Approximations of Some Numbers

 

Approximations

 

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Approximations of Some Numbers

Using ATutor: My Own Online Physics Class

2008. I was having trouble with keeping up with classes. The reason: every teacher’s chronic request – more time. At that time, I was teaching secondary General Science. So I decided that I need a blog. The blog was about General Science, tailored to what I wanted to cover in order to catch up with lessons.

A few months later, I needed better functionality than what a free blog could give. So I decided to buy a web domain. Same deal, but with more interactivity. I felt it was going somewhere. And so the idea grew in my head, that web-based content would be very useful in teaching.

Now, a few years after starting the website, I have decided to take a new direction. I have bought a new domain, and this time I have full control of the site. Doing this felt good, as I have installed ATutor into the site.

ATutor is a learning management platform for the web, and I have been playing around and tweaking with it to get familiar with how it works. So far, it has allowed me to give the proper content to the students, both in General Science and Physics. Though a bit intimidating at first, ATutor is easy to use once you get the hang of things.

There are other learning platforms out there in the Internet, so don’t take my word for it. I have tried two other learning platforms, and they were great in their own regard. In my experience, ATutor has the easiest install and setup of all the ones I tried. Problems also arose, and this is where ATutor shone more than the others. Google searches for solutions had excellent content, and had, as of this writing, a 100% success rate in fixing issues.

And the best part? It’s open-source software, so it’s free to download and use!

If you have any suggestions or questions, feel free to comment below and I’ll answer as promptly as I can. Hope to hear from you soon!

Using ATutor: My Own Online Physics Class

Quantum Mechanics and (Future) Internet Security

The News

German physicists working on secure data connection have developed an improved method to transmit data securely from one computer to another, using the ideas of quantum mechanics.Some institutions, like banks and certain agencies of government, have started using quantum cryptography to ensure that data transmitted through their networks are secure.

How it Works

Encryption is the securing of data transmitted from a source. There are many ways to do this, ranging from a simple code to a complex mechanical device to computer codes.

In essence, encryption is used to make a message unreadable by anyone without a key. Let’s say that Alex has a message for Bob.

APPLES ARE SWEET.

To encrypt this message, Alex needs a key to translate this into what looks like gibberish. To illustrate the point, let’s use a simple encryption key: A becomes B, B becomes C, and so on. The encoded message should look like this.

BQQMFT BSF TXFFU.

The encrypted message now looks like gibberish. Bob then needs the key, and use it in reverse to read the message.

Messages sent through encryption can be as simple as this. A more likely scenario for using encryption in our daily routines is the usage of the Internet, with all the usernames, passwords, credit card information, and a plethora of other personal information.

Historically, all encryption was done either mechanically or mathematically. This means that with enough time and the proper resources, most simple encryption is crackable. This is very applicable today, where computers can simply try to use every possible combination to find the key. So to help prevent this, several security systems based on mathematical ideas were developed, and are still used now. Essentially, two keys are used by a computer: a public key that everyone can access, and a public key that only the computer knows. These methods are collectively known as asymmetric encryption.

There is still a problem with this. Anyone that somehow gets both keys can theoretically steal the data without you being the wiser.

The Basic Physics

This is where quantum physics comes in. The key idea that applies in data security here is Heisenberg’s uncertainty principle, which states that for any particle, both its velocity (more accurately, momentum) and position cannot be known with 100% certainty at any particular time. This is due to the fact that everything exhibits wave-like and particle-like behaviour at all times. This is more apparent with molecules, atoms, and anything smaller; the tinier the particle, the more wave-like it is.

Well, that’s how most physics sources explain it anyway, but it’s a little difficult to imagine. Here’s another way of looking at the uncertainty principle. Let’s look at an electron, which is a very tiny particle. So tiny, it can be affected heavily by quantum mechanics.

Let’s keep our electron in the dark, literally. Just the electron in space, moving about. Let’s pretend that we, as the observers, do not affect the electron in any way.

If we assume that the electron’s velocity is known with 100% accuracy, then there is no way we can know where it is. It’s like saying, “Our car is going at 100 km/h, but I don’t know where my driver took it now.” Same thing with the electron: since we only know how fast it is going, we may be able to calculate where it is (using classical physics that does not work in the quantum world), but we still cannot be 100% sure that it is there at that time.

To know for certain where the electron is, we need to look at it. To do so, we need to shine some light on the subject. Most of us know light as a wave (an electromagnetic wave, to be precise). But since light moves very fast and has a small wavelength, we can also consider this to be a particle, called a photon.

The difficulty now is that when we observe something, a photon has to come from that something to our eyes. So for us to actually know where the electron is, a photon coming off an electron has to be sensed. In order to do that, either a photon has to come directly from the electron, or has to bounce off the electron.

We know that when two things bounce off each other, their new motion paths are different from the old ones. And as with regular collisions, an electron and a photon bouncing off each other will change each other’s momentum. So we may now be able to “see” the electron, we cannot know where it is now headed. Furthermore, the diagram shows that we know where the photon is coming from. But in practice, we never know where exactly the photon comes from.

And finally, the time that passes by between the collision and the observation will also come into effect. The more time between the collision and the observation, the more uncertain we are of both the position and momentum of the electron, since the electron can still collide with other photons. This all adds up, and therefore the electron’s state of motion has now changed.

In summary, the mere act of observing anything on the quantum level changes the information associated with it. So how does this link to data security?

Application

Quantum cryptography is still based on the same mathematical principles behind asymmetric encryption. The additional security we get from this stems from the fact that observation changes the state of the data.

Let’s look at two scenarios with quantum cryptography. In the first scenario, no data is stolen. In the second, data was stolen.

Scenario 1: No data taken

• Data is transmitted.


• No outside observer, so no change in quantum state of keys.


• Everything’s A-OK!

Scenario 2: Data was stolen

•  Data is transmitted,


• Thief has to observe data. Quantum states of data change due to observation. Thief has unreadable data due to changes in quantum states.

Here’s an infographic on how this works, in more detail.

A graphical explanation of quantum encryption.

It would be helpful to think of the polarisation of each photon as the quantum states. In fact, it is one of the quantum states we are talking about. As seen with Eve the eavesdropper, an attempt to intercept the message with the wrong decoder changes the quantum state of the data, making it unreadable.

That, dear readers, is how physics is related to your online security. In the future, we’ll see what we can come up with

Sources

• http://phys.org/news/2013-04-physicists-successfully-transmit-quantum-code.html


• http://en.wikipedia.org/wiki/Quantum_cryptography


• http://www.howstuffworks.com/encryption.htm


• http://www.computerhope.com/jargon/b/brutforc.htm


• http://www.webopedia.com/TERM/P/public_key_cryptography.html


• http://www.scientificamerican.com/media/inline/000479CD-F58C-11BE-AD0683414B7F0000_quantum.gif

Quantum Mechanics and (Future) Internet Security

Test Post from Freaky Physics

Test Post from Freaky Physics http://www.freakyphysics.com

Test Post from School Science Site

Test Post from School Science Site http://www.schoolsciencesite.com

Teaching Physics Without Too Much Effort, and Another New Look!

I’ve been teaching physics to kids for at least seven years. I know that’s not a long time in absolute terms, but it’s pretty amazing what you can pick up and learn over such a time span. There’s a lot of things that can be done, either to link different areas of study, or to make one point last long. And so, here’s the big pitch: Not only will I be posting stuff related to learning physics (and science in general), but I will also be posting stuff on how to teach physics in a manner that works efficiently.

There’s also gonna be a new look to the site, as I have received feedback that the last one did not have an intuitive feel to it, especially in terms of clicking and reading through articles. Most of that feedback came from my students. I do feel that there is some wisdom in a young one’s requests (like this story about Harry Potter author J.K. Rowling), so I have turned it back into a click-and-read site.

Finally, I now have some time I can use to update the site again. Since the last time, I have had several ideas, which I wanted to either write down or share, but just could not do so. So here’s to a few new things to look forward to. Thanks for sticking around!

Teaching Physics Without Too Much Effort, and Another New Look!

xkcd What If? Series

As I have previously posted, I read the comics posted on www.xkcd.com. The humor, at least for me, is great in that it makes you think. But sometimes, you need something new in life.

A few months ago, that something new came up as a section: the What If? page. It’s as simple as it sounds. What if _________________? Most of the time, site readers submit the questions and one gets answered every week.

Here’s one of my favourites. It’s such a simple question, but with a lot of physics in it. Here you go…

If you enjoyed that, just keep reading. There’s a lot to go through, and more coming every week!

xkcd What If? Series