## 1 Quantizing Spacetime

Science has been offering us a view of reality as if space and time is continuous and infinitely divisible. But this is not true of energy. It comes as indivisible quanta. Similarly, matter comes as indivisible particles. The main contents of spacetime are quantized. This suggests that spacetime, the unity of space and time, is also quantized. If so, our view of reality changes. We have to discard certain assumptions, and paradoxes, that originate from the assumption that spacetime is infinitely divisible.

To see the implications of indivisible quanta of spacetime, suppose each quantum provides three minimum dimensions of space and one minimum repeating interval of time. This interval, synchronized within a local group of quanta, provides the intrinsic time of its region. Across the universe, variations in local time and length caused by gravity average out so that we can define different locations in the universe and investigate its overall history. Assuming spacetime quanta are packed into a matrix filling the universe, we can define the location and motion of every elementary particle. Each one is either at rest in a quantum or transferring from one quantum to another.

The minimum length of the quantum and its minimum time interval impose an absolute limit to the divisibility of space and time. They also set an absolute limit to particle speed in transferring from quantum to quantum. It is found by dividing the minimum length by the minimum time. In our spacetime, this is the speed of light. No higher speed exists, because that would require a fraction of a time interval, which we have defined as indivisible.

Remarkably, for particles transferring between quanta, no slower speed exists either. That would require a fraction of a minimum length, which we also defined as indivisible. So, particles transferring from quantum to quantum move at just one speed.

So, how do particles, in isolation or as group, move slowly in quantized spacetime? The only way is by mixing transfers between quanta at light speed with pauses within quanta at zero speed. This requires quanta to be capable of two states. One holds a particle at rest, the other transfers a particle to the next quantum. The speed of a particle is governed by a pattern of pauses and transfers. The speed of a composite objects like atoms, molecules and macroscopic structure is governed by the pattern imposed on their elementary particles.

Such a pattern is defined digitally. The pause state of a quantum might be defined by 1, and the transfer state by a 0. Then an average speed is defined by a sequence, or string, of 1’s and 0’s, derived from a digital computation. This sequence travels along with the particle, which passes repeatedly through it. The spacetime quantum length becomes the smallest length in spacetime able to store a single bit of information in the short string defining particle speed.

Quantum mechanics and general relativity have ways of calculating the
minimum length able to store a single bit, based on different effects of
particle mass on spacetime. Fortunately, their calculations agree
reasonably closely at the Planck mass of 0.0218 mg. From this we infer
that the quantum has the Planck length of 1.62 x 10^{-35} m. And as the
minimum length divided by the minimum time equals the speed of light
(defined as 299,792,458 m/s), the minimum time must be 5.39 x 10^{-44} s,
the Planck time.

I assume the quantum shape capturing these dimensions is a sphere of Planck-length diameter with an intrinsic time pulse of the Planck time. Only a sphere provides equal lengths and transfer times in any direction, satisfying the observed absence over astronomical distance of any variation of path length or speed with direction.

Two Types of Time

The two different states of spacetime quanta require two different types of time: intrinsic time in which a particle is paused, and transfer time in which a particle transfers from one quantum to another at the speed of light. To maintain time synchronism in the QST matrix, the transfer time interval must have the same duration as a pause interval, because one replaces the other. The particle state is quite different in the two intervals

A photon, displays transfer state properties. It has no mass. It
always moves at the speed of light. It does not decay radioactively
(does not age). It is associated with a wave of length inversely
proportional to its energy. When energy is expressed in terms of mass by
the relationship E= mc^{2}, the wavelength of the photon becomes inversely
proportional to its momentum (mass time velocity).

A muon, which acts like a heavy electron, displays pause state properties. It has mass. It always moves below the speed of light. It decays radioactively (it ages), and it is accompanied by a wave of length inversely proportional to its momentum. The electron shows no sign of aging.

So, this is where quantized spacetime presents a radically different view of reality than continuous spacetime. To achieve an average speed slower than light, a particle in quantized spacetime must enter the transfer state when moving between two quanta. This means it has zero mass and does not age. Then when it changes to the pause state in a later quantum, it gets its mass back and starts aging again. Losing mass in this way is not countenanced in continuous spacetime.

However, each of these two versions of spacetime have their own basic assumptions. And there can be no dispute between the validity of a set of assumptions, unless they contain self-contradiction. If they pass this test, their validity becomes a matter of whether they are consistent with the experimental evidence. On this basis, the assumptions of quantized spacetime are valid. When we calculate how aging slows and mass increases as average speed increases. 6/29/2020