Welcome to MiTiempo

From observation of type Ia supernovae, people perceive that the cosmic expansion is accelerating. The interpretation is under the invariant light speed since the Big Bang to the present. Has the light speed been constant for whole the process of cosmic expansion? Before examine light speed and cosmic expansion, we have to elucidate key features and definition of the time.

Starting from energy as vibration in multiple dimensions, I investigated requirements for a dimension to work as a time. Subsequently, I proposed a 4-dimensional spherical model of the universe, in which cosmic energy spreads with expansion in a 3D surface of a 4D sphere. Our observable energy like light and quantum particles is vibration of the intrinsic space energy in the 4D space. The radius of the 4D sphere is our observed Time that can be a common time for any locations of the 3D space. The model nicely fits the observed data of supernovae without introducing acceleration of space expansion or the dark energy.

In this website, you will find the new proposed concepts. Please click a menu in the above menu bar or the left column.


Invitation to the Energy Circulation Theory (ECT)        

Nature of the time and
4D Spherical Universe

(1) Nature of the time, 4D spherical model



Michelson-Morley experiment

(2) Light speed

3) Hubble Diagram from 4DS universe and observed data of Supernovae


Published paper

Energy circulation theory

Energy Circulation Theory

Evolution to 4D spherical universe

Light Radiation

Kinetics of an Energy Circulation

Quantum particles based on ECT

Galactic Evolution w/o Dark Matter

Quantum Mechanics from ECT


Described full-text explanation including how to come to the proposed concepts.

MiTiempo My Time

Part-1: What the time is(PDF)

1) Start of a tour around the time

2) Time and movement

3) Decrease of dimension

4) Tracing dimension and imaginary order of freedom

5) Properties of a dimension having the imaginary order of freedom and definition of the time

6) Another important property of the time

7) 4-D spherical model of the universe

8) Measuring time

9) Measurement of movement and the clock

Part-2: Verification of the 4-D spherical model of the universe(PDF)

1) All the issues started from Michelson-Morley experiment

2) Michelson Morley experiment

3) Special relativity

4) Acceleration factor of a stationary wave

5) Light propagation speed

6) Redshift of light

7) Light propagated distance and redshift

8) Frequency-based redshift for cosmological obervation, Hubble diagram, Comparison with Supernovae data

Click a term or press an arrow of keyboard to show explanation.
existence :
"Existence" means there lies energy. Energy exists only at a single point of time, which is the "present". The time exists only at the present. The past is a record of past existing at the present. The future is a present expectation on what to happen in future.
space :
Space (of universe) is the area where energy is distributed.
space energy / apparent energy :
Intrinsic energy fills in the vacuum space of universe. Call it "space energy". Vibration of the space energy in the 4D space vests additional energy, which we call "apparent energy" and is our observable energy in the 3D space as light or quantum particles. Call the space energy and the apparent energy collectively as the "cosmic energy".
time and space :
Time is basically equal to a space dimension in term of existence and interaction. However, the cosmic energy is located only at a single point of time whereas it spreads out in a tremendously huge area of 3D space. 3D surface of a 4D sphere is a potential geometry giving such a distribution.
time :
Time is a dimension to trace values in space dimensions.
tracing dimension :
Define the "tracing dimension" as a dimension, by variance of which a value-change (movement) of the resting other dimensions is expressed. In order for a dimension to work as a tracing dimension, any single value of it should correspond to a single value of any resting dimension for a movement.
imaginary order of freedom :
The "imaginary order of freedom" is defined as that there is no freedom of selecting a value, and furthermore the value is not a constant but moving in a single direction (increase or decrease). A dimension showing the imaginary order of freedom when traced by other can act as an alternative tracing dimension.
original time :
The initial cosmic energy was vibration in multiple dimensions. In order to describe it as vibration, a tracing dimension is essential. The dimension showing the longest cycle in relative value change can work as a tracing dimension to express value-changes (movements) of the all other dimensions. Refer it to as the "Original time".
4D spherical universe :
The initial energy separated to two universes, in which the energy distribution spreads in 3D surface of a 4D sphere (Cosmic Separation). Then it turned to expand in the 4D space (Space Expansion).
observed Time :
The radius of the 4D sphere for the distribution of cosmic energy exhibits the imaginary order of freedom when traced by the Original time. Therefore, it can be a new tracing dimension to trace a movement in the 3D space. Refer it to as the "Observed Time".
common time :
Tracing an object (energy) targets only a single point where its space location and the time cross each other. Each place of 3D space has its own distinctive 4D vector of radius, but the absolute value is common at any location. Therefore, the Observed Time as absolute value of the radius can work as a common time for any locations of 3D space. While a movement is a change of location, we can trace it by a common time if we use the Observed Time.
chronological recording and remote tracing :
For measuring a movement, it is necessary to record respective positions of space at individual time points ("Chronological recording"). By recording measured values successively, we can measure a movement via comparing the current one with past values remaining at present. We cannot directly trace a movement because an object and its observer are different in the location. We indirectly trace it by measuring position information of an object using a device ("Remote tracing").
common measuring time and the clock :
Individual persons recognize their own time passage. Each one cannot recognize its correlation with the Observed Time, which is a common tracing dimension to all observers. Should take a movement, which varies at a uniform speed by the Observed Time, as a standard, each observer can correlate its time passage with movement of the standard. Therefore, such a standard can work as a common measuring time, which is the key nature of the "clock". By connecting plural clocks, we can share common time passage.
light :
Light is a propagation of an energy circulation in one hidden and one space dimensions. In the parallel direction to propagation, the rest mass is zero having kinetic energy. In the perpendicular direction, the energy turns to be the rest mass without kinetic energy.
light speed :
Light speed is the phase velocity, constant toward the medium (space energy) independent from emitter's movement. Along with the space expansion, the light speed slows down due to decrease of the space energy density.
quantum particle (matter) :
Energy circulation of the space energy reaching a steady state with the radius of the largest hidden dimension can be treated as a particle. The total energy works as the rest energy for further movement. A composition of one or plural energy circulations is a quantum particle.
acceleration factor :
When a circulation of the intrinsic energy moves linearly, the motion of the intrinsic energy is spiral to the medium. There is the maximum speed of energy movement, that is the phase velocity of the medium (space energy) equal to the light speed. Accordingly, the acceleration by a force depends on the speed to the medium. I newly propose an acceleration factor in the equation of motion, instead of the Lorentz factor in the special relativity.
Life and time

Given a new definition of life

Publication
  1. Quantum mechanics from the energy circulation theory - wave function showing an energy location in the 3D real space, Reports in Advances of Physical Sciences 5 (2021) 2150001
  2. Galactic evolution showing a constant circulating speed of stars in a galactic disc without requiring dark matter, Reports in Advances of Physical Sciences 4(2) (2020) 2050004
  3. Structures and interactions of quantum particles based on the energy circulation theory, Reports in Advances of Physical Sciences 3(1) (2019) 1950001
  4. Energy circulation theory to provide a cosmic evolution, electric charge, light and electromagnetism, Reports in Advances of Physical Sciences 2(3) (2018) 1850007
  5. Frequency-based redshift for cosmological observation and Hubble diagram from the 4-D spherical model in comparison with observed supernovae, Journal of Physics: Conference Series 880 (2017) 012058
  6. Light propagated distance and redshift of a distant star, Journal of Physics: Conference Series 626 (2015) 012068
  7. Acceleration factor for propagation of a stationary wave in its wave medium: movement of energy in the 3-D space, Journal of Physics: Conference Series 442 (2013) 012067
  8. Light speed and the expansion of the universe, Journal of Physics: Conference Series 306 (2011) 012073
  9. Nature of tracing dimension, imaginary order of freedom and our observed time passing at constant speed, Journal of Physics: Conference Series 174 (2009) 012069