The Jedell Report: August 2019

By David William Jedell UPDATED August 24,, 2022

Time is a delusional construct created by our single point reference. We will call this Time "Time-A" for the reason that we could not discuss the concept in the English language without using the familiar word Time. It is our everyday concept of Time on earth.

However, we exist in our local Space-Now point reference wherever we are. The delusion of the Time-A construct is created by our single point reference on earth. The ticks of a watch are only made by gears that are coordinated with a fraction of the earth's rotation we call a "second." It is not keeping track of "Time." It is the relation of two motions.

The "speed" of these motions are not inherent in Time-A as a thing in and of itself, but rather, in the ratio of the distance the object travels to an arbitrary fraction of the earth's cyclical rotation as a constant

(i.e., the ratio of one to 24, or an "hour").

When there is an event, like a collision of two objects in front of us, we store it in memory. When that event has moved out of our local Space-Now, and there is another event in an ordered sequence, we delude ourselves into believing that the conscious perception of the first sequentially ordered event happened in the "past," as a result of the fact that the event is no longer generating sensory impulses (i.e., you no longer see it in front of you). However that event and its energies still continue in their effects in Space-Now that is non-local. Since our conscious mind can review the perceptions of memory and the lack of the same immediate sensory perceptions simultaneously occurring (i.e., you don't see it anymore), the mental construct is created that there is a past and a present. This is not factual but flawed. As far as the "future," the motions and coincidences in "events" (i.e., the paths of two objects colliding) have not occurred in our local Space-Now reference. The future can only be imagined, predicted or hoped for, but if the future did exist, it would be in our Space-Now.

A major obstacle to the general acceptance of the fact that Time-A is a mathematical convenience or tool to compare relative motions in everyday life, and not a

thing in and of itself, is that languages, such as English, are pervaded with words that express Time as a thing in and of itself, such as "happened," "was," "yesterday," tomorrow," and many other expressions of past and future tenses. Calendars, clocks and appointments are other obstacles to the comprehension of Space-Now.

Instead of trying to think this out with our flawed verbal language system, try to think in a spacial way of what is actually happening. Here is a simple example of spacial comprehension of this; a thought experiment. A jet liner located on the equator takes off due west. When it reaches 35,000 feet it is traveling 1,000 mph ground speed. The pilot has only a sun dial in front of the cockpit that he can see from inside. Nobody on the plane has a clock or watch. The sun dial shadow indicates it is 3pm upon reaching 35,000 feet. The sun can be seen high above. Subsequent to the plane traveling 6,000 miles, the sun dial is in the same 3pm position and the sun hasn't moved. Its still high in the sky. The pilot and everyone on the plane think that time has stopped during the flight. They even confirm this assessment when they land and take a few minutes to walk into the airport. All the clocks on the walls and all the people's watches indicate 3:05pm. On the ground at the airport that the plane departed from, the ground crew personnel look at their watches and see that they indicate 9pm. It is also night, the stars are shining. They compare their memory of a sunny day with the present sensory input of night and no sun. They construct the delusion of time. Whereas the pilot and passengers have current sensory input of a shining sun and a sun dial that has not moved during the flight. Finally, the pilot and passengers are informed that they are moving through Now from one area of Space to another, and that they passed 6 "Time Zones." The pilot and passengers accept this explanation after some thought. But the ground crew believe that it is 9pm and that 6 hours of "Time" have passed because the hands of their watches moved and the sun set and it is night. The crew holds on to delusion like people did when the earth was flat and the earth was the center of the universe, rejecting Columbus and Copernicus on his death bed, and burning Guido at the stake for heresy. THE SO CALLED ARROW OF TIME Since there is no time there is no arrow of time. Moreover, it's just as logicical to say that this arrow of time moves from future to past as much as it is to say it moves from past to future.

Special Relativity

The thought experiment of Albert Einstein to explain time dilation is a space ship traveling at relativistic speeds (close to the speed of light 'c') with a pulse of light moving up and down in a straight line within the space ship, from the emitter to the receiver and back. Relative to an outside stationary observer on earth, the light pulse is moving over a greater distance than just up and down (it is traveling the hypotenuse of a right angled triangle because of the train's motion on the x-direction), but because light travels at 'c' in every reference frame, the pulse must still travel at the same speed 'c' relative to the outside observer. Hence, according to the theory, because it travels a greater distance with the same speed, it must take longer to do so and hence time will appear to be running slower within the rocket - relative to the man outside.

However, Einstein doesn't apply his own postulate that all inertial frames are equivalent. So, the observer on the spaceship sees the clock on earth going slower while the observer on earth sees the clock on the spaceship going slower at the exact same rate. Since all inertial frames are equal, when the two observers are joined back together, the number of clicks of their clocks are physically the same. Otherwise, the observer on the space ship would see the earth spinning like a top.

Moreover, in accordance with Einstein's Special Relativity, light always moves in a straight line. In his famous thought experiment, the light leaves the emitter and heads straight up towards the receiver at an angle. This is impossible. Actually, the beam must be moving straight up and down. It is the spaceship that is moving, that's all. [4]

A different perspective on the theory of Einstein that does away with his equivalent frames postulate would be that the spaceship is moving within the vacuum energy of space with respect to the "fixed stars."

In other words, the earth is in the framework of the fixed stars and the spaceship is too but it is not within the framework of the earth as an enertial frame moving the opposite way. With this clarification, time has a different connotation. Since inertia (mass) is shown to increase at relativistic speeds, the ship and all that is in it is affected by the slower speed at which objects move in that local Space-Now ("Time-B"). Special Relativity does not exclude Space-Now.

Gravity and Curved Spacetime - General Relativity

The Einstein field equations (EFE) may be written in the form:

R_{\mu \nu }-{\tfrac {1}{2}}Rg_{\mu \nu }+\Lambda g_{\mu \nu }={\frac {8\pi G}{c^{4}}}T_{\mu \nu }

where

R μν

is the Ricci curvature tensor,

R

is the scalar curvature,

g μν

is the metric tensor,

Λ

is the cosmological constant,

G

is Newton's gravitational constant,

c

is the speed of light in vacuum, and

T μν

is the stress–energy tensor.

Despite the fact that it's over a century old, Einstein's theory of general relativity is our current understanding (physicists' consensus) of how gravity operates. In this view, space and time are merged together into a unified framework known as (no surprises here) space-time. This space-time isn't just a fixed stage but bends and flexes in response to the presence of matter and energy.
That bending, warping and flexing of space-time then goes on to tell matter how to move. In general relativity, everything from bits of light to speeding bullets to blasting spaceships want to travel in straight lines. But the space-time around them is warped, forcing them all to follow curved trajectories — like trying to cross a mountain pass in a straight line, but following the peaks and valleys of the topography.

Einstein's equations can be loosely summarized as the main relation between matter and the geometry of spacetime (describing gravitational motion). On the right hand side of the equation, the most important thing is the appearance of the energy-momentum tensor

T_{μ ν}

. It encodes exactly how the matter---understood in a broad sense, i.e. any energy (or mass or momentum or pressure) carrying medium---is distributed in the universe. For understanding how to interpret the subscript indices of the

T

, see explanation of the metric tensor below.
It is multiplied by some fundamental constants of nature (the factor

\frac{8 π G}{c^{4}})

but this isn't of any crucial importance: One can view them as book-keeping tools that keep track of the units of the quantities that are related by the equation. In fact, professional physicists typically take the liberty to redefine our units of measurements in order to simplify the look of our expressions by getting rid of pesky constants such as this. One particular option would be to choose "reduced Planck units", in which

8 π G = 1

and

c = 1

, so that the factor becomes

1

On the left hand side of Einstein's equations, we find a few different terms, which together describe the geometry of spacetime. General relativity is a theory which uses the mathematical framework known as (semi-)Riemannian geometry. In this branch of mathematics, one studies spaces which are in a certain sense smooth, and that are equipped with a metric. Let us first try to understand what these two things mean.
The smoothness property can be illustrated by the intuitive (and historically important!) example of a smooth (two-dimensional) surface in ordinary three-dimensional space. Imagine, for instance, the surface of an idealized football, i.e. a 2-sphere. Now, if one focuses ones attention to a very small patch of the surface (hold the ball up to your own face), it seems like the ball is pretty much flat. However, it is obviously not globally flat. Without regards for mathematical rigor, we can say that spaces that have this property of appearing locally flat are smooth in some sense. Mathematically, one calls them manifolds. Of course, a globally flat surface such as an infinite sheet of paper is the simplest example of such a space.
In Riemannian geometry (and differential geometry more generally) one studies such smooth spaces (manifolds) of arbitrary dimension. One important thing to realize is that they can be studied without imagining them to be embedded in a higher-dimensional space, i.e. without the visualization we were able to use with the football, or any other reference to what may or may not be "outside" the space itself. One says that one can study them, and their geometry, intrinsically.

The metric

When it comes to intrinsically studying the geometry of manifolds, the main object of study is the metric (tensor). Physicists typically denote it by

g_{μ ν}

. In some sense, it endows us with a notion of distance on the manifold. Consider a two-dimensional manifold with metric, and put a "coordinate grid" on it, i.e. assign to each point a set of two numbers,

(x, y)

. Then, the metric can be viewed as a

2 \times 2

matrix with

2^{2} = 4

entries. These entries are labeled by the subscripts

μ, ν

, which can each be picked to equal

x

y

. The metric can then be understood as simply an array of numbers:

(g x x g y x g x y g y y)

We should also say that the metric is defined such that

g_{μ ν} = g_{ν μ}

, i.e. it is symmetric with respect to its indices. This implies that, in our example,

g_{x y} = g_{y x}

. Now, consider two points that are nearby, such that the difference in coordinates between the two is

(d x, d y) .

We can denote this in shorthand notation as

d l^{μ}

where

μ

is either

x

y,

and

d l^{x} = d x

and

d l^{y} = d y .

Then we define the square of the distance between the two points, called

d s,

d s 2 = g x x d x 2 + g y y d y 2 + 2 g x y d x d y = \sum μ, ν \in {x, y} g μ ν d l μ d l ν

To get some idea of how this works in practice, let's look at an infinite two-dimensional flat space (i.e. the above-mentioned sheet of paper), with two "standard" plane coordinates

x, y

defined on it by a square grid. Then, we all know from Pythagoras' theorem that

d s 2 = d x 2 + d y 2 = \sum μ, ν \in {x, y} g μ ν d l μ d l ν

This shows that, in this case, the natural metric on flat two-dimensional space is given by

g μ ν = (g x x g x y g x y g y y) = (1001)

Now that we known how to "measure" distances between nearby points, we can use a typical technique from basic physics and integrate small segments to obtain the distance between points that are further removed:

L = \int d s = \int \sum μ, ν \in {x, y} g μ ν d l μ d l ν - - - - - - - - - - - - - \sqrt

The generalization to higher dimensions is straightforward.

Curvature tensors

As explained above, the metric tensor defines the geometry of our manifold (or spacetime, in the physical case). In particular, we should be able to extract all the relevant information about the curvature of the manifold from it. This is done by constructing the Riemann (curvature) tensor

R_{ν ρ σ}^{μ}

, which is a very complicated object that may, in analogy with the array visualization of the metric, be regarded as a four-dimensional array, with each index being able to take on

N

values if there are

N

coordinates

{x^{1}, \dots x^{N}}

on the manifold (i.e. if we're dealing with an

N

-dimensional space). It is defined purely in terms of the metric in a complicated way that is not all too important for now. This tensor holds pretty much all the information about the curvature of the manifold---and much more than us physicists are typically interested in. However, sometimes it is useful to take a good look at the Riemann tensor if one really wants to know what's going on. For instance, an everywhere vanishing Riemann tensor (

R_{ν ρ σ}^{μ} = 0

) guarantees that the spacetime is flat. One famous case where such a thing is useful is in the Schwarzschild metric describing a black hole, which seems to be singular at the Schwarzschild radius

r = r_{s} \neq 0

. Upon inspection of the Riemann tensor, it becomes apparent that the curvature is actually finite here, so one is dealing with a coordinate singularity rather than a "real" gravitational singularity.
By taking certain "parts of" the Riemann tensor, we can discard some of the information it contains in return for having to only deal with a simpler object, the Ricci tensor:

R ν σ : = \sum μ \in {x 1, \dots x N} R μ ν μ σ

This is one of the tensors that appears in the Einstein field equations. the second term of the equations features the Ricci scalar

R

, which is defined by once again contracting (a fancy word for "summing over all possible index values of some indices") the Ricci tensor, this time with the inverse metric

g^{μ ν}

which can be constructed from the usual metric by the equation

\sum ν \in {x 1, \dots, x N} g μ ν g ν ρ = 1 if μ = ρ and 0 otherwise

As promised, the Ricci scalar is the contraction of the Ricci tensor and inverse metric:

R : = \sum μ, ν \in {x 1, \dots x N} g μ ν R μ ν

Of course, the Ricci scalar once again contains less information than the Ricci tensor, but it's even easier to handle. Simply multiplying it by

g_{μ ν}

once again results in a two-dimensional array, just like

R_{μ ν}

and

T_{μ ν}

are. The particular combination of curvature tensors that appears in the Einstein field equations is known as the Einstein tensor

G μ ν : = R μ ν - 1 2 R g μ ν

The cosmological constant

There is one term that we have left out so far: The cosmological constant term

Λ g_{μ ν}

. As the name suggests,

Λ

is simply a constant which multiplies the metric. This term is sometimes put on the other side of the equation, as

Λ

can be seen as some kind of "energy content" of the universe, which may be more appropriately grouped with the rest of the matter that is codified by

T_{μ ν}

.

Einstein's equation relates the matter content (right side of the equation) to the geometry (the left side) of the system. It can be summed up with "mass creates geometry, and geometry acts like mass".
For more detail, let's consider what a tensor is. A two-index tensor (which is what we have in Einstein's equation), can be thought of as a map which takes one vector into another vector. For example, the stress-energy tensor takes a position vector and returns a momentum vector, mathematically

p_{ν} = T_{ν μ} x^{μ}

The interpretation is that the right side of Einstein's equation tells us the momentum which is passing through a surface defined by the position vector.
The left side can be interpreted in this manner as well. The Ricci curvature

R_{μ ν}

takes a position vector and returns a vector telling us how much the curvature is changing through the surface defined by

\vec{x}

. The second and third terms, both having factors of the metric

g_{μ ν}

, tell us how much distance measurements are changed when traveling along the vector. There are two contributions to this change in distance - the scalar curvature

R

and the

Λ

. If

R_{μ ν}

is "curvature in a single direction", than

R

is the "total curvature".

Λ

is a constant which tells us how much innate energy empty space has, making all distances get larger for

Λ > 0

.
So, reading the equation right to left, "Einstein's equation tells us that momentum (moving mass) causes both curvature and a change in how distances are measured." Reading left to right, "Einstein's equation tells us that curvature and changing distance acts just like moving mass."

Despite its intricacy, relativity remains the most accepted way to account for the physical phenomena we know about. Yet scientists know that their models are incomplete because relativity is still not fully reconciled with quantum mechanics. which explains the properties of subatomic particles with extreme precision but does not incorporate the force of gravity.

That's it for Relativity. Now we explore how the internal feeling of the amount of "Time-C" gets smaller as our body ages.

$Subjective Feeling of Time Accelerates as We Get Older. Getting "older" is correlated with Objective Time but it is only the biological division of cells and other harmful health factors that are truly "aging."$

Subjective Time ("Time-C) is interactive memory and recall of the distance between "events" that is mistaken as the duration of "Time-A" in and of itself. Our largest subjective feeling of Subjective Time is when we are first aware of being conscious, sometime in the first Objective Year of life.

Moreover, in 2005, Wittmann & Lehnhoff [1] systematically asked large samples of younger and older people how they experienced time. In the study, 499 German and Austrian participants aged 14 to 94 were asked how fast time usually passed for them. The study indicated that this set of people feel time passing more quickly as they get older.

Wittman and Lehnhoff found that everybody, regardless of age, thought that time was passing quickly. The question, “How fast did the last 10 years pass for you?” yielded a tendency for the perception of the speed of time to increase in the previous decade. This pattern peaked at Objective age 50, however, and remained steady until the mid-90s. [2]

Dr. William Friedman [3] proposed a theory, originally proposed by William James in 1877 (labelled the "Father of American psychology"), to explain this phenomenon as follows (I thought of this when I was 8 years old myself as it is self evident to me):

“As we get older, each year is a smaller proportion of our lives. For example, a year is 1/10 of the life of a 10 year old, but 1/70th of the life of a 70 year old. Therefore each year feels shorter relative to all the time we've lived and thus seems to be going by faster.”

Mathematical Treatment of Dr. Friedman's Statement and its Implications
The t-axis represents Objective Time;

Objective Time (as a mathematical tool) is represented by t (based on "ticks" of an objective "clock" at 1 objective year intervals);
The y-axis represents Subjective Time;
Subjective Time represented by y is defined as a function of t;
y(t) = 1/t , t > 0;
F(t) is the area under y(t), which is the perceived cumulative Subjective Time;
F'(t) is the rate of change of the area under y(t).

F(t) = ∫y dt – 0 = ∫y dt

We may infer that the Subjective Area of Perceived Time during the Objective Time interval (t1, tn) is the integral of y(t) between (t1, tn).

∫ y dt

The curve represents the Subjective Time as a function of Objective clock t. The shaded area under the curve is the Area of Subjective Perceived Time. The smaller the Area, the faster Subjective Time is perceived to pass.
At 80 years of Objective age, looking back to the Objective year “1” we find that the Subjective Area of Perceived Time is,

∫ y dt = ln (80) = 4.3820266347 ≈ 4.4 Subjective Years.

Furthermore, whereas most people sleep for 1/3rd of their first conscious year, lives, we do not adjust for sleep. This is a general number and subject to minor differences and aberrations with each different person.

4.4 Subjective Years is virtually all that is lived in a lifetime.

The Area of Subjective Time begins to become imperceptible from about 50 objective years to 80 objective years, because it is sufficiently small. This idea is consistent with the findings by Wittman and Lehnhoff, as stated above, that everybody, regardless of age, thought that "Time" was passing quickly and this pattern peaked at age 50, however, and remained steady until the mid-90s.

In conclusion, the theory of Subjective Time under consideration is consistent with the empirical study. Dr. Friedman's statement that “As we get older, each year is a smaller proportion of our lives,” and that “each year feels shorter relative to all the time we've lived and thus seems to be going by faster,” further implies the mathematical result that a full 80 Objective Year lifespan results in only 4.4 Subjective Years.

Your Subjective Time = Natural Log of your chronological age in objective years.
So, if you want to know your specific amount of Subjective Time that you have lived, use this Natural Log Calculator. Ex. ln (80)= 4.4

https://www.rapidtables.com/calc/math/Ln_Calc.html

Natural log calculator | ln(x) calculator online

Natural Logarithm Calculator. Natural logarithm calculator. ln(x) calculator. The natural logarithm of x is: ln x = log e x = y. Enter the input number x and press the = button:

www.rapidtables.com

In conclusion, the idea that there are three types of Time is a fiction to deal with the misconceptions involved in the use of the word "Time." In reality, these are three different phenomena fictionally subsumed under the rubric of the common notion of "Time."

References

[1] Wittmann, M. and Lehnhoff, S., (2005), Age effects in perception of time, Psychological Reports 97: 921-935
https://www.researchgate.net/publication/7266174_Age_effects_in_perception_of_time
[2] Lewis , Jordan Gaines, Why Does Time Fly as We Get Older, Scientific American, (Dec. 18, 2013).
https://blogs.scientificamerican.com/mind-guest-blog/why-does-time-fly-as-we-get-older/
[3] Based on Aging and the Speed of Time presented by Dr. Friedman on 10/14/2010 at Oberlin College. Ibid.
[4] Ricker III, Harry H., Refutation Of Einstein's Principle of Relativity, General Science Journal, (May 28, 2011)
http://gsjournal.net/Science-Journals/Research%20Papers-Relativity%20Theory/Download/3494

Other Resources
Jedell, David W., Einstein's Field Equation Explains Faster than Light Warp Drive
https://thejedellreport.blogspot.com/2019/09/theoretical-alcubierre-warp-drive.html

Sutter, Paul, The Universe Remembers Gravitational Waves — And We Can Find Them,
Space.com (12-6-2019)
https://www.space.com/gravitational-waves-memory-space-time.html

Bergmann, Peter Gabriel; Einstein, Albert, Theory of Relativity, Dover Publications, Inc., (1976); Stanford General Relativity Lecture Series, Leonard Susskind, https://m.youtube.com/watch?v=JRZgW1YjCKk

Mann, Adam, What is Space-Time, Live Science (Dec. 19, 2019)
https://www.livescience.com/space-time.html

Copyright © 2022 David William Jedell
Email: d.w.jedell@gmail.com

The Jedell Report

Thursday, August 8, 2019

What you never knew, but thought you knew, about "Time," "Now," "Curved Spacetime General Relativity" and "Special Relativity 'Time Dilation'"

The cosmological constant

Time

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