The *Theory of Physics in 5 Dimensions* includes hypotheses that result in different perspectives of the current fundamentals of classical-, quantum- and
relativistic-mechanics. These hypotheses are shown to apply to many different fields of physics yet still agree with the fundamentals of physics for parameters with values typical of classical
physics.

**Superposition of seven cosine waves**^{35}

A prime hypothesis of *Physics in 5 Dimensions* states: *The origin of all matter is electro-magnetic- radiation (emr) in the form of many matter waves of different wavelength producing
groups of waves with particle-like-nature of mass m and energy E* as described by de Broglie^{54} in 1929. De Broglie predicted the
phenomena of superimposition of many sinusoidal matter waves (seven in the previous figure^{55}) which produces matter in the form of a *group of
waves* (lower plot in the figure opposite) to which is assigned the de Broglie - Einstein relations of energy E, momentum p, wavelength λ and frequency ɣ.

Point sources of emr are considered to be located in a 5^{th} dimension^{56} without space in
the sense of a Cartesian system of coordinates and are therefore sources of energy *before-the-start-of-matter* in our universe. The mechanism associated with the generation and
combination of these emr matter waves producing groups of waves (matter) is outside the scope of the research into *Physics in 5 Dimensions.*

The *Space* of our universe is created by the paths of the groups of waves (particles & bodies) each moving relative to the source of emr with a common constant velocity that
determines the speed of light c. As Einstein noted in 1952 *physical objects*^{57} *are not in space, but these objects are spatially
extended* and, given the above hypothesis of *Physics in 5 Dimensions*, are dynamically moving along their individual paths with the velocity of light c.

With the emr parameters of wave amplitude A and frequency ɣ associated with the source of the emr matter waves, the parameters associated with the resulting particles or bodies (groups of waves)
and their dynamic movement in the universe are: - length (ref. Einstein’s measuring rods^{58}), - time t, - wavelength λ, - mass m and – the velocity
of light c.

*Physics in 5 Dimensions* proposes further hypotheses that determine the fundamental structure of the universe namely that:

- All particles and bodies move along closed paths (an orbit) with a common constant velocity c (speed of light) and therefore have fixed *intrinsic values of angular
momentum. *Initially all bodies are on the surface of a *universal reference sphere* of radius Ru in a *pre-local-space-state* with the bodies entangled with their own
matter waves.

- As shown in the figure opposite, the vector c of body O has two component velocity vectors v4 and v5 defined to be respectively aligned with the x and y
axis of a Galilean coordinate system. The path of body O with velocity vector c subtends an angle θ with the path of observer P with the velocity vector c, defined to be aligned with the y axis.
When the body and observer have parallel paths then it follows that θ=0, v4=0 and v5=c and the body is deemed to be *at rest* in a frame of reference rigidly attached to observer P. The
magnitude of the velocity vector v4 aligned with the x-axis is defined to be equivalent to the observed velocity of a body in classical mechanics and we have the scalar relationship c^{2 }= v4^{2 }+ v5^{2 } of *Physics in 5
Dimensions*.

- The figure below illustrates the *Structure of the Universe* and a *local space* as viewed from a universal four dimensional Galilean coordinate
system (x, y, z, t). Two objects of mass M4 and m form a *local space* of radius R5s (dotted line). The *matter waves* of all member bodies of a *local space* orbit a space
of common radius R5 coincident with a body of mass M4 and with orbital velocity w4. The associated body of mass m has its own orbit with radius R4 and radial velocity v4 centred
on an extended axis of M4; where according to de Broglie w4 v4 = c^{2}. So object m has a dynamic path within its own *local space*, as judged
from a frame of reference rigidly attached to mass M4.

- When a body changes from *pre-local-space* to the *start-of-local-space*, the matter waves of a body separate from the surface of the *universal reference sphere* and
become part of a *local space* close to the surface of the universal reference sphere moving with, or close to, the common constant velocity c, and the mass M4 *develops or arrives*
(see previous figure).

- The fixed angular momentum of the body m is given by h5 =2 𝝅 m R4 v4 and the condition of fixed angular momentum requires that R4 v4=R5 w4=Rc c, where Rc is the radius of orbit of m when v4 = c. The expression for the fixed angular momentum of all electrons (e) is given by he = 2 𝝅 me R4e v4e where he where he is Planck’s constant.

- *Matter* is continuously created in the form of elementary particles (for example quarks and leptons) and similarly at *end-of-local-space*
continuously returns to the originating source of emr, for example by the burning of material where a solid body is reduced to ash while emitting emr. The *end-of-local-space* is also
associated with an object smaller than its Schwarzschild radius which is called a *black hole*. The surface at the Schwarzschild radius acts as an event horizon and neither light nor
particles can escape through this surface from the region inside, hence the name *black hole*. The Schwarzschild radius of classical physics is identical to the *Physics in 5
Dimensions* expression for the end-of-space^{59}, namely when R5s = 2 R5 = 2 G M4/c^{2 } where
R5s is the radius of local space when v4 = v5 = c/√2 and G is a constant of dimensions of *Physics in 5 Dimensions* and the gravitational constant of classical *Physics in 4
Dimensions*.

With *Physics in 5 Dimensions* the structure of the universe has a finite physical boundary at the surface of the universal reference sphere of radius Ru and around which matter can move
for an unlimited period of time with the velocity of light c. So a starting point for a view of the stars and galaxies of our universe is to consider the complete Milky Way to be orbiting
close to the radius Ru and with the Sun and Earth forming a local space with bodies of mass M4 and m respectively; to which we can add all the other planets orbiting the Sun.

While the hypotheses of *Physics in 5 Dimensions* determines the structure of our universe, many universes may exist each with their own characteristics, especially in connection with the
common constant velocity that sets the *speed of light* for each universe.

**References:**

(35) Ref. Fig 3.9 Quantum Physics, Robert Eisberg & Robert Resnick, John Wiley & Sons Inc., ISBN 0-471-87373-X

(54) de Broglie’s “ The wave nature of the electron” – Nobel Lecture December 12, 1929 https://www.nobelprize.org/uploads/2018/06/broglie-lecture.pdf

(55) Ref. Fig 3.9 Quantum Physics, Robert Eisberg & Robert Resnick, John Wiley & Sons Inc., ISBN 0-471-87373-X

(56) The emr origin of matter waves is called the 5th Dimension because it is in addition to and different from the usual concept of 4-dimensional space with 3 coordinates plus time.

(57) Relativity - The Special and the General Theory by Albert Einstein - First published in 1920 ISBN 0-415-09104-7 – 15th Edition published in 1952

(58) Page 115 – The space-time Continuum, Einstein, The Principle of Relativity, standard book no. 486-60081-5, Dover Publications, Inc. New York

(59) Page 426 Physics in 5 Dimensions ISBN: 978-3-96014-233-1 https://www.researchgate.net/publication/266794606_Physics_in_5_Dimensions_Bye_bye_Big_Bang

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