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 2018 in optics and photonics

It's that time of the year again, the time to look back on what was accomplished. I couldn't find the time or the energy to write this sooner, and I kind of left this to the last minute. But well, here it is now, the photonics news that really caught my eye this year:

OSA Photo Contest winner

Here is the photo that won this years annual OSA Photo Contest! 


Shot by Tobias Tieß from Leibniz-IPHT, Germany, the photo features a glass cup filled with fluoresciing liquid and a UV-laser is coupled into the handle of the cup. Quite nice effect, I must say. The rest of the contestants can be found here.

Nobel prize

The Nobel prize in physics was awarded "for groundbreaking inventions in the field of laser physics," To Donna Strickland, Gerad Mourou and Arthur Ashkin. I made a whole post on this, which you can find here for more info.

SI system redefinition

The SI system underwent a major overhaul! Or to be more precise, it was decided that it will be overhauled, but meh, close enough. You may have heard that the kilogram was redefined, but the consequences were actually more far-reaching than that.

Speeding up diffractive design

These days people can design astounding diffractive optical elements, for example via inverse design. But these methods are always computationally very demanding, and complex designs have become possible only recently, due to increase in processing power. Even with very powerful computers, we are still constrained to the domain of nanophotonics and millimeter sized structures are far out of reach. However, a new approach has sped up the process astoundingly. For example, a calculation that would take 60 000 years and demand 3 822 TB of RAM memory, can now be done in 11 hours and with 244 MB of memory! Of course, the new method comes with restrictions, but it's a big step in the right direction.

One way Möbius strips, for light

You've probably heard of the Möbius strip, the geometrical object where you can travel on both sides of the strip without going over the edge. Did you know that you can achieve a similar geometry with light as well? Well, you can with a twisted cavity, and now a group of researchers have used such a cavity to produce a one way path for light. It's kinda like a Möbius strip where you can travel only towards one direction, a diode for light if you will.

When doughnuts fly

Ever seen a flying doughnut? Maybe you have, but not one made of light. They are bascally complex, doughnut shaped electromagnetic pulses and they have been theoretically predicted over 20 years ago. However, no one has figured out how to actually make them, until now. Mind you, the research is still theoretical, but it proposes a plausible way of creating these pulses, by using an array of metamaterials. Finally, doughnuts may fly! 

Entangled photons from Q-dots

Quantum entanglement is a fancy trick that can be used for many next generation devices, especially in quantum communication and cryptography. But the problem is that producing entangled photon pairs with parametric down conversion requires bulky equipment. It has been known for a while that quantum dots (tiny devices that can even be found in new televisions) can produce entangled photons pairs, however, their efficiency is quite low. Now a team of researchers has found a way to fabricate dots that have an efficiency comparable to parametric down conversion. This could drive research towards next generation quantum internet, among other things.

Quantum cryptography distance record

Speaking of quantum stuff, researchers achieved a new record in the transmitting distance of quantum crypted signals. The new record is a whopping 421 km, which is a somewhat modest increase from the earlier 404 km. Although, the distance record came together with a speed record as well, and the team demonstrated quantum key distribution rates over 100 times higher than before.

Location, location, location

This year also saw the advent of a new location measurement scheme for nanoparticles. The scheme can be used to measure the location of hundred nanometer -sized particles with a resolution of \( 3 \times 10^{-10}\) m, which is about three times the diameter of a hydrogen atom. To top it off, the uncertainty in the measurement was just \(0.6 \times 10^{-10}\) m. This is quite exciting, since conventional wisdom states that you can't measure something that is smaller than the wavelength of the probing light.

Tabletop X-ray spectroscopy

High harmonic generation is a non-linear process, where an intense pulse of light is shot into a target material (gas, plasma, ion shower, you name it) and the pulse generates new pulses with wavelengths that are several times shorter than the original pulse. Now, the scheme has been extended to x-rays, and namely x-ray spectroscopy. This type of measurement may provide a large amount of information about matter, but to employ such modalities usually requires large synchrotron or free-electron laser facilities. On the other hand, a high harmonic generating scheme is a table-top setup and rivals the precision of large facilities, opening up many possibilities.

Let it rain!

Inducing rain is usually done by sprinkling chemicals over potential rainy clouds. The sprinkled chemicals act as nucleation centers, which kick start the precipitation process, and this way it is possible to control where a cloud rains down. However, concerns have been on whether the use of chemicals in this way is safe. Worry no-more, because we now have laser to do it! Or at least there is patent claiming that it can be done. The idea - it seems - is to shoot an extremely intense laser pulse into the cloud, ionizing the air, and water vapor and whatever, which also has the ability to kick start the precipitation. Cool, huh? 


That's pretty much it for the research that caught my eye this year. If you have any gems you want to add to the list, don't hesitate to comment! IHappy new year to everyone, see you next time!

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