It contained a $5 note and a plea from an elderly man, asking the University of Melbourne computer scientist to explain how the Kindle e-reader he'd been given for Christmas could possibly store dozens of literary tomes without getting any heavier.

"Although my Kindle is a wonderful present, there is one thing that is really puzzling me," the 75-year-old wrote.

"I now have more than 30 books and many of these contain several hundred pages ... Despite this, the Kindle seems to be no heavier than when it had no books. Surely I must soon be getting to the stage when the Kindle will become quite heavy?"

Many readers would assume the query was a joke; in fact that's exactly what Professor Sinnott wondered.

He kindly returned the man's money and replied that he needn't worry about overloading his Christmas gift with reading material, unless he planned on clocking up tens of thousands of books – in which case the data storage capacity may eventually run out.

But do all the apps and files stored on our devices, such as our iPads, actually weigh something after all?

That's what University of California professor John Kubiatowicz argued in comments in a 2011 New York Times article, which has recently been doing the rounds again after CultofMac, an Apple news website, published a post entitled "An iPad filled with apps weighs more than one with nothing installed".

We put that claim to several Australian academics, from physicists to electronic engineers, with mixed responses.

One said the theory was "baloney"; another labelled it an "urban myth".

All said that if it were true, the increase would be so infinitesimal as to be immeasurable – more or less what Professor Kubiatowicz argued.

It all rests on Einstein's theory of relativity, which converts energy into mass using the formula E=mc².

Professor Sinnott said storing data using flash memory – commonly built into tablets, smartphones and e-readers, including the Kindle – involved holding electrons in a certain position to record the binary code that a computer could read (i.e. 1s and 0s).

Holding that position required more energy, therefore mass, according to the formula.

Professor Kubiatowicz's conservative estimate of just how much energy that would be was 10^{-15} joules per bit, converting to 10^{-18} grams for a 4GB Kindle.

That's an attogram; and for readers who don't know what those negative numbers mean, it can also be written as 0.000000000000000001g.

In other words, nothing a human being can notice, let alone measure.

But while Professor Sinnott supports the Berkeley computer scientist's theory, other experts are doubtful.

Macquarie University's Mike Heimlich said the charge of an electron – amounting to "one billionth of a billionth of a billionth of a kilogram" – may in theory add weight in one part of a device, but "someplace else" there would need to be a voltage deficit.

As Adelaide University electrical engineer Michael Liebelt put it: "When you store stuff on a USB drive or Kindle, or anything like that, all you're doing is moving electrons around."

Professor Liebelt added that while Einstein's formula was valid, "in practical terms you never convert between the two".

Whether the device used flash memory or any other type of storage made no difference, he said.

Wollongong University's Roger Lewis agreed with Professor Liebelt on the Einstein factor. "That tells you how to convert between energy and mass, but having more energy doesn't necessarily mean having more or less mass," Professor Lewis said.

He said the theory that electrons in different energy states could have more or less weight was "far-fetched" but, in principle, "possible".

Whatever side of the weight-watchers camp you're on, it helps to put the debate into perspective.

Curtin University's Cesar Ortega-Sanchez said the weight difference in question was about "as small as the diameter of a red blood cell compared with the distance from Earth to Jupiter".

"It does exist," Dr Ortega-Sanchez said, "but it is too minuscule to be of any relevance or practical use."

Except, of course, to make a good headline.

Update:

On Friday, another expert, Associate Professor Andrea Morello, a quantum physicist and electrical engineer at the University of New South Wales, said Professor Kubiatowicz was correct.

"An iPad loaded with apps weighs more than an empty one. But you need to highlight that the difference is really small!! 10^{-18} grams, which means a billionth of a billionth of a gram. So it's a funny curiosity, not anything meaningful for a user who carries the iPad around."

Professor Morello also said "the academics who said this is baloney have probably confused the way a flash memory works with the way a RAM or a hard drive work". Below is his full explanation:

• In a flash memory, data is stored by charging some very small capacitors. This means that, to write a "1" on a flash drive, you need to load it with some electrons, which then stay there for as long as the memory is kept. A blank flash memory would have "0" written everywhere, so no electrons loaded. This has therefore nothing to do with E = mc^2 or anything related to charge motion. It's really just adding electrons, which have weight of their own, albeit extremely small.
• In a RAM, data is stored by turning transistors ON or OFF. So, the difference between a "0" and a "1" is whether current flows or not. There is no extra mass permanently stored, just "flow"/"no flow" of mass.
• In a hard drive, data is stored by changing the orientation of small magnetic domains. The material of the hard drive is magnetic, and its magnetic direction can be rotated locally. Of course, inverting the magnetisation makes no difference for the mass.