Is 0.999... = 1? (spoiler alert: no it is not)

You may have encountered the popular claim that \( 0.999... = 1 \), where the three dots signify that the decimal continues forever. This is a somewhat weird claim, since it would mean that mathematics is broken. There should be no way for two different numbers to have the same value. What makes it weirder is that this is quite popular claim. I've even seen mathematicians say that it's true! But is it though? One popular proof is to first denote \( S = 0.999...\) and then multiply by \(10\) to get \( 10S = 9.999...\) and subtract \( S \) from it, to get  \( 10S - S = 9.000...\) and finally dividing by \(9\) yields  \( S = 1.000... = 1 \) and we see that  \(0.999... = 1\)! However, there's a problem. This short derivation is not strictly speaking correct. It is veeeery close to being correct, and to see why let's look at finite decimals first. Let's say that \(S = 0.999\) (note that this is not the same as \(S = 0.999...\) ). Let's do the same trick as before, so

The year 2019 in optics and photonics


Another year, another review. 2019 was quite a wild year for me, and whew, what a decade it has been! It's hard to imagine that at the beginning of the decade, I was still in high school. In chronological order, starting from 2010: I graduated from high school, served in the army, moved across the country, got my BSc, met five Nobel laureates, started a scicomm platform, got my MSc, moved abroad for work, moved back, got my PhD, got married, moved again across the country, and got a postdoc position. I don't think there will be another decade quite like this one for me!

What was your year/decade like? Share in the comments!

The winner of this years OSA photography contest, by Dr. Pascale Müller and Prof. Dr. Dan Curticapean: the cross section of a bean, imaged with a scanning electron microscope and digitally colored.

Anyway, let's get to the sciencey stuff; here are the news that caught my eye from the past year:

Nobel prize in physics

This years Nobel prizes went to James Peebles (one half), Michel Mayor (quarter) and Didier Queloz (quarter). Peebles is known as the father of modern cosmology, and his first major contribution to cosmology was that he derived the likely properties of the cosmic microwave background radiation from first principles, and discussed its implications for the thermal history of the universe and the amount of baryonic matter it contained. He followed this up with another contribution in the same year on the blackbody radiation content of the universe.

Michel Mayor and Didier Queloz shared the other half of the prize for their work on Doppler spectroscopy. With this method, it is possible to determine whether a star is orbiting around some nearby point in space by looking at the Doppler shift of the emission spectrum. If there is a stable periodic redshift followed by a blueshift, it implies that the star has a massive nonluminous companion, which orbits the same central point as the star. Their work allowed for the first detection of exoplanets.

How to shape a single photon

This topic close to my heart: single photons and their spatiotemporal shape. We know from earlier experiments that it is possible to shape the spatial distribution of a photon (popsci article on the subject: https://phys.org/news/2016-07-birth-quantum-holographymaking-holograms-particles.html), and now, new research is showing that in addition to spatial extent, photons also have some temporal structure. The researchers were able to take an incoming photon with a temporal width of 500 μs, and shrink it three orders of magnitude to 0.5 μs. Afterwards, they were also able to stretch it back to original. This is actually quite big news, because it yields information on one of the oldest and most fundamental problems in modern photonics, what is the shape of a single photon?

Quantum interference across an astronomical distance

This is another really exiting fundamental result this year, researchers were able to take two photons - one from the sun (yes, the sun) and another from a quantum dot in a lab - and show that they in fact do interfere!

Light seems to pull electrons backward

In some specific conditions, light that hits metals can propel electrons away from the direction of the beam. How this happens is actually still an open question, and now a team has found that certain surfaces allow backward propagating electrons, but only if they are in a vacuum. When the surface is exposed to air, the electrons start flowing normally, towards the direction of the light beam. Go figure.

Longer movies at trillion frames per second

A new technique for super high speed video recording has allowed researchers to make up to 12 picosecond videos, with about 200 femtosecond temporal resolution. The method involves a strongly chirped probe pulse, and spectral imaging. Chirping a pulse causes it to stretch and temporally separate the different frequency components; when imaged with synchronized spectral cameras, it becomes possible to make out very fine temporal details.

Squeezing more precision from LIGO

Squeezed light finally got into action! Although the name is kinda goofy, the technique is very advanced and now it is going to be used in an actual measurement device for the first time. Squeezing light means that the uncertainty quadratures are modified so that the one we want (for example phase sensitivity) is "squeezed" to achieve better resolution, while the other one (in this example, number of photons) will be stretched out. In other words, the uncertainty of one observable is increased in order to decrease the uncertainty of another, keeping their product constant. It is expected that the squeezing boosts LIGO performance by 20-50 %, making it possible to detect even weaker gravitational waves.

Laser-Cooled Plasmas Chill Out to Record Levels

A new record in cooled plasmas was achived, and it is a chilling 50 mK. The research could open up new experimental avenues in strong coupling regime of plasmas, which could help illuminate the states of matter in giant planets, super-dense stars and the cores of fusion reactors.

Radiative Cooler Leaves Rivals in the Shade

With a clever mix of insulation, and a material that reflects visible light but emits infrared, a team has demonstrated passive cooling in direct sunlight, with a cooling power of 96 W/m\(^2\). This translates to a cooling of up to 13°C below ambient temperature around solar noon, showing promise in low power food storage, for example.

Quantum Satellite Probes Exotic Space-Time

Jian-Wei Pan and co have yet again shown their superiority in ground to space quantum tests with their Micius satellite. This time, they probed whether some versions of event formalism could be correct. The theory predicts that a pair of entangled particles decorrelate (or equivalently, de-entagle) as they pass through different regions of a gravitational potential. The team presents results of a quantum optical test using their quantum satellite. They sent one of the entangled photon pair to the satellite and the other was kept on Earth, and found no evidence for the predicted decorrelation effects. Another small step forward in the unification of quantum theory and relativity, I guess.

Laser-Beaming Sound to a Recipient’s Ear

Now it is possible to beam sound directly to the recipients ear, with no need for a receiver! How? by using air as a receiver! With a suitable near-infrared laser, it is possible to shake the water in the air to produce very, very, weak sound waves, that can be heard only when the laser is pointed at the intended recipients ear. I'm just hoping this never makes it into advertising, I didn't want directed ads on the internet, and I sure as hell don't want them in public spaces or stores either!

Thermal Vibrations Can Move Through a Vacuum

Since we started with fundamental results, let us also end at one. A team of researchers has discovered a new phonon transport mechanism at nanometer scales. This represents a previously unknown mechanism of heat transfer in addition to the well-known triplet of conduction, convection and radiation. The team brought two membranes with different temperatures to close proximity of each other, and measured whether there was any change in their temperatures. After the membranes were closer than 600 nm, they started to exchange heat, and surprisingly enough, at a separation of about 300 nm, they settled to the same temperature.


There we go, some of the optics and photonics news from this year. If I forgot something, feel free to add in the comments section. Happy new year, I hope you have a good one!

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