Echo-Echo and Offer-Offer Wave Coupling

[Reiku]

Echo Wave and Offer Wave Coupling Theory

Not sure if this has ever been proposed before, but let’s investigate the notion that two echo waves can couple (much like the mathematical discipline Evanescent Wave Couplings – I say much like, as they deal with electromagnetic waves *)

• In this theory, we have electromagnetic waves, but find that they decay with distance. In a sense, an echo wave, if it does not meet its conjugate with the correct quantum information, the wave will simply cancel out, or as I have speculated, continue to oscillate the imaginary time dimension, or real space until it finally ‘’finds’’ it’s correct conjugated partner.

In a Near Field Conjecture (and Far Field), between two moving waves that are subtly close that their quantum waves can couple, through the theory of ‘’Interference.’’ This may be well known, through the nature of the Double-Slit Experiment, first experimentally conducted by Thomas Young.

When two quantum waves couple, they interfere with each other, and in the case of the Double Slit Experiment, the results where that even if two slits where open, logic would have suggested that more particles would hit the screen, but instead, the waves of probability found themselves entangled, and less particles reached the screen.

If the proposal has never been made before, then I propose it now. Echo waves may couple, in correspondence with two coupled Offer Waves, with all four waves corresponding to each other as a conjugate of each other. In other words, only one of these waves in the coupled echo state can satisfy the correct field of probability found in one of the coupled offer wave’s states.

When two waves like this come together, such as an echo-echo state wave coupling, or interference, coherent in reference to each other, either because they come from the same source (1) or because they have the same or near enough the same frequency.
(1) – This, is I think is related to the quantum action at a spooky distance, where two photons have been created from a single source, and therefore, must be identical… so it stands to reason that two echo-waves can be created also from the same source: Which according to Cramer, exists here and now.

Those who are wise to ‘’ constructive interference’’ of QM, would explain the echo wave to have a constructive interference, whilst (destructive interference), would only work in this case, if the two echo-waves did not have suitable conjugates which contained the correct information… and simply, cancel out, or possibly oscillate into infinity, until it does find a suitable squaring result, if there would ever be one.

So, if the waves are not in phase, such as an echo-echo coupling, then it must be regarded they are either not in phase with each other, or in this other case, the echo-echo waves are not compliant with the offer-offer wave coupling.

Integrating this now, into a mathematical guide:

$$E=E_1+E_2$$

Where E has a state value that is in a constructive interference, and therego, couples the waves. But as stated before, there is also a destructive intereference, where in one case, the undulating waves do not coincide mathematically, and this can be given through the amplitude theory:

$$E=|E_1+E_2|$$ only if $$E_1=E_2$$

So the result leads the information to have a zero amplitude, and destruction of the wave coupling itself. When two sinusoidal waves superimpose, like the Echo Wave demonstration, the wave coupling depends on the frequency amplitude of the waves and relative phase of the two waves. But here, in this work, two echo waves are created, with these characteristics, so long as two offer waves are also created with exactly the same information, but of a negative time direction.

So, using these known facts of physics, we can now deduce that:

A) $$\psi* \psi_i=<i|\psi><i|\psi*>$$

Where

B) $$\phi_i=<i|\phi>$$

… which state the final system as coefficients, defining the equation A) as being an operation where they reduce the $$\psi \psi*$$ as giving a final solution though equation B).

Now…

These operations so far, couple echo wave states |S>, given by the state field value, so we can concentrate on applying the same for two coupled offer waves, working as a negative time wave direction:

A) $$-\psi*-\psi_i=<i|-\psi><i|-\psi*>$$

So the correct mathematical expression for describing the coefficients is best given as:

B) $$\phi_i \pm <i|\phi>$$

So it naturally allows the solutions for both a negative time direction value, and a positive time direction.

When any two of these waves meet, they should be expressed by Dirac Notation as:

$$<(t,1)E|O(t,2)>$$

Which gives a value of 1, that is real.

Why should an Operation even operate in This Fasion?

It depends on what kind of information is being processed in the present time. According to Cramer, it is upon a measurement, on let’s say an electron, do two waves, an offer moves into the future, and an echo into the past, moving in a sinusoidal manner back to the present, switching their terminology where the echo wave now becomes an offer wave from the past, and an echo wave from future.

But if the probability of the measurement somehow ‘’makes the system,’’ have two outcomes, then echo wave coupling and offer wave coupling, now take on new values, so that whatever wave is ‘’accepted when the return to the present state time,’’ the other two waves cancel out. So, to make that simpler, it depends on the amplitude of probability given by the wave function that will inexorably determine a correlation that will either cancel all other probabilities out, or cancel all the information contained if all four wave-couplings don’t have the exact values for the probability field.

 

[AlphaNumeric]

A) $$\psi* \psi_i=<i|\psi><i|\psi*>$$

Where

B) $$\phi_i=<i|\phi>$$

If $$\phi_{n} \equiv \langle n | \phi \rangle$$, ie the coefficient of the n'th basis of $$|\phi\rangle$$ then $$\phi_{i}^{\ast} = (\langle n | \phi \rangle)^{\ast} = \langle \phi | n \rangle$$. This is needed so that $$\phi_{n}^{\ast}\phi_{n} \in \mathbb{R}$$. This is not true for your equation.

A) $$-\psi*-\psi_i=<i|-\psi><i|-\psi*>$$

So the correct mathematical expression for describing the coefficients is best given as:

B) $$\phi_i \pm <i|\phi>$$

Since $$|-\psi\rangle = -|\psi\rangle$$, $$-\psi_{n}*-\psi_n= (\psi_{n}*\psi_{n})$$

So the correct mathematical expression for describing the coefficients is best given as:

B) $$\phi_i \pm <i|\phi>$$

So it naturally allows the solutions for both a negative time direction value, and a positive time direction.

No, because you've just said that either 0 or $$2\phi_{n}$$ is the best coefficients, since $$\phi_{n} = \langle n |\phi \rangle$$ by your post further up. You have to connect two things, one a function of space and one a function of time, in order to have any hope of having a wave-like propogration. You've connected two things which are the same, up to a sign.

When any two of these waves meet, they should be expressed by Dirac Notation as:

$$<(t,1)E|O(t,2)>$$

Which gives a value of 1, that is real.

Where t appeared from? There's no 't' given in $$\phi$$. Besides, even if you hadn't just made the error with the $$\phi_i \pm <i|\phi>$$ thing, $$\phi_i \pm <i|\phi>$$ is, by construction, a number. You are now claiming they are states, which they are not.

You cannot talk about quantum mechanics and waves if you don't know how to construct wave solutions and you don't know the fundamentals of Dirac notation. We've been over this many times. And yet you persist.

Maybe you'll reply with "I've got you on ignore" but it doesn't matter. Someone was going to demolish your work for all to see. I got here first due to my terrible sleep patterns.

 

[Reiku]

I accept that this was a speculation, rather than a mainstream science... so i understand why it is here. Gowd knows what Dr Alphanumeric said, but anyone who will continue following this, i haven't finished, and i am planning to ask Dr Cramer if he has ever considered echo-echo wave coupling, because i haven't seen such a probabilistic relation in his work...

 

[Reiku]

I wonder... Ben. Would you consider moving it back, if he finds this perfectly fine in his theory?

 

[Reiku]

Anyway, i had more to explain, and i will do it in bits.

The state vector equals |S> the primary states of a system, like a wave, so we can talk about intervals of differential vector states, and are integrated always as real processes, the integral giving the function between y and x, where y will represent the Echo Wave, a positive time wave, and x as an Offer Wave, a negative time wave.

$$\int_x^y$$

The integral of x and y, must find themselves by theory to square upon arrival. However, normally we when using a single integral like this one with two points, x and y, we are actually talking about, is x and y having actual relationships as being a measurement between an interval. So a=x and a=b

$$\int_x^y f(x)$$

So since we are dealing with two wave that must multiply, we must find one operating in the positive and negative time directions, give as:

$$\int f(\int f_1,. . .f_2)$$

And

$$\int f(\int f_{-1},. . .f_{-2})$$

So we can make

$$\int_{x,-y}^{y,-x} f(x)$$ →$$\psi \psi*$$ →$$|\psi|^2$$$$=1$$

 

[Reiku]

Of course, the reduction of 1, is when the conjugates have arrived together, but the above in ps. 5, is only a mathematical description of two waves, an Echo and an Offer. I will continue this soon, because there is quite a bit to write about.

 

[Reiku]

In a coupling equation,it would look like this instead;

$$\int_{x,-y+y,-x}^{x,-y+y,-x} f(x)$$ →$$\psi \psi*^{2}$$ →$$|\psi|^{2}^{2}$$$$=1$$

Only if the initial waves contain the correct information in deriving the result of 1. There are a few solutions why it can't, and i'll tackle it later.

 

[Reiku]

It can also be said, that we may even be able to apply the mathematical discipline of the Dirac Delta Function into how we come to see the waves of information in time. They certainly travel at infinite speeds, with the least amount of energy possible, and yet contain an infinite amount of energy at their lowest speeds possible (1).


(1) – A few might disagree with actually saying these waves use or even have an energy, but, the way I see it, is that they certainly contribute to the very ‘’collapse’’ of states which contain energy (like a particle), so in a sense, they may have some type of imaginary energy instead of real energy.

Let’s have a look at the next equation:

$$\int_{-\infty}^{\infty} \delta(x) d(x)=1$$

In this case, we can use this equation to describe the nature of the distribution of the waves, being Echo and Offer Waves by terminology.

And we can even use a measure equation, when dealing with the spacetime theory concerning the relationship to a measurement theory, which are basically the conditions of a spacetime like having x, y and z directions. Such as length, area and volume. The main use of measure theory is as I understand it, to define concepts of integration over a hierarchy of domains with more experiences of using complex systems rather than that existing in real time. This actually opens up the usage of probability curve theory, to express probabilities in the nature of measurements.

$$(\mu_a(S))=(\chi_S(a))=[a \in S]$$

If we could know these things from more intensive math, we could predict them through probability curve theory to measure and possibly map out some kind of system in i how quantum waves operate, even though total knowledge of |S> (the state vector), is absolutely forbidden to be known entirely due to the Uncertainty Principle.

But in a branch of probability theory that does relate with measure theory, is called the Characteristic Function, where we can use probability distributions made in real dimension, hence its usage also with consciousness, since no measurement is ever made but in real time:

$$\varphi - X(t)= \operatorname{E}\left(e^{itX}\right)\,$$

The Delta Function for a measure, is given as

$$\int_{-\infty}^{\infty} f(x)d \delta(x)=f(0)$$

If we are talking about the wave introduced into the spacetime theory, then we can indeed say that it represent the transaction of two waves moving at infinite speeds, as a function that is limited, being the collapse in the wave function by definition.

$$\delta(x)=\lim_{a\to 0} \delta_a(x)$$

It would be interesting to see what would come out of the predictions of such equations when measuring statistics behind them, when concerning the observer. And why the importance? Because Cramers Transactional Interpretation is an Observer-Dependant theory and is an anti-parallel universe thesis, originally.

 

[Reiku]

So here we have

$$\psi (x)\psi*(x)$$

Leads to allow us to reduce this as

$$\psi (x)\psi*(x)=|\psi(x)|^2=1$$

These are of course, able to describe the probability amplitude to be collapsed into a single state.

The variable $$(x)$$ is to allow the outcome to be renormalization, or not.

In further teaching of what I know on this subject, is that the integral is finite $$\psi \psi*$$, Also known as Bohr’s Law, and this is subsequent over a three-dimensional vacuum. Really interesting thing is how reduce this law $$\psi \psi*$$ into a single value of one, isn’t only by finding the absolute square, but by allowing $$c\psi$$ which makes the integral equal to 1 exactly.

The Equation used in Amplitude Theory to describe the probability of a measurement, is given as:

$$P(\varepsilon)= \int_{(\varepsilon)} |\psi(x)|^2 dx$$

Takes us right back to my probability equations i created, showing the probability between not only duration, but also found by squaring the conjugates,

1) $$P_{12}|t_1(a_2,b_2)|^2=|(\Delta S)t>,|(\Delta S_f)t*$$

And for the conjugate

2) $$P_{12}|t_2(a_2,b_2)|^2=<t(\Delta S),|<t*(\Delta S)|$$

To solve this, as a field of probability, when amplitude is involved in the notions, or works... what have you, i state:

$$|P(\psi)|=B exp(iab-i*a*b*)$$

As an equation that can help reduce the probability when upon a measurement.

 

[Reiku]

Can't get a hold of Dr Cramer, however... I asked Dr Wolf why i haven't ever seen this proposal, and this was his response:

''Fred Alan Wolf: Because they don't add together. I do admit that although
I have brought Cramer's idea to the popular audience that I think it
deserves, I do have some conceptual difficulties with it such as the one
you've raised here. Each wave in the pair starts from a different place and
time. That part is OK as far as interference is concerned, but one wave
(echo) travel backwards in time and already modulates the other (offer) at
every point of space and time along the common spacetime pathway. Hence
they are already (interactively) combined the instant the offer wave
appears. The only difference is how and where the echo modulates the offer
which depends on the final state of the experiment (the observation that is
carried out).
So this already modulated wave cannot interfere with anything else.
Cramer's idea was invented to account for the 2-slit experiment and the EPR
effect and other paradoxical thought experiments. In what follows
probability =offerXecho.
In the 2-slit experiment the offer wave goes through both slits, but
(case I) in the event the particle is observed through one slit (say slit-A)
and the final screen the echo only travels back in time through that slit-A,
while (case II) if the particle is not observed at either slit (slit-A and
slit-B) but only on the final screen, the echo travels back through both
slits. So we have in case I offer=A+B, echo=A*. In case II offer=A+B as in
the first case, but echo=A*+B*. Results are for case I,
offerXecho=probability=A*A; case II
offerXecho=probability=(A+B)(A*+B*)=AA*+BB* +BA*+AB*. The last two terms
(BA*+AB*) in case II are the interference terms which give rise to the
different pattern on the screen. If the quantum physics interference was
not present we would only have the normal distribution of either slit
(AA*+BB*) as in the case of baseballs or classical objects where in the
interference terms are too small to be seen due to the high frequency of the
waves themselves effectively canceling each other out over any finite time
interval in which the observation of the baseball is carried out. ''