spacetime inverses and 1-to-1 mapping

[AntonioLao]

If spacetime charges are analogous to that of 4D vectors then the spacetime continuum is simply a 4D vector space. The properties of this mathematical space can be described by certain transformations or certain mappings say from R⁴→R⁴ or R⁴→R³ or R⁴→R² or R⁴→R¹ or R³→R³ or R³→R² or R³→R¹ or R²→R² or R²→R¹ or R¹→R¹. There are also the same numbers of reverse mappings: R¹→R¹ or R¹→R² or R¹→R³ or R¹→R⁴ or R²→R² or R²→R³ or R²→R⁴ or R³→R³ or R³→R⁴ or R⁴→R⁴. The sets of real numbers to the left of the mapping arrows are defined as the domains while sets to the right are defined as the codomains (ranges). All these mappings are called “onto” mappings. However, if each different point of the domain maps only to a unique point in the codomains then the transformation is called a function and the mapping is called 1-to-1. By their precise definitions, only one-to-one mappings have inverses. Their corresponding functions also have inverses. The collective transformations form symmetry groups of mappings.

Unfortunately, spacetime charges as squares of energy represented by square symmetric Hadamard matrices do have any inverses. Mathematically speaking, they are called singular matrices such that their determinants are identically zero. The implication is that mappings from squares of energy to matter and ordinary energy do not imply one to one correspondence. This is also true for all reverse mappings from matter and ordinary energy back to squares of energy. Fortunately, these Hadamard matrices as spacetime charges are mathematically suitable for formulating a quantum theory of the spacetime continuum by giving the products of matrices as generators of physical mass and matrix additions the generators of physical charges (notably more so for fractional electric charges).

[labelwench]

If spacetime charges are analogous to that of 4D vectors then the spacetime continuum is simply a 4D vector space. The properties of this mathematical space can be described by certain transformations or certain mappings say from R⁴→R⁴ or R⁴→R³ or R⁴→R² or R⁴→R¹ or R³→R³ or R³→R² or R³→R¹ or R²→R² or R²→R¹ or R¹→R¹. There are also the same numbers of reverse mappings: R¹→R¹ or R¹→R² or R¹→R³ or R¹→R⁴ or R²→R² or R²→R³ or R²→R⁴ or R³→R³ or R³→R⁴ or R⁴→R⁴. The sets of real numbers to the left of the mapping arrows are defined as the domains while sets to the right are defined as the codomains (ranges). All these mappings are called “onto” mappings. However, if each different point of the domain maps only to a unique point in the codomains then the transformation is called a function and the mapping is called 1-to-1. By their precise definitions, only one-to-one mappings have inverses. Their corresponding functions also have inverses. The collective transformations form symmetry groups of mappings.

Unfortunately, spacetime charges as squares of energy represented by square symmetric Hadamard matrices do have any inverses. Mathematically speaking, they are called singular matrices such that their determinants are identically zero. The implication is that mappings from squares of energy to matter and ordinary energy do not imply one to one correspondence. This is also true for all reverse mappings from matter and ordinary energy back to squares of energy. Fortunately, these Hadamard matrices as spacetime charges are mathematically suitable for formulating a quantum theory of the spacetime continuum by giving the products of matrices as generators of physical mass and matrix additions the generators of physical charges (notably more so for fractional electric charges).

Hello Antonio, and I ask you to forgive my posing you with such a question, yet my curiosity is engaged, and I would follow it.

You are the forum member with the greatest number of thread starts, yet few of them seem to find lengthy discussion.

In view that there may be few who can engage you on these topics, why do you not stay the course yourself on a thread, as per example Wick, with his 'Resting Light' thread?

Perhaps as you developed some of these ideas, others might find an edge to grasp and join in.

Just a thought......

[SteveA]

Hi, Antonio.

As a couple additional comments. Notice that 1 to 1 mappings appear to be the only deterministic/physical and non-theoretical form of mapping as the ability to verify a specific inverse form allows the two to be connected together without any information required to decide which states in the domain gave rise to states in a specific range.

For example, if we mapped 2 states in one representation to a single state in another, this gives rise to uncertainty and would require some additional information/energy to determine which of the initial states caused the observed state. Of course because the model was not actually deterministic, then either original state was possible, but this would require a destructing of information and be impossible to describe or verify as something physically deterministic.

Also, if we assume there exists an evolution of a deterministic mechanism over time to construct space, then there should fundamentally be a 1-D structure in time.

If we had more than a single direction/dimension of motion, without some deterministic manner to determine what components of that single dimensional motion were allocated to each of these dimensions, then the dimensions are not connected to each other within the same space and would exist as separate structures.

In order to possess some degree of freedom within a common space, a variable velocity (# of quanta per perceived event) in a single dimension could be used. The spread of perceivable ranges of velocity would provide the quantity of information for a perceived event and these could all exist within a single space and be mapped to a multidimensional perceptual space (with a finite, though growing range of perceptual dimensions and a single fundamental infinite "universe" of 1-D time).

The range of possible discrete accelerations would be equal to the number of discrete possible motions available along this. The precision of control over this would be proportional to this quantity as well and perceptual information would have to allow this quantity to be conveyed as well.

So, for example, if we had a fundamental evolution of time as events 1,2,3,4, ...

An uncontrolled motion in this would just progress as 1,2,3,4, ...

But if there existed, for example an ability to select between +1 or +2 motions, then in order to have these deterministically controlled, that binary value would need to be perceptual present, as well as an ability to map this to that selection process. So we could see this space as a binary+time form, with an average velocity of 1.5, but any finite quantity of information would not appear capable of conveying an unbounded perception of time, though specific qualities present at each of these states 1,2,3,4,... could provide that, though I'm certain there would be a bit more to this, but those are just some ideas to kick around.

Another quick consideration - there's more contextual information available in conscious experiences than what exists solely as "externally" measurable events and so there's a broader range of possible "motions" when it's not simply the observation by the manners and contexts in which those are perceived to occur are considered. This gives more information to "play with" ... (a tad more options in terms of deterministic/controllable accelerations in spacetime? )

[AntonioLao]

Anna, i can only speak for myself. My main objective is to post topics that in someway related to cold fusion. I call these research in progress. I notice from the beginning That i do lack certain communication skills. But tried my best to relate all the ideas I have in mind. However, there are some ideas in this forum that would require a lot of efforts for me to discuss properly in connection to mine. So i dont pursue them further. But the more I posted the clearer the ideas about cold fusion become. So it does progress slowly but surely.

Steve, if all the relationships in the world were all one to one correspondence, then these functional relationships would have simplified life's problems a lot better than any mathematical idealization can provide.

[labelwench]

Thank you for your reply, Antonio. I understand now that you are searching, in your own way, as do we all.

Your communication skills are just fine. The lack of scientific wherewithal is entirely my own shortcoming, and I appreciate the patience of yourself and many other posters in helping me to understand your methodology.

I wish you the best in your search for the key to cold fusion.

As always,

Anna

[SteveA]

Steve, if all the relationships in the world were all one to one correspondence, then these functional relationships would have simplified life's problems a lot better than any mathematical idealization can provide.

I assume every thing in existence is unique and only an identity to itself ... sounds like a good start for a one to one mapping

Time, as change, appears to be unable to be ever described in any such form. If A became B, then we've got problems (next thing we know B would become C and ... yikes!!! A whole "number line" compressed into a singularity)

My guess is that everything has always fit in perfectly. We happen to not be able to see it - and even if ignorance is not specifically bliss, it allows for a lot of free play and thrill rides.

In a sense though, time includes more than such an idealized state and include illogical, indeterminant and paradoxical things into "everything" ... so it could be a way to pack in more than just a logic structure could provide (though recognize that such things would not appear required to be connected to any specific structure - "change" is not inherently synchronized, though it could be. If the rules of thumb is absolute freedom, then if two things happen to track each via. a common reference in time, under those conditions it would have to be because each "desired" to be there at the same time, so we could still have a "universe" of completely random motion, as long as a common unit of motion was used, and each thing could both be free to move as well as interact etc. and you could construct the appearance of collisions and forces, though it wouldn't fundamentally be such ... that's the direction I've been looking at, though there's an issue in that it would appear the origins or properties of every thing in such a space would be unknown, except for the properties of interaction within that space - notice that this would then have to be a space one selected, even if it wasn't a controlled selection, though we could assume whatever the initial motivation would have been would have been continual - if you ever did a first thing, what would it be? I'd assume it would have been something you wanted to do - hence time, the desire to do what one wants. Specifically what would it be? Within that context, I'd have to assume nothing specific at all, though it's interesting how an accumulation of these actions could lead to various more complex contexts and it could be possible to look at these similar to the manner in which we develop more complex systems of values from lower level desires - for example, someone might like working because they enjoyed an income because it pays for food and shelter because the body required these to grow, because one was born ... or something along those lines. I've been mapping out some interesting structures for emotions and trying to see if there's a nice way to optimize things a bit I guess that's my version of "cold fusion" - basically, I realized that there were a ton of things I could enjoy doing but it was frustrating to see that none of them specifically were really enough - life has been a rather never ending series of projects (it both me and my wife a while to realize the recurring pattern) and anyway I wanted to break out of that cycle and I think if you look ahead a bit you might find something more ultimately satisfying. Is it truly cold fusion that's the destination or something beyond that? Give it a bit of thought. I bet you've got bigger ideas around ... some transformations can be optimized by using block operations on a large quantity of information, for example a Fast Fourier Transform is exponentially faster than a serial version, but it takes a bit more time to collect all the information before the transformation ... but it gives great results ... just ideas to kick around)

[SteveA]

Thank you for your reply, Antonio. I understand now that you are searching, in your own way, as do we all.

Your communication skills are just fine. The lack of scientific wherewithal is entirely my own shortcoming, and I appreciate the patience of yourself and many other posters in helping me to understand your methodology.

I wish you the best in your search for the key to cold fusion.

As always,

Anna

I'm going to take a wild guess and say that he doesn't mind at all ... am I right Antonio?

[AntonioLao]

Anna, I seem to have a lot of keys but none yet fit the CF lock and Steve, as a researcher, time is all I need and more of it. But I'm running out of time. For doers they would prefer to do things quickly so they can take a longer vacation doing nothing.

[labelwench]

Anna, I seem to have a lot of keys but none yet fit the CF lock and Steve, as a researcher, time is all I need and more of it. But I'm running out of time. For doers they would prefer to do things quickly so they can take a longer vacation doing nothing.

Somewhere along the way I was taught, that everything takes the time that it takes.

We are presently living in an era of 'instant gratification', that we look to our technology and corporate retail to satisfy.

Nature works on cycles far different than we choose to respect.

Renewable resources are renewable, yet not at the rate we are depleting them.

Yes, Antonio, I concede that you may be running out of time, but then again, I'm concerned that we are all running out of time.

Each of us can only weave our own thread and trust that, in the end, the threads will come together to make something of significance, though we may be blind to the pattern and texture, even unto the end of our journey.

[AntonioLao]

that everything takes the time that it takes.

This would apply perfectly to many wine makers who are not concerned about profits but the quality of the wine. 'Instant satisfaction' would apply more to a wino than to a social drinker. For those who drink alone, they can drink themself to death and still get no satisfaction.