matches all the measurements.
See also Figure 4.2 The author should give the details exactly what is predicted and what is measured. IMO what is measured is CMB radiation.

5.4 Eternal Inflation - page 111

Q: What caused our Big Bang?
A: The repeated doubling in size of an explosive subatomic speck of inflating material.
You can not explain something by introducing concepts which are not clear.
How does this doubling in size happen?
Q: Did our Big Bang happen at a single point?
A: Almost: it began in a region of space much smaller than an atom.
The mainstream opinion is that it happened everywhere.
The answer implies that our universe is finite.
Q: Where in space did our Big Bang explosion happen?
A: In a tiny region - but inflation stretched it out to about the size of a grapefruit growing so fast that the subsequent expansion made it larger than all the space that we see today
The issue is not what we can see, but how large our universe, which started at the Big Bang, presently is.
By introducing "a tiny region" our universe is finite, implying that the total universe is much larger.
Q: How could our Big Bang create an infite space in a finite time?
A: Inflation produces an infinite number galxies by continuing forever. According to General Relativity an observer tc, perceiving space as having been infinite already when inflation ended.
What an observer observes is of no importance. The importance is to describe the evolution of our universe and is our universe finite or infinite. To answer these questions you must know what finite means.
In summary, inflation has transformed our understanding of cosmic origins, replacing Friemann's Big Bang Model by a simple mechanism that creates our Big Bang from almost nothing.
Can the auther please describe this simple machanism in detail?
It has given us more than we asked for: space that isn't just huge but truly infinite, with infinite numbers of galaxies, stars and planets.
Our universe, which started at the Big Bang is finite and contains a finite number of galaxies and stars.
The author should answer the following question: Immediate after the Big Bang there were no galaxies. At a certain moment the first galaxy formed. More and more but the number was finite. What is the moment that they became infinite? Our point of view if we can observe them has nothing to do with this.

6. Welcome to the Multiverse - page 119

6.1.1 What's a Universe - page 120

Physical Reality:
Everything that exists
Yes. If this means all of what exists at present.
This is a concept independent if we exist Yes or No.
Our Universe:
• The part of physical reality we can in principle observe.
• The spherical region of space from which light has had time to reach us during the 14 billion years since our Big Bang
This difinition is misleading, because definitions dependent about what we humans can observe and where we are not well defined. For humans living in the Andromeda galaxy their "Our Universe" is different and partly overlapping with our "Our Universe". What is also important that the Big Bang that caused their and our "Our Universe" are one and the same,
In particular, some people use the phrase I eschew (synonym: avoid) "the universe" to mean everything that exists, in which case, by definition, there can't be any parallel universes.
 There is nothing wrong with the terminology "the universe" meaning: Everything that exists. The problem is with the terminology "Our Universe" meaning: all that we can observe. This definition is in fact in contradiction with the ERH Hypothesis. See page 254 , because it reflects the human point of view. What "Our Universe" should mean: is the physical reality "created" or caused by Our Big Bang. What we observe is an image of the state of "Our Universe" in the past. See also page 48 This leaves the possibility open that the size of "Our Universe" caused by "Our Big bang" is smaller than the size of "the Universe" (meaning everything) and that there occured more Big Bangs.
At page 121:
This is certainly a lot of stuff, but could there exists even more, farther away in space? As we saw, inflation predicts that there is.
See page 103
1. Such a claims are easy to predict but very difficult, so not impossible to verify that they are true. See also To predict .
2. It is highly possible that "The Universe" is larger than "Our Universe". You do not need inflation to make such an assumption understandable. The issue is at the moment of "Our Big Bang" was there already something or was "Our Big Bang" "created" out of nothing.
By our very definition of universe, one might expect the notion that our observable Universe is merely a small part of a larger multiverse to be forever in the domain of metaphysics.
By using the definitions of "Our Universe" and "The Universe", as explained in the Yellow box above, you do not have to refer to metaphysics.

6.1.1 Are Parallel Universes Unscientific - page 123

Page 124:
Physics is all about testing mathematical theories against observation: if a theory can't be tested even in principle then it's logically impossible to ever falsify it, which, by Popper's definition, means that it's unscientific.
If a theory cannot be tested against observations than what is the purpose?
Laws describe the behaviour of (similar) physical processes. Laws are described by mathematical equations, by parameters (some of which are constants) and by initial conditions. Similar processes are described by different parameters and initial conditions. Laws are develloped by means of experiments and observations. Laws are tested by performing experiments or predicting observations.
Theories are the same as laws except that the predicted observations are not yet performed.

In some cases the details of the processes involved can not be directly observed. This is the case for example when elementary particles are involved. To unravel these inner details different experiments have to be performed with different outcomes to deduce these details.

Parallel universes are not a theory, but a prediction of certain theories.
That is correct. However a clear definition of what is a parallel universe should be supplied. Immediate next:
Of theories such as inflation.
That means parrallel universe are a prediction and part of inflation theory.
However this raises serious problems:
• What is the inflation theory?
Allan Guth in his book discusses four. See Book Review Reflection 1 and there are more. What this means that there exists no clear definition.
Next at page 124:
For a theory to be falsifiable, we need not be able to observe and test all its predictions, merely at least one of them.
That depents about what the theory involves.
In order to claim that a theory is true you should test all its predictions specific (by means of different experiments) if the predictions are indepent on each other.
The theory is correct if the actual observations are the same as the predicted observations.
That does not mean that if you can not test a prediction presently that the theory is false.
If the theory involves a sequence of events than at least the final outcome should be tested i.e. observed.

Let us define the inflation theory in 3 steps:
1. The inflation theory assumes a short very rapid period of expansion.
2. As a result the CMB radiation will be almost homogeneous.
3. As a result there will be parallel universes.
The CMB radiation is almost homogeneous but that is no proof that this is caused by very rapid expansion, mainly because the details of the supposed internal relations are not clear. With relations I mean chemical reactions. See also Book Review Reflection 1
The same is also true for parallel univeses: the details are not clear.
That means we have no prove that there are parallel universes.
At page 125:
Analogously, the succesful predictions of inflation that we've described in the last two chapters make inflation a scientific theory, which makes it seriously its other predictions as well - both testable predictions such as what future CMB experiments should measure and seemingly untestable predictions such as the existence of parallel universes.
At page 103 are described the horizon problem and the flatness problem.
IMO the process of inflation is deduced to solve the horizon problem and the flatness problem. The issue is: that it is easy to write/invent what should have happened but difficult to test what has actual happened. IMO it is even impossible.
Alan Guth describes this inflation process in his book as a rather discontinuous process with two specific start and ending events. In reality many different scenarios are possible. What happened very short after the Big Bang is very difficult to test specific the different scenarios.
What happened 300000 years after the Big Bang as a consequence of inflation is also difficult if not impossible to test except if Lambda is equal to 0. In that case the density is equal to the critical case but that is in contradiction which is currently as standard accepted.
Another important thing about physics theories is that if you like one you have to buy the whole package.
• If the inflation theory predicts both uniform CMB radiation and parallel universes than both should be observed.
• If the inflation theory assumes parallel universes as an option than not.
General relativity is a rigid mathematical theory with no adjustments possible; you have to either accept all its predictions or you have to start from scratch etc
All the predictions of General relativity are demonstrated. In fact General relativity better can be called a law in stead of a theory. The same as Newton's Law within its own limitations.
In the same way, parallel universes aren't optional in eternal inflation. They come as part of the package, and if you don't like them, then you have to find a theory that solves the bang problem, the horizon problem and the flatness problem etc
After the Big Bang a very complex range of physical processes happened which after 13.7 billion years resulted in the state of the Universe we are observing today.
A detailed description of these processes is complex. To predict the influence of a period of large expansion is even more difficult.

6.2.3 Fine-Tuning as Evidence for the Level II Multiverse - page 138

Basically we've discovered that many of those knobs that we discussed appear tuned to very special values and if we could change them even by quite small amounts then life as we know it would become impossible.
The only thing we know is that the conditions for life to evolve at a planet are rather specific. There are no knobs to control these specific conditions. On the other hand we can easily assume that there are more planets with the same conditions prone for life, but this is difficult to verify.
Tweak the dark-energy knob and galaxies never form.
What does the author tries to demonstrate with this?
There are galaxies and there is the Friedmann equation which describes the evolution of the universe. One parameter is called dark-energy and different values describe different evolutions. The problem is to calculate the correct value which describes the evolution as observed. There are no knobs available.

6.2.4 Fine-Tuned Dark Energy page 140

As we saw in Chapter 4our cosmic history has been a gravitational tug of war between dark matter trying to pull things together and dark energy to push them apart.
Because galaxy formation is all about pulling things together; I think of dark matter as our friend and dark energy as our enemy.

7. Cosmic Legos - page 157

And the book just said that every quantum system changes deterministically accordingly to the so-called Schrödinger equation.
Quantum system do not behave deterministically only probablistic (from the outside!)

7.6 Above The Law - page 168

So are microscopic particles above the law? No they obey a different law: Schrödingers.
Schrödingers Law is a very clever law but the law does not describe the behaviour of each particle accurate, only on average ie probablistic.
Part of the problem is that more you want to know the more you interfer.

7.8 Making Waves - page 172

This is the essence of Heisenberg uncertainty principle: etc.
In other words, an object can't simultanously have an exact position and an exact velocity.
By using a camara at two different moments you can calculate "exactly" the velocity of a falling raindrop. See also: to measure and to calculate
The reason is because the measurement (which uses photons) does not disturb the object being measured (raindrop).
 In the case when a hydrogen atom is considered (H1 which consists of 1 proton and 1 electron) the claim that the electron can't simultaneously have an exact position and velocity is rather misleading. The issue is that both can't be measured simultaneously, because measuring the position also influences the behaviour. This means that the Heisenberg uncertainty principle is mainly a human measurement problem and not a Law of physics The problem is more subtle: You can not measure the position of an electron twice (in order to calculate the velocity) because measuring the position changes the direction of the electron and influences the velocity.

7.9 Quantum Weirdness - page 175

Schrödinger was even more radical: he abandoned the very idea that a particle has a well-defined position and velocity.
The concept of a well-defined position and velocity is not practical, because it can not be measured.
Instead he described the state of a particle by a new mathematical beast called a wavefunction, which describes the extent to which the particle is in different places.
The wavefunction describes the average position of a particle. A particle is never at different places at once. In that sense the comment near Figure 7.5 at page 171 is wrong.
Specifically, if you experimentally go looking for the electron, you find that the square of the wavefunction gives the probability that you'll find it in different places, so some physicists like to think of the wavefunction as describing a probability cloud or probability wave.
The wavefunction describes the probability of finding the electron at a certain place. The function does not describe to find the electron at different places at once.
In particular you'll never find a particle in places where its wavefunction equal zero.
You'll never find a particle in a place where its wavefunction is zero.
At page 176 bottom:
If you want to stir up a cocktail party by sounding like a quantum physicist another buzzword you'll need to drop is superposition: a particle that's both here and there at once is said to be in a superposition of here and there,
How do you know that the particle is here and there at once? How do you know that the particle is in two different positions at once? Or is it better to say that you do not know?

7.10 The Collapse of Consensus Page 177

In summary, Schrödinger altered the classical description of the world in two ways:
1. The state is described not by positions and velocities of the particles but by a wave function.
2. The change of this state over time is described not by Newton's or Einstein's laws but by the Schrödinger equation.
The Schrödinger equation describes the outcome of an experiment when a measurement is done. Not before the measurement.
At page 178:
Specifically if something is not being observed then its wavefunction changes according to the Schrödinger equation, but if it is being observed, then its wave function collapses so that you find the object only in one place.
This depends about the specific process involved and how the measurement or observation is performed.
If a particle moves in a circle and you measure the position at one position you will find the particle there.
If you measure the particle at two positions at 180 degrees there is a 50% chance for each.
Next:
This collapse process is both abrupt and fundamentally random and the probability that you find the particle in any particular place is given by the square of the wave function.
In the case of Schrödingers Cat the "collapse" is at the moment when the radioactive element decays. The chance is calculated by calculating the half live time of this particular element. To calculate this duration you need a stopwatch and a counter (in order to monitor 1000 decays)
Next at page 178:
Not everyone was thrilled,however. If wave function collapse really happened then this would mean that a fundamental randomness was built into the laws of nature.
All what this means that the outcome of certain experiments is not 100% sure. In certain experiments the outcome can only be predicted with a probability of 50%. In other experiments the outcome will be more accurate, specific if they can be described using Newton's Law.
Einstein was deeply unhappy about this interpretation and expressed his preference for a deterministic unverse with the remark "I can't believe that God plays dice"
The whole issue is that the physical reality can not be considered deterministic (meaning that the physical processes follow strict physical laws, described by mathematics) but is only partly deterministic.
After all the very essence of physics had been to predict the future from the present and now this was supposedly impossible not just in practice but even in principle.
 Newton's and Einstein's Law do not predict the future from the present. That is impossible. In order to use Newton's Law to predict the future you must include observations from the past. The whole issue is an accuracy issue. That means you can not predict the future with 100% certainty.
At the bottom of page 178:
Even if you were infinitely wise and knew the wave function of the entire Universe you couldn't calculate what the wavefunction would be in the future, because as soon as someone in our Universe made an observation the wavefunction changed randomly.

7.11 The Weirdness Can't Be Confined - page 180

Loosely speaking the Copenhage interpretation of quantum mechanics suggests that small things act weird but big things don't. Specifically things as small as atoms are usually in several places at once but things as big as people aren't
Small things are not at different places at once. We don't know where they are, but if we take a measurement we know and performing a measurement drastically influences their behaviour (and often this is like a dead sentence if we want to measure photons)
For large things this is different because the act of a measurement does not influence their behaviour implying that more measurements are possible. The result is that future behaviour can be calculated with high accuracy.
At page 180
Schrödinger himself shattered such hopes with a diabolical thought experiment: The Schrödingers cat is trapped in a box with a cyanide canister that's opened if a single radioactive atom decays.
You can not perform in general science by performing thought experiments. Only real experiments. See also: thought experiment at page 187 Anyway you have to perform your experiments as simple as possible to explain what you want.
• For example a radioactive element is not required. You can also replace the cat by a human being which puts on a green or a red hat. The other person (the observer) can do the same. The state of the system becomes fixed as soon as when both persons have decided what they want to do.
• A different experiment is only to use a radio active element, a geiger counter and a Stopwatch. The experiment starts when the Stopwatch is started. After 10 decays the Stopwatch is stopped. The purpose is to calculate the half life time

8. The Level III Multiverse - page 184

In this thought experiment that I'll call "Quantum Cards", you take a card with a perfectly sharp bottom edge, balance it on a table and bet \$100 that it's going to land face-up when it falls
Physics can not be based on thought experiments. See also: thought experiment discussed at page 180. Next:
You keep your eyes closed until you hear that the card has fallen, then look to see whether you've won or lost your bet. According to classical physics it will stay balanced forever.
Because this does happen, classical physics is "wrong". Remember this is a thougt experiment.
Next:
According to the Schrödinger equation it will fall down in a few seconds even if you do the best possible job balancing it, because the Heisenberg uncertainty principle states that it can't be in only one position (straight up) without moving.
The fact that the card falls down depends on the material of the card and on the thickness. This has nothing to do with the Schrödinger equation nor with the Heisenberg uncertainty principle
Yet since the initial state was left-right symmetric, the final state must be so as well.
This is a typical sentence without any scientific value
This implies that it falls down in both directions at once, in superposition.
With both eyes closed.
When you open your eyes and look at the card, you're making an observation. So according to the Copenhagen interpretation the wave function would collapse and you'd see the card either face-up or face-down with 50% probability for each outcome.
The Copenhagen interpretation cannot make this claim. In order to make any claim you have to perform this card experiment 1000 times. If the outcome is 502 head 498 tail than you can claim that the chance of each is 50%. In fact you do not need any Schrödinger equation or wavefunction nor is there superposition involved You can keep your eyes open. The best way is to perform this experiment by a robot.

8.2 The Illusion of Randomness - page 191

Quantum mechanics won't predict the outcomes, merely the probability of different outcomes.
Quantum mechanics can not predict the outcome of throwing head or tail. If you want to know the probability you have to perfomed an experiment. Many.
Next at page 192:
There is nothing random at all about the Schrödinger equation: if you know the wavefunction of our Universe right now, it will in principle let you predict what the wave function will be at any time in the future.
See also: wave function universe discussed earlier at page 178. In practice what that does mean? If you know and if you don't know.
Well if you repeat this experiment with four cards there will be 2^4 = 16 outcomes (Figure 8.2) and in most of these cases it will appear to you that the queens occur randomly with roughly 50% probability.
The second half should be:
and when you observe all results in 50% the outcome is a queen.
Almost all of the copies of you in the final superposition will therefore conclude that the laws of probability apply even though the underlying physics (the Schrödinger equation) isn't random at all.
When I throw dice a 1000 times and when the result is 499 head and 501 tail than my only predictament will be that the chance of throwing head or tail is equal. No superposition is involved nor Schrödinger equation.
High Everett's work is still controversial, but I think that he was right and that the wavefunction never collapses.
 In order to describe the outcome of experiments with a fixed number of outcomes ( 2 with a coin, 6 with a dice, 37 with roulette) you do not need the concept of wavefunction and collapse. The only thing (in most of these cases) is that you want to be sure that the chance of each outcome is identical. The only way to figure this out is by performing many experiments.

8.3 Quantum Censorship - page 197

For example, if something can be in only two different places, my knowledge about it can be described by a two-by-two table of numbers, as in these two examples:
 ```(0.5 0.5) "It's here and there (0.5 0.5) at the same time" (0.5 0 ) "It's here or there (0 0.5) I just don't know which" ```
The problem is in the top part ie the concept: "at the same time". What does it mean that something is at two different places "at the same time"?
Before you do the measurement something, at any split instant, is either in one or the other state, (and can be continuously changing between the two states) but you do not know in which one.
After the measurement you know in which state.
So if you manage to replace these off-diagonal numbers by zero's then you have turned and into or and collapsed the wave function!
After you have performed a measurement, for example made a finish photo, you have frozen something what is changing and dynamic into something fixed and static. Nothing more nothing less.
Next:
The Copenhagen interpretation of quantum mechanics says that an observation somehow makes these off-diagonal numbers zero. I wondered if there might be some less mysterious physical process that did the same.
You make everything overly complex. The answer is: No
Next at page 199:
I concluded that quantum mechanics requires secrecy: an object can only be found in two places at once in a quantum superposition as long as its position is kept secret from the rest of the world.
 First an object can never be found in two places at once, you could write in principle: assumed. To be found implies a measurement. Secondly the concept of "to keep something secret" is typical a human based concept and is not in agreement with the ERH concept. See also page page 3 (What is reality) and page 254 (External Reality Hypothesis)
next at page 199:
If the secrets gets out, all quantum superposition effects become unobservable and it's for all practical purposes as if it's either here or there and you simply don't know which.
The physical reality has nothing to do with secrets. Our human capabilities have limits. That means not all what is real can be observed (measured) accurately, but that definitivily does not mean that it does not exist ie is not real.
Next
Now I was convinced that consiousness had nothing to do with it.
That is correct. Cousiousness has nothing to do with any physical process or the evolution of the universe. Except here on Earth where the influence of human conduct is studied.
Next
I realized that quantum observation isn't about consciousness, but simply about the transfer of information.
After any physical measurement (as part of an experiment) you acquire information.
Next at page 200:
And if you can't make the information secret again then the quantum superposition can't be restored.
Now I finally understood why Level III parallel universes stay parallel!

8.4 The Joys of Getting Scooped - page 202

I still had enough new stuff in my paper ( http://arxiv.org/pdf/gr-qc/9310032.pdf)

8.5 Why Your Brain Isn't a Quantum Computer 205

In recent years, there's been a surge of interest in building so-called quantum computers, which would exploit the weirdness of quantum mechanics to solve certain plems faster
Until now (2014) no one has actual build a general purpose quantum computer.
For example etc your credit-card number was encrypted with a method based on the fact that multiplying two 300-digit prime numbers together is quick, but factoring the resulting 600-digit number (figuring out which two numbers it's the product of) is hard and would take longer than the age of our Universeon today's best computers.
The largest number currently factorized is in the order of 10^230. See Nature 11 July 2013
The higest number factorized using Visual Basic 2010 and Parallel programming is in the order of 10^27. See Quantum Factoring Performance Evaluation - Using Parallel Programming - VB2010
Next:
If a large quantum computer can be built, then a hacker could use it to get the answer quickly, using a quantum algorithm invented by Peter Shor.
And IF the quantum computer performs as expected.
As David Deutsch puts it: "Quantum computers share information with huge numbers of versions of themselves throughout the multiverse" and get answers faster here in our Universe by in a sense getting help from these other versions.
Quantum Computers like any other PC have nothing to do with with multiverses. They operate based on Quantum Mechanical principles in our Universe. Seeing is believing and it is still a long way to go.
Next:
Many modern computers calculate faster by using multiple processors in parallel.
That is correct. But that implies that also the algorithm used should be suitable.

8.8 Multiverses Unified at page 220

In some fields, coauthors on a paper traditionally list their names in alphabetical order. In cosmology, however, we usually let the author ordering reflect who has contributed most to the paper.
This makes sense
I finally suggested a solution that both we liked: deciding the author-order with a quantum random-number generator.
In this particular universe, he's the first author ( http://arxiv.org/pdf/1008.1066.pdf ), but if our paper is correct, then I'm first author not only in half of the Level III parallel universes where we used this procedures, but in half of the Level I parrallel universes as well.
The title is: "Born in an Infinite Universe: a Cosmological Interpretation of Quantum Mechanics" by Anthony Aguirre and Max Tegmark June 2012
IMO this experiment does not make sense

10. Physical Reality and Mathematical Reality - page 243

10.1 Math, Math Everywhere - page 246

At page 249, As part of Figure 10.3 we read:
Figure 10.3: When something is orbiting something else due to gravity, its orbit always has the same shape, called an ellipse, which is simply a circle that's stretched in one direction (that's if there is no source of friction and you ignore Einstein's corrections to Newton's gravity, which are usually tiny unless you're near a black hole)
In general this picture is not so simple because all the objects in the universe influence each other.
We humans have gradually discovered patterns in nature etc involving motion, gravity, electricity, magnetism, chemistry, radioactivity and subatomic particles. These patterns are summarized by what we call our laws of physics. Etc. all these laws can be described using mathematical equations.
Only a small part of all the process in nature can be described by mathematical equations. In many cases the mathematical equations are only approximations of real life situations. Weather prediction is such an example.

10.2 The Mathematical Universe Hypothesis - page 254

External Reality Hypothesis (ERH). There exists an external physical reality completely independent of us humans.
It is enough to claim: There is a physical reality subject of change.
The object of humankind is to describe this physical reality independent of humans.
Mathematical Universe Hypothesis (ERH). Our external physical reality is a mathematical structure.
Such a claim has no value.
The issue is to describe the physical reality as accurate as possible. One tool to be used is mathematics.
Mathematical objects are mathematical structures which are build using strict mathematical rules. Examples are
Polyhedrons _ Wikipedia but I expect that is not what the author has in mind.
A hypothetical ideal supercomputer could calculate how the state of our Universe changes over time without interpreting what's happening in human terms, simply figuring out how all the particles would move or how the wavefunction would change.
The biggest problem of such a calculation is the initial condition. That means you have to know the position and velocity of all the particles involved.
A second huge problem is that the supercomputer self changes the state of the universe.
In practice such a calculation is impossible.
The auther is not the first with this idea.

10.3.2 Symmetry and Other Mathematical Properties - page 265

In fact it does: symmetries! In physics, we say that something has a symmetry if it remains unchanged when you transform it in some way.
That is correct. But you have to be carefull not to mix physics with mathematics.
For example, we say that your face has mirror symmetry if it looks the same after being reflected left to right.
 My face is not symmetric. My face is only symmetric roughly speaking.
In the same way, the mathematical structure in Figure 10.8 (A cube) has mirror symmetry etc
A cube is a mathematical structure because it is designed accordingly to strict rules and has perfect mirror symmetry. You can not compare it with a face.
Next:
A famous issue is the so called infinite regress problem For example: if we say that the properties of a diamond can be explained by the properties and arrangements of its carbon atoms, that the properties of a carbon atom can be explained by the properties and arrangements of its protons, neutrons and electrons, that the properties of a proton can be explained by the properties and arrangements of its quarks etc forever etc
At each level such an explanation requires a whole different physical story.
The mathematical Universe Hypothesis offers a radicial solution to this problem: at the bottom level, reality is mathematical structure.
The fact that you can divide the physical reality in different levels of complexity, going from large to small, is a physical issue and has nothing to do with mathematics.
The fact that there exists a periodic table and what the differences are between the different elements and isotopes is a physical issue and not the mathematical issue.
If the MUH is correct then our Universe is a mathematical structure and from its description an infinitely mathematician should be able to derive all these physics theories. How exactly would she do this? We don't know.
Our Universe is a physical structure subject of change and you need first of all a physicist to discover the laws that describe these changes.

11. Is time an illusion - page 272

11.1 How Can Physical Reality Be Mathematical - page 272

Einstein thaught us that there are two equivalent ways of thinking about our physical reality: either as a three-dimensional place called space were things change over time or as a four-dimensional place called spacetime that simply exists unchanging never created and never destroyed.
Which one of these two points of view is the most practical if you want to describe the laws of nature? IMO the first.
Mathematically spacetime is a space with four dimensions, the first three being our familiar dimensions of space and the fourth dimension being time.
However you have to be again very carefull here. Time is an abstract concept and is no dimension like the concept of length or distance. Time becomes a dimension when you multiply the elepased time between two events with the speed of light. Then it becomes a distance.

12. The Level IV Multiverse - page 319

12.1 Why I believe in the Level IV Multiverse - page 319

Could there really be a fundamental etc, splitting mathematical structures into two classes - those with and without physical existance.
Complex have no correspondance to the physical reality.
At page 321:
I argued to Bill Poirier that complete mathematical democracy holds: that mathematical existence and physical existence are equivalent, so that all structures that exist mathematically exist physically as well.
The author should have written this sentence in reverse order: all structures that exist physically exist mathematically as well.
The problem is if this is true it has no scientific value.
A sentence like: "Not all physical processes can be described riqoursly by scientific equations" has scientific value because it shows that the world is not black or white.

12.3.2 The Illusion of Initial Conditions page 339

At page 339:
Nobody captures the traditional view of initial conditions better than Eugene Wigner: "Our knowledge of the physical world has been divided into two categories: initial conditions and the laws of nature. The state of the world is described by the initial conditions. In a sense the physicist isn't interested in the initial conditions, but leaves their study to the astronomer etc."
This view is wrong. If you want to understand the laws of nature in the form of mathematical equations you have to do observations at regular intervals. These observations at t=0 are the initial conditions of the equations. Using the observations the first step is to calculate the parameters of the equations. The second step is to make predictions. This is important for every scientist. See also prediction
In other words, we physicists traditionally call the regularities that we understand "Laws" and dismis much of what we don't understand as "initial conditions"
This view is totally wrong as explained above.
The law let us predict how these conditions will change over time, but give no information about why they started out the way they did.
Laws, in general, never answer the why question.
In contrast, the Mathematical Universe Hypothesis leaves no room for such arbitrary initial conditions, eliminating them altogether as a fundamental concept.
To call initial conditions: arbritrary, is wrong. If you want to predict the positions of the planets using Newton's Law, accurate initial conditions are of uttermost importance.

12.4 Are we Living in a Simulation? - page 346

My guess is that this would be a tiny effect at best, so if asked: "Are we simulated" I'd bet my money on "No"
How do you figure out that you are right?
If you can not, what is the point.

12.6 Testing the level IV Multiverse - page 351

and that the recent successes of the standard model etc that our ultimate physical reality, whatever it is, fundamentally revolves around us humans and can't exist without us.
The physical reality (the laws of nature) in general has nothing to do with our human behaviour, except for what we are doing on the planet earth.
Next:
In particular, we saw that some of the strongest evidence for level II multiverse comes from the observed fine-tuning of the dark-energy density.
There exists not such an evidence. See also: dark energy discussed earlier at page 139.

13 Life Our Universe and Everything - page 358

13.1.1 The case for a Smaller Reality page 360

A nice example of this is a recent anti-multiverse article in Scientific American by the relativity pioneer George Ellis, which I highly recommend reading (see http://tinyurl.com/antiverse )
The article has the title: "Does the Multiverse Really Exist" and is from August 2011.
The SA article starts with the sentence:
" The word “multiverse” has different meanings. Astronomers are able to see out to a distance of about 42 billion light-years, our cosmic visual horizon. We have no reason to suspect the universe stops there."
Next in the book at page 360 we read:
the spherical As discussed in Chapter 6, we use the term Our Universe to mean the spherical region of space which light has had time to reach us during the 14 billion years since our Big Bang.
Accordingly to the Schrodinger equation the size of Our Universe is 42 billion light-years.

13.1.2 The case for a Greater Reality - page 363

Suppose that the ERH is correct. Then most multiverse critique rest on some combination of the following three dubious assumptions:
• Omnivision Assumption
Physical reality must be such that at least one observer can in principle observe all of it.
• Pedagogical-Reality Assumption
Physical reality must be such that all reasonable informed human observers feel they intuitively understand it.
• No-Copy Assumption
No physical process can copy observers or create subjectively indistinguisable observers.
The problem is that non of these assumptions are clear.
The critique against the multiverse comes from a complete different corner.
The problem is that Our universe is, most probably, only a part of the total cosmos. With Our Universe meaning all that is formed since the Big Bang, implying something that is finite. With total cosmos we mean that outside Our Universe there is more space. In this space, inprinciple, different Big Bangs could have happened. The problem is we have no prove for this now or never.
It should be pointed out that in case there are more Big Bangs (Something similar as that there are more Black Holes) each of these is a physical explosion or process. They have nothing to do with mathematics.
page 3 (What is reality) page 199 (Quantum Censorship) and page 254 (External Reality Hypothesis) and

Our Mathematical Universe - Reflection part 1

One main issue regarding the whole idee of a Big Bang is the difference between Our Universe versus The universe. Our universe is that part of The universe that is modified as a result of the Big Bang. Our universe is finite, That means it is only a part of the universe. The universe is infinite in the sense that it is larger than Our universe.
The concept of observable universe is a misnomer specific when part of the definition is based from the human point of view. Physics (astronomy) should be studied (specific the laws and equations involved) indepent of any human point of view.
Along that same line concepts like temperatures and colors should also not be used.

The emphasis in the book is on two concepts: Multiverse (That there is more than 1 Universe) and mathematics.
The conclusion of the book is the statement: "Our Mathematical Universe". IMO such a conclusion does not improve our understanding of the evolution of the universe. This evolution is a sequence of physical actions or processes. Part of this processes you can describe using mathematical equations but not with great accuracy. The further back in time the greater this uncertainty.
We know that Our Sun collects comets. Each of these collisions will disturb the movement of the Sun slightly. As such will the exact position of the Sun stay a mystery in the past and also in the future.

The Mathematical Universe - Reflection part 2

Near Figure 4.2 at page 72 is written: "without worrying about the details." The reverse is true: the author should describe the evolution of physical world in as much mathematical detail as possible.
The author calls "Our Universe" a "Mathematical Universe". He can do that, but this is of almost no significance. What he should do is describe the mathematical equation that descibe the physical world and how the parameters are calculated using observations.

The Mathematical Universe - Reflection part 3 - flat universe

The concept flat universe is discussed at Gold in the Hills at page 75.
At the bottom of that page we read:
A microwave telescope called Boomerang, showing a beautiful first peak at exactly the place for a flat universe. So now we knew the total density of our Universe (averaged over space) ie six hydrogen atoms per cubic meter.
The issue is how important is the concept of "flat universe". How important is a concept that is universal true. How important is the physical significance?
The opposite is that the universe is not flat ie bended. What does this bended means? are there different gradations?
Part of the problem is that how do you know that the first peak in the Power spectrum of the Cosmic Micro Wave Background radiation is a function of the total density of the Universe and specific that the position of the peak is a function of the flatness of the universe. Apperently the gradation factor is zero.
IMO you cannot prove such a relation nor can you perform any type of experiment.

IMO the whole flatness problem is much more a mathematical problem than a physical problem.

Created: 8 March 2014
Modified: 29 June 2014
Modified: 15 June 2016 Back to my home page Contents of This Document