Dr Katie Spalding, a mathematician and science writer, set out to answer this question.
Information in your computers or mobile phones is stored as electrons, those tiny subatomic particles orbiting the outer shells of an atom.
They have a mass in grams of 9.1×10-28
From Einstein’s equation, E = mc2 , this mass can be converted to energy and vice versa.
When you are encoding information in your device they become more energetic.
So, if we work out the change in energy levels between a “full” phone and an “empty” one, we can know the weight of the data it contains.
From Einstein’s equation, E is energy, mass is M and C is the speed of light which is approximately 3 × 108 metres/second. So, lots of energy can come from a very tiny mass.
Dr Katie Spalding quoted John D. Kubiatowicz, a Professor of computer science in the University of California, Berkeley: “A conservative estimate for the difference in energy between a trapped electron and a free one is around 10–15 joules per bit. Plugging that into Einstein’s equation, he calculated that a full 4-gigabyte Kindle e-reader will weigh more than an empty one, but the amount is very small, on the order of an attogram or 10–18 grams. This amount is effectively immeasurable.” It is less than one-tenth the weight of a single HIV-1 virus.
This is too small to be noticed.
Sense, sensation, and perception is measured by psychophysicists as “just-noticeable difference”, or JND: the amount a value must be changed in order for a difference to be detectable at least half the time.
Dr Katie Spalding used the Weber–Fechner law: The ratio of the increment threshold to the background intensity is a constant. That is, if you have two small quantities, you need less of a difference for it to be noticeable than if you have two larger quantities – it is easier to tell a louder sound from a quieter one in a quiet library than in a noisy marketplace.
When applied to weight, the law says: To be “noticeable,” the difference between two objects must be five per cent or more of one of their weights.
The new iPhone 14 weighs about 172 grams – meaning that it would take a weight increase of 8.6 grams before you notice that it had been made heavier. If 512 gigabytes weigh about 10-16 grams, that would mean you will need about 44,000,000,000,000,000,000 gigabytes, or 44 million extra zettabytes of information stored on your phone.
So, your device weighs more with data but it is too tiny that you cannot feel it or notice that change in weight using any instrument.
