Quantum-Geometry Dynamics: The Slowing Down of Clocks as Explained by QGD

This article assumes basic knowledge of quantum-geometry dynamics; minimally the concepts presented in the short article Quantum-Geometry Dynamics in a Nutshell.

QGD considers time to be purely a relational concept. In other words, time is not an aspect of physical reality. But if time does not exist, how does QGD explain the different experiments which results support time dilation; the phenomenon predicted by special relativity by which time for an object slows down as its speed increases.

To explain the time dilation experiments we must remember that clocks do not measure time, they count the recurrences of a particular periodic system. The most generic definition possible of a clock is a system which periodically resumes an identifiable state and a counting mechanism that counts the recurrences of that state.

Clocks are physical devices and thus, according to QGD, are made of molecules, themselves made of atom composed of particles all of which are ultimately made of bounded $preon{{s}^{\left( + \right)}}$ .

We know that the magnitude of the momentum vector of a $preo{{n}^{\left( + \right)}}$ is fundamental and invariable. The momentum vector is denoted by $\vec{c}$ the momentum is $\left\| {\vec{c}} \right\|=c$ . We have shown that the momentum vector of a structure is given by ${{\vec{P}}_{a}}=\left\| \sum\limits_{i=1}^{{{m}_{a}}}{{{{\vec{c}}}_{i}}} \right\|$ and its speed by ${{v}_{a}}=\frac{\left\| \sum\limits_{i=1}^{{{m}_{a}}}{{{{\vec{c}}}_{i}}} \right\|}{{{m}_{a}}}$ . From these equations, it follows that the maximum possible speed of an object $a$ corresponds to the state at which all of its component $preon{{s}^{\left( + \right)}}$ move in the same direction. In such case we have $\left\| \sum\limits_{i=1}^{{{m}_{a}}}{{{{\vec{c}}}_{i}}} \right\|=\sum\limits_{i=1}^{{{m}_{a}}}{\left\| {{{\vec{c}}}_{i}} \right\|}={{m}_{a}}c$ and ${{v}_{a}}=\frac{{{m}_{a}}c}{{{m}_{a}}}=c$ . Note here that $\sum\limits_{i=1}^{{{m}_{a}}}{\left\| {{{\vec{c}}}_{i}} \right\|}$ corresponds to the energy of $a$ so the maximum speed of an object can also be defined as the state at which its momentum is equal to its energy.

From the above we see that the speed of an object must be between $0$ and $c$ while all its component $preon{{s}^{\left( + \right)}}$ move at the fundamental speed of $c$ .

Now whatever speed a clock may travel, the speed of its component $preon{{s}^{\left( + \right)}}$ is always equal to $c$ . And since a clock’s inner mechanisms which produces changes in states depend fundamentally on the interactions and motion of its component $preon{{s}^{\left( + \right)}}$ , the rate at which any mechanism causing a given periodic state must be limited by the lowest inner motion speed which is transversal speed of its component $preon{{s}^{\left( + \right)}}$ .

Simple vector calculus shows that the transversal speed of bound $preon{{s}^{\left( + \right)}}$ is given by $\sqrt{{{c}^{2}}-v_{a}^{2}}$ where ${{v}_{a}}$ is the speed at which a clock $a$ travels. It follows that the number of recurrence of a state, denoted $t$ for ticks of a clock, produced over a given reference distance ${{d}_{ref}}$ is proportional to the transversal speed of component $preon{{s}^{\left( + \right)}}$ , that is

$\frac{t}{{{d}_{ref}}}\propto \sqrt{{{c}^{2}}-v_{a}^{2}}$ . It is thus easy to see that as the speed at which a clock travels is increased, the rate at which it produces ticks slows down and becomes $0$ when its speed reaches $c$ .

We have thus explained the observed slowing down of periodic systems without resorting to the concepts of time or time dilation.

So we see that though the predictions of special relativity in regards to the slowing down of clocks (or any physical system whether periodic or not, or biological in the case of the twin paradox) are in agreement with the predictions QGD, QGD’s explanation is based solely on fundamental aspects of reality. Also, since according to QGD, mass, momentum, energy and speed are being intrinsic properties of matter, their values are independent of any frame of reference it precludes the paradoxes, contradictions and complications associated with frames of reference.

However, though both QGD and special relativity predict the effect of speed on clocks, there are important differences in their explanation of the phenomenon and the quantitative changes in rate. While for special relativity the effect is caused by a slowing down of time, QGD explains that it is a slowing down of the mechanisms clocks themselves.

If $t$ and ${t}'$ are the number of ticks counted by two identical clocks counted travelling respectively at speeds ${{v}_{a}}$ and ${{{v}'}_{a}}$ over the same distance ${{d}_{ref}}$ then QGD predicts that

${t}'=t\frac{\sqrt{{{c}^{2}}-v_{a}^{'2}}}{\sqrt{{{c}^{2}}-v_{a}^{2}}}$ .

This prediction sets QGD apart from special relativity’s prediction that ${t}'=t\frac{1}{\sqrt{{{c}^{2}}-{{v}^{2}}}}$ . However, it is important to note that the two predictions of the QGD and the special relativity equations cannot be directly compared. The speed in the relativist equation is the relative speed of the clocks while the QGD equation makes uses the distinct and intrinsic speed of the clocks.

Slowing Down of Clocks due to Gravity

Since ${{v}_{a}}=\frac{\left\| {{{\vec{P}}}_{a}} \right\|}{{{m}_{a}}}$ then $\displaystyle \frac{t}{{{d}_{ref}}}\propto \sqrt{{{c}^{2}}-v_{a}^{2}}=\sqrt{{{c}^{2}}-{{\left( \frac{\left\| {{{\vec{P}}}_{a}} \right\|}{{{m}_{a}}} \right)}^{2}}}$ . We have also shown that gravity affects the orientation of the component $preon{{s}^{\left( + \right)}}$ of structure so that $\Delta {{\vec{P}}_{a}}=\Delta G\left( a;b \right)$ and $\Delta {{v}_{a}}=\frac{\Delta G\left( a;b \right)}{{{m}_{a}}}$ and since ${{{v}'}_{a}}={{v}_{a}}+\frac{\Delta G\left( a;b \right)}{{{m}_{a}}}$ in order to predict the effect of gravity on the rates of clocks, all we need to do is substitute the appropriate value in ${t}'=t\frac{\sqrt{{{c}^{2}}-v_{a}^{'2}}}{\sqrt{{{c}^{2}}-v_{a}^{2}}}$ and we get ${t}'=t\frac{\sqrt{{{c}^{2}}-{{\left( {{v}_{a}}+\frac{\Delta G\left( a;b \right)}{{{m}_{a}}} \right)}^{2}}}}{\sqrt{{{c}^{2}}-v_{a}^{2}}}$

where $\Delta G\left( a;b \right)=G\left( a;b|{{d}_{1}} \right)-G\left( a;b|{{d}_{2}} \right)$ .

As we can see, the greater the gravitational interaction between a clock and a body, the slower will be its rate of recurrence of a given periodic state. This prediction is also in agreement with general relativity’s prediction of the slowing down of clocks by gravity.

Conclusion and Implications

We have shown that the slowing down of clocks resulting from increases in speed or the effect gravity is explained not as a slowing down of time, but as a slowing down of their intrinsic mechanisms.

The effects of the time dilation predicted by special relativity and general relativity are both described by $\frac{t}{{{d}_{ref}}}\propto \sqrt{{{c}^{2}}-\frac{\left\| {{{\vec{P}}}_{a}} \right\|+\Delta G\left( a;b \right)}{{{m}_{a}}}}$ since it takes into account both the effect of the speed and gravity on a clock. Thus, if QGD is correct, the predictions of SR and GR are approximations of particular solutions of the QGD equation.

We will see in a later articles how QGD can predict the behaviour of binary pulsar systems and explain and predict the decay of atmospheric muons, both phenomenon supporting special relativity and general relativity.

The decay of muons is particularly significant as it provides indirect evidence supporting QGD’s prediction that they (and all other particles believed to be elementary) have structure and are composed of $preon{{s}^{\left( + \right)}}$ .

Quantum-Geometry Dynamics

Monday, May 12, 2014

The Slowing Down of Clocks as Explained by QGD

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