The Weight of the Technological Age

With the holiday season still hanging around in our rear view mirrors, many of us have embarked on the quintessential New Year’s resolution, the one that serves to line the pockets of fitness centre owners everywhere.  That is, we ate too much during our winter solstice revelling and now we feel compelled to make at least a token effort to lose some weight.  Well, some of us are, while some others (myself included) continue to stuff our faces well into the New Year.

We – that is to say some of us – are, it seems, obsessed with our body weight.  Having had some experience with the arena of amateur bodybuilding in my younger days, I am all too familiar with the mechanism that serves to make us overly focused on how much we weigh (though I am no longer afflicted so).  What happens to that weight when you “lose” it though?

No, this is not the introduction to a new weight loss scheme or a fad diet, but rather a discussion of the physics of weight, or mass to be specific.

What is weight?  It is the product of gravitational pull on the mass of an object.  Every object has mass, from the smallest organisms to the largest planets, but weight depends on those objects being close enough to each other to combine their natural gravitational pull.

Sir Isaac Newton, who was the first to describe and measure the force of gravity, expressed the gravitational pull of spherical objects (where the majority of their mass can be assumed to be at their core) in terms of the following equation:

F = G (M1*M2/R²)

• F is the force of attraction between them.
• G is a constant that is 6.67259 x 10-11 m3/kg s2 (known as the Gravitational Constant).
• M1 and M2 are the two masses that are attracting each other.
• R is the distance separating the two objects.

So, again, everything has mass, so everything has a measurable weight relative to another object.  On Earth, that other object is generally given as Earth.  When you step on that bathroom scale, the number given is a representation of the result of the above equation.  It gives you a measurement of the gravitational pull between you – your body – and the Earth, expressed in the common terms of pounds or kilograms.  But as you might now be asking, if the scale tells you your weight relative to the Earth, then what does the Earth weigh?

Using the above, one can in fact work out the weight of the Earth, or, more accurately, the mass of the Earth.  And it turns out this is one heavy planet.

The Earth’s mass is approximately 6×10²⁴, or 6,000,000, 000,000,000,000,000,000 kilograms. And one might add that it’s gaining weight, albeit ever so slowly.

In addition to the tons of space dust and meteorite material that enters our atmosphere annually, there is a phenomenon occurring now that is directly related to us and our technology, believe it or not.

It can be argued that Earth’s biosphere is a closed system.  That is to say we, as a planet, neither lose nor gain appreciable amounts of matter or energy as time goes on.  Our material resources are finite, and the use of those resources amounts to a huge exercise in recycling.  This is true, to a point, but it’s inaccurate.

Every bit of energy used on this planet comes from our sun, as in solar radiation energy.  It is used either directly, as in photosynthesis or solar power collection, or even heat, or indirectly as in fossil fuels, or through the consumption of plant materials by animals etc. (There are other ways, of course, but this will suffice for the current discussion.)  The same is true for electricity, whereas it’s either direct or indirect solar energy that initiates the flow of electrons in electric circuits, which by definition is electricity.  Electrical systems make use of this flow by either powering components and thereby using up the indirect solar energy, or storing the potential of the energy in capacitors or batteries for later use.

Believe it or not though, this is contributing to the fluctuation of the mass of the planet.

According to John Kibiatowicz, professor of computer science at the University of California, Berkley, a Kindle e-reader weighs more when it’s fully loaded with e-books than when it’s empty.[1]  Admittedly, the weight difference is so slight that it’s technically unmeasurable in a single e-reader device.  The difference is said to be approximately 10^-18 grams, which is about a billionth of a billionth of a gram, or what is known as an atogram.  Since today’s most sensitive scales have an effective resolution of about 10^-9 grams, it’s beyond negligible, but there is a difference.

It can be scaled up though, and according to Michael from Vsauce in a video on his YouTube channel (see below), when you apply the same logic and mathematics to larger collections of digital information, say the internet as a whole, it turns out that such data weighs on the order of 12 grams or as much as the average strawberry.

This may not make much sense to you, as it didn’t to me until I looked into it.  After all, digital data is just a particular arrangement of imaginary 1’s and 0’s on a hard drive, or on a more fundamental level, the specific arrangement of electrons on the surface of a memory device.  Where they are on the disk shouldn’t amount to a hill of beans in terms of the weight of the device on which they’re stored.  However, as mentioned above, even electrons have mass, and if they have mass, they have weight.  In the case of electrons that weight is beyond infinitesimal, but when there’s a lot of them it can start to make a difference.  Thus, adding more information means adding more electrons, and more weight.

The same is apparently true for fully charged electronic devices vs. devices with no battery power, since charged means only that there are more electrons stored in the devices battery or capacitors.

So how does this mean the Earth is getting heavier?

As mentioned, the Earth is considered a closed system, but it really isn’t.  We’re bombarded on a second by second basis with particles from the sun.  All manner of particles, including electrons.  Some of these particles pass right through, others bounce off our magnetosphere, and others are absorbed in the form of solar energy.  In general this is a two-way street, as heat energy and electromagnetic energy are constantly ejected into space from our atmosphere, however, with the advent of electronics, much more of that energy is retained in our devices than has been released historically.

As has been illustrated though, energy has mass has weight, therefore the more energy is retained in our massive planetary system, in the form of electric potential, the more the planet weighs.  It would never be an extreme weight gain, but compared to other ages of our planet, our penchant for electronic toys has had a measurable impact on the weight or mass of the planet Earth.  This of course has no real impact on anything resembling reality, it’s just interesting food for thought.  Mmm…food.