The Physics Behind the Nonsense: Kilograms and Instagrams

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.

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 these excess 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 5×1018 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. Since the mass of an electron at rest is known to be 9.11×10-31 kg, we can therefore calculate the equivalent mass of an Instagram by:

    \[m_I = N \times \frac{8 \text{ bits}}{ \text{  byte}} \times \frac {1\text{  cell}}{ \text{  2 bits}} \times \frac {40000 \text{  electrons}}{ \text{  cell}} \times \frac {9.11 \times 10^{-31}  \text{  kg}}{ \text{  electron}}\]

where m_I = mass of the Instagram and N= file size in bytes. The fraction \frac {1\text{  cell}}{ \text{  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. Solving this, we can find the mass of the electrons comprising an Instagram to be:

    \[ m_I =  41,000{\text{ bytes}} \times \frac {8 \text{  bits}}{ \text{  byte}}  \times   \frac  {1  \text{  cell}}{2 \text {  bits}}  \times \frac  {40,000 \text{  electrons}}{ \text{  cell}} \times \frac  {9.11  \times 10^{-31} \text{  kg}}{\text{  electron}}\]

    \[m_I=0.00000000000000000000597616 \text{ kg}= 5.97616 \times 10^{-21} \text{ kg}\]

For comparison, 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 10-21 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 does not add too much to the mass of a device.

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 device.

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

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