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The Physics Behind the Nonsense: Kilograms and Instagrams

The Question

On one hand, the kilogram. The SI unit of mass (NOT WEIGHT!). Currently defined as the mass of a certain platinum-iridium cylinder, the kilogram may receive a new definition, or another, soon. For simplicity though, the mass of 1 litre of water is 1 kg.

One of the current proposals for the definition of the kilogram

On the other hand, Instagram. A photo-sharing service, used by millions. Take a photo, apply a filter on it, and share it with the world. Furthermore, an Instagram (note the article an) can denote that said photo sent to the service.

Behold, an Instagram of Instagram!

The question is: how many kilograms are there in an Instagram? In a stricter sense, what is the equivalent mass, in kilograms, of an image sent to Instagram?

How it Works

To answer the question, we need to know what exactly do we mean by equivalent mass. To do so, we need to know how modern computers work.

Instagram – or any electronic service and device for that matter – works on the idea that electrons can be used as a means to store data. Most of the data we currently use is saved either on magnetic hard disks (MHDs) or in solid-state devices (SSDs) such as USB flash disks and SD cards. Instagram is most commonly used with smartphones, which use external or built-in SSDs; hence these storage devices will be the devices of interest  for this

A few examples of solid-state devices.

In essence, an SSD  directly uses electrons to store data in a flash memory (hence the term flash drive). The flash memory has small cells built in it, which store electric charges in the form of excess electrons. These cells are then either  full (1) or empty (0) of electrons. These combinations of 1′s and 0′s, called bits, is what stores the information about the Instagram.

In computing, bits are arranged in groups of 8 to form a larger unit of information called the byte. This term may be more familiar, since this is how electronic file sizes are measured. For instance, a typical Instagram may have a file size of 40 kilobytes, or about 41,000 bytes (1 kilobyte is 1024 bytes). This translates to around 330,000 bits. This means, therefore that the SSD has to use around 330,000 cells in the flash memory to store an Instagram.

The Basic Physics

When a cell in the flash memory is full (1), it contains roughly 40,000 excess electrons. This may seem like a large number, but this number of electrons is nothing to the amount of electrons passing through a light bulb every second (amounts to about \(5 \times 10^{18}\) electrons).

An electronic file like an Instagram normally has about the same number of 0′s and 1′s in it; half of the cells would therefore contain excess electrons. Thus, 330,000 bits will be divided approximately equal numbers of empty cells and full cells.

The mass of the electron at rest is known to be  \(9.11 \times 10^{-31}\) kg.

Now, let’s commence the determination of the equivalent mass of an Instagram.

\(m_I = N \times \frac{8\:bits}{byte} \times \frac{1\:cell}{2\:bits} \times \frac{40,000\:electrons}{cell} \times \frac{9.11 \times 10^{-31} kg}{electron}\)

where

\(m_I = mass\: of\: the\: Instagram\) and \(N = file \:size,\: in \:bytes \)

The fraction \(\frac {1 \: cell}{2 \: bits}\) takes into consideration the approximately equal distribution of bytes between empty and full; that is, 2 bits has the equivalent mass of an empty cell and a full cell together.

\(m_I = 41,000 \: bytes \times \frac{8\:bits}{byte} \times \frac{1\:cell}{2\:bits} \times \frac{40,000\:electrons}{cell} \times \frac{9.11 \times 10^{-31} kg}{electron}\) this, we can find the mass of the electrons comprising an Instagram to be:

\(m_I = 0.00000000000000000000597616 kg= 5.97616 \times 10^{-21} kg\)

This mass is so small, no measuring technique has been developed yet to determine this mass. The smallest mass ever measured is that of a group of xenon atoms, with a mass of a few bilionths of a trillion of a gram, or in the order of \(10^{-15}kg\).  This is similar to the proportionality in the masses between a human and an oil supertanker, or a human and a flea. So the mass of an Instagram is barely there.

So, where do all these additional electrons come from? They all come from a power source, which place the cells in the flash memory in their proper states. This also explains the nature of flash memories, which have no mechanical parts and therefore could last much longer than CDs or MHDs. Electrons are the only things that move about in a flash memory.

Application

This is one instance wherein the application was in place before the question, as flash memories and smartphones have been around far longer than Instagram. However, the ideas behind the answer are what drive current technologies such as the aforementioned smartphones, tablets, USB flash drives, solid-state hard drives, and other file-storage devices. All these devices have enabled us to be more mobile, having to carry a lot less mass than what we would do in the past.

Just 20 years ago, most books were printed on paper and had no electronic equivalent. Music was limited to cassette tapes and CDs which could carry one album from a recording artist. Movies had to be shipped as film to various cinemas, resulting in uneven release dates. Office work that had to be brought from one place to another required huge boxes. Now, one device about 200 g in mass can contain everything mentioned in the list above, and can be accessed easily and instantly. Instagram just happens to be one of the applications of electronics that has dominated our lives over the past few decades.

Final Thoughts

This is going to be the first of a series called The Physics Behind the Nonsense, where we take seemingly weird and whimsical questions and answer them with Physics concepts.

Sources

• http://discovermagazine.com/2007/jun/how-much-does-the-internet-weigh#.UaNCQED040E


• http://wiki.answers.com/Q/How_many_bits_are_in_a_byte


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


• http://instagram.com/


• http://www.universetoday.com/38394/charge-of-electron/


• http://searchinstagram.com/


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


• http://science.slashdot.org/story/05/04/01/2323209/scientists-weigh-smallest-mass-ever


• http://asburyandasbury.typepad.com/.a/6a010535893544970c017d3ef41caa970c-800wi


• http://phys.org/news/2011-02-kilogram-approaching-avogadro-constant-enriched.html


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

The Physics Behind the Nonsense: Kilograms and Instagrams

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Classification_Terms

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Adventure Time!

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The Misconception of Mathematics and Women

A pretty common misconception about mathematics is that women and girls are not that good in it. As a teacher, I know this is not true.Here is an infographic about mathematics and women.

 

Makes you ponder, doesn’t it?

The Misconception of Mathematics and Women

Immovable vs. Unstoppable: What's Gonna Happen?

The Question

A few days ago, some students asked what would happen when an unstoppable force meets an immovable object. It was an innocent question, but one that caused the whole class to stop work and ponder on the answer. Since the class was supposed to cover a whole different topic on physics (thermal transfer),  I decided to answer the question, under the condition that we had to finish the topic before going through the physics behind the force and the object.

The Situation

An object is immovable. Something that is unstoppable comes along. What happens when they meet?

This is actually a common metaphor used in the English language, where two large entities collide in an epic showdown. But aside from common usage, this is actually a very common question in introductory Physics courses in university.

So what would happen, theoretically, when this does happen?

The Physics

For simplicity, let’s call the unstoppable force the Ball,and the immovable object the Wall.

The Ball is unstoppable. This means two things. First, it is moving. Second, it cannot stop. In physics terms:

The Ball is always in a state of constant velocity, and will never experience a reduction in its velocity. It will never experience deceleration.

When acceleration is being considered, then force must also be accounted for. Newton’s second law of motion guarantees it.

Let’s take a closer look at this. If the ball has any finite value for its mass, any force can make it accelerate. Hence, anything with a finite mass cannot be the unstoppable ball. This then leads us to the conclusion that the ball has to have an infinite mass.

Now, let’s look at the Wall. Since it does not move, its velocity (relative to us observing it) is always zero. Again, using some physics terms:

The Wall is always in a state of zero velocity, and will never experience an increase in its velocity. It will never experience acceleration.

Let’s analyse the Wall. If it had a finite mass, it would accelerate when a force is applied. It’s almost just like the ball. So we can get to the same conclusion that the Wall has infinite mass.

Many physical laws, especially Special and General Relativity, will have to broken to get infinite mass. However, since we are simplifying everything by ignoring other laws of physics, let’s make the Wall and the Ball collide.

Since the two entities cannot accelerate, nothing should happen when they collide. And by “nothing”, we do mean it. The Ball does not decelerate, so it passes through the Wall. But the Wall does not accelerate in any way (including breaking down), so it must stay whole and unmoving. This means that there should be no interaction between the Wall and the Ball.

Here’s another way of looking at this problem.

A bit anticlimactic, but what can we expect? The whole problem breaks every law of physics that we know.

A Possible Way About This

Since the Wall and the Ball passing right through each other is not too realistic, it’s time to approach this another way.

Immovable is simple enough. The Wall cannot move at all. However, just because the ball is unstoppable does not mean it cannot be deflected. In other words, the problem is not clear as to the Ball has a constant speed or a constant velocity.

If the Ball has a constant speed, then it is still unstoppable, but can still be deflected. The end result now would be that the Wall still does not move, but the Ball is moving one way and then the other.

This time, another law of physics is broken: The law of  conservation of  momentum. Essentially another form of Newton’s third law of motion, this is now the final blow to the scenario.

In Summary

The scenario of an unstoppable force and an immovable object is not only physically impossible, but mathematically nonsense (a paradox). If both exist, nothing else does, and we would not be here to discuss this problem.

I know most of this would be unsatisfying, but don’t worry. You’re not alone, as I am still wondering about the Wall-and-Ball situation even after I have finished writing this article. You have to admit though, that was a good topic to discuss.

Immovable vs. Unstoppable: What's Gonna Happen?

When I was taking a break in Bali, I came across a place with a glass tank for a ceiling. The water in the tank was oscillating with the wind, and the sun was in the perfect place its light to shine down from the sky to the floor. It was a marvel by itself, and then I looked at the floor.

Physics is simply beautiful.

The Beauty of Physics: Waves and Light

Approximations of Some Numbers

 

Approximations

 

Source

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

An Insider: Homework for Radioactivity

This post contains the homework for my Secondary 4 students on radioactivity. Click here to download it.

S4 Homework

An Insider: Homework for Radioactivity