Fractal Quantum Mechanics (FQM) & Time

[alexross]

Criteria for a valid dimension

This thread is started just to answer the question of why Complex Space is viable and how we should evaluate any new dimension that is put forward. :cool:

Epsilon= One, I accept your position and reconise that this discussion is not new but still open.
I have followed the discussion myself between eminent persons.
I can see your reservation.
However I take a position based upon these observations:

1> Einstein's theory of Special Relativity rests largely upon my assertion.
This is not obvious at first and it is a hidden facet of his work.
However he was able to describe time as an extra dimension since it behaved
in a similar manner to our 3D dimension. Time has 3 dimensions, not directly associated spatially but present, past, and future.
Our 3D dimension is defined, in large part, by Number Theory. In other words
it underpins what Einstein said. So QM and relativity will be seriously
effected if time is treated in the same manner (by disallowing Number Theory
to describe its validity). This allowed Einstein to use space/time as indivisible.

2> Setting the criteria for consistency in the properties of a new dimension is
reasonable. Suppose our 3D dimension did not obey such rules. Then we could, say, envisage a universe in which a black hole could open and close randomly in any place! Of course such dimensions might exist. They will, however, not be of as much interest as a dimension which does not exhibit such metaphysical behaviour.

3> Time obeys Number Theory in as much as it mimics 3D space and so some
argument for it being a dimension is still feasable.
Einsteins Relativistic Equations for length and time are another example.
In fact QM uses a probalistic complex wave to describe the path of, say, a
quantum at any particular time. This is very, very close to what I have
said, although I am pushing the boat out farther. I am saying in effect I
can better describe this behaviour (although I prefer to concentrate on
length rather than time) by giving time more (numerical) properties than Einstein did.

4> Set theory is another criteria (admittedly poor) for the existence and validity of a dimension.
This tends towards being very abstract. It is necessary to ignore the fact
that some criteria are not very helpful (and very abstract) and look at how
they can help us.
Aside: One thing I have noticed is that despite the fact that Set theory helps very little it can help to check the validity of a situation. For example compare the Uncertainty Principle against Russell's Paradox (the Barber Paradox restated: "I know the probability for the position of those quanta, and all those quanta, whose probability for the position is not known").
This helps to show that the set for the probability of knowing its position is the same set as that of the probability of not knowing its position.
I believe that the Uncertainty Principle follows a similar paradoxical argument.

I consider any dimension as needing to comply with a comprehensive collection of Set Theory rules (conditions) when you come to operate within
it as giving an additional means of checking its behaviour.
In this way the more we define a dimension (even our own) then the more we
learn about it.
These may not be the existing rules (but this becomes fraught with difficulty)
we are familiar with in our 3D world but should show how we can expect such
a dimension to behave.
Complex Space obeys the same Set Theory Rules (and in fact all the criteria I give) as our 3D space/dimension.
This does raise a problem for time. It has not been shown that time obeys
some but not all of the Set Theory Rules as our 3D space/dimension.
Einstein did not go as far as describing time in 3 dimensions using Number
Theory. Time now appears more as a sub set of our 3D dimension.

5> Time is a linear dimension:
It may be possible to show that the behaviour of time MIGHT obey the same Laws of Arithmetic and Algebra as our 3D space/dimension.
Perhaps I should give a simple example. Time does not obey the
multiplicatiom rules in the Laws of Arithmetic and Algebra such as a * b = c
or t * t = t^2. At least as Star Trek fans would say: "not as we know it".
Another consideration is that there is no real number that does not obey
all the basic arithmetic rules (but obeys some) apart from zero. This gives
us a paradox if we say time is described by real numbers as there is now no
real sub set it can belong to.
I suppose there is some milage in saying time is a separate dimension so it
does not need to obey all the rules. The problem is in proving that.
The solution is to say time is a linear dimension.
I am sorry to labour these points. I am just aware of the old discussion.
This demonstrates the serious ramifications even for present theories.
It also shows the reasoning Einstein used was based upon Number Theory.

6> Fractal Quantum Mechanics (FQM): Despite all this time usually 'decays'
in three dimensions! So these techniques help to delve deeper into the
nature of time. It was natural for Einstein to consider time acting linearly
upon a quanta. The problem is that time also acts upon stationary bodies and
not just linearly. I am saying the linear action of time mimics a linear
path in 3D space. The conventional approach is to say a linear time operator
acts three dimensionally in 3D space without giving any supporting argument.
So now I see an unexpected way of introducing FQM (perhaps prematurely) and throwing my hat into the ring.
The solution to this last hurdle is to let time act BOTH linearly and fractally. Time can be considered linearly but like a snow flake or fractal tree which branches linearly to fill not just 2 dimensions as a snow flake but in all 3 dimensions. Note that this allows time to decay constantly as it branches.
This gives a better correspondance between space and time than did Einstein.

7> For the benefit of other readers: The use of Number Theory to underpin
science validates all scientific experiments such as a cannon ball being
fired. The cannon ball always follows a predetermined path because of the
behaviour of our 3D space.
If you want to fire a cannon ball (or particle, say) in another dimension
you need Number Theory to help you determine what, if any, its change in
behaviour will be (for example in complex space). There is no other alternative practice for dealing with unknown dimensions.

Sorry, to be so long winded in getting to FQM for new readers.
Alex

[Epsilon=One]

This thread is started just to answer the question of why Complex Space is viable and how we should evaluate any new dimension that is put forward.Excellent idea.

First, carefully define “Complex Space” so that its “viability” can be discussed.

Second, carefully define “dimension” so that there is no confusion between the concepts of location and fundamental phenomena.

It is your view of “dimension” as a fundamental orthogonal phenomenon that interests me.

…I take a position based upon these observations:

1> Einstein's theory of Special Relativity rests largely upon my assertion.

This is not obvious at first and it is a hidden facet of his work.
However he was able to describe time as an extra dimension since it behaved in a similar manner to our 3D dimension.”In a similar manner” is not good enough; as it does not behave "in a similar manner."

Now that you are into “time,” also, carefully define what kind of time you are referring to. Time is merely a tool for counting; the concept is defined by the “clock” that creates the phenomenon. At the level of your discussion, I assume you will want to describe “fundamental, intrinsic time” (FIT), which is the "time" that synchronizes the inner and outer actions of fundamental quanta.

Time has 3 dimensions, not directly associated spatially but present, past, and future.The operative words are “not directly associated.” Also, only the “past” and “future” exists; the “present” does not.

Speaking of a “counting” device and “dimensions” is a difficult comparison.

Our 3D dimension is defined, in large part, by Number Theory.And, what defines Number Theory?

Numbers and their arithmetic manipulations, as well as: orthogonal phenomenon, are each fundamental; however, neither defines one another. They are both equally defined by fundamental motion.

In other words it underpins what Einstein said. So QM and relativity will be seriously effected if time is treated in the same manner (by disallowing Number Theory
to describe its validity). This allowed Einstein to use space/time as indivisible.Einstein would be the first to agree that his theories were rife with error.

Setting the criteria for consistency in the properties of a new dimension is reasonable.Your interchangeability of the definition of “dimension” is confusing.

One concept of “dimension” allows unlimited dimensions; while another concept would make finding a “new” dimension a justifiable qualification for a Nobel.

Time obeys Number Theory in as much as it mimics 3D space and so some argument for it being a dimension is still feasable.Time does not mimic 3D space. Time is “counting”; so, it is not too surprising that there is a relationship with number theory.

Einsteins Relativistic Equations for length and time are another example.An example of what; other than: the relative effect of changing motion?

In fact QM uses a probalistic complex wave to describe the path of, say, a quantum at any particular time. This is very, very close to what I have said, although I am pushing the boat out farther.…QM is only an irreconcilable theory; “pushing” it further seems a bit risky.

…I can better describe this behaviour…by giving time more (numerical) properties than Einstein did.What is meant by “more (numerical) properties”???

Set theory is another criteria (admittedly poor) for the existence and validity of a dimension.
This tends towards being very abstract. It is necessary to ignore the fact that some criteria are not very helpful (and very abstract) and look at how they can help us.???

I consider any dimension as needing to comply with a comprehensive collection of Set Theory rules (conditions) when you come to operate within it as giving an additional means of checking its behaviour.???

Complex Space obeys the same Set Theory Rules (and in fact all the criteria I give) as our 3D space/dimension.How does Complex Space differ?

This does raise a problem for time. It has not been shown that time obeys some but not all of the Set Theory Rules as our 3D space/dimension. You are comparing apples and oranges; they are both kind of spheres.

Time now appears more as a sub set of our 3D dimension.It’s not.

It may be possible to show that the behaviour of time MIGHT obey the same Laws of Arithmetic and Algebra as our 3D space/dimension.Well, yes. As does everything else that exists, if the “Laws” are understood.

Perhaps I should give a simple example. Time does not obey the multiplicatiom rules in the Laws of Arithmetic and Algebra such as a * b = c or t * t = t^2.It does “obey”; depending upon the concept of time you’re discussing. Have you considered accelerating acceleration?

I suppose there is some milage in saying time is a separate dimension so it does not need to obey all the rules. The problem is in proving that.You can’t prove the illogical statement.

It also shows the reasoning Einstein used was based upon Number Theory.There isn’t anything much more fundamental to start from.

Fractal Quantum Mechanics (FQM): Despite all this time usually 'decays' in three dimensions!The following statement is not only ludicrous; but, it is also very weak: “time usually 'decays' in three dimensions!”

So these techniques help to delve deeper into the nature of time.Why is help needed to delve into the nature of “counting”? Possibly, you need help with the nature of fundamental, intrinsic time’s (FIT) defining “clock”?

The problem is that time also acts upon stationary bodies and not just linearly.There is no such thing as an absolute stationary body for anything to act upon.

The conventional approach is to say a linear time operator acts three dimensionally in 3D space without giving any supporting argument.”The conventional approach” for defining fundamental time has no acceptable “supporting argument.”

The solution to this last hurdle is to let time act BOTH linearly and fractally. Time can be considered linearly but like a snow flake or fractal tree which branches linearly to fill not just 2 dimensions as a snow flake but in all 3 dimensions. Note that this allows time to decay constantly as it branches. If “time” is anything it consists of consistent “units” of something.

This gives a better correspondance between space and time than did Einstein.Two wrongs don’t make a right. And, AE had a lot better excuses . . . and understood his dilemmas better.

The use of Number Theory to underpin science validates all scientific experiments such as a cannon ball being fired. The cannon ball always follows a predetermined path because of the behaviour of our 3D space.Yes, numbers are fundamental to most all else; however, the cannon ball’s path depends upon many factors.

If you want to fire a cannon ball (or particle, say) in another dimension you need Number Theory to help you determine what, if any, its change in behaviour will be (for example in complex space).As you are using “in another dimension” you are dealing with fiction, illusion, and metaphysics. Do not fault Number Theory for the erroneous impressions of mathematics.

There is no other alternative practice for dealing with unknown dimensions.Nor is there an “alternative practice” for dealing with heaven and hell than religion.

[alexross]

Hello Epsilon=One,
I will get back to you on this, if I may please.
One thing I would say in passing is that I am not in competition with
AE or anyone else.
I have actually started from my own basic propositions.
They have been successful - at least to the extent that they engage and
question our peers.
I do not therefore want to argue I am better than AE or not.
I am sure AE set a good example and had high standards of ethical,
moral, and professional behaviour. He is an hard act to follow.
If I do half as well, I will be happy.
Regards,
Alex

[Epsilon=One]

I have actually started from my own basic propositions.
They have been successful - at least to the extent that they engage and question our peers.Great. Wish there were more like you who question . . . everyone!!!

[alexross]

Hi,
Sorry for the delay, I thought I had posted this.
Here is my answers to your comments:

Time is defined by the "clock" that establishes its "unit."

First, carefully define Complex Space so that its viability can be
discussed.

Answer: This is a huge area. No-one has seriously attempted to map out
another dimension before. I proceed to build up a picture as a jigsaw.
Although time has been accepted as another dimension its complex nature
makes it very difficult to describe accurately.
This is an abstract process as we have little direct observation of complex
space. It therefore leads you on a 'paper trail' in which you get closer
and closer to your goal of validation but always leave room for
interpretation. The goal should be remembered as being to give a 'valid' in
the sense as 'mathematical consistent and self sustaining' rather than
eliminating every uncertainty. Explanations our own dimensions still contains
some mysteries. A realistic goal is to advance our understanding and achieve
an ability to manipulate the new dimension mathematically if possible.

Second, carefully define dimension so that there is no confusion between
the concepts of location and fundamental phenomena.

Answer: I leave room for others to introduce other types of dimension and
have therefore left my criteria broad. Perhaps another approach, to answer
your phylosophical question, is to ask what the difference between a universe and a dimension is?
Looking at my post grad text on fractals (which I have only half read) it dicusses the definition of a dimension.
Leading mathematicians in fractal mathematics use the Hausdorf dimensions.
My selection criteria do not upset this view. Ideally I should finish the book and try to bring a greater harmony here.
Our universe contains three known dimensions. Those dimensions define its
structural character and rules of integrity thus making it a valid space.
Once you engage on the search for these in Complex Space (CS) you can either consider CS as a seperate entity from our 3D space or alternatively as
interacting or impinging upon it.

It is your view of dimension as a fundamental orthogonal phenomenon that
interests me.

Answer: It is a subject which in some respects is greater than myself or
anyone. You can approach CS from a host of different perspectives. It is
like looking through a mathematical or scientific looking glass.
Initially the response of most people would be to assume it to be too time
consuming. In a way that is true but it is the way to make progress.

Quote:
Originally Posted by alexross
…I take a position based upon these observations:
Time is merely a tool for counting

Answer: Is it? or is it more than an abacus?

At the level of your discussion, I assume you will want to describe
fundamental, intrinsic time (FIT), which is the "time" that synchronizes the
inner and outer actions of fundamental quanta.

Answer: Yes that will do fine. Remember I said I created my version of CQM,
then FQM, and finally time. The work on time is unlikely to finish do to
is ethereal nature. I will set more modest goals of advancing our
understanding and constructing a way forward.

Speaking of a “counting” device and “dimensions” is a difficult comparison.

Answer: I agree that is why I suggested coming at this from a different
direction and understanding CQM and FQM first.

Quote:
Originally Posted by alexross
Our 3D dimension is defined, in large part, by Number Theory.

And, what defines Number Theory?

Numbers and their arithmetic manipulations, as well as: orthogonal
phenomenon, are each fundamental; however, neither defines one another.
They are both equally defined by fundamental motion.

Answer: As we probe for a UFT we find ourselves facing the need to relate to
the most fundamental aspects of our existence. These are defined, as best we can, by mathematics and established scientific theories.
There is a chicken and egg aspect to this if we probe as deep as you are
doing. However, I approach this myself by taking a phylosophical view of
General Relativity. If you apply General Relativity to all aspects of
science you will find everything can be relative to everything else.
The difference, here, is that when so widely applied it is to varying degrees.
The degree of relativity between two scientific subjects can be very close
or widely apart.
This does not help us in our reductionist approach. Hence the need to narrow
my approach towards mathematics alone as far as practical.
Perhaps I should say that defining reality is a harder task than defining
what a dimension should be.

Quote:
Originally Posted by alexross
Setting the criteria for consistency in the properties of a new dimension is
reasonable.
Your interchangeability of the definition of “dimension” is confusing.
One concept of “dimension” allows unlimited dimensions; while another
concept would make finding a “new” dimension a justifiable qualification for
a Nobel.

Answer: I have given a broad means of selection. This allows Complex
Space to exist in a spatial dimension as my criteria favour spatial dimensions.
At the same time it does not say another dimension cannot exist non=spatially.
In one sense I take a practical approach now. Why not take a particular case
(CS) and start to fit a framework for it? Rather like constructing the face
of a dead Pharoah from his skull?

Quote:
Originally Posted by alexross
Time obeys Number Theory in as much as it mimics 3D space and so some argument for it being a dimension is still feasable.

Time does not mimic 3D space. Time is “counting”; so, it is not too surprising
that there is a relationship with number theory.

Answer: I am basing my correlation of time with space on Special Relativity
in which the equations are interchangable. I see this as an area ripe for
investigation. If you like you can regard inumber theory as one feature of
time.

Quote:
Originally Posted by alexross
In fact QM uses a probalistic complex wave to describe the path of, say, a
quantum at any particular time. This is very, very close to what I have
said, although I am pushing the boat out farther.…

QM is only an irreconcilable theory; “pushing” it further seems a bit risky.

Answer: It is not so risky if you take my approach. It seems more reasonable
now that I should accept only the firmly established and conventional
aspects of QM? What others criticised, in this, of my approach now becomes a virtuous! In my opinion QM has some inherently risky parts. Why not remove them if you can substitute something better?

Quote:
Originally Posted by alexross
…I can better describe this behaviour…by giving time more (numerical) properties than Einstein did.

What is meant by “more (numerical) properties”???

Answer: Without the numerical properties in SR we would not see that time
changes as the SOL increases.
Einstein showed how a body at the SOL behaves he did not focus upon the fabric of space around it. This is where my view of space/time diverges from AE.

Quote:
Originally Posted by alexross
Complex Space obeys the same Set Theory Rules (and in fact all the criteria
I give) as our 3D space/dimension.

How does Complex Space differ?

Answer:

Quote:
Originally Posted by alexross
Time now appears more as a sub set of our 3D dimension.

It's not.

Answer: I split hairs here. I said "appears".

Quote:
Originally Posted by alexross
It may be possible to show that the behaviour of time MIGHT obey the same Laws of Arithmetic and Algebra as our 3D space/dimension.

Well, yes. As does everything else that exists, if the “Laws” are understood.

Answer: Unfortunately 'action at a distance' does not obey these rules.
I regret in part that I approach this abstractly. The true value of setting
forth new criteria is not in dealing with known and understood events but in
applying them to other possibilities to broaden our understanding.

Quote:
Originally Posted by alexross
Perhaps I should give a simple example. Time does not obey the multiplicatiom
rules in the Laws of Arithmetic and Algebra such as a * b = c or t * t = t^2.

It does “obey”; depending upon the concept of time you’re discussing.
Have you considered accelerating acceleration?

Answer: I overlooked this. Acceleration units are in distance per time squared.
I think (it has mentioned before by others?) that acceleration uses INVERSE
time 1/(t^2). Point taken though.
This explanation gives me a new problem to solve though. How do we have
Inverse Time and what is it? I think FQM will help.
Unfortunately I have left CQM and FQM alone for 7 years and would need to
dig out my old work.
I also believe that I will (eventually but not now) be able to show how
(t^2) * 1/(t^2) = 1.
Your ideas do challenge me to exert myself and attempt a more mathematical
basis to describe time. I have shown you its fractal nature but fractal
mathematics is not simple. This needs a lot more work and my natural
tendancy is to go away and get a better picture for myself first.
I know this is very abstract when taken out of context from FQM. Sorry.

Quote:
Originally Posted by alexross
I suppose there is some milage in saying time is a separate dimension so it
does not need to obey all the rules. The problem is in proving that.

You can’t prove the illogical statement.

Answer: I always try to give counter arguments their full scope. I am
prepared to accept that a critic may put forward a plausable concept even if
they cannot prove it.

Quote:
Originally Posted by alexross
Fractal Quantum Mechanics (FQM): Despite all this time usually 'decays' in three dimensions!

The following statement is not only ludicrous; but, it is also very weak: “
time usually 'decays' in three dimensions!”

Answer: Yes it is true. However the present view of time does not give any
reason for its decay in three dimensions! It is also supposed to operate
linearly. I supposed this seems like nit picking but I suppose I digging a
bit deeper.

Quote:
Originally Posted by alexross
So these techniques help to delve deeper into the nature of time.

Why is help needed to delve into the nature of “counting”? Possibly, you
need help with the nature of fundamental, intrinsic time's (FIT) defining “
clock”?

Answer: Time as counting is only one possible view. Can we really saying
that an accelerating body is just counting? If it is counting then perhaps
we need to know where it keeps it's records?
Another idea comes to me. A clock just measures time. What if we look for
other non-mechanical clocks? To do this we look for evidence of the
footprints of time in FQM or any of the spaces we have been considering.

Quote:
Originally Posted by alexross
The problem is that time also acts upon stationary bodies and not just
linearly.

There is no such thing as an absolute stationary body for anything to
act upon.

Answer: That is a good answer. The relativistic aspects of time are very
difficult to deal with. We have AE views but beyond this it is hard going.
So time must be relative as well as the body you mention.
I extend Einstein's principle of relativity applying to bodies. Clearly
time is not a body but Einsteins showed it displayed relativistic effects.
No-one I know seems to have noticed this. Why or how should time behave
relativistically? I cannot give you all the answers but perhaps some more.
As I said before time is my unfinished symphony.

Quote:
Originally Posted by alexross
The solution to this last hurdle is to let time act BOTH linearly and fractally. Time can be considered linearly but like a snow flake or fractal tree which branches linearly to fill not just 2 dimensions as a snow flake but in all 3 dimensions. Note that this allows time to decay constantly as it branches.

If “time” is anything it consists of consistent “units” of something.

Answer: I concur with you that Time is defined by the "clock" that establishes
its "unit" seconds.
Thats all for now,
Regards,
Alex

[Epsilon=One]

I appreciate the effort and insight that you have provided in Post #5.

You have opened up many avenues of discussion, which I will address, as time allows, in sections, at this thread.

I will try to consolidate your thoughts and begin where we seem to have some agreement.

I do understand the great difficulty in recalling prior details once a conclusion has been decided.

Don't worry about delays in responding. I would rather wait for something thoughtful rather than the usual mindless babble of alternative theorists.

In general, your thoughts are in the proper areas and you have been able to identify fundamental problems. However, it appears your solutions tend towards increasing the enigmas, much like most of the pomo elite theorists, rather than seeking simplicity.

When the forces are reconciled, and TOE is approached, the final solutions will tend towards almost obnoxious simplicity.

The first steps towards understanding our environment include a simple, clear definition of the source of orthogonal dimensions, arithmetic (numbers and their manipulation), and fundamental, intrinsic time (FIT); rationalizing Light and gravity will then easily fall into place.

[alexross]

Hello Epsilon=One,
Sorry for the delay. I have been typing the rest of my work on gravity.
You seem to be spot on now. You can see we are aiming to poineer a trail.
Just like the old 49ers following the gold rush trail we need to seek markers like Johnny Appleseed left.
Most people expect physicists to solve problems in 2 easy steps.
When all the work is done you can often explian it simply that way. However when you are trying to convince other physicists they like to have a comprehensive explanation.
Regards,
Alex :cool:

[Epsilon=One]

When all the work is done you can often explian it simply that way. However when you are trying to convince other physicists they like to have a comprehensive explanation.So much for vision and curiosity of most "other physicists."

How else to explain their "tangled strings."

[alexross]

Hi Epsilon=One,
Sorry I have been very busy lately. String theory has not lost its way but by refusing to accept my ideas of complex forces they cannot progess any farther.
They are looking at the situation from the wrong angle.
I do support M theory as a step forward to basic string theory.
As a clue: M theorists define their strings as quantum or planck sized bits of energy. It is not too big a step to redefine them as forces.
Regards,
Alex :)