Time

is time an illusion?

we only live for 2.3 billion seconds, don't be shocked!

the average global life expectancy is 74 years.

if we were to calculate it:

$$total\ seconds = 74 \cdot 365.25 \cdot 24 \cdot 60 \cdot 60 \approx 2.3 \times 10^9 seconds$$

clocks create cosmic mess

while I was going through this article, it really caught me off guard, and I wanted to share it as well, so please bear with me.

as per the article:

• a clock cannot exist without actively making the universe more chaotic.
• to measure a single tick of time, a clock's counter must undergo an irreversible physical reaction.

what it means is that every clock increases the entropy of the universe.

the fundamental limit of a clock's precision $\Delta t$ is given by:

$$\Delta t \geq \frac{h}{E}$$

where $h$ is the Planck constant and $E$ is the energy of the clock.

so to make a clock twice as accurate, you must generate twice as much heat and entropy.

14,000-Foot mountain time experiment

article

here the scientists took ultra precision clocks up to 14,000-foot summit of Mount Blue Sky in Colorado to measure time dilation against ground clocks. Optical clocks have broken precision barriers, measuring time shifts down to 1 part in $10^{18}$.

the fractional frequency shift is given by:

$$\frac{\Delta f}{f} = {g \cdot h \over c^2}$$

where $c$ is the speed of light, $L$ is the distance between the clocks, and $v$ is the velocity of the clock.

for a 4,348 meter high mountain, the time dilation is given by:

$$\frac{\Delta f}{f} = \frac{9.8\,\text{m/s}^2 \cdot 4348\,\text{m}}{(3 \times 10^8\,\text{m/s})^2} \approx 4.73 \times 10^{-13}$$

converting to nanoseconds per day:

$$4.73 \times 10^{-13} \times 86{,}400\,\text{s/day} \approx 4.09 \times 10^{-8}\,\text{s/day} = 41\,\text{ns/day}$$

this means the clock on the mountain summit will run faster than the clock at ground level by about 41 nanoseconds per day, tiny but real and measurable proof of einstein's general relativity.