About thirty years ago I realized that time could very well
be discontinuous without us knowing. That is so because we
need time in order to measure time.
If time should stop then there would be no time to find out about it.
Not being able to stop speculating about what traces there would be to look for if this were a fundamental aspect of time, or try to figure out how it could work, I eventually found an answer a few years back that also may explain some remaining questions concerning relativity and quantum mechanics.
In view of later developments in physics where a growing
number of physicists now look for a way to quantize time, I
feel obliged to communicate my ideas on the subject.
If time is discontinuous we need to reconsider our
understanding of the time dimension.
So, what is time, when and why do we need it and how does it work?
The standard model treat time as if it were an extra 4th
dimension, one that presents an additional degree of freedom
along with the usual three.
This may be needed in order to make sense of situations that involve movement, but the way I see it, time, as we usually think about it in the sense of a steady flow from the past to the future does not exist other then in our mind.
The reason we regard time as real is probably due to the fact that we have a memory which allows our brain to use the input from our senses to maintain our bodies.
This is how we operate ourselves, using the remembered input from a previous moment to act during the present one.
With our comparably slow mind we do however need the input from many moments before reacting, thus bringing about a sense of continuity which, in turn, would be interpreted as a flow of time. In other words, I think time is just a remembered diagram of the status of what goes on. It has no real physical existence apart from what in discontinuous time would be a dynamic transformation of the present moment during the course of its - probably very brief - duration.
The speculations below hopefully illustrate how space
itself could serve as a memory that brings about the
dynamics of our universe due to the type of discontinuity I
have in mind.
While it may be easy to understand the need of time when
one think about a moving object, the need of time in empty
space is not so obvious since we do not see anything that
move. However, if space itself is elastic, then time would
be needed for its elastic properties to work. You cannot
have elasticity without time.
Or… could it be the other way around so that the elasticity of space is the cause of what we experience as time?
Let’s see what could come out of this idea.
No one should be surprised about space being elastic. It
was Einstein with his theory of general relativity who
taught us that.
According to general relativity we live in a four
dimensional universe with three space- and one time
coordinate where gravity is explained to be a topographic
phenomenon with moving bodies that follow geodetic tracks in
the four dimensions of space time while bending and altering
the metric of the same space as they are proceeding. Neither
special nor general relativity does however reveal anything
about what makes time tick, so discontinuous time may well
lurk under the cover of general relativity.
How can that be?
Well, assume that time would stop. Would we notice? -Could
we notice? The answer, of course, is no. When time
eventually starts ticking again we would be none the wiser,
living on as usual. As far as concern what we know of
physics up till now, nothing prevents time from behaving
When one try to figure out what might be the cause of quantum physics the possibility that time is discontinuous is even more obvious.
To my eyes the quantum of action looks suspiciously much like a manifestation of elastic force in a space that is oscillating some way.
That would account for the discontinuity of quantum physics and its quanta.
It would also account for the phenomena of non-locality.
The question then is why and how space oscillates?
Answering the first question, the why, is impossible. Let
me only say that whatever event it was that induced enough
energy into space to overcome the elastic stiffness required
in order to account for the speed of light must have made a
big bang indeed…
Perhaps it was a collision with another universe..?
Anyway, those who maintain that time were born the moment the Big Bang happened are probably right although the present ideas about time and how it works need some refinement.
The second question is easier.
One only has to find out what mode of oscillation would
cause the physical phenomena we see around us.
That is the subject of this document.
About 20 years ago I had settled for a mode of oscillation that promised to work. The only problem was whether it was physically possible.
Then I learned about acoustic pressure waves in the sun and about sonoluminescence.
That gave me some confidence about my model. Working out the details took some time since this was- and is- a hobby project.
However, after having retired in august 05 I decided to
dedicate a little more time to the project, so in order to
refresh my knowledge on the subject I decided to sign up for
some short courses at GU.
One of which was “Modern Cosmology“with Marek Abramowicz and Gustaf Rydbeck.
When Professor Abramovicz held his first lecture I was
reminded about MOND. Remembering I had read about
MOdified Newtonian Dynamics in Scientific American back in
1983 when Professor Mordehai Milgrom proposed this
correction as an alternative to the Dark Matter model, I now
realized that my ideas about the dynamics of discontinuous
time could eventually provide the missing foundation for
As a consequence I feel that also from this point of view I have an obligation to bring my ideas to attention. The mode I propose has the form of a spherical oscillation similar to that of a standing longitudinal sound wave where the fabric of space rapidly oscillates in a pulsating way between rarefaction and compression.
Discontinuous time would then be the full cycle from maximum compression past rarefaction and back to maximum compression.
That is, actually a “live” and reusable variable to the three space dimensions that affect all of space simultaneously.
If this is true then it seems we live in a reoccurring
moment which, it appears, contain the only “time” that
actually exists. -A discontinuous and elastic present, the
size of which would encompass the entire known universe.
The duration of that moment, the period of the bulk oscillations of space, would presumably equal the 5.4 x 10ˉ⁴⁴ s time span known as Planck-time. According to present understanding this is also the shortest possible duration of time.
Why the spherical pulsating oscillation mode?
Apart from providing a possible answer to the questions of
the arrow of time and the flow of time, there are at least
two other reasons. One is the ability of particles and waves
to move in any direction and the other is the properties of
Louis de Broglie introduced the concept of matter waves and if matter is a manifestation of the elasticity of space, then E=mc² suddenly make sense.
It does not require much imagination to realize that if space itself oscillates in a way that allows for standing spherical matter waves to resonate with those oscillations they will pack a lot of energy.
The spherical wave of the fabric of space that constitutes
the particle will slosh back and forth during each cycle of
the universal space oscillation at the speed of light.
The number and amplitude of such oscillations during one second is the same that would bring a transverse wave the distance covered at the speed of light.
Hence the c² in E=mc².
What about the mass, m?
Again the spherical oscillation mode provides an
A spherical particle wave, resonating with the bulk oscillation mode of space will not move relative to the oscillating background as long as it is truly spherical.
This is because the elastic wave that makes up the particle has equal distance to travel between turnaround each “slosh” between the circumference and the center.
Since the wave front is moving at the speed of light due to the elastic properties of space the act of pushing the particle in order to accelerate it in a certain direction is instead a matter of blocking the expansion of the part of the particle’s wave front that is moving in the counter-direction.
In order to do so one has to overcome the elasticity of space.
That is the origin of Planck’s constant – the Quantum of Action – the least force sufficient to overcome the elasticity of the fabric of space.
Given that the blocking applied is firm enough, this part of the wave front will now contain more elastic energy then the other parts of the wave, thereby allowing it to reach a new center a small distance past the original.
The rest of the elastic wave making up the particle will adjust accordingly and eventually all of the now not quite spherical wave front will be sloshing back and forth towards this new constantly displaced center.
A mental picture could be that of a football being kicked by a player with the wave front represented by the spherical surface and the blocking positioned where the foot hits the ball.
Since all parts of the wave still move at the speed of light, the center of the particle wave can never be displaced past the distance covered at the speed of light.
This is why the speed of light is a universal speed limit not only for transverse waves, but also for the particles of matter.
In the light of the above I guess nobody will be surprised
to learn that mass consequently appears to be the “grip on
space” exerted by the spherical waves of the particle.
No surprise either that relativistic mass growth apparently is due to the firmer grip on space that is a result from the elastic energy added to the particle when it is accelerated….
-Or that inertia also is due to the same grip on space, making the particle harder to accelerate in any direction the more of this grip on space or mass it has.
At this point if not earlier, I imagine the reader have at
least one very large objection to all of this.
Suggesting that discontinuous time has the form of a very
brief reoccurring universal moment with the duration of
about 10ˉ⁴⁴ s would seemingly contradict both special and
According to these theories there is no such thing as simultaneity since time runs at different rates depending on the velocity of the reference frame.
This makes it more or less impossible to agree between frames about eventually simultaneous events.
I can only agree about the difficulties between different frames to pinpoint a simultaneous event, but this difficulty is due to traditional ideas of time which require the use of different frames of reference.
Instead the idea of discontinuous time makes it possible to explain the relativistic effect that is being used to reject the idea of simultaneity - why clocks run slower when they move faster.
At the point of maximum compression in the cycle of
universal oscillation all movement has stopped due to the
elastic resistance against further compression of the fabric
As the cycle continue, the energy stored during the compression phase now makes the universe “bounce” and expand outwards along with the longitudinal waves of matter and the transverse oscillations of light as the cycle accelerate towards a state of maximum rarefaction.
At this point the strain in the fabric of space will
reverse the process and force space to rebound back towards
the state of maximum compression where the cycle is
completed only to proceed into a new present in the same
The clock used in the relativist examples is running slow
when moving at higher speed because it must spend a larger
portion then otherwise out of the 10ˉ⁴⁴ s long universal
cycle of oscillation in order to first accelerate and then
to decelerate its speed in the direction of travel during
each cycle of compression and rarefaction.
Since this acceleration and deceleration will stretch the fabric of space each cycle the force delivered from the springs and gears of a clock, or from chemical reactions will diminish in relative effectiveness the faster the system moves.
As a consequence a larger number of cycles of oscillation are needed to do the same job in order to complete chemical reactions or to turn the arms of a clock in a faster system the same angle as a clock in a slower system would need.
A clock that could be locked to the background oscillations
of space would keep the time no matter what the speed of the
observer happen to be.
Does this mean that there is anything wrong with the principle of relativity? Not at all! What needs to be reconsidered is only our concept of time.
Before returning to the properties of particles something
should first be said about gravitation. I referred above to
the elastic deformation of space exerted by the spherical
wave of a particle as the particle’s “grip on space”, or
The very same “grip” would also be responsible for gravitation as it pulls the surrounding space towards the particle during each oscillation.
For a mental picture of the effect, think of what would happen if you pull upward on the center of a tablecloth.
If there is a hole at the center of the table as might be the case in a garden table where you can place an umbrella type sunshade, pushing the sheet down in the hole with a rod will give the same effect, pulling the surrounding cloth with cups and all toward the center.
The equality between the outcomes of the two methods is to illustrate that anti matter, which I suspect differs from matter only by its phase of oscillation in space, would cause and be subject to the same type of gravitation as matter.
The gravitation caused by the “grip” or mass of only one
particle would be tiny to say the least, but the effect of
many particles pulling in unison on the surrounding space
would of cause accumulate.
This has two consequences.
The first is obvious. Space itself within a sphere centered on the congregation of particles will stretch during every universal oscillation towards that center so that a particle that enters this sphere finds itself oscillating on a fabric of space whose background universal oscillations are directed towards that center.
The result will be that the particle’s center is displaced an increasing distance each oscillation in the same direction without any need to overcome the elasticity of the fabric of space by pushing the particle against its “grip” on space.
That is why the particle “feels” no force of acceleration as its speed increases.
However, since the particle is incorporating the background
oscillations with its own original oscillation, stopping it
is a matter of using force against the background induced
displacement of its center.
This is why we experience acceleration forces when we stand on the surface of a planet.
The next consequence is not so obvious.
The space in the sphere of gravity resulting from a large
aggregation of matter will have its elastic properties
somewhat altered by the fact that it stretches during each
Similar to a string instrument giving off higher tones when fretted up the neck.
At the end of the day this effect could perhaps turn out to be responsible for some of the missing energy that our cosmologists are doing their best to find.
The rest, the proposed effect from the mysterious dark matter is probably due to one or perhaps two other not so obvious consequences.
Vera Rubin was the first person to systematically
investigate the effect.
She showed that the angular speed of orbiting stars in galaxies did not drop quite as one should have reason to expect from a measure of the mass that is supposed to control their orbits.
Instead it seems the stars in the galaxies rotate around the center of the galaxy almost as if they were sitting on a wheel.
The MOND effect as proposed by Mordehai Milgrom in 1983 is one way of evading the need for dark matter to account for her observations.
It is a correction to Newtonian dynamics that introduces a basic universal constant of acceleration of the size approximately one angstrom per second per second.
What could motivate that?
I think the best candidate would be the “bounce” when the
oscillating fabric of space enters the expanding phase. That
is the point when space and everything it contains is
If the reverse process when the strain in the fabric of space later pulls everything back is a little less effective then the bounce one might have a small difference that could account for the size and existence of MOND.
Below is however a slightly different effect outlined that also might exist.
That is the acceleration induced by moving spheres of gravity.
The stretching of space within the sphere of gravity is an
instant elastic phenomenon that originates with the various
aggregations of matter and takes place every 10ˉ⁴⁴ s.
If this matter is moving in any direction, then the local stretch everywhere inside the sphere will have a component of direction every 10ˉ⁴⁴ s pointing the same way and moving at the same speed as the matter is traveling.
This is because the complete oscillating sphere of gravity moves as fast as does the matter it originates from. It follows then that the field of gravity within the sphere does not point directly at the aggregation of moving matter, but towards a resultant direction in the future path of the matter aggregation.
As a consequence, any body within the sphere of gravity will also be partly accelerated towards the direction that the aggregation of mass is moving.
The accumulated effect from a large number of such aggregations of matter, like the orbiting stars of a galaxy, or the individual members of a galaxy group with a common center of orbit, could therefore simulate a rotating background, making it appear that space itself is rotating.
Or, rather, that the stars we see has a more or less common angular speed around their center of orbit almost as if they were in a sense nailed onto a wheel.
Before returning to particles I would like to mention
These objects are among the earliest artifacts of our universe as may be understood from the Hubble redshift involved. They are also the most energetic so far discovered delivering far more energy then can be easily explained in the context of the standard model.
In the scenario on hand they may however have a place.
The way I see it quasars could explain the large, mainly
spherical regions of empty space along the surfaces of which
one find filaments of galaxy clusters.
Suppose that the Big Bang happened as I have suggested with energy being introduced as violent vibrations/oscillations of the fabric of space. One might then imagine that violently oscillating spots could have formed here and there throughout the universe, akin to the phenomenon of sonoluminescense.
Suppose further that these “hot-spots” are the quasars and that the energy we now see them produce is the dispersion of their vibrations. One might then speculate that after a long, long time, these vibrations could have met up with other vibrations from neighbouring quasars, in the process forming the filaments we now observe.
When the quasars eventually were fully dispersed they would have left the voids of empty space behind.
According to string theory particles may be seen as small
Their mode of vibration then decides what particle they represent.
Regarding this I would only like to point out that a string theorist would be well suited to explore the mathematical consequences of the above since the ideas outlined here also build on vibrations and oscillations.
There is a slight difference however.
There are only three spatial dimensions in discontinuous time.
Three simultaneously vibrating background dimensions that drive the oscillation of the waves making up matter by resonance.
This resonance effect will keep the matter waves oscillating until the background vibrations die out as they eventually must.
What makes me think the universe would stop oscillate some time in the future?
If our universe started out with a Big Bang as we already is pretty certain it did, and if this Big Bang happened more or less according to the ideas presented above, with a cataclysmic event that induced a lot of energy in the form of elastic oscillations, then the stiffness of the oscillating fabric of space would eventually damp the oscillations.
This would have some consequences that we can observe.
With a very stiff fabric of space, the damping of the
initial oscillations would bring these down in amplitude at
a speed that could well be in parity with the supposed speed
The continuing damping of the amplitude of the oscillations would then show as a relative expansion of the fabric of space to the observing denizens.
The reason is that the diminishing amplitude of the universal oscillations also happens to double as our measuring rod.
This is because as I understand it, things cannot move any farther during one oscillation then a distance that is twice the amplitude, which in a way is what we do when we take a measure.
So, in other words, the universe is really not expanding. Instead it appears that we and the rest of the content of the universe are shrinking.
The property of spin has a simple explanation in the
context of this type of pulsating universe. It is due to
relative phase and frequency differences between the modes
of oscillation of the various particles in question and the
pulsating background oscillations of space itself.
To be more specific - there is a systematic difference
between the resulting oscillations of transverse and
longitudinal waves when they are overlaid on the
longitudinal background oscillations.
This difference is what we measure as spin.
Finally, if time really does consist of sequential elastic
transformations of a universal moment with a periodic
duration of 5.4 x 10ˉ⁴⁴ s as I propose, then the frequency
of this fundamental oscillation of our universe would be
about 1.85 x 10⁴³ p/s.
No wonder we never noticed.