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1. Introduction to Three-Dimensional Vector Time.


Time seems like it is a very familiar concept, but if we spend a bit of time thinking about it, it is difficult to wrap our heads around it.   Our measurement of time is really a measurement of the change in time.  This change in time is normally in the form of a measurement of a rotation.  The most common timing is the rotation of the earth around its axis to mark out a day and the rotation of the earth around the sun to mark out a year.   We take this change, and subdivide it into smaller units to make it practical for everyday use.  On the other end, an atomic clock is based on the rotation of an electron around an atomic nucleus.  The units are so small that it is not very practical for our everyday lives, but is practical in science and engineering where our new technology demands this type of resolution of time.


In our universe time is everywhere.  There is no place in the universe that we can think of that time is not, from the smallest parts of the atom to the largest parts of the cosmos. Yet we currently treat scalar time as an equivalent one-dimensional variable.   Even then, we only understand it as increasing, that is, going forward.  Why is time so elusive?  Temperature is only one-dimensional and it is everywhere, but we do not have the same difficulty understanding temperature.  Why is this? We think in terms of moving in time, but do we truly understand what this means.  We talk of a place in time, but it is just described as a point on a line.  


Can time be multi-dimensional? If so, what does it mean to have a location, direction, or even a velocity in three-dimensional time.  Dewey Larson, in his Reciprocal System Theory, postulated that time can be three dimensional.  I have taken Dewey Larson's ideas, and integrated some of my own ideas to derive four additional Maxwell equations based on Vector Time. In this introduction are ideas that should be considered in your own exploration of the concept of 3D vector time.



2.  Dimensional Vector Time and Velocity [ref 1]


The concept of location in 3D Vector Space is very familiar to us and so is the concept of moving in 3D Vector Space.  In 3D Vector Space, the dimensions of length [L], area [L^2] and [L^3] are well understood.   These variables define static space.  To move in 3D Vector Space requires time.  Without Scalar Time, it is not possible to move in space, since movement is change in space divided by change in time.  A change in space divided by a change in space, that is, dx/dx is not movement.  It is just the measurement of the rate at which space changes at that point, the slope.  To move in space requires a change in space divided by a change in time, that is, dx/dt.


What does 3D Vector Time mean?  The concept of 3D Time can be imagined and we can even imagine moving from one location in time to another, just like in 3D Vector Space.  We even struggle to intuitively understand the equivalent of time as one-dimension , but what about two dimensions of time [t^2], or even three dimensions [t^3].    The measurement of length would be in seconds, the area in seconds^2 and volume in seconds^3.  Now this concept of measuring in terms of time is not foreign to us.  We often talk about a trip in terms of either distance or the time it takes.  But describing the living area of a house in three-dimensional time as so many seconds^2, or minutes^2 is a bit strange to us.


I have read many books and ideas on time, and even multi-dimensional time.  It was not until I ran across the ideas of Dewey Larson, in his Reciprocal System Theory [ref 2], that I found an interesting insight that really helped me think differently about 3D vector time and 3D vector space.  In his theory, space and time are coupled via velocity where velocity is just a ratio of space to time.  When we think of the velocity of light, this means the ratio is 186 thousand miles, or 299 million meters, for each second.  If you think about it, one second it something we can relate to and even count out.  But 299 million meters is just a huge number.  The only practical use of a unit that large is out in space, where it quickly becomes too small and scientists have to multiply it by 31.5 million seconds to get a light year to have a practical unit of measurement.  What I found is that velocity, this ratio of space to time, can be very informative if you use it to evaluate spacetime as this ratio. 


When considering motion in spacetime, it becomes obvious that increasing time has the same effect as decreasing space.  Both decrease velocity.  The same is true about decreasing time and increasing space.  Both increase velocity.  The most fundamental relationship of space to time is that they are reciprocal.  Increasing one is the same as decreasing the other when it comes to motion, or velocity. 


One property of matter in spacetime is that all of it is in constant motion.  From the smallest components in particle physics to the largest galaxies out in space, everything is in motion. Even if you do not move in 3D Vector Space, time is constantly changing.  There is no place in 3D vector space you can find where time is not constantly changing.  So, it is true for space.  Even if you are now sitting still, you are rotating around the axis of the earth, rotating around the sun and rotating around the center of this galaxy at hundreds of thousands of miles per hour.  Everything is always in motion since both space and time are constantly changing. The only choice is how much space we move, or we move an object, relative to all the other constant velocities we are part of.


Now motion comes in two forms.  One is speed, the other is velocity.  Speed is a scalar, so only has magnitude and no direction.  The speed of light [c] is one example.  Light is in all directions, so c can only have magnitude.  Velocity normally refers to a motion that has direction, a vector.  In velocity, space is three-dimensional vector and has both magnitude and direction whereas the other component, time, has only magnitude.  But only one component in necessary to give velocity direction. 


The difference between scalar and vector is very important, so I want to give an example.  Think of temperature.  It can go up and down but it has no direction. If someone states the temperature is 23C, or 73.4 F, it tells you only the magnitude but there is no information about direction.  From this bit of information, you have no idea how temperature is going to change if you move North versus East.  But temperature can have a unique value for every point in 3 dimensions.  A three-dimensional map of temperature can be made.  The gradients, or change in temperature, in any direction can be calculated, but now you have converted a scalar value into a vector, since you now have mapped a change in temperature to a change in location.   The same is true if you map an area of three-dimensional space as one variable, height above sea level.  This height is scalar.  But if you are interest in how steep a trail on this map when walking in the NW direction, you need to calculate the change in height relative to the change in distance.  Now you have the gradient, or slope in that direction.  So each point in three-dimensional space has a value associated with a particular direction.  In three-dimensional space, you can tell someone to drive 65 miles in the east direction and then 40 miles in the north direction.  These are vectors in multi-dimensional space. What is important to remember is that spacetime is a combination of a vector [space] and a scalar [time].  In the new ideas expressed in the papers and links on this website, additional dimensions of spacetime are included, where the new vector is time and the new scalar is space.


Time, like temperature, is a scalar variable that can increase and decrease in magnitude.  Time is not limited by any physics to only increase, but we only experience it as increasing.  Again, it begs the question, why.   Time has no direction even though we regularly talk of increasing time as going forward, a property typically associated with direction. But this term, forward, is only a figure of speech.  


Another interesting property of time is that it is everywhere in our three-dimensional world.  Fortunately, this scalar time has extremely high uniformity since, no matter what direction in this three-dimensional world we move in, it behaves in exactly the same way.  Without this extreme uniformity, the physics we use would become even more complicated than the effects of relativity on time when considering velocities close to the speed of light.   


So, to reiterate, motion in vector space is; Change in Vector Space / change in Scalar Time = velocity or motion in Vector Space


In order to move in Vector Time, a change in space is required which is represented as; Change in Vector Time / change in Scalar Space = 1/ velocity or motion in Vector Space.   


But what is the Scalar Space variable?  In 3D Vector Time there has to be a comparable scalar variable like time is in 3D Vector Space.  Scalar Space is the obvious variable since these new dimensions appear to be a direct swap of space and time.  But what does Scalar Space mean?  In order to move in Vector Time, as has been stated, requires a change in Scalar Space.   So, locations in 3D Vector Time can be mapped out just like locations in 3D Vector Space.  In our familiar spacetime if we move, we measure this movement in meters/second and the change in time component is measured with a watch.  But now in 3D Vector Time, if you are in one location of 3D Time and you want to move to another location in 3D Time, you have to have a change in space.  To measure a change in space, your watch would measure meters instead of seconds.  A bit of a strange concept to us.  Movement in Vector Time requires Scalar Space, resulting in a reciprocal velocity [1/velocity] from the perspective of 3D Vector Space.  Just like the Scalar Time field manifests as a uniform scalar field, that is, as a uniform density in 3D Space, so it could be imagined that Scalar Space field is a uniform density in 3D Vector Time.    I imagine Scalar Space to be an extremely uniform fog of matter distributed throughout 3D Time just like Scalar Time is distributed extremely uniformly throughout 3D Space.   In 3D Time, matter would have different shapes, but there would be matter that would be measured in terms of a unit of time.


In terms of electrodynamics, in 3D Space and Scalar Time, the source of electric fields are charges, or electric monopoles.  The source of magnetic fields are dipoles, or pairs of north and south poles.  These poles pairs are never separable, so the idea of a magnetic monopole, an independent north and south pole has yet to be measured. There cannot be a magnetic field without time, since magnetic fields are generated by the movement of electrical charges and movement in space requires time.  So magnetic fields are linked to time.


 When 3D Time and Scalar Space is included in electrodynamics, specifically Maxwell's equations, the source of magnetic fields are individual north and south magnetic monopoles but electric positive and negative charges are not separable. They always appear as dipoles, just like magnetic charges in 3D Space and Scalar Time.  Including 3D Time and in electrodynamics gives a theoretical basis for dual symmetry in electrodynamics that physicist always believe should be there [ref 1].

What this points to is that the basis of electrodynamics in 3D Space and Scalar Time are electric monopoles and the basis of electrodynamics in 3D Time and Scalar Space are magnetic monopoles. I therefore refer to 3D Space and Scalar Time as Electric Space and 3D Time and Scalar Space as Magnetic Time.


3.  Zero Point Energy [ref 3]


In 1901 Max Planck published his first paper on the radiation of a black body.  In his paper, Plank introduced a new constant, h which came to be known as Planck’s constant, to accurately calculate the radiation emitted from a black body.  What was disturbing at the time was that the radiation had to be quantized.  This quanta of energy is small, but the field of physics up to that time believed energy to be a continuous phenomenon.   At the macro level this has little impact, but at the microscopic level, specifically the level of atoms and particles, it has a radical impact.   Planck was not comfortable with the format of his equation.  He worked on it for another 10 years and then published a new paper in 1911.  In this second paper he had two terms instead of one in his equations, as shown below.  In the first term in this equation, energy is dependent on temperature and in the second term [hf/2] it is not dependent on temperature, only frequency.  The result of this equation is that matter always has a residual amount of energy, even at zero degrees.  Because of this, this second term became known as the Zero Point Energy [ZPE][ref 3].


The concern with this term was that although the energy generated by each individual frequency is extremely small, the universe is expected to support an infinite number of frequencies so the amount of energy density from all these frequencies is infinite.   To solve this problem, the frequencies are limited to the point where the fabric of space breaks down, known as Planck’s length.  This frequency, which is on the order of 1044Hz, is inserted into the equation 1 and the amount of energy density is recalculated. The result is still extremely huge, an energy density on the order of 1093g/cm3.   Atomic energy, the most dense form of energy we knew before this, only has an energy density of only 1014g/cm3.  This energy density is so large it has the capacity to vaporize all the known matter in the universe.  The reason that the Zero Point Energy does not destroy matter is that it is extremely uniform, so there are no forces to create this destruction [ref 4].  It is like a box which is closed and sealed at sea level.  At sea level, there is uniform pressure inside or outside the box.  But if the box is taken deep under the ocean, it will be crushed by the outside force generated by the in-balance of pressures outside versus inside the box.  Likewise, if the box is brought into the upper part of the atmosphere, it will explode because force generated by the larger pressure inside the box relative to the low pressure outside.  So, the uniformity is critical to the balance of the universe as we know it.



4.  Stochastic Electrodynamics [ref 5].


Out of this second equation of Max Planck, a second interpretation of quantum behavior is developing, a field called Stochastic Electrodynamics [SED].   Stochastic Electrodynamics postulates that the Zero Point Energy is an energy that manifests from a gradient, or change in the balance of the Zero Point Field [ZPF].   As noted above it is the difference in potentials, or pressure in the analogy, that creates the energy and forces. This Zero Point Energy is a jitter motion that is imparted to matter at the most fundamental level.  The Zero Point Energy consists of virtual particle pairs, in the form of electron-positron pairs, that oscillate between an undetectable presence in this Zero Point Field and a very brief detectable presence as photons in the universe of matter.  During the brief time as photons, these photons can absorb and emit electromagnetic radiation, and so interact with matter.  At a given Zero Point Energy energy density, the amount of virtual particle density is fixed.  This virtual particle density fixes the amount of energy imparted to real particles during the brief interaction.


Physicist H. E. Putoff asked the question why all the electrons in the universe have not run out of energy and crashed into the nucleus of the atom since as they orbit the nucleus they are constantly radiating energy.  He calculated that the electron has the orbit radius it has because the electron absorbs just the right amount of energy from the Zero-Point Field to maintain this exact orbit.  If energy density of the Zero Point Energy increases, the electron’s path will get smaller and the electromagnetic attraction of the nucleus will slowly pull the electrons in, unless it absorbs enough energy to counterbalance this electromagnetic attraction.   Likewise, if the energy density of the Zero Point Energy decreases, the orbit of the electrons will increase and they will escape the electromagnetic attraction, or coulomb force, of the nucleus.


Since the atomic frequencies detected by our instruments is dependent on the radius of the electrons orbit, and the Zero Point Energy effects the orbits of the electrons in all matter, this means that the energy density of the Zero Point Energy impacts the precision of the atomic clocks we use. 


5.  Mass [ref 3]


In an article called Zero Point Energy, by the Calphysics Institute, their scientists reminds us that the Higgs field does not explain the origin of inertial mass of ordinary matter.   The article states, “The Higgs field applies only to the electro-weak sector of the Standard Model.  The mass of ordinary matter is overwhelmingly due to the protons and neutrons in the nuclei of atoms.” In the same article, it states, “The origin of inertial mass of ordinary matter is thus a wide open question.” [ref 6]


In the Reciprocal System Theory [ref 2], mass is defined in terms of inverse velocity.  That means mass is a time phenomenon since inverse velocity is related to 3D Time.  The theory postulates, and as shown in in the paper ‘Concepts of Three-Dimensional Time in Electrodynamics’, motion in space is not possible without time.  But the theory takes this a step further.  Motion in 3D Space is not possible without units of time involved, that is, a dx/dt.  In the equation F=ma, mass is represented as 1/c3, that is time^3/space^3, a unit of motion in 3D Time.  In this same paper, that authors use inverse velocity as a coupler between force and acceleration. The acceleration is part of motion in 3D Space. Force, like energy, cannot be seen in 3D Space, but their effects on matter can be measured in 3D Space. Force in Reciprocal System Theory is a Time phenomenon.  Space and time are coupled via the scalar form of motion, in this case, c, the speed of light. As stated, the authors use mass, in the form inverse scalar motion, as the coupler between acceleration and force, just as the Reciprocal System Theory does.


In papers on the Zero-Point Field and Zero Point Energy, authors have worked out formulations to show that mass is due to a reaction of the Zero-Point Field to accelerated motion.  This reaction to accelerated motion of charge is inertia, which is measured as inertial mass in vector space and scalar time. So, mass is not an innate property of matter, as theory states.  In the Zero-Point Field paper “Beyond E=mc2”, the authors state “In our formulation, the m in Newton’s second law of motion, F=ma, becomes nothing more than a coupling constant between acceleration and an external electromagnetic force.”[ref 7].  In my paper, Energy was derived as a property of the 3D Time Field with units of time/space, or 1/c, as postulated by the Reciprocal System Theory.  If the equation E = mc2is solved for mass, then mass = E/ c2, and E has been shown to be equal to 1/c, so mass is 1/c3.  Therefore, mass is energy in the three dimensions of time.  


Again, in the same paper “Beyond E=mc2”, the authors state the following based on the derivation of mass from Zero Point Field.  “In the view we will present, Einstein’s formula is even more significant than physicists have realized.  It is actually a statement about how much energy is required to give the appearance of a certain amount of mass, rather than about the conversion of one fundamental thing, energy, into another fundamental thing, mass”. Later in the same paper they are more explicit, “Mass is energy” [ref 7].  The 3D Time derivation of mass says exactly the same thing, where energy is a property of time.  So, mass is not an innate space property of matter, it is a result of energy generated by motion through the field of time. [ref 7].  In addition, the Reciprocal System Theory states that motion in time is in opposition to motion in space. The theory of Zero Point Energy and time appear to correlate pretty well.  


6.  Potentials [ref 10]


Writing electrodynamic equations in terms of potentials not only gives them a nice symmetry, but also allows for keener insight into the source of electromagnetic fields.  Initially, potentials were considered mathematical constructs to help with the calculations of electrodynamic fields.  But the Bohm Aharanov effect demonstrates that vector potentials have real effects on electrons, shifting their phase, validating that potentials effect matter [ref 8].     


When electrodynamic equations for 3D Space and Scalar Time as well as for 3D Time and Scalar Space are derived, it becomes apparent that the form of the scalar potential is the same for 3D Time as it is for 3D Space. The units for potentials in 3D Time are the same as for 3D Space. This suggests that potentials are more fundamental than fields in both spacetimes. 



7.  Summary


It is clear that Physics does constrain time to being a scalar.  Representing time as multi-dimensional does not change the current physics, but it expands what insight can be had about matter in our universe significantly.  The extra 4 equations of electrodynamics that I derive that come from time in 3 dimensions and space as a scalar variable can open a whole new way of looking at the interactions of space and time.  It points to the foundations of electromagnetism in Vector Space and Scalar Time being electric monopoles and the foundations of electromagnetism in 3D Time and Scalar Space being magnetic monopoles. This concept aloo gave me insight into ideas such as Electric Space, Magnetic Time, and photons that can be called Electric Photons and Magnetic Photons. The concepts we understand about anti-matter I have also applied to 3D Time [ref 8]


With Three-dimensional time introducing so many extra degrees of freedom in spacetime, it helps to keep an open mind and explore what the implication can be. The many papers on the 'White Paper' tab of this website introduce these and many more concepts to readers who are interest in exploring time in more detail.




1.      Concept of Three-dimensional Time in Electrodynamics, Robert Kersten, Paper 1,

2.      Nothing but motion, Dewey Larson, North Pacific Publishers, 1979. ISBN 0-913138-07-x.  Information can also be accessed at 

3.      Three-dimensional Time and Zero Point Energy, Robert Kersten, Paper 4,

4.      Beyond E=mc2, Bernhard Haisch, Alfonso Rueda, H.E. Putoff, The Sciences, Vol. 34, no. 6, p 26-31, Nov/Dec 1994.

5.      Quantum Fluctuations of empty space; A new Rosetta Stone in physics, Dr Halorld Putoff, Insitute of Advanced Physics.

6.      Zero Point Energy, Calphysics Institute,

7.      Measureability of vacuum fluctuations and dark energy, Christian Beck, Michael C. Mackey, Dec 11, 2006,

8.      Three-dimensional Time,Monopoles,Photons and  Anti-matter, Robert Kersten, Paper 4,





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