## What is Space-Time, Really?

Motion and awareness seem to be aspects of each other. Please see **What is Awareness, Scientifically?**

In Physics, the most fundamental form of motion is the electromagnetic radiation. This motion is understood to be varying fields with wavelike characteristics. It has wavelength, period and frequency. The frequency provides a measure of the energy present per the relation, *E = hν.*

The wavelength of this motion can be said to provide a sense of extent, which we know as space. Space is basically an awareness of extent.

The period of this motion can be said to provide a sense of duration, which we know as time. Time is basically an awareness of duration.

But neither space nor time are absolute. They are even transformable into each other. There is no absolute unit of time. Therefore, frequency cannot be defined simply as an inverse of period. Frequency is related to space-time.

Thus, frequency, which provides a sense of energy, must lie in the dimension of space-time. In other words, space-time is not empty. Space-time is filled with the sense of energy.

**Space-time is basically an awareness of energy.**

If there is no energy there shall be no space-time.

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There is an overall awareness of motion. Motion may be described in terms of wavelength (extent), period (duration), and frequency (energy) as its characteristics.

Thus overall awareness of motion may be described in terms of space (awareness of extent), time (awareness of duration), and space-time (awareness of energy) respectively.

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December 16, 2014 at 9:41 PM, under

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V:”Space is basically an awareness of extent.”

Or how about “space is the extent of awareness.” It is brought about by the “extension of awareness”.

Awareness can “make” space.

Thank you for your suggestion, 2ndxmr.

Overall “awareness” is simply an awareness of motion. It does not “make” space. There is simply a relationship.

Motion has wavelength (extent), period (duration), and frequency (energy) as its characteristics.

The “awarenesses” of these characteristics are space, time and space-time respectively, in my view.

V:”Overall “awareness” is simply an awareness of motion.”

I believe awareness is capable of being aware in the absence of motion. This would be at the level of thought.

Do you separate thought out from awareness?

I see “aware of being aware” as introversion at human level. It is just a very complex motion.

Using this form of awareness as a measuring stick of all possible awareness is a human-centric view in my opinion.

I have modified the above post to clarify it and correct the typos.

I know that what I have presented is a radical view in that it goes against the idea of “creation”.

The problem I see with a non-creation scenario for the universe is that it is too well structured at the quantum level to have been the result of a random wave motions. It does not fit an Occam’s razor reduction to have something this complicated spontaneously arise. The probability is the product of numerous remote probabilities, i.e. smaller than the probability of a single necessary event.

However applying Occam’s razor to the emergence of awareness from “nothing” does work because that is a singly probailistic event i.e. it depends on no other event.

So, with emergence of awareness being much more probable than the emergence of a well defined quantum structure, I will maintain my view that awareness could evolve to the point of being able to create a “matter” based sub-universe within a larger universe (or void).

Of all the dichotomies in this Universe, the most interesting dichotomy is “awareness – non-awareness.”

“Non-awareness” is like a curtain. We do not know what is behind that curtain. We only know what is in front of it. When something emerges from that curtain we become aware of it. Until then we may only speculate about what is behind that curtain.

POSTULATE: The Universe begins as it emerges from behind the “curtain” of non-awareness..

Like any dichotomy, “awareness – non-awareness” may represent a single continuum, and the two ends extend to infinity in either direction. The “curtain” described above is a transition point on this continuum, and not a point of creation.

We cannot tell whether the universe was ever created or if it has always been there..

The state of the Universe behind the “curtain” can only be speculated. If there is a Divine Principle that stands above the Universe, it would lie behind the “curtain,” and would only represent a speculation.

Any Divine Principle that stands above the Universe may be relegated to speculation..

Since the Universe begins when it transitions from non-awareness into awareness, the common denominator of the entire Universe may be established as AWARENESS. Awareness is, however, only half of the dichotomy. The Vedic process of “Neti, Neti” (not this, not that) essentially asserts that the basis of this universe lies beyond awareness.

The Universe is made up of AWARENESS, the basis of which lies in non-awareness..

The idea, “God created this world” arbitrarily divides the awareness of Universe into “God” and “world.” God cannot be excluded from the awareness of Universe.

The Universal awareness shall include awareness attributed to gods or God..

The universe begins with awareness. It has evolved entirely out of awareness. It may end by transitioning back into non-awareness. The universe has to be aware of itself because it is all that there is.

The Universe is aware of itself..

Reference: Universe and AwarenessV:”But neither space nor time are absolute. They are even transformable into each other.”

While forward and reverse transformations are common in math, I don’t think you’ll find a way to transform time into space.

I would hold with my long-term argument that “time” is the artifact of expanding and contracting space.

That is to say, the minimum time unit – the Planck time unit – is produced by a sinusoidally expanding and contracting space dimension, or dimensions.

These pulsing or vibrating space dimensions would likely act like waves of water in the way they carry “stuff”.

“Stuff” without mass would behave like a surfer following the wave and is carried along at the speed of the wave. This is why massless EM energy always travels at the speed of light.

“Stuff” with mass would behave like wood chips floating on the water. This massy stuff always moves slower than the wave speed. This is why particles with mass always travel slower than light speed.

This also shows the mechanism of propulsion. In essence, this moving space forms a “reaction platform” and this shows why neither massy nor massless particles can exceed the speed of light. To understand this concept, think of the surfer and think of the wave is his “reaction platform”. All his propulsion comes from creating a reacting, propulsive force against the advancing wave. Since all his usable energy is coming from the advancing wave, he cannot advance faster than the wave.

As for time, this space-wave structure sets the time unit by virtue of the wavelength of the space-wave.

Time is measured by the “ticks” of passing wave crests.

This then shows why time slows as you move faster. If time is measured by wave-crest “ticks”, the faster you move, the fewer wave-crests pass you and the slower your time gets – compared to a stationary observer.

As you reach light speed, no wave-crests pass you and your time goes to zero – as far as the stationary observer is concerned.

Thus it may be said that a photon either does not experience time or is experiencing a time of zero.

This zero-time effect may explain the “spooky effect at a distance” experienced by entangled photons.

I have come to see space and time as forms of awareness, and thus they can transform into each other as also shown by mathematics.

The dimensional analysis shows energy to be M (L/T)^2. It includes the concept of mass or inertia. But electromagnetic energy involves the concept of frequency (space-time). What needs to be worked out here mathematically is how frequency and inertia are transformable into each other.

Point of interest, Voyager experiencing interstellar motion of waves catching and passing it by. http://science.nasa.gov/science-news/science-at-nasa/2014/16dec_voyagercme/

This was interesting but it looks like the buffeting was due to magnetically-excited interstellar ions rather than perturbations of “space”.

“As you reach light speed, no wave-crests pass you and your time goes to zero – as far as the stationary observer is concerned.”

I have been thinking this for a while now. This is the reason for Heisenberg’s Uncertainty. Possibly if an object position is located precisely, it velocity would be found to be zero.

The entire universe is in motion so you will have a very remote chance of finding anything with a “zero” velocity, except as relative to an observer moving at an identical speed.

What I described was how one could get a perception of “zero” time.

Another thing to consider is that “matter” and “mass” at the first fractal will likely be units of vibrating space-dimension. So even at that level you wouldn’t be able to pin down an absolute position of the fractal.

The concept of speed (distance / time) becomes confusing when one finds that space and time are relative rather than absolute. There are no standard units of meter and seconds applicable in the interstellar space.

When we talk about speed of light being a constant, I don’t think we know exactly what we are talking about.

In my view the Theory of Relativity suffers from some human-centric assertions and assumptions.

Frequency is a better parameter for space-time than speed.

How would you apply that idea to creating a trajectory for a space capsule?

Classical mechanics will work fine for creating a trajectory for a space module.

V:”When we talk about speed of light being a constant, I don’t think we know exactly what we are talking about.”

In the model I have proposed, the speed of light will be as constant as the wavelength of the space-dimension acting as the carrier for the light photon.

Since this space-dimension can be curved by gravity, and gravity is virtually omnipresent and varying, what you say about light speed not being “constant” is essentially true. But like the measurement of an inch, you have to discriminate whether you want 1.0″ or 1.00000″. To the carpenter wanting to measure his boards to 1.0″, his board lengths will look constant despite being different of .01″ or less.

I have registered for the following on-line course offered by MIT. This course starts in 8 weeks.

Mastering Quantum MechanicsI am studying the first four chapters of the following book, as advised, to prepare for this course.

Introduction to Quantum MechanicsHope this leads to some intelligent questions. 🙂

The above book starts out with the following in its PREFACE:

Unlike Newton’s mechanics, or Maxwell’s electrodynamics, or Einstein’s relativity, quantum theory was not created—or even definitively packaged—by one individual, and it retains to this day some of the scars of its exhilarating but traumatic youth. There is no general consensus as to what its fundamental principles are, how it should be taught, or what it really “means.” Every competent physicist can “do” quantum mechanics, but the stories we tell ourselves about what we are doing are as various as the tales of Scheherazade, and almost as implausible. Richard Feynman (one of its greatest practitioners) remarked, “I think I can safely say that nobody understands quantum mechanics.”

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“Every competent physicist can “do” quantum mechanics, but the stories we tell ourselves about what we are doing are as various as the tales of Scheherazade, and almost as implausible.”

Good quote. This is all I am saying about “what is spacetime really?” Not as an objection to study but as a warning to hold loosely to our understandings. I will never be a contributor to these great researches, but I do enjoy spectating and cheering from the sidelines.

I am optimistic that any understanding can be improved, even when there may not be some absolute understanding. 🙂

Vin, thanks for putting this up. Looks interesting. Are you going to do it for credit or will you audit it?

I’ll audit it.

“In my view the Theory of Relativity suffers from some human-centric assertions and assumptions.”

These are called abstractions. As Korzybski says, they are not illusions but abstractions. It is not that there is nothing there, it is that what we abstract is what we abstract (a tautology). There is a universe, is it self-aware? There are the nodes on the surface of this awareness called individual entities. Are they self-aware? Somewhat, yes. Is all self-awareness the same as all other self-awareness? To me, not at all. The subset seems unaware of, unable to fathom what is outside, in excess of its own set. Efforts to add more correct abstractions to the knowledge of Man is the engine of speculation, conjecture, supposition, innuendo, and guessing. The superset cannot be successfully resolved from within the subset and this may be hold true. Is Man doomed to walk the Earth continuously contemplating his own navel? Partly, but possibly not completely. The subset seems able to expand in awareness, in abstraction, in knowledge. Man’s awareness can expand, but mathematically, to me it seems not entirely as a wet-meat sack. There seems logically to me to be something more expansive going on, there seems to be a superset to my own subset. We can call this “immanence without hope of transcendence” which on the surface might sound forlorn, but it needn’t be. There is a tremendously rich life to be lived and immanence to be enjoyed while we live for a brief moment. What is space-time really? It is all there is or ever will be, world without end, (more tautology) – amen.

I am simply pointing out inconsistencies, and effort is to resolve them. It doesn’t matter whether they are abstractions or illusions.

I just mean that something is going on. It is not an illusion that something is going on. Abstraction is the best resolution that we can make of what is going on. And that is a personal reality which might or might not coincide with objective reality. When these abstractions gets broad agreement, then we say we are nailing down an objective reality. Yet when we look more closely that abstraction needs modifying as well to make it more consistent. It is a big undertaking to conjecture a unifying theory of everything. It seems our knowledge and our mastery of physics will increase. We seem able to continually create magic from relatively advanced understandings of physics. So what is spacetime really? It is the expanding opposite of neti neti, as in “yes this and yes that.” There may be many correct vectors to take spacetime understandings. An example is our understanding of the photon as a particle and a wave. These are both correct and yet this understanding is not complete. A closer look will bring about new and possibly quite different understandings of what is going on until the idea of “particle” and of “wave” seem archaic notions.

That’s my effort.

CT:”What is space-time really? It is all there is or ever will be, world without end, (more tautology) – amen.”

Unfortunately all good things come to an end.

For this expanding universe that end is a long ways away, but eventually our sun will burn out and the stars will similarly wink out.

Entropy wins.

If you let it.

Back at MIT in 1970, I got lost when I came across the Schrodinger equation during my Nuclear Engineering curriculum. It is funny that I have to start with this equation in the book above. The following makes good sense.

The Schrodinger equation plays a role logically analogous to Newton’s second law: Given suitable initial conditions [typically, Ψ(x, 0) for wave function], the Schrodinger equation determines Ψ (x, t) for all future time, just as, in classical mechanics, Newton’s law determines x(t) for all future time.

Here the wave function Ψ (x, t) is being treated logically analogous to the position function x(t). The book says,

But what exactly is this “wave function”, and what does it do for you once you’ve got it? After all, a particle, by its nature, is localized at a point, whereas the wave function (as its name suggests) is spread out in space (it’s a function of x, for any given time t). How can such an object be said to describe the state of a

particle?It seems that what is causing conceptual confusion here is the fixation on the concept of a particle as a point like structure, and that wave is sort of a path traced by a particle.

My conjecture is that a “wave” is a diffused particle, or that particle is a condensed wave.Wave is not necessarily a path traced by some “point” particle.

This tells me that the “space” in which wave moves is contained entirely inside the particle; and that the particle moves in an entirely different space.V:”This tells me that the “space” in which wave moves is contained entirely inside the particle; and that the particle moves in an entirely different space.”

You’re now getting into the folded-space realm of the Calabi-Yau manifold.

There is a certain jump that I would suggest you take and that is to look at the mathematics of black holes. The nub of the matter is that when an atom “falls” into a black hole, the circumference of the black hole increases by the diameter of the atom.

To me this indicates that the atom has been segmented into “space containing” bits (as the 3-space event horizon has enlarged) and mass/gravitaton components which merge appart from 3-space at the “bottom” of the black hole.

This seeming separation of atomic “space component” and mass/gravity component is consistent with my hypothesis that the gravity component has the form of a vortex that is dimensionally orthonormal to 3-space.

I find that math is being given so much importance that it is creating its own reality. Nobody seems to be making sure that mathematical reality is consistent with the reality that is sensed and observed. I am simply looking for consistency among various concepts without getting lost in math.

sigh… Ψ

Did you use an external editor to create your post? Having some math symbol and editing capability – like LaTex – would be nice, at times.

No. Just used Microsoft Word.

The wave function seems to determine the “shape” of the “particle,” which seem to extend in some “inner” space.

In reading Section 1.2 I seem to have the following questions.

(1) Is the idea that a particle must be localized at a point correct? Can a particle be like a snake, where the position of snake is spread out in some “particle space”?

(2) Can the “wave” be a diffused particle, or particle a condensed wave?

(3) Is it possible that the “space” in which wave exists is contained entirely inside the particle? The particle then moves in an entirely different external space?

I have put these questions on Quora in a comment.

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V:”(1) Is the idea that a particle must be localized at a point correct? Can a particle be like a snake, where the position of snake is spread out in some “particle space”?”

That is pretty much the string theorists idea. I recently looked at a YT vid where the premise of the string was expanded to include “branes”, sort of a membrane that the string would be found on. This was very similar to the proposition I’ve made that a space geometry in the form of a plane would exist.

In string theory they have the brane doing a single oscillation over its surface as if you took a piece of thin sheet steel and made a wave pattern from it.

I find this brane theory limiting in that they have not yet given a plausible explanation of the continued resonance of the plane/brane. In my model the plane expands and collapses (contracts) modeling the elastic medium necessary for continued oscillation.

The final needed point for sustained self resonance in my model is supplied by the “space-picture” of the Real component of the wave which is captured by the orthonormal “imaginary” space plane during the collapse phase of the wave.

Because each quantum component requires a self-resonant structure to sustain itself, this means that each self-resonant component has this “picture” making capability, i.e. every time it collapses it makes a picture of the state it was in at the time of the collapse.

This means that every resonant particle in the universe has a picture making capability and has been making “pictures” (of its collapse from a state) ever since the moment of its creation.

V:”(2) Can the “wave” be a diffused particle, or particle a condensed wave?”

I think it is best to look at all quantum structures as sets of orthonormal dimensions or geometries of spaces.

Yes, the plural “spaces”, all with different geometries.

A very simple analogy for this is a wood house. All the different members are made of the same “stuff” (wood), but they are prepared in different geometries (planks, beams, sheets) that assemble in an orderly way to make a stable structure.

Similarly a “particle” is a composite of geometries of space.

The “hardness” of a particle may well have to do with the magnitude of the Real (3-space) components of the composite geometry.

That would be why we see no “hardness” (particle-ness) in a photon which has just simple E and M components i.e. its Real components are zero.

That does not mean that the photon has fewer dimensions than a harder particle, it just means that the dimensional vectors that contribute to hardness (the Real space dimensions) are all zero valued.

The virtual proof of this is the observation that two gammas (E-M dimensioned bosons) colliding will produce a positron and electron from the collision. Since the lepton products (positron and electron) have attributes of mass, charge and spin very different from the gamma photon, it clearly indicates that a fundamental set of dimensions exist and that there is a way for the transformation to occur from boson-boson to lepton-lepton.

It is these fundamental dimension sets, or matrices if you prefer, and the magnitudes of the geometries (vectors, if you prefer) that establish the properties of the particle: its charge, mass and relative connectivity to 3-space.

Quantum Mechanics basically boils down to the question of things that we are taking for granted in our present reality, and what are they?.

One thing we are taking for granted is that observer is not a part of the reality being observed.

The following excerpt from the book explains the concept of collapse. It is the first time that I have understood this concept fully.

But what if I made a second measurement, immediately after the first? Would I get C again, or does the act of measurement cough up some completely new number each time? On this question everyone is in agreement: A repeated measurement (on the same particle) must return the same value. Indeed, it would be tough to prove that the particle was really found at C in the first instance if this could not be confirmed by immediate repetition of the measurement. How does the orthodox interpretation account for the fact that the second measurement is bound to give the value C? Evidently the first measurement radically alters the wave function, so that it is now sharply peaked about C (Figure 1.3). We say that the wave functioncollapsesupon measurement, to a spike at the point C (Ψ soon spreads out again, in accordance with the Schrodinger equation, so the second measurement must be made quickly). There are, then, two entirely distinct kinds of physical processes: “ordinary” ones, in which the wave function evolves in a leisurely fashion under the Schrodinger equation, and “measurements”, in which Ψ suddenly and discontinuously collapses.This figure is a description of quantum inertia: the next state of a particle will be most likely to be the same as the last state. Position is also included in this concept.

In the first position spectrum (top wave), ‘A’ is the most probable location, but ‘C’ isn’t improbable, so the function can ‘collapse’ at ‘C’.

A physical observation of this phenomena has been observed in a special chamber where an electron has been shown to be in multiple locations ‘at once’. This would be the equivalent of finding the electron at ‘A’ and’C’ and other probable locations) at the “same” time.

While that phenomena has been observed and been used to support the superposition theory, I believe that a better explanation comes from my model where the particle takes a “picture” of every location where it has condensed and it is these pictures that form the probability spectrum. Thus, when an external condition causes a collapse, the collapse will occur with the most recent picture being the highest probability. In the case of the description above, after a collapse at ‘C’, the most probable next collapse would near ‘C’.

Per the above excerpt the condition that causes collapse is the

second measurementwhen made quickly.Yes, that is understood. The longer the duration between measurements, the more external factors occur that change the position.

This is even true with quantum computers where they are attempting to maintain a Qubit state. The lifetime of that state is given a name that I can’t currently pull from the probabilistic dictionary. 🙂

Getting back to the OP:

“Space-time is basically an awareness of energy.

If there is no energy there shall be no space-time.”

This is true up to a limit.

As I proposed earlier, time would be “sensed” by the passage of waves of space (energy, of a form). The upshot of this is that when you are moving at the same speed as the space wave, time goes to zero. This is consistent with the theory of relativity.

What that implies is that the observer traveling at light speed (or space-wave speed) sees a static condition energy-wise and his elapsing time would go to zero – at least as perceived by an external observer and likely so based on observations of clocks in orbiting space platforms.

So, for the observer traveling at light speed thinking “Space-time is basically an awareness of energy” this might well appear true as that observer should not be able to observe energy. However, if this observer is able to “think” for a duration, then he will at least have a sense of personal time.

On the other hand, an external observer sees the light-speed observer going by very fast and having the apparency of kinetic and potential energies but zero time.

Paradox.

In a way “velocity” is an awareness of energy too, but through the concept of mass

“space-time” is an awareness of energy through the concept of frequency. I am assuming, of course, that de Broglie’s frequency is somehow functions the same way as mass.

V:”I am assuming, of course, that de Broglie’s frequency is somehow functions the same way as mass.”

That was his proven assertion, however he didn’t link the mass effect to dimension. You have to account for the mass differences between a photon-boson and a W or Z gauge boson and I don’t think that can be done other than by considering other dimensions.

Please see Problem 1.5 on page 11 of this book.

Introduction to Quantum MechanicsI am having trouble understanding the solution for this problem given in this manual.

Solution ManualCan somebody explain how the problem is set up in this solution? I simply cannot picture it.

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Start by picturing the parallel lines of separation L on a Cartesian grid with line 1 at Y=0 and line 2 at Y=L.

The needle falls.

The eye position is given value y.

The point falls anywhere in a 360 deg arc but only 180 deg needs to be considered. (Ergo the appearance of 1/pi in the expansion)

The contribution to the +Y component by the needle resting at some angle between pi/2 and pi equals root(L^2 – delta x^2). The problem solver has simply called this value “x” which makes it somewhat ambiguous with delta x.

A similar function exists for the -Y component.

P(y) is the sum of probabilities for a +Y crossing and the -Y crossing.

Do you get the integrals now?

“The contribution to the +Y component by the needle resting at some angle between

pi/2 and piequals root(L^2 – delta x^2). ”That should have been “between pi/4 and pi/2”.

Can you draw a picture and explain to me the limits of the integral?

Thanks.

The needle can fall between the two lines without crossing either of them.

I don’t have an easy means of making a picture that will embed in WWP right now, so it might be a while.

Which set of limits is the troubling set: first set of equations or second where limits go from 0 to l?

V:”The needle can fall between the two lines without crossing either of them.”

Yes, but that is fully taken into account by the domains established by the path projection onto X. (-l<=x<l for positive y term)

Do you get the meaning of "projection"?

You may send me your answer and the diagram through email.

vinaire@yahoo.com

I shall then post it here.

2ndxmr, You can draw the diagram and write your solution along with it. Then scan it and send me the scan.

I have now worked out my own solution for Problem 1.5

I have just updated the following essay.

The Eighth DynamicThe picture of the universe is gradually coming into focus. The Quantum Mechanics is clarifying the relationship between sixth and seventh dynamics at a very fundamental level.

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Quantum Mechanics is looking at the relationship between motion and awareness.

MOTION is not a particle moving in space.That is a wrong human-centric view. The correct view is

MOTION is interchange of space and time expressed as frequency.This frequency appears as energy, and when extremely high, it takes the appearance of a particle.

Energy is a form of awareness, and so is the particle..

Matter, Energy, Space and Time (MEST) can simply be stated by one word MOTION, because they are nothing but aspects of motion. If there is no motion then there would be no matter, no energy, no space and no time.

In Classical Mechanics motion is defined by Newton’s Laws of Motion. In Quantum Mechanics, motion is defined by Shroedinger’s Equation.

Per Wikipedia,

In quantum mechanics, the Schrödinger equation is a partial differential equation that describes how the quantum state of a physical system changes with time. It was formulated in late 1925, and published in 1926, by the Austrian physicist Erwin Schrödinger.

In classical mechanics, the equation of motion is Newton’s second law, (F = ma), used to mathematically predict what the system will do at any time after the initial conditions of the system. In quantum mechanics, the analogue of Newton’s law is Schrödinger’s equation for a quantum system (usually atoms, molecules, and subatomic particles whether free, bound, or localized). It is not a simple algebraic equation, but in general a linear partial differential equation, describing the time-evolution of the system’s wave function (also called a “state function”).

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In classical sense, motion is described by a mass particle moving in space. This view falls short at atomic scales because there is no longer anything that can be grasped cleanly as a particle. Instead, the motion appears to be very different.

The Shroedinger equation attempts to describe motion at atomic scales through the concept of a wave function. It is a density of something that is varying in the space, and has wavelike properties. It is described as probability density of the particle.

But the classical concept of a particle no longer serves.

Spaceis defined in Wikipedia as follows:Space is the boundless three-dimensional extent in which objects and events have relative position and direction.[1] Physical space is often conceived in three linear dimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum known as spacetime. In mathematics, “spaces” are examined with different numbers of dimensions and with different underlying structures. The concept of space is considered to be of fundamental importance to an understanding of the physical universe. However, disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework.

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We are most familiar with space in terms of an awareness of extents. The key characteristics of space are location, direction, and distance. There are infinite locations. From each location there are infinite directions. In each direction there are infinite distances. A location can be pinned down only by means of an object. The direction, and the distance, can be pinned down by placing another object relative to the first object. Space is not something absolute.

Note that space cannot be stated to be permanent and absolute as Newton thought. If there are no objects anywhere, and no energy to be sensed, it is difficult to have the concept of location, direction and distance, and, therefore, of space.

From Wikipedia,

Later, the metaphysician Immanuel Kant said neither space nor time can be empirically perceived, they are elements of a systematic framework that humans use to structure all experiences. Kant referred to “space” in his Critique of Pure Reason as being: a subjective “pure a priori form of intuition”, hence it is an unavoidable contribution of our human faculties.

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Space is quite objective when physical objects are there. When there are no physical objects, space can only be imagined in a subjective manner.

But there can be mental structure, which are existing by themselves, such as in mathematics. These mental structures can be perceived objectively by the mind. In this case there is space.

From Wikipedia,

In the 19th and 20th centuries mathematicians began to examine geometries that are not Euclidean, in which space can be said to be curved, rather than flat. According to Albert Einstein’s theory of general relativity, space around gravitational fields deviates from Euclidean space. Experimental tests of general relativity have confirmed that non-Euclidean space provides a better model for the shape of space.

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Here space is being looked at in terms of awareness of energy, in addition to the awareness of objects. The idea of “curved space” comes from the awareness of energy fields.

Getting back to the wave function portion of Scrodinger’s equation, namely

iℏ ∂/∂t ψ,

what we have defined is the wave function ψ as a changing, or changeable function – the changeability implied by the calculus operator ∂/∂t. (All this operator says is that for any change in time 1/∂t, there exists a possibility of change in ψ.)

The factor ℏ is a constant, very small value so can be largely ignored in the context of any absolute change.

The ‘i’ is the important factor.

It has been my proposition that the appearance of the imaginary operator, ‘i’, in the Schrodinger equation must be accounted for by a dimension, even if it is a dimension that cannot be grasped by the mind.

It has also been my proposition that there is a continuous translation, or cycle, that goes on between the Real phase of the universe and the “imaginary” phase, and that the “imaginary” phase represents a picture of the Real phase, and that it is from these pictures that energy and particles condense to create the Real phase.

This is basically saying that there is a one-to-one correspondence between points existing in the Real phase and the (imaginary phase) picture of those (Real phase) points.

We could approach a model of this translation if we took an apple and made a 3-D hologram of that apple. We’d have essentially the Real (the apple) and the “imaginary” (the hologram) components. The translation that would mimic the way the physical universe operates would be to have the Real apple convert to the hologram (Real-to-imaginary) and then the hologram to collapse back into the Real apple (imaginary-to-Real). This would be a repeating cycle.

It is the imaginary-to-Real translation that that is the equivalent of the collapse of the wave function. In this translation we have a picture collapsing (or condensing) into an actuality. The most probable picture for a condensation will be the picture that was just taken. However, external factors could also influence the picture chosen to become the next Real apple, so the next apple does have a probability of being altered to the state of an earlier picture.

The equations representing the apple could be written as:

apple = 1 x Real(apple) + 0 x imaginary(apple)Real phase of the apple,and

hologram = 0 x Real(apple) + 1 x imaginary(apple)the picture phase.These equations represent vectors of Realness or picture-ness.

These two equations (vectors) define a space and can therefore be defined in a mathematical matrix:

The matrix

[1(Real) 0(imaginary)]

[0(Real) 1(imaginary)]

could be reduced to

[1 0]

[0 i]

to show the translation.

The laws of mathematics say that in this space a mapping exists between the two axes (Real and imaginary) that is defined by the “dot product” and that product is 1 x i + 0 x 0 = i.

Therefore I would proffer that the Schrodinger equation could be shown as

iℏ ∂/∂t ψ = ℏi ∂/∂t ψ ≡ (is equivalent to) ℏ[1 0] ∂/∂t ψ

[0 i]

and this shows that the state translation from Real to “imaginary” is consistent with the form of the equation.

(Unfortunately I could not get a nice copy of the equations from Word into this WordPress window so my apologies for the poor understandability of this.)

“iℏ ∂/∂t ψ = ℏi ∂/∂t ψ ≡ (is equivalent to) ℏ[1 0] ∂/∂t ψ

[0 i]”

(This didn’t come out well at all. Let’s see what a slight formatting change can do.)

iℏ ∂/∂t ψ = ℏi ∂/∂t ψ

≡ (is equivalent to)

[1 0] ℏ ∂/∂t ψ

[0 i]

where

[1 0]

[0 i]

is the translating matrix.

Here is course 8.04, which is the prerequisite of the course 8.05x

Quantum Physics IAll the lecture notes and videos are provided here. Also the recommended text books are available.

David Albert – Quantum Mechanics and ExperieEisberg, Robert M., and Robert Resnick. Quantum Physics of Atoms, Molecules, Solids, Nuclei, and ParticlesLiboff, Richard L. Introductory Quantum MechanicsGasiorowicz, Stephen. Quantum PhysicsShankar, Ramamurti. Principles of Quantum MechanicsI now have to immerse myself in these lectures and books.

I read about the Stern–Gerlach experiment from Wikipedia. It allowed scientists to conduct measurements of deliberately superposed quantum states for the first time in the history of science. I also read about pure and mixed quantum states. A mixed quantum state corresponds to a probabilistic mixture of pure states.

From Wikipedia:

Before a particular measurement is performed on a quantum system, the theory usually gives only a probability distribution for the outcome, and the form that this distribution takes is completely determined by the quantum state and the observable describing the measurement. These probability distributions arise for both mixed states and pure states: it is impossible in quantum mechanics (unlike classical mechanics) to prepare a state in which all properties of the system are fixed and certain. This is exemplified by the uncertainty principle, and reflects a core difference between classical and quantum physics..

I don’t have any disagreements. I now see that classical resonances can also be seen as quantum states. Also, I am getting a better understanding of Quantum Superposition.

From Wikipedia:

Mathematically, it refers to a property of pure state solutions to the Schrödinger equation; since the Schrödinger equation is linear, any linear combination of pure state solutions to a particular equation will also be a pure state solution of it. Such solutions are often made to be orthogonal (i.e. the vectors are at right-angles to each other), such as the energy levels of an electron. In other words, the overlap of the states is nullified, and the expectation value of an operator is the expectation value of the operator in the individual states, multiplied by the fraction of the superposition state that is “in” that state (see also eigenstates). Such resolution into orthogonal components is the basis of what is known as “quantum measurement”, a concept that is characteristic of quantum physics, inexplicable in classical physics.Physically, it refers to the separation and reconstitution of different quantum states..

Many of my questions resolve when I see “resonances” as quantum states. The mathematics in Quantum Physics seems to have been developed to deal with these experimentally observed quantum states.

I hope to understand the part that frequency plays in the explanation of quantum states.

I am currently studying

Chapter 1, Mathematical Introductionfrom the bookShankar, Ramamurti. Principles of Quantum Mechanics.In my opinion this is the best place to start if one wants to see Quantum Mechanics the way intelligent minds are looking at it.

There is a caveat, however. Mathematics provides a certain structure to awareness. It may be looked upon at as training of the mind to perceive and analyze what is there. But it can also become conditioning if one starts to implicitly believe in this structure. Mathematics is unbelievably consistent, and that is the brilliance of it. However, mathematics shall always be limited by its fundamental postulates. This was pointed out in the essay

THE FUNDAMENTAL INCONSISTENCY.Therefore, mathematics is best utilized as a trusted and efficient tool but with full awareness of its limitations. That is the view I am taking while training myself on the mathematical structure developed to look at Quantum phenomenon. But, I believe that this training is a must, and the best place to start.

Good find. Decades of disuse seem to have left my own lin alg skills with an additive inverse! Hopefully some Christmas study will bring kets back within my ken.

LOL!

Bra-ket

All this stuff is new to me.

Do you understand the proof for Schwarz inequality given on page 17? I have no clue.

Take any triangle. The length of the hypotenuse can never be longer than the sum of the two sides. Same for a vector triangle ABZ,

|A+B| + |B>)

Same thing with products: a vector of length 2 multiplied by a scalar of 3 will give a vector length of 6 but never greater than 6.

Same holds with the product of two vectors: the product along any axis is never greater than the product of the components of the axis, so

<= |V| |W|

I see that the angle brackets are going to be a problem as WP uses them for in-line commands. I’ll see if {} will work in place of them.

For the vector triangle ABZ made of vectors |A}, |B}, |Z}

where |x| is the magnitude of |X}

|A+B| <= |A| + |B| and

|Z} <= |A} + |B}

Same thing with products: a vector of length 2 multiplied by a scalar of 3 will give a vector length of 6 but never greater than 6.

Same holds with the product of two vectors: the product along any axis is never greater than the product of the components of the axis, so

|V x W| <= |V| |W|

or

|{V|W}| <= |V| |W|

I know it intuitively. I just don’t understand the proof given on page 17.

OK, I see that (1.3.17) is just an example and not some equation from before.