A few remarkable events or observations, Part III.

Date : 18 Januari, 2022
Version: 0.0
By: Albert van der Sel
Status: Just starting.
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Chapter 1. A few notes on "Reality".

1.1 Could one speak of (personal) "local realism" and (independent) "objective realism"?

Tons of articles have been published, on the "misty" subject of "Reality".

Or..., is it not "misty" at all...? And is it just me, who thinks it's all a bit foggy?
Well, you do not have to hesitate to call me a silly guy... Really !

It's indeed quite established that our brain, "filters" and "massage" information, originating
from "outside" us. Whatever way you turn it, there seems to be a "local realism" which applies
to you (and me, and everybody else). So, it's your personal local reality.
Ofcourse, say there are two persons in a room, and a chair. Both will agree that a chair is present.
But, there are more sophisticated situations, where personal education, experience, and
personal character (?) may play a role. For example, quite a few people are able to exploit others,
for personal gain. Others may be more ethical, and will never do such a thing.
Also, as from another angle, there is a extensive science dealing with "perception".

Apart from the (personal) "local reality", there exists consensus about the existence of "objective reality",
which is independent from you. Indeed, the Earth, the Sun, the Universe...., it simply exists...

So, you might agree, or you might not agree, that we have (at least) two types of realities:
(personal) "local reality" and (independent) "objective reality".

However, the upper statements cannot be fully correct. For example, in Quantum physics, we have in certain
microscopic observations, that the Quantum system (under investigation), and the Observer, cannot be
viewed as fully seperated. Yes...., ofcourse the Interpretation of the measurement and the outcome
is critical too.

1.2 An Emulated, or virtual Universe (Reality), is likely not to be "true".

Some folks advocate, that we exist in an emulated Universe, and you are an emulation too.
As if a super computer is running, which have this all in memory (or in something else).
This would place "reality" in quite some other context.

Why is this not likely?

1. It's not mandatory to assume that "hyper being(s)" have set up this emulation, but generally
it is assumed to be the case. But then..., at a higher level "ultra hyper beings" might have
set up an emulation where the (lower) "hyper being" are in, that is, emulated.
It's quite evident that this would quickly lead to causality conflicts.
If "hyper being(s)" can setup an emulation, then why not have "ultra hyper beings"?
That would be a massive emulation, within a massive emulation. Would it break down?

2. In a Universe (emulated Universe?), where "true" stochastic events occur, it is not likely
that it can be succesfully emulated. This would be different (but still unlikely), if all
events were deterministic.
Yeah... but why? Again, if causality still must hold, then stochastic events would quickly
desync the emulation. Ofcourse, you might find the reasoning nonsense.

Note: "true" stochastic is meant to be fundamentally different from a computing random generator,
since the latter is just an algolrithm.

- It's not too hard to find many other pro- and contra arguments.

- One pro argument could be that "reasoning is like a form of computing..." or an argument like
"Our reality is really quite similar to the worst B movie....".

- Another often heard pro argument is, that the Universe is a big Quantum Computer, since Quantum effects
are everywhere and it could be indeed so that (e.g. all fermions) form an insanely large "Computation".
I don't buy it..., but who knows....?

Indeed, I have an objection. The point namely is, that "c" is the max speed at which information can travel.
The Universe is "rather large", so "far out" regions can (probably) considered to be causaly "disconnected".
This would especially hold, if the Universe undergoes an accelerated expansion (as many astronomers currently believe),
so that waves would (over large distances) so much stretched, that information cannot reach other far out regions anymore.
That would be a weak point for the idea of the Universe as a Quantum Computer.

1.3 A pseudo equation.

Let's try a simple pseudo expression, to relate (personal) "local reality" and (independent) "objective reality":

|φ (local reality) > = |θ(filtering, massage, state, limitations senses etc..)>   *   |Ω (objective reality)>

Due to the effect of filtering, massage, biological inheritence, limitations of the senses etc.. on Objective Reality,
we end up with Local Reality, which is what someone "perceives" as the World (or what is true).

It must be written in terms of factors, since θ should be in the form of an "operator" (see below).

It is ofcourse so, that |θ(filtering, massage, state, limitations senses etc..)> will never be "1", otherwise
we would have

|φ (local reality) = |Ω (objective reality)>

thus local reality equals objective reality, which is (most certainly) impossible.

The expression above, suggest a function. Ofcourse, better seems to be a vectorial or tensor relation,
since the human factors which lead to a personal local reality, are many, such as
mental state, biological inherentance, limitation of the sensory inputs, experiences of the past, massage of information
by the brain, filtering information etc.. etc..
Also, the objective reality where the person is in, can only be described by a larger n-tuple, or n,m tuple,
which then leads to a matrix relation.
Thus, a more appropriate relation seems to be:

φ (local reality) = θ(filtering, massage, state, limitations senses etc..)   *   Ω (objective reality)

where φ, θ, Ω are matrices.

Note that θ "looks" (or works) like an operator, projecting objective reality to a personal local reality.

The proposition of these expressions should be "reasonable", since operators are used almost everywhere in Physics
and other sciences, whenever "transformations" are used.

Ofcourse, these are all pseudo expressions.

As a very simple example from math, illustrating a projection, might be this: suppose you have a vector (1,2,3) in 3D Space,
represented by a coordinate system. Usually, this means we have representation of an arrow, from (0,0,0) to (1,2,3).
An arbitrary point (vector) in 3D space, can then be written as (x,y,z), where x, y, z can all have certain values.
You can write down an "operator" which projects the vector (x,y,z) to the vector (x,y,0), which then becomes
the projected vector in the XY subplane.

It seems reasonable to think that the human mind works in a similar way. Only the features of Reality which
"fits" the scope of a biological entity, with all filtering/massage/etc.. in place, leads to a Reduction (or projection).

1.4 A few remarks about Modern Theories on Physical Reality.

I decided to place that in Chapter 2, below.

Chapter 2. A few remarks about Modern Theories on Physical Reality.

Well..., I am not an arrogant person (I hope....).

I say that, since "A few remarks about Modern Theories on Physical Reality", can only lead to a rather weak story
without substance, and actually is (or virtually is) impossible.

Indeed, physicist active on the forefront of modern theories, have to do work like just a few
other occupations do. Just one aspect: the number of relevant, weekly articles, are dazzling,
and he/she simply must stay informed.

However..., I believe that the "absolute core" of some important theories, which has something to say about Physical Reality,
can be fairly short (not really short, ofcourse), and still has some substance.
You doubt that??? I hope you are not right, this time.... But It's true: I am often wrong.

2.1. A certain convergence of Philosophy and Physics, the last decades?.

It seems to me, that, say the last 40 years or so, philosophers and physicists, somewhat grew to each other.
What I mean to say is, is that quite a few philosophers attended courses and seminars with regards to more advanced physics.
It seems to be more than it used to be in the past (say, before 1970).

Ofcourse, the findings of other sciences were always important for philosophers, all along, but a certain increase
in attention (in Physics, Cosmology) could be observed since the '80's (or thereabout).

Needless to say, that Philosophy is an enourmous wide domain, touching every aspect of Human thinking.
There are streams which are mostly related to ethics, politics..., etc..., you name it.

However, a deep core is centered around any question about existence, like any question which revolves
around why, how, when with respect to Reality, conciousness, physical existence, Nature, the Universe...
But it seems that Philosophy and Physics are more close, than it used to be, in our modern times (say as of 1800).
Especially the modern front theories, like Branes, strings, quantum, quantum gravity, Cosmology etc.., are important for
the scientists from Philosophy, as well.

So, it could well be, that a more complete "view" will emerge some day, from philosophy, and not so much
directly from the hard β sciences. Who knows... ?

In the next sections of this chapter (chapter 2), it's going to be dull, or boring, since I like to present
some key points from modern theories of Physics, which may say something about objective reality.
So, maybe, if you have a hard time to fall asleep at night..., you might try this chapter.

2.2. More dimensions needed than the Classical ones? Makes it sense?

It might not be a "bad idea" at all, although we experience a 3D Space, like depicted in point descriptions as in e.g. (x,y,z).
Considering time (t) as well, as in Minkowski SpaceTime (relevant in Relativity Theory),
we arrive in point descriptions as (ct,x,y,z), which is 4D.

Once, during the '70's, '80's, and '90's, the unification of interactions (like gravity, electromagnetic force, weak interaction),
seemed to be an important queeste.
Nowadays, among the most productive physicists, it could still be (partly) important, but seems not to be the "number 1" target anymore.
You should know, that during the '20's of the former century, Kaluza (and later Klein), did a very serious attempt
to unify> Einsteins gravity, with the ElectroMagnetic interaction.

It's no doubt true that Kaluza-Klein theory, is a remarkable theory, and is an attempt to unify Einstein's GR,
and the ElectroMagnetic (ElectroDynamics) Theory of Maxwell.
The arena where that seems to work, is a 5-dimensional SpaceTime, which was very remarkable at that time.

The ideas in Kaluza-Klein, inspired many other Theories, even very modern ones.

It seems that "the fuller" the description of matter and interactions get, the more dimensions you need for that to work.
Well, not in all theories, but for some parts in theoretical physics, it is true (like Superstring theory).

2.2.1. Example 1: Would having more dimensions make sense? Kaluza-Klein

Let's try to say something usefull about the Kaluza-Klein model. In a way, it stood partly as a model for modern theories,
although the original Kaluza-Klein model has some serious flaws.

A small testmass "m" in the Gravitational field of a larger mass "M", experiences a (classical Newtonian) Force
given by FGrav=constantGrav . mM/r2. A small testcharge "q" in the Electrostatic field of charge "Q", experiences
an Electric Force given by FEl=constantEl . qQ/r2. Note that these classical expressions
are quite similar. Ofcourse, when all masses move (or even relativistic), the situation is more complex.

Anyway, the two apparently different physical environments, seems to have "something in common"...?

Sure, the statements above, are really to simple.

The crux is, that by adding an extra dimension to the 4 dimensional metric (as is used in Einstein's equations),
it is possible to describle the motion of a charged particle, as to follow a "geodesic" as well, very similar as
to the original proposition of a motion in Einstein's General Relativity.

-In General Relativity, the presence and amount of mass "M" (or energy), determines the curvature of 4D SpaceTime.
This in turn determines how a "testparticle" with mass "m" will move.

-If you think of it, a distributed charge "Q" somewhere in SpaceTime, will determine how a charged "testparticle",
with charge "q", will move.

Even these two simple lines of text, show that there is a degree of analogy between the effects of Mass and Charge,
in the surrounding SpaceTime, and on the motion of a "test particle".

In fact, the manifestation of "force" due to curvature of SpaceTime, called "gravity", now is aligned with the forces
which were classically associated with ElectroMagnetic fields. Most often, this unified "force" still is called gravity,
but we must understand that this "superforce" includes "gravity-" and the "ElectroMagnetic" force.
You may also see it as a 5 dimensional Gravity.

Please note that the qualification "force" is not exactly as we should see it in GR. Namely: acceleration and gravity
are (as consensus exist among physicists), indistinguishable.

Some folks name Kaluza's theory "the Fifth dimensional Relativity theory".

In retrospect, we can see why Kaluza was motivated to try to unite both fundamental theories.

Note: In modern views, the unification of Electrodynamics and the "weak interaction" seems to be valid
at high energies, instead of Electrodynamics and Gravity. But, Kaluza went on along a new exiting path.
Although, according to modern insights, Kaluza was wrong.

However, the two theories differ quite significantly, from a mathematical prespective.
Maxwell's field equations for the E and B fields (or the vector- and scalar potentials), are
rather regular linear differential equations, while Einstein's tensor equations are from another order.
Indeed, rather dis-similar.

Reconciling both worlds can be done, using a new insight, namely that of the metric.

Then, in 1926, Oscar Klein proposed a modification to Kaluza's theory. In effect he managed to align the theory
with Quantum Mechanics, by scaling and quantifying this extra dimension to Planck's constant.
This extra spatial dimension was quantified, and curved in such a way that space comes back on itself like a circle.
In fact, this was the first introduction of a "compactified dimension". In this view, the "width" of the extra dimension
is absurdly small, making it unnoticable for observations. However, it exists (in this theory).

The study of the metric is often a starting point in the study of SpaceTime. For example:

- The equations of motion can be derived from the metric.

- Or, it can been seen that it has the consequence, that a testparticle must follow a certain trajectory, like
a geodesic in GR, in curved SpaceTime.

- Or, it follows from the metric that events can only be causally connected, like in STR.

In most cases (and here too), the metric can be represented by a "matrix". So, in 3D we have a 3x3 matrix,
and in 4D we have a 4x4 matrix.

Kaluza showed, using a 5 dimensional approach of Einsteinís GR, how both Electromagnetism and Gravity
could be treated in a uniform fashion, namely in the sense that both are described as parts of a five-dimensional metric.

While the 4D curvature of SpaceTime, which can be derived from the metric:

┌ g11 g12 g13 g14
│ g21 g22 g23 g24
│ g31 g32 g33 g34
└ g41 g42 g43 g44

Kaluza (and later Klein) used analytics to device a 5D framework, uniting both interactions (gravity, electromagnetism).
In matrix language, a rather daring proposition then would be that our 5 dimensional metric looks like:

┌ g11 g12 g13 g14 ω15
│ g21 g22 g23 g24 ω25
│ g31 g32 g33 g34 ω35
│ g41 g42 g43 g44 ω45
└ ω51 ω52 ω53 ω54 ω55

Note the "new" ωij elements in this 5 dimensional metric.

Now, all elements in this new metric must contain information for the unified Theory, but the last column
and the lowest row, should express specifically the unified ElectroMagnetic components.
In the framework, particles follow a "geodesic" as well, just like in traditional 4D Gravity.

Skipping lots of mathematical formulation, it all turned out to be highly remarkable:

Does this all prove anything? No..., but having additional dimensions may help in theoretical Physics
to solve hard problems. In this example, it helped to "unify" Gravity with ElectroDynamics.

Much later, it became clear, that new models actually better suited a unification of Electrodynamics
and the socalled "weak interaction". However, the approach of Kaluza (in the '20's of the former century),
stand model for many ideas that followed in later decades.

2.2.2. Example 2: Would having more dimensions make sense?

The story below, is an extreme form of a "Jip and Janneke" demonstration.

Suppose we live in a 1 dimensional world, thus, on a line (or curve). In the figure below, suppose
"our world" is the red line, or the x-axis.
Now, suppose we know of a force Fx which can act on particles with mass "m" along our 1 dimensional world (see the red arrow),
to the left or right on the x-axis. That is all OK, since going to the left, or right, fits exactly in our 1D world.

Now, Pricilla, an inhabitant of the 1 D Space, and a briljant physicist, had noticed that sometimes,
particles with charge "q", mysteriously dissapear. It's just is if they are swept away from the 1 D world.

According to a current Cosmological Theory, the 1 D world came into existence, after a Big Bang, and a period
of rapid expansion of the 1 D Universe. Then, at later phases, it seems plausible that various states
of SpaceTime/Vacuum existed, which rolled down to less energetic states, and matter and a range of forces
materialized. So, one assumption was that in an early phase, various forces were united into one Superforce.

So, she deviced a model, where Fx exists (as is clearly shown by the observations), and a
theoretical component Fz, working along an unknown, perhaps hidden, dimension.
Then, her model suggsted that Fx and Fz, were actually low-energy manifestations
of one unified Superforce.

Silly story perhaps, but the heart of this Jip and Janneke story is, that multiple degrees of freedom
(like unknown, but nevertheless real extra dimensions) might result in a Theory which explains
our Universe better than before.

2.2.3. Example 3: What is a central idea in Superstring theory? More dimensions makes sense?

- About the number of Dimensions

A higly remarkable Theory.., and I am afraid.., also fairly complex.

In the framework, quite a large number of "algebra's" are used, and the subject is still "moving".
You might take a look at the arxiv library, and see the large number of articles, published over decades by now.

However, some core ideas can be presented in a relatively short text. Ofcourse, that effort lacks true "substance".

One fundamental idea, is that a string replaces the idea of a "point particle". Now, quite brilliant is the
theorem that different quantum states of a string, can account for the different particles we observe.
This is indeed an enourmous step in Unification, since there exists one unique object, while "vibration modes",
determine the type of particle (we may observe).

Historically, in the '60's, strings we used to describe the particles of atomic nuclei, thus protons, neutrons,
and also the scattering of these particles in collisions.

Later, the quarkmodel came to life, and also Chromodynamics (and string theory became a bit out of grace).
Later on, with the desire to reconcile important fundamental theories, Superstring theory got momentum,
especially since the late '70's, early '80's.

However, to also describe Gravity, the order of stringsizes "L" now needed to be near the Planck Length,
so L was roughly about [hG/c3]½, which is about 10-35m.

The string is an one-dimensional object, which can move in various ways. This movement, sort of sweeps out a two-dimensional sheet,
called the World-Sheet. This sheet is not directly synonymous for the Regular SpaceTime.

For furher analysis, you cannot get away without objects as spinors and other concepts.
However, if you look at the "action", or pathintegral "S", to determine the path of a particle, then classically
it travels along the shortest path. For a quantum particle, multiple paths are a probability, so we must
integrate along the area (instead of a classical path):

S = -T ∫ ds

The expression above, is extremely simplified. In many literature, or articles, a correct expression can be found (like for example
JOSEPH POLCHINSKI, Vol. II, Superstring Theory and Beyond).

I must also say that the first Superstring version, analyzed bosonic strings, in the same way, while later on, fermions
(the well-known particles) came into the picture, while slightly later, a sort of integrated "Supersymmetry" was build in.
For the bosonic analysis, it became clear that D=26, while for fermions it must be so that D=10.

The calculation of the integral, is complex (spinors, superconformal transformations etc..), but which is not
so much of interest to us.

In the calculations, ghost field constructs are used (a temporary utility), but in the end, the total charge must dissapear.
This leads to the notion of "critical dimension" D, as in the relation 0 = 3/2 D - 15. This means that D=10.
Thus that is 9 spatial plus one time dimension, and a total of 10.

However, we are quite used to 3 real spatial dimensions, a 1 time dimension. What happened to the other 6 spatial dimensions?
As we will see later on, they are compactified to an immensely small scale (Planck Length like).

As a confirmation of the "sanity" of D=10, it can be established that with D=10, the theory is Lorentz invariant, which
you may see as equivalent to as "preserving causality".

What is fabulous, that the physicists started with (sort of) nothing. Usually, in science, you have experimental
observations, and you may formulate a theory, which is in line with those observations.
With superstring theory, it is almost (or entirely) 100% theoretical work.

What shamefully is missing in the text above, is how the string theories, unify Gravity and Quantum theories, which actually
is one of the main strenghts. Sorry for that.

- About the compact Dimensions.

Actually, there are 5 slightly different theories, which were later Unified (so to speak), in M-Theory.
M-Theory, which is 11 dimensional, really is some piece of nice work, with fabulous (theoretical) implications.

Before we go into that, what was the original idea of compactified dimensions in pure Superstring Theory (or theories)?

How is it possible that we have a 4 D world, and physics, that it is "somehow" related to underlying 10 D world, and physics?

In fact, do we thus seem to have a M4 manifold (our usual 4 D World), tied in, or related to a
hidden or compactified "K" manifold (with hidden, supersmall Spatial dimensions, 6 in total.

In such a way, you could say "Full_SpaceTime = M4 x K".

Some motivations why the 6 extra dimensions "should be" compactified, that makes them essentially hidden (on scale
near the Planck Length, which is around 10-35m.

-Already Klein, in the Kaluza-Klein Theory (a few sections above), had no other choice than to postulate
that the 5th extra dimension, was unnoticably small.

- 4D SpaceTime is Poincare-Lorentz invariant. For example, Rotations etc.. does not change Physics. Also, 4D Relativity
is actually based on Poincare-Lorentz invariance. Superstring theories, may not conflict with that, at all scales.

- We cannot observe any extra Spatial dimensions, since they are compactified, on a scale of 10-35m.
So, it's quite understandable they are "hidden". So, the main motivation here is, that they must be un-observable.

-Superstring Theory is 10 D theory, six of which should be curled up in some small internal compact manifold.
The science of linking/relating this compact manifold to our well-known four-dimensional physics, is called string compactification.
This theory neatly lines up, and is a motivation for 6 compact dimensions.

- Some string physicists regard the compactified dimensions, as a "low energy" limit, of possible other solutions.

- Some string physicists regard the compactified dimensions, as the correct number and "size" needed
for the ranges of vibration modes (looks like degrees of freedom).

- An argument in articles, often (more or less) tells us that a "wrapped" string has a minimum mass, determined by the size
of the circular dimension/cilinder (tori), and the number of times it wraps around. The string's oscillatory motion, then adds more mass.
However, "the start" is wrapping (related to the compact dimensions of the K manifold).
This results in a low energy limit.

So, these were some motivations, for having 6 compact spatial dimensions, while D=10 was already established.
Ofcourse, all of the above, was a bit in Jip and Janneke language. Sorry for that.

Often it is suggested that the compact manifold correspond to socalled Calabi-Yau manifolds (as many articles state),
but such solution is certainly not unique. That is, there are more classes of manifolds, as many physicists argue.

2.2.4. A few elements of Physics.

2.2.5. Example 4: What is a central idea in M-Theory theory? More dimensions makes sense?

2.2.6. Does Superstring/M-Theory describes (uses/generates) an emergent SpaceTime?

2.2.7. Could Superstring/M-Theory theory be a valid model of Reality? A true model perhaps?

This should be the heart of section 2.2.

Unfortunately, experimental data for any confirmation seems to be missing (?), except for some rather advanced simulations.
But "real" data, does not exist yet. However, one needs to be rather carefull with such statements.