# 7d Physics

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7d physics [1][2] is a mathematical theory of physics that describes particles in 6 dimensions of space and one of time. It uses confirmed physical theories to present a new, simplified view of what these theories describe.

The theory itself is simple: Space has axis(s) orthogonal to the standard 3 dimensions of space we observe in day to day activities. Matter is composed of photons with a velocity component in an additional dimension (or dimensions) of space.

No amount of experimentation can ever prove me right; a single experiment can prove me wrong. Albert Einstein[3]

## Definitions

3dspace: 3-dimensional space.

Orthogonal dimension: Another dimension of space in which photons travel.

${\displaystyle \theta }$ : angle from 3dspace axis
${\displaystyle \lambda _{\text{orthogonal}}}$ : a particle's Compton (or orthogonal component) wavelength
${\displaystyle \lambda _{\text{3d space}}}$ : a particle's de Broglie (or 3dspace component) wavelength
${\displaystyle \lambda _{\text{total}}}$ : the photon's complete wavelength

## The relationship of Compton and de Broglie wavelengths

Let's start out with a mathematical demonstration of the theory, with an electron.

Electron mass: 510,998.910 eV/c2 [4][5]

Electron (rest mass)energy: 510,998.910 eV [4][5]

Planck constant in eV s: 4.13566733 × 10−15 eV s [4][5]

Speed of light in vacuum (c): 299792458 m/s [4][5]

Let’s find the frequency and Compton wavelength [6] of a photon with this energy.

ƒ = E/h = 510,998.910 eV / 4.13566733 10−15 eV s = 1.23558998 × 1020 Hz

Compton wavelength [6] = c/f = 299792458 m/s / 1.23558998 × 1020 Hz = 2.42631021×10−12 m

Now we are going to accelerate the electron to .5 c (cos 60 * c) and calculate its de Broglie wavelength [7][8]. The equation for the de Broglie wavelength is:

${\displaystyle \lambda ={\frac {h}{mv}}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}$ [7][8]
${\displaystyle \lambda =4.20249256\times 10^{12}{\text{ m}}}$

Let’s determine what the total wavelength of the photon (the electron) is.

To find the total wavelength, we have to invert the wavelengths, square them, add them together, take the square root of the result, and invert the result of this. Note that the deBroglie wavelength of the particle is the particle’s 3dspace wavelength component and the Compton wavelength is the particles orthogonal component (it is more descriptive to use the terms 3dspace and orthogonal).

Here is the equation to check ********:

${\displaystyle \lambda _{\text{total}}={\frac {1}{\sqrt {({\frac {1}{\lambda _{\text{3d space}}}})^{2}+({\frac {1}{\lambda _{\text{orthogonal}}}})^{2}}}}}$
${\displaystyle \lambda _{\text{total}}={\frac {1}{\sqrt {{\frac {1}{4.20249256\times 10^{-12}m}}^{2}+{\frac {1}{2.42631021\times 10^{-12}m}}^{2}}}}}$

so:

${\displaystyle \lambda =2.10124628\times \ 10^{-12}{\text{ m}}}$

Let’s calculate our total energy from the wavelength:

${\displaystyle E={\frac {hc}{\lambda }}}$

so:

${\displaystyle E_{\text{total}}=590050.717{\text{ eV}}}$

Let’s go ahead and check this against the result from the standard relativity energy equation[9][10][11][12]:

${\displaystyle E={\frac {e}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}}$
${\displaystyle E={\frac {510998.910eV}{\sqrt {1-{\frac {(.5c)^{2}}{c^{2}}}}}}}$
${\displaystyle E_{\text{total}}=590050.716{\text{ eV}}}$

It's the same, except for a slight error due to rounding. We can see a direct mathematical relationship linking a particle's Compton Wavelength (orthogonal or rest mass component equivalent energy) and its de Broglie Wavelength (3dspace component) which accurately gives us the particle's relativistic energy.

The significance of the de Broglie wavelength's relationship to the Compton wavelength is that this wavelength is physically expressed in 3dspace (electrons diffract according to their de Broglie wavelength which implies it is an actual wavelength rather than a mathematical equivalence). Of course, this makes the relationship with the Compton wavelength all the more important, as we can see that this relationship directly implies vector addition- exactly as the velocity equation in the next section does. Basically, it looks as if de Broglie wavelength's confirmation via electron diffraction is evidence for at least one more dimension of space.

## Some simple trigonometric relationships

We can also determine the angle of the photon from the 3dspace axis and all of its component vector magnitudes with simple trigonometric functions. If we know the velocity of the photon along the 3dspace axis, we can do something relatively simple. Since the total velocity of the photon is broken up into these components:

${\displaystyle v_{\text{total}}={\sqrt {v_{\text{3d space}}^{2}+v_{\text{orthogonal}}^{2}}}=c}$

We can take the inverse cosine of the velocity unit vector component along the 3dspace axis divided by the total velocity of the photon. In other words, the inverse cosine of (.5c)/c (the scalar is taken out) gives us the angle away from 3dspace (for a particle moving a .5*c (or c/2)). If we know the total relativistic energy of the photon (particle) we can use the angle to generate its 3dspace and orthogonal component vectors.

${\displaystyle \theta =\arccos {0.5}=60}$

Say we know the relativistic energy of this particle, how do we find its rest mass energy (the orthogonal component of the photons energy)? Simple trigonometric calculation in 7d physics:

${\displaystyle e_{\text{rest mass}}=\sin \theta \times E_{\text{total}}}$

${\displaystyle e_{\text{rest mass}}=\sin 60\times 590050.717{\text{ eV}}=510998.910{\text{ eV}}}$

Likewise if we know the photons rest mass energy component and its velocity, we can take the inverse cosine of the unit vector (v3dspace/c), get the angle, divide its orthogonal (rest mass) energy by the sin of the angle and get its relativistic energy:

${\displaystyle v={\sqrt {0.96}}c}$
${\displaystyle e_{\text{orthogonal}}=510998.910{\text{ eV}}}$

${\displaystyle \theta =\arccos {\sqrt {0.96}}=11.5369590\,}$

${\displaystyle E_{\text{total}}={\frac {510998.910}{\sin {\theta }}}=2554994.55{\text{ eV}}}$

Go ahead and check this result against the standard relativistic energy equation.... you'll see that the results are the same.

Energy is a vector in space with 6 dimensions, rather than a scalar quantity (I prefer to define it this way as the direction of expression is a property of the particle and effects all of its interactions- perhaps I am semantically challenged but...).

Eventually we will talk about how fermions can be reflected using photons, reversing their charge while the photon reflector’s momentum is redirected orthogonal to 3dspace (the photons no longer have presence in 3dspace, although their momentum in 3dspace may be transferred to the fermion, as the fermions orthogonal momentum is transferred to the photons which become dark photons (photons with velocity component only in orthogonal space)).

## A couple more demonstrations

If we have the velocity of an object in 3dspace, how do we calculate the angle of the photon from the 3dspace axis?

The velocity component of the photon along the 3dspace axis can be used to calculate the photons angle (θ) from the 3dspace axis.

${\displaystyle v_{\text{3d space}}=\cos \theta \times c}$
${\displaystyle \cos \theta ={\frac {v_{\text{3d space}}}{c}}}$
${\displaystyle \theta =\arccos {\frac {v_{\text{3d space}}}{c}}}$

If we have the orthogonal (rest mass) energy and total (relativistic) energy of a particle, how do we calculate the velocity of the photon along the 3dspace axis?

First, we need to realize that the orthogonal (rest mass) component of a photon’s energy is:

${\displaystyle e_{\text{orthogonal}}=\sin \theta \times E_{\text{total (relativistic)}}}$

From this we can deduce the angle of the photons travel relating it to the 3dspace axis:

${\displaystyle \sin \theta ={\frac {e_{\text{orthogonal (rest mass)}}}{E_{\text{total (relativistic)}}}}}$
${\displaystyle \theta =\arcsin {\frac {e_{\text{orthogonal}}}{E_{\text{total}}}}}$
${\displaystyle v_{3dspace}=\cos \theta \times c}$

How do we find the de Broglie wavelength (3dspace component of a photon’s wavelength) with only the photon’s total energy (relativistic) and angle of travel from the 3dspace axis?

${\displaystyle \lambda _{\text{total}}={\frac {hc}{E_{\text{total (relativistic)}}}}}$
${\displaystyle \lambda _{\text{3d space(deBroglie)}}={\frac {\lambda _{\text{total}}}{\cos \theta }}}$

Likewise, how do we find the photons orthogonal (Compton) wavelength component?

${\displaystyle \lambda _{\text{orthogonal}}={\frac {\lambda _{\text{total}}}{\sin \theta }}}$

From this, how do we find the photons orthogonal (rest mass) energy component?

${\displaystyle e_{\text{orthogonal}}={\frac {hc}{\lambda _{\text{orthogonal}}}}}$

## An orthogonal perspective

### On dark energy and dark matter

Dark energy[13] and Dark matter[14] interact with matter and photons in 3dspace, creating the apparently random quantum fluctuations that are currently referred to as vacuum fluctuations or vacuum energy. Einstein is right: God does not play dice with the universe.

These variables aren’t hidden: they are detectable, in fact, the “random” paths traveled by 3dspace particles are indications of Dark particles interacting with 3dspace particles (not some inherent magical property of particles that allows them to behave without cause).

Dark Photon: a photon with momentum (and thus velocity) only in a dimension orthogonal to our own.

### On the shape of the universe

As dark matter is simply matter anchored in a 3dspace dimension adjacent to our own, we can perceive that these other "dark dimensions" are slices of the universe as a whole with their own portion of the universes energy and space. Dark energy is just anchored in the orthogonal dimensions so there could be many orthogonal dimensions as well (single slice orthogonal dimensions).

#### The early universe

Another 3dspace dimension orthogonal to our own provided the gravitational pattern that caused early star formation in our otherwise "pristine" or uniform dimension. If you feel like infinite regression shall ensue, perhaps you are right. Suppose that there are many 3dspace universes parallel to our own, offset orthogonally, each one seeding the universes located next to its gravitational fields with patterns (shifting from universe to universe, the fields appearing as if they originated from dark matter). So an initial uniform distribution of energy in an early state universe will eventually be effected by the gravitational fields of universes beside it, which in turn effects the universes beside it. From far off (many universes away) the gravitational fields will average (say several trillion light years distant in the orthogonal direction) so that there is a uniform force upon the early state universe. As the universes are seeded and seed the universes next to them, the pattern of gravity becomes sharper and eventually when a formed universe (with gravitational clusters, galaxies, etc.) is close enough to an early state universe the early state universe is seeded. The question is, if this scenario is true, what happens to old universes?

### On gravitation and the expansion of spacetime

All matter, dark and "normal", pulls space into itself at a rate determined by its mass, stretching existing space. This creates an acceleration towards matter when matter is close together (gravitation), however when matter is far enough apart the stretching of space caused by space consumption leads to expansion of space between groups of matter. This expansion of space due to stretching is uniform throughout all space, however the "consumption" of space is localized around matter (space "consumption" being the reason for gravity). The rate of stretching exceeds the rate of consumption.

### On proton (and W, Z+, and Z− bosons) mass and composite particles in general

One 'orthogonal viewpoint' is that the mass of composite particles is due to an additional type of elementary particle that exists orthogonal to (or alongside) our 3dspace dimension, a particle of dark matter that is bound to the quarks of the proton (quarks are particles that exist in both orthogonal and 3dspace dimensions in 7d physics) or the photon (3dspace) component of the W, Z+, or Z- Boson.

There is another explanation for a proton's mass: the quarks are moving at relativistic speeds (orbiting one another, etc.) and the mass is due to the 3dspace energy component of the quarks. However, if 3 particles "stick" together (having their relativistic kinetic energy added to the composite particles total energy/mass) it may indicate that the particle gains more orthogonal energy.

Composite particles can have components that exist entirely in the orthogonal dimension (there may even be completely orthogonal composite particles and completely 3dspace composites). Keep in mind that the particle can be seen as a single entity (although it is made up of more than one photon moving in various directions through the dimensions of space) for the purposes of determining its total energy and/or de Broglie (and Compton) wavelengths.

### On the simplification of physics

Many of us recall learning how complicated the Ptolemaic (geocentric model[15]) equations for the movement of planets are compared to the Galilean (heliocentric model[16]) equations. The complicated geocentric equations, with their extra variables, etc. were not the most efficient means of predicting the movement of the planets, nor were they entirely correct. This was simply because of an incorrect perspective (geocentric) that the equations were built around, and indicates nothing faulty in the reasoning leading up to them (other than an incorrect assumption). In fact, the generation of these equations involved far more thought (and perhaps greater intellectual capacity) than the simpler heliocentric equations that followed.

Likewise, the current physical models centered around the perspective of 3 dimensional space may be more complex than necessary- even though they accurately describe probabilities of certain occurrences. If we shift our perspective from 3dspace to 6dspace we may find that these complex probabilistic models can be replaced with simpler deterministic models that take into account the action of dark photons and their fields upon the paths of quantum scale particles. We might even find the 3dspace-centric perspective is incorrect- rather the orthogonal dimension is the originating dimension of energy. As we already know that particle energy, charge, spin, etc. are quantized (except for 3dspace relative velocity energy), perhaps we will develop an energy/particle model similar to Bohr's model of the atom [17][18] with orbital quantization.

### On spin, charge, and quasicharge

Particles (fermions) with presence (or velocity) in both 3dspace and the orthogonal dimensions have a spin of ½. Their angular momentum (a quantized quantity) is divided equally between the dimensions (as a photon, they have a spin of 1, while "travelling" in both dimensions they have a spin of ½). As to the spin 1 particles with mass (which indicates an orthogonal component of velocity), they could be composite particles made of photons in our dimension (spin 1) and fermions (which accounts for their mass) in our dimension. Note that fermions move about in 3dspace, but are anchored to it relative to orthogonal dimensions so instead move space into or out of 3dspace (for this portion of their velocity).

The charge of particles is simply the direction of "travel" in the orthogonal dimension.

Quasicharge: similar to charge, but along another axis of the orthogonal dimension

Demicharge: similar to charge and quasicharge, but along the third axis of the orthogonal dimension

The quasicharge and/or demicharge of particles such as neutrinos is only directly felt by particles with like or opposite quasicharge/demicharge. Oppositely charged particles attract, same charged repel- likewise oppositely quasicharged particles attract and same quasicharged repel one another. Quarks with 1/3 charge could have 2/3 quasicharge, or 1/3 quasicharge and 1/3 demicharge, or 2/3 demicharge. Neutrinos can interact with the quarks of protons (but only ones with similar, albeit opposite, orthogonal direction: quasi or demi).

## Testability, falsifiability, etc.

It's very important to check this, and all theories, for testability, to see if they are truly scientific.

Is there a method with which to test this theory (or aspects of it)?

Can this theory be proven to be wrong?

Does it cover to broad of a scope to be falsified?

Is it correct to keep the basic premise of the theory (more spatial dimensions) and alter the theory to account for new information learned, gathered, and compared to previous knowledge?

### Test methods

Gravitational tests: Dark matter should have an exact orthogonal distance from 3dspace matter (in addition to 3dspace distances). This should allow us to detect the mass of the dark matter, it's distance, etc. by its effects upon 3dspace matter. The problem is sensitivity of test instruments- and length of time for tests that rely on galactic observations.

A gravitational test should indicate the center of mass of an object made of dark matter, even if its center of mass is offset orthogonally, its total mass would cause its speed to change in relation to other mass that it passes by/through so we should be able to determine if it is an object of larger mass with an orthogonal offset (the distance its 3dspace dimension is from ours), or an object of mass that is simply moving through our 3 dimensions of space without interacting with "regular" matter.

Could dark matter simply be particles with such small wavelengths that they miss everything? Would this allow them to slip past regular matter without being in an orthogonal dimension?

"Anti"-gravitational tests: Dark energy could have exact 3dspace and orthogonal distances from specific locations as well as specific field strengths. Can we find local concentrations of dark energy or is it evenly distributed throughout spacetime like the CMB? We already know that the universe (space) is expanding more or less evenly anywhere we look (on average, except for gravitational effects), and dark energy has been postulated to be the cause of this.

#### Note to astrophysicists

It is probably already known, but we can determine whether or not dark matter is simply present in a compactified form in our dimension of 3dspace (as in KK theories) or it is present in a "large" dimension some distance orthogonal to our own (as in this theory, and other higher dimensional theories with large dimensions).

If it is present at some distance orthogonal to our 3dspace dimension, we should be able to tell by the dark matters gravitational effects.

Dark matter with a center of mass offset orthogonal to 3dspace would have a slightly different gravitational geometry than 3dspace objects. The radius from the object's center of mass would have a set minimum in 3dspace (the distance from 3dspace to the dark matter's center of mass). At this minimum radius, the gravitational acceleration due to the object would approach a mathematical limit (equaling zero at this point as the object cannot accelerate orthogonally). This minimum radius would be the closest point in 3dspace to the object.

The radius from the object's center of mass is calculated with these formulas:

r_3dspace= Distance from point closest to dark matter in 3dspace to measurement location in 3dspace.

r_orthogonal= Distance from point closest to dark matter in 3dspace to location of dark matter's center of mass orthogonal to 3dspace.

${\displaystyle r_{\text{total}}={\sqrt {r_{\text{orthogonal}}^{2}\ +\ r_{\text{3d space}}^{2}}}}$

With this radius, we can calculate the gravitational acceleration due to the object (assuming we know the object's mass). Even if we don't have the mass of the dark matter object, we should see a gravitational geometry that indicates a constant (orthogonal distance squared) added to a distance in 3dspace squared.

This is different from 3dspace gravitational geometry. If the dark matter resides wholly in 3dspace (but as a mini black hole, a KK particle, or simply matter that doesn't interact with (the "normal" form of) matter) it would have a gravitational geometry that does not include a constant added to the radius squared.

The 2 different geometries would basically obey these equations (the first the standard equation for 3dspace, the second designed for an object offset from 3dspace in an orthogonal direction):

${\displaystyle g_{\text{3d space acceleration}}=-{\frac {mG}{r^{2}}}}$

${\displaystyle g_{\text{higher- dspace acceleration}}=-{\frac {mG}{(r_{\text{orthogonal}})^{2}+(r_{\text{3d space}})^{2}}}}$

You can see that the latter equation will generate a different geometry as it approaches the point in 3dspace that is closest to its orthogonal location (due to the presence of the unchanging orthogonal distance from the center of mass that is part of its geometry).

Of course, these equations are basically toy models- we would have to take into account other things as well (you know that at the center of the Earth, the acceleration due to the gravitational field of the Earth= 0), but this assumes an orthogonal offset from our 3dspace dimension greater than the actual radius of the object (such as the radius from the surface of the Earth to its center).

If dark matter is simply matter than doesn't interact with "normal" matter as you approach the center of the gravitational field you should have a steady drop in acceleration (like you would observe if you could travel towards the center of the Earth). If it is offset orthogonally, gravitational acceleration would steadily increase as you approached the center of the field (however at the very center of the field it would be zero after reaching the limit acceleration at a point infinitely close to the center of the field).

In addition we should be able to determine the objects distance from 3dspace with trigonometry: finding the location of the gravitational limit, we can measure the gravitational limit (the limit acceleration) by moving close to the point of zero acceleration (the point at which the object is closest to 3dspace). The point at which the gravitational acceleration is 1/2 the limit acceleration is the same distance from the point of zero acceleration as the center of mass of the object is.

#### Testing quasi- and demi-charge

We would have to observe attraction or repulsion between non charged particles. If there isn't any (besides gravitational effects), we can discard this aspect of the theory until we see something that can only be explained by it.

### Falsifiability

This is a problem. At the moment it appears completely impossible to rule out extra dimensions of space, whether or not they actually exist. Specific predictions (as to whether we can use specific wavelengths of radiation to reflect the orthogonal momentum of electrons to reverse their charge) need specific techniques to be established in order to be falsified. Predictions may not be completely falsifiable, but techniques are testable, so we shall see what optical specialists come up with.

## References

1. As noted by Alice Calaprice (ed. 2005) The New Quotable Einstein Princeton University Press and Hebrew University of Jerusalem, ISBN 0-691-12074-9 p. 291. Calaprice denotes this not as an exact quotation, but as a paraphrase of a translation of A. Einstein's "Induction and Deduction". Collected Papers of Albert Einstein 7 Document 28. Volume 7 is The Berlin Years: Writings, 1918-1921. A. Einstein; M. Janssen, R. Schulmann, et al., eds.
2. http://www.physicstoday.org/guide/fundconst.pdf CODATA Recommended Values of the Fundamental Physical Constants – 2006
3. "Planck constant in eV s". 2006 CODATA recommended values. NIST. Retrieved on 2007-08-08.
4. http://en.wikipedia.org/wiki/Compton_wavelength (only reference I could find, is this correct method of citation?)
5. http://en.wikipedia.org/wiki/De_Broglie_hypothesis (The equation is not cited on this page, so must not be copyrighted: it is de Broglie’s equation, however)
6. L. de Broglie, Recherches sur la théorie des quanta (Researches on the quantum theory), Thesis (Paris), 1924; L. de Broglie, Ann. Phys. (Paris) 3, 22 (1925). Reprinted in Ann. Found. Louis de Broglie 17 (1992) p. 22
7. Albert Einstein in letter to L Barnett (quote from L. B. Okun, “The Concept of Mass,” Phys. Today 42, 31, June 1989.)
8. Tolman, R. C. (1934). Relativity, Thermodynamics, and Cosmology. Oxford: Clarendon Press. LCCN 340-32023. Reissued (1987) New York: Dover ISBN 0-486-65383-8.
9. Larmor, J. (1897), "A dynamical theory of the electric and luminiferous medium — Part III: Relations with material media", Philosophical Transactions of the Royal Society 190: 205–300, doi:10.1098/rsta.1897.0020
10. Lorentz, Hendrik Antoon (1899), "Simplified theory of electrical and optical phenomena in moving systems", Proc. Acad. Science Amsterdam I: 427–443; and Lorentz, Hendrik Antoon (1904), "Electromagnetic phenomena in a system moving with any velocity less than that of light", Proc. Acad. Science Amsterdam IV: 669−678
11. http://en.wikipedia.org/wiki/Dark_energy
12. http://en.wikipedia.org/wiki/Dark_matter
13. http://en.wikipedia.org/wiki/Geocentric_model
14. http://en.wikipedia.org/wiki/Heliocentric_model
15. http://en.wikipedia.org/wiki/Bohr_model#Electron_energy_levels
16. N. Bohr, Philosophical Magazine 26, 1-25 (1913)