We witnessed the invention of atomic clocks of incredible accuracy, whose physical properties differ very much from the clocks Einstein imagined. This will be discussed in some detail in Chapter 3. Let us mention here a real difficulty resulting from internationally adopted definitions. The unit of length is based on the wavelength of a spectral line of krypton-86 under carefully specified conditions with accuracy $10^8$ and the unit of time is based on the frequency of a spectral line of cesium with accuracy $10^{12}$. Hence, the same physical phenomenon, a spectral line, is used for two different definitions: length and time, and the velocity $\,c\,$ of light remains undefined and looks arbitrary. It should be stated, once and for all, whether a spectral line should be used to define a frequency or a wavelength, but not both!

Indeed, according to Wikipedia: "in 1967 the

Let $\,m_0\,$ be a reference elementary particle mass as it is here and now at a timestamp $(0)$ and let $\,m\,$ denote the same elementary particle mass mass after some change. Then we thus have: $$ \frac{\Delta L}{\Delta L_0} = \frac{\Delta L/c_0}{\Delta L_0/c_0} = \frac{m_0}{m} \hieruit \frac{\Delta t}{\Delta t_0} = \frac{m_0}{m} $$ As a consequence of all this, according to Brillouin: the velocity $\,c_0\,$ of light [..] looks arbitrary. Worse, the speed of light has been more or less

Click on Pic

# Gravitational constant G := 6.6743*10^(-11); # Mass of the earth M := 5.9722*10^(24); # Radius of the earth R := 6378*10^3; # Period of clock T := evalf(2*Pi*sqrt(R^3/(G*M)))/60; T := 84.48611832From Wikipedia: The

Let's revisit the equation $\,\omega = \sqrt{GM/r^3}\,$. Suppose that quantities are affected by Variable Particle Mass. If we substitute back in Newton's equations, then we have, with primed (') the changed quantities and otherwise the original ones here and now: $$ \omega' = \sqrt{G\frac{M'}{r^3}} \slechts \omega\times\sqrt{m/m_0} = \sqrt{G\frac{M\times m/m_0}{r^3}} \slechts \omega = \sqrt{G\frac{M}{r^3}} $$ From this the following should become clear:

*With Newton's laws alone - that is: with*.**inertia and gravity**and nothing else, in**orbital time and empty space**- then it makes no difference whether (elementary) particle (rest) mass is varying or not

Conclusion:

More important, however, is the following.
**Orbital time** and **Atomic time** can only be distinguished from each other
*in combination* - provided, of course, that Halton Arp's hypothesis is indeed true.
You can measure one with the other, but a variable time tick - orbital or atomic - cannot be measured with itself.
For **the two pure clocks** - orbital and atomic - this leaves us with only two possibilities:

- Atomic time is measured with Orbital time
- Orbital time is measured with Atomic time

- The formula $\,dT/dt=\sqrt{m/m_0}\,$ shows how Orbital time $T$ is measured with Atomic time $t$
- The formula $\,dt/dT=\sqrt{m_0/m}\,$ shows how Atomic time $t$ is measured with Orbital time $T$

There is evidence. According to Wikipedia,
there exists an **Anomalous increase of the astronomical unit**: *Recent measurements indicate that planetary
orbits are widening faster than if this were solely through the Sun losing mass by radiating energy.*
Let's see. Because $m > m_0$ in the future we simply have:
$$
\frac{dT}{dt} = \sqrt{\frac{m}{m_0}} > 1
$$
Therefore planetary orbits - *being* gravitational clocks - should indeed be more increasing than expected,
that is: *widening faster*. The reverse might be true as well. Far aways (younger) objects in outer space
have lower elementary particle rest mass $m/m_0 < 1$ and therefore are expected to orbit faster.

*A New Approach to Special Relativity* is suggested in Léon Brillouin's book Relativity Reexamined, as we have seen already in
Length Contraction. The "new approach" starts with the mass-energy relation, and variable mass
is in there from the very beginning:
$$
E = mc^2 \EN m = \frac{m_0}{\sqrt{1-v^2/c^2}}
$$
So we have, according to the findings above, for *atomic time*:
$$
\frac{\Delta t}{\Delta t_0} = \frac{m_0}{m} = \sqrt{1-v^2/c^2}
$$
This means that clock ticks become smaller as velocity increases. Hence more clock ticks are needed in order to measure
the same time span as with "a particle at rest". Thus corresponding with Time Dilation according to Special Relativity.

Last but not least, let's talk about time according to Einstein, or Einstime for short. The picture below is from Spacetime- Right or Wrong? by Doug Marett (2013). The well known Time Dilation from Special Relativity is shown on the right.

There exists a critical essay, written by Léon Brillouin
at the end of his life. The title of the booklet is *Relativity Reexamined*.
Quoting without permission from page 33:
Einstein's clocks were supposed to emit extremely short signals and to
accurately measure time intervals between signals emitted and received.
In a word, *an Einstein clock was a radar system*, and its requirements
were thus very different from those of a frequency standard.

With varying elementary particle mass according to UAC there is another time dilation in addition to the relativistic one.
It is already known that the arm length $\,d\,$ of the device (in the above picture) is shrinking,
so we have:
$$
\Delta t = \frac{2d}{c_0}=\frac{2d_0}{c_0}\frac{m_0}{m} \hieruit \frac{\Delta t}{\Delta t_0} = \frac{m_0}{m}
$$
Thus even the Light Clock as conceived by Albert Einstein (defining "Einstime") is no exception to the rule.

Right from the start, Sean Carroll says: For example, the early universe has low entropy. That's where the arrow of time comes from.

At 40:30 minutes, Sean Carroll and companion start talking about time reversibility. At 41:30 minutes: [ Space and time ] are different, obviously, because, unlike space, time has a direction. And I wrote a whole book on this [ .. ]: From Eternity to Here.

It actually

The laws of physics seem to be in support of time reversibility. But that is only the case if these laws can be considered apart from initial and boundary conditions. Now let us only agree upon the fact that, in the end, all classical calculus boils down to Numerical Analysis, for the simple reason that you must get numbers out. But Numerical Analysis is not continuous: it is discrete. Within a discrete substrate, it's not at all obvious that the laws are independent of the boundary conditions: The only