#Fused Quartz Etched by Femtosecond Laser

Some articles on this technique [here](http://live.iop-pp01.agh.sleek.net/2016/05/19/optical-memory-enters-5d-realm/), [here](http://spie.org/news/6365-eternal-5d-data-storage-via-ultrafast-laser-writing-in-glass) and [here](https://spie.org/about-spie/press-room/press-releases/background-on-billion-year-5d-storage-breakthrough-published-by-spie?SSO=1), and a wikipedia article with more references [here](https://en.wikipedia.org/wiki/5D_optical_data_storage). According to that first article, 

>The current data-writing system is not much different from that found in CD or DVD drives. Ultrashort laser pulses with a wavelength of 1030 nm are focused inside a spinning glass disc and the position, power and polarization of each pulse are simultaneously modulated depending on the encoded information – leaving a trace of pits with different optical characteristics. Reading the data is more complicated because it requires a microscope-based birefringence measurement system, but we are now working on how to solve this problem.

The [original paper](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.033901) says that they estimate how long the data will last by looking observed decay rate of the nanovoids (the 'pits' made by the laser as mentioned above) at "several annealing temperatures in the range from 1173 to 1373 K", and then using the [Arrhenius equation](https://en.wikipedia.org/wiki/Arrhenius_equation) to extrapolate the decay rate at other temperatures. In fig. 4 they present the following chart showing the "thermally activated decay time" $\tau$ (which they mention is equal to $1 / k$, where $k$ is the decay rate in the Arrhenius equation) as a function of the temperature $T$:

[![enter image description here][1]][1]

So, though one would have to preserve the fused quartz records in a place where they will be extremely well-protected from shattering (as fused quartz is a type of glass), the time that would pass before the information would degrade due to ordinary thermal decay is extremely long--longer than the current age of the universe (13.8 billion years) at a temperature of 462 K (189 C) or less, and $3 * 10^{20}$ years at a room temperature of 303 K (30 C).

Edited to add: Ultimately if you are concerned about preserving the information indefinitely on cosmological timescales (as suggested by your comment about heat death), you will want the civilization to periodically make new backups and store them in different locations throughout the universe, so that the probability that *all* records of some information are destroyed is continually decreasing over time. If the probability of all records of some information getting destroyed *isn't* decreasing this way, if you wait long enough it becomes a virtual certainty you'll lose that information. Say in a given million-year timespan the probability is $q$ that the civilization loses some item of information due to all records of it getting destroyed, so the probability the information is preserved in that timespan is $(1 - q)$. Then naturally if the probability is same in the next million years the total probability the information will be preserved for 2 million years will be $(1 - q)*(1 - q) = (1 - q)^2$, if the probability remains constant for 3 million years the probability the information is preserved in that time is $(1 - q)^3$, and so forth. No matter how close $(1 - q)$ is to 1, there's going to be some sufficiently large exponent $N$ such that $(1 - q)^N$ becomes arbitrarily small. 

On the other hand, suppose the probability the information is preserved in the first million years is still $(1 - q)$ but the probability it's preserved in the next million year span is $(1 - q^2)$ and the probability it's preserved in the next million year span after that is $(1 - q^3)$ and so forth. So here the probability the information is preserved for 3 million years is $(1 - q^1)*(1 - q^2)*(1 - q^3) = \prod_{k=1}^{3} (1 - q^k)$, using [Pi notation](https://mathmaine.com/2018/03/04/pi-notation/) for products akin to [Sigma notation](https://en.wikipedia.org/wiki/Summation#Capital-sigma_notation) for sums. Then if that pattern continues indefinitely the probability the information is preserved approaches a nonzero limit $\prod_{k=1}^{\infty} (1 - q^k)$, which according to [this mathematica page](http://mathworld.wolfram.com/q-PochhammerSymbol.html) is given by the Euler function $\phi (q)$, and the page also shows a graph of its value for different values of $q$.


  [1]: https://i.sstatic.net/fafC6.jpg