A spectrum to space - the view from inside a crystal radio receiver?

[SteveA]

I had an interesting idea that I intend to pursue more but it's interesting enough in the areas it could potentially link together that I wanted to post the beginning of it here.

The first thought is we should have some simple mathematical operations to describe at least the apparent motion of objects in space from a first person perspective.

The obvious one is of horizontal and vertical rotation, in which case these are easily described by circles in trigonometry and we can begin with trying to describe a simple mechanism to move a circle around in various manners in space relative to an observer.

We have a few operations like determining the elliptical ratio as well rotations and offsets.

Now we can also consider such a circle to be drawn at some frequency or wavelength and effectively it could be a single point sweeping over a cycle. This would make moving these circles around similar to viewing the progressive growth, or shrinkage of a spiral over time.

Now let's compare this with the operation of a radio receiver - we can tune to various stations and this alters the base/reference frequency. If we perform a simple multiplication of this, we get heterodyning http://en.wikipedia.org/wiki/Heterodyne and we're computing basically the sums and differences of our reference frequency with the signal we're analyzing.

This creates redundant mirror images in the signal and the general technique then is to construct a lowpass filter in order to isolate only one version of this signal. (We can ignore the IF amplifier in a typical radio if we have components that are perfect resonators)

The simplest filter is constructed by simply summing two samples in time together. This creates a "comb filter" http://en.wikipedia.org/wiki/Comb_filter, but a comb filter generates periodic repetitions in a spectrum, though if we simply string together a very large number of such filters, similar to a transmission line we can remove this artifact.

What we then have are a series of what I believe are called "half cosine filters". Basically we're just summing together two "adjacent" points in a signal and constructing another signal for which similarly we sum together two adjacent values and we simply repeat this.

If we look at the frequency response of such a filter, we can see this delay in time to be equivalent to summing two phase shifted points of a sine wave (this can be closely associated with memory).

a(t)=sin(f*t)+sin(f*(t-1))

Notice that the peak value of a occurs when f*t and f*(t+1) are symmetrically centered around pi/2, in which case we have an amplitude of sin(pi/2+f/2)+sin(pi/2-f/2) and these two values are equal, so we can rewrite this and normalize the gain to a maximum of 1 at a frequency of 0 and rewrite this in terms of a cosine as cos(f/2).

If we stage n of these filters serially, the response then becomes an exponential decay of cos(f/2)^n.

Now we had previously offset the frequency via. a multiplication with a reference frequency, p, which is sin(p) and this multiplication with the source signal, sin(s), creates the response (via. the product to sum identity http://en.wikipedia.org/wiki/List_of...ric_identities):

sin(p)*sin(s)=(cos(p+s)+cos(p-s))/2

Now we must assume our signal p is significantly larger than 0 (in other words, we're not looking near the "origin" of space as we would then see a mirroring of our signal within the "passband" of the filter) and that our filter response, cos(f/2)^n is sufficiently narrow to reject the cos(p+s) component, such that we have a "small" value of p-s, near 0.

Then the apparent response of this with respect to changes in the frequency, p approximately follows the form cos((p-s)/2)^n.

Let's rewrite this as d=(p-s)/2 to denote the distance or difference between our reference point in a spectral space and let's also write the cosine function in terms of its Taylor series expansion http://en.wikipedia.org/wiki/Taylor_series:

cos(d)^n=(1-d^2/2!+d^4/4!-d^6/6!+...)^n

The most significant term for d~=0 is the d^2/2! term. To keep things simple, we can assume a rescaling of d by sqrt(2) and remove the division by 2.

Now we have a first order approximation of cos(d)^n=(1-d)^n and notice also that on infinitesimal scaling we also have 1-d~=e^-d, and similarly for d~=0, we have, for a constant scaling value, a, cos(a*d)^n~=1-(a*d)^(2n)~=e^-(a*d)^2n (and again, these are under the previous assumptions (in order to construct the first order appearance of a "flat" Euclidean space ) of n>>|p|>>|p-s| ... as always, it's important to keep our infinities sorted out , though I left their specific relationships unspecified, but constructing various relationships between these could, in itself, provide a "signal" to receive and considering that n is constructed of the equivalent of quanta and we have 3 "dimensions" to view as determined by n, f and g, where f(n)~=g(n) and similarly n >> p=f(n) >> |f(n)-g(n)| ).

Also, many consider space time to be describable by 4 dimensions, but this is not inherently true relative to an observer as an observer, such as the Earth can specific all events in space in terms of a time (similarly altitude) and two angles of rotation. Notice that time and distance are equated in physics, hence it is redundant to both contain time and a distance value as a description of an event. The only reason this is done is to "objectify" the view in physics and attempt to simultaineously describe many observers views, but this later fails when we then consider ourselves to both be able to localize them at a distance as well as synchronize the time (and then we have created two unknowns, where there is only one).

So we have a description that constructs a potentially finite and closed 1-D "universe" with positions specified in terms of spectral characteristics and a "local" bandwidth gain approximating a gaussian form (close associations with atomic properties and Pascal's triangle here)

Let's consider that we have a highly chaotic spectrum and that we're trying to isolate some signal within this. In this case we can assume a very low signal to noise ratio http://en.wikipedia.org/wiki/Signal-to-noise_ratio.

If we have a constant amplitude signal at some frequency, s, and we "move"/tune our reference, p, near s, then the amplitude of this signal changes relative to (I'm skipping constant scaling factors and generally working with just the first order approximations, though these details are not insignificant over large distances and can create distortions to the perception of space when n is finite) cos(|p-s|)^n~=e^-|p-s|^2n.

Now if we look at the theoretical lower limit for the capacity of detecting information, we have a Shannon limit http://en.wikipedia.org/wiki/Shannon...artley_theorem of:

C=B*log(1+sig/noise), where B is the bandwidth of the signal (though we should similarly include a constant scaling factor if we want to determine a level of confidence), s and n are the amplitudes of the signal and "noise" respectively and C is the equivalent quantity of information.

With a fixed bandwidth (and level of confidence), we then have C proportional to:

C~=log(1+sig/noise) and sig~=(e^-d^2n)^2=e^-d^4n, so
C~=log(1+(e^-d^4n)/noise)

With noise>>sig, once again ignoring scaling, we have (e^-d^4n)/noise near 0 and log(1+sig/noise)~=sig/noise

In this case, with a large noise (we can assume a chaotic vacuum energy) the minimum theoretical signal is proportional to the energy of it, though large signal energies can appear distorted in size and "shrink" due to a large "mass"/energy of it is not true that noise>>sig, because we then approach the logarithmic "distortion" to the linear approximation.

There are still lots of additional things to look at, but overall it's a very interesting model how motion in space could be perceived as sweeping through a spectrum of "channels" of information and the associated distortions that would appear to exist "moving" past these along with properties associated with distortions arising from a finite "universe"/spectrum as well as distortions arising from a "saturation" of energy in a space creating an appearance of a non-linearity in its information content as it begins to approach densities of a potential chaotic vacuum energy.

And all this from something, in many ways, more simple than an old crystal radio set.

I've also previously found some rather interesting structures embedded with chaotic noise sources, such as this from analyzing various delayed versions of the evolution of a logistic function.

Look at the 6th image in this:
http://www.toequest.com/forum/member...art-logic.html

This is also similar to my comments regarding folding a "time line" of a single deterministic algorithm to generate different dimensions of data.

Anyway, there do appear to be many correlations with physics in this, though if this model is correct, then there are also many areas of distortions that can be looked at, including what occurs when p~=0 and we look at the "origin" of space (That could be a fun spot to check) as well as how the divergence between the parabolic form ("flat" or Euclidean view) and the cosine form ("closed"/warped space) can affect the appearance of physical properties on different scales.

There should also be simple mechanisms that can be added to this to generate rotations in perspective (and this could potentially arise if we use the imaginary components of rotation as well).

P.S.: No, I don't think a truly "objective" universe is closed, but in terms of a finite set of physical properties making the measurements, then yes, we should expect that to only describe a finite component of it.

[greenbug]

angular momentum?

http://en.wikipedia.org/wiki/Angular_momentum

or linear momentum?

http://en.wikipedia.org/wiki/Linear_momentum

[SteveA]

angular momentum?

http://en.wikipedia.org/wiki/Angular_momentum

or linear momentum?

http://en.wikipedia.org/wiki/Linear_momentum

Perfect comment! Thank you

I think it's fundamentally a linear momentum in an infinite space (or at least beyond distances we can physically measure), and this mismatch in scales makes the universe seem cyclic, curved or closed but that's more of a distortion created by the structures used to describe it because it's only properties of those structures that allow for an extended measurement to be made.

An expanding circle or spiral might better describe some of the properties of how the two views mesh.

[greenbug]

Relativity is spherical, it acts from a central point out in all directions.

Lets say we have a fish tank. If you think of light as moving threw the medium of air and hitting the dense medium of water it bends inward toward the water. If that fish tank was wrapped around in a circle, rather then a flat plane, light will always bend inward toward the center. Now if you consider that matter bends space-time and time is slower at the surface of our planet then any object moving in space is moving threw a medium of time less dense then what is at the surface. Then you can see why gravity is the property of bent space-time. It is a spherical interaction and not just linear. Yet their are cases where because information can not be faster then the speed of light, space maybe bent, folded or creased along a line that is not spherical to where it began. It is something you have to consider.

We do live in a 3 dimensional universe and allot of the actions we see will be procreated along all of those dimension instantaneously. But From what I've seen, like the example given above due to the speed of light, is that there are actions that take place using less dimensions and not all three. So what we should take notice of is why and how the singular dimensions work and act in laws or rules that combine to give the effects that we see in the physical world we experience.

[SteveA]

Some of your comments reminded me of thoughts I'd had regarding properties that could make the appearances of vortices expected from a bending of space.

Let's first say for a second that we have a point origin to a signal that is spread out through chaotic pathways and similar to a bat or dolphin using sonar, we want to view the environment via. reflections. If there are many background sources of "noise" then the signal needs to have a precise manner to be detected and let's assume for a second that it is of a specific frequency.

Now if there are multiple reflections, then these can cancel or reinforce each other in different ways, though we should never see a larger amplitude of energy than what was emitted and if we look at the phase shifts that could be present, we could map all expected reflections in terms of amplitude and phase as lying within a circle with the radius being equal to the emitted energy and the angle of rotation being the measured phase shift relative to our reference phase.

(I have to leave soon, so I'll try to make this quick)

If our, believed to be singular, path of emission was actually diffusing over multiple pathways, then we could experience cancellations.

If we had multiple pathways orbiting in different manners around an observation point then we could witness the appearance of discrete pathways of space as being the subset of pathways for which only reinforcements in the phases occured.

For for example, let's say we emit light in some direction to see an object and then we witness the reflection. If there are multiple pathways this light is travelling and these continually reintersect in space, then we have many pathways that will cancel in influence. The greater the number of "reintersections" the greater the influence of each cancellation is and for example, two versions of our reference that are phase shifted by 10 degs (or 1/36th of a wavelength) reduces the amplitude of the returning signal by cos(pi/36)~=.984 or approximately 1.5%, but if this continually recurs through space and let's say we have 100 such reintersections, then we only detect (.984^100)~=.2 or an 80% reduction in the amplitude. If we have 1000 such reintersections, this drops to ~1x10^-7, which could be practically undetectable.

If we took two parallel lines and constructed a lattice of interactions between them and emitted a signal along this, we could see coherent interactions along its length and a complete reflection of the emitted signal, but now if we bent this, we could generate the appearance of discrete angles of interaction for which no visibility occurs between.

Similarly if we had a large number of concentric circles and such a lattice structure connecting between these, we could find the appearance of discrete orbitals or self sustaining loops external to the origin as well (those these would not necessarily be directly obvious or interactable with, by modulating the reference it could be possible to indirectly detect the existence of them, similar to an inertia or time constant to the system).

Anyway, I think along similar lines we can generalize most any form of medium and computation and construct the equivalent of such forms of reinforcing and non-diffusive transportation of information as well as "obstructions" with spectral characteristics when information interacts with itself destructively.

[SteveA]

Here's an interesting correlation between atomic orbital shells, quantized spectral information and a spacial vortex.

If we assume a constant velocity motion through space, such as light speed, and a discrete quantization to space, such as plank units as well objects that possess discrete quantities of energy that come with spectral characteristics and can be equated to a quantities of information in terms of 1 of n selections, consider the model of a vortex with discrete rings.

We have a central origin and objects orbiting around it. If they're moving at a constant velocity and can convey information in 1 of n states, then they must be moving through discrete positions located symmetrically around the center (at displacements of 2pi/n) and the radius or distance from the center should be proportional to n (in a 2 dimensional plane).

If we combine together two objects, one having 1 of n states and the other having 1 of m states, then together they could determine 1 of n*m states. This could be similar to an excited orbital of an electron (and also describe to an extend the shape of the orbital shell).

If we have n as a prime number, then n could not be factored into anything smaller and would be the lowest orbital shell or if we had two rings in this describing 1 of n and 1 of m states, then if n and m share no common divisors, there is no single jump possible between these two rings (unless they combined with a pair of objects describing a ratio) and they would appear similar to two distinct spectral lines.

Something else to consider is the manner in which these orbital positions around a nucleus could be determined (if there's no way to differentiate between these positions, then they would not be detectable as distinct).

If we have some quantity of protons in the nucleus and at any point in an orbital a distinct relationship to this set of protons could exist then we have it very likely that larger numbers of protons allows for larger numbers of orbitals (and this is the case). As a possible example, imagine that we have an electron "viewing" a nucleus with 3 protons and we'll label them A, B and C. If it was able to determine an ordering of nearest to furthest, then we have six possible positions that an electron could be relative to the atomic nucleus as ABC, ACB, BAC, BCA, CAB or CBA.

For a chemical interaction, imagine that we have two atoms, each describing 6 possible orientations in space and their combined information in that respect is a total of 1 of 36 possible configurations. In order to conserve information (not required, but consider that we could not determine much of anything regarding physical events that destroyed information because the information would not be available to verify whether or not it was conserved! It's cheating if we tried to "remember" the information, because then we're already interacting and extracting the information and so we'd be replacing the information it contained and not duplicating it).

We could have a single electron orbiting the pair at the "36th ring" or, if we could distinguish which was which (which we may not be able to do), we could have a pair orbiting at a distance of 6 each, or various combinations for which n*m=36 (sort of a superposition of possible orbitals).

An object describing 1 of 5 states would be chemically non-reactive relative to this because we can't factor 36 into 5th precisely (though we might assume the existence of a virtual particle describing an rational ratio such as 5:6 could be present), though an object in 1 of 3 states could potentially interact coherently with this pair of "atoms" describing 1 of 36 states and, for example, "pull off" a factor of 3 from 36 making the pair describe one of 12 states instead and move that ratio of 3 into raising/exciting the "orbital shell" of the second atom to become 1 of 9 states (there's another issue with synchronization in time here and how these might appear to be interleaved in time).

Anyway, if we looked at this in terms of a vortex, we could see a highly complex multidimensional structure of interactions across rings at various distances appear to exist as well as exchanges of particles or information across these and if we assumed it was all done in a constant velocity space, then these rings could appear to fold back into complex toroidal shapes and having irregular prime related spacings in their distances.

.... I know this isn't necessarily easy to follow, but I have found these features tend to arise in most forms of (non-linear) computation and I even suspect there's a way to translate computations into an equivalent shape of a uniform computational medium. For example, it's likely we could even have something like a bottle of water perform computations and alter those just by shaping the bottle differently and determining the spectral characteristics over time.

Oh well, that's just some ideas that I've been kicking around for a while, but it's definitely a complex subject and relates to many of the leading areas of research in science.

[greenbug]

This reminds me of my idea for gravimetric viewing. The idea is that gravity is detectable, hard to detect small amounts but if you could cancel out all the other gravimetric waves it would be easy to detect them. My idea for canceling out other gravimetric waves..

If you had three atomic clocks attached to a device, yet each on their own arm, and in triangular fashion. If you spin each of these arms fast enough the time on the clocks will slow down. Because matter bends space time, time would be slower nearest to an object. You could then slow each arm down detecting differences in time and triangulate where those differences are coming from.

The cool thing about this is that gravimetric waves move threw objects. So you could create a virtual image of the surrounding aria, even threw walls. Depending on how fast you spin the arms and how precise each clock is, you can remote view any where and every where.

In continuation you could also use the same concept to communicate over long distances with the device at the speed of light with no noise or interference, because you would be effectively canceling it all out by focusing the triangulation precisely.

Originally I thought you might communicate faster then the speed of light, but gravimetric waves move at the speed of light so..

[SteveA]

Your idea reminds me of something similar I'd thought of as well

With regard to gravity traveling the speed of light ... I'm still mixed on that one. I don't think gravity is due to a single force either but a statistical result of many chaotic influences (that primarily cancel in influence, hence gravity appears weak, but I assume that's because we haven't untied the knots yet).

As an example of saying gravity travels at the speed of light, if black holes can exist, then how can gravity escape where light cannot?

Notice on the other hand that if gravity was not a single force but a chaotic collection, then we could have gravity communicate faster than light, but not coherently (no gravity waves yet either, which makes sense if it is not a coherent motion through space) and in that sense we would not necessarily be able to communicate faster than light using gravity because though components could be faster than light, we could not control those components (at least not yet).

[greenbug]

I did think at first perhaps gravity was faster then light. What would this mean. It would mean that all things are relative instantaneously. In some cases this is true in QM but there is a bottle next in exchange of information, only so much information can pass so fast and this eventually brings about the speed of light. The problem is with relation, when too may things are in relation, relation brakes down. Reality becomes a matter of contrast.

I've been reading some articles recently one man speaks of time being an illusion, that it does not exist. Trying to think of how this would work perception becomes contrast that warps reality and that in turn creates the perception of time. Time then becomes the perception latency, lag, or inability to understand all the information at the same time. Which with out an observer reality might exist but time would not. But physics explains the world threw perception so I don't see how explaining the world that way would do any good. That and the information threw contrast is infinite, no point of the real would is ever stable, the only thing that would be stable would be the perceptions. In which relativity explains how the perceptions remain relative to each-other vaguely. I think commonality would be precedence for perceptions, in which a common ticking of a clock is born. Other wise we would all float off into infinity never able to reach commonality.