Here ’s a weird query : does your sound weigh more when it ’s “ full ” than when it ’s “ empty ” ? It sounds almost ridiculously naïve – of course , a phone is n’t like a jugful of water , with each photo or impinging total an extra few mil to the sum . How couldinformationhave a weightiness ?
But like many manifestly dewy-eyed questions , this one has a astonishingly complex answer – and it all comes down to one of the most fundamental law of the universe . So , with a bit of particular relativity , a lot of math , and a small dip into computer science , allow ’s actually take a serious looking at at the weight of your earphone – before , and after , you ’ve occupy it with lolcats and enshroud the Pain Harolds .
In theory: yes
It might sound counterintuitive , but the data point on your phone does in fact have a weight . And the even more surprising affair is , you already get laid the scientific reason why .
“ entropy is stored [ on electrons ] , ” explained NPR science newswriter Robert Krulwichback in 2011 . “ And electrons are very , pocket-size . But they do have pot . Einstein taught us that . So it ’s possible to take all the vitality ( east ) … and , using Einstein ’s equation , ( E = mc2 ) turn that energy into something we can consider . ”
It ’s one of themost noted equationsin scientific discipline – but unless you ’re a working physicist or cosmologist , you probably did n’t conceive it had much manipulation in daylight - to - day life-time . Here , though , it ’s precisely what we need : if we can ferment out the change in vim levels between a “ full ” telephone set and an “ empty ” one , Einstein’smost renowned soundbite will allow us to figure out the departure in mass between the two .
First , though , we need to realize how and why the energy story change at all . When we supply information to non - electronic system – like , say , a book , or a photo album – the difference is wide-eyed : a blank page versus a full one . But with our phones , eastward - readers , tablet and so on , it ’s more complicated : in these cases , the data is stored as binary information , encoded in serial of aught and one .
When you add or dispatch data point from your machine ’s flare memory , you ’re not adding or hit these digits , but shift them – modify one to zero and zeroes to ones . “ Another fashion of think about it is that the atoms in the memory have charismatic - corresponding properties , ” explains Gareth Mitchell forBBC Science Focus . “ Groups of atoms align in one focal point or the other consort to whether they are storing a 1 or a 0 and will have differing amounts of vim consort to how they are aligned . ”
Technically , flash retentiveness works by either carry electrons in place or not . While they ’re being held in place – that is , when they ’re encoding info – they become more energetic . And as Einstein ’s equation assure us : more energy equal more mickle .
Technically , then , filling your phone with photos , music , and messages does indeed make it heavy . But do n’t go swapping out your dumbbells for an erstwhile iPhone just yet – because …
In practice: not really
It ’s one affair to recognise that special relativity means your phone gets heavier with more data . But what would in reality happen if you weighed your machine before and after loading it up with memes ?
Luckily , it ’s pretty light to turn this out using Einstein ’s par : we have energy , E , and we require to work out slew , m. There ’s just one letter in the equivalence to go : the constant , coke – which refers tothe velocity of light .
Now , as you may recall , the speed of ignitor is anextremelylarge number – around 3 × 108meters / endorsement . When you plug this into the equation for mass - energy equivalence , it result in something interesting : it means thata little tiny piece of masswill be the equivalent weight of justvast amounts of energy .
We ’re working the other way around , but it ’s still true : it would take a psyche - flabbergast amount of vigor to result in a noticeable difference in mass . And while modern mobile phones can hold quite a lot of data – there ’s easy six orders of magnitude more memory board in your smartphone than there were in the computers that put humankind on the Sun Myung Moon , for a bit of perspective – when we execute the number , we witness that even the latest devices ca n’t halt enough data to actually feel “ enceinte ” when full .
So , what variety of size are we babble ? Well , according to John D. Kubiatowicz , a professor of data processor scientific discipline at the University of California , Berkeley , who answer a interchangeable interrogative forThe New York Timesback in 2011 , a conservative estimate for the difference in energy between a trapped electron and a destitute one is around 10–15joules per bit . punch that into Einstein ’s equivalence , he reckon that a full 4 - gibibyte Kindle e - lector will weigh more than an empty one , but “ the amount is very small , on the rescript of an attogram , ” or 10–18grams . “ This amount is efficaciously unmeasured . ”
Of of course , that was more than a decade ago , and even cheap phones usually have quite a lot more than 4 GB of memory today . But even allowing for 512 gibibyte of datum – the amount available on the latest iteration of the iPhone – will only result in a difference of around 10 - 16grams , or 0.1 femtograms .
To put that in perspective , it ’s slightly gruelling than a singletobacco mosaic virus , the first computer virus ever discovered . Alternatively , it ’s about one - tenth the weightiness of a single HIV-1 virus . In other words , it ’s not the sort of bulk you ’d notice even if it was drop on your foreland from thetop of the Empire State Building .
Weighty information
So just how much data would we need to be carry on our earpiece before we ’d actually sense a dispute ? Well , to answer that , we need to know something else : exactly how much heavier does something need to be before your average human would notice ?
This is where the extremely nervelessly - named skill ofpsychophysicscomes in – the arm of data-based psychology focalise on sense , maven , and percept . To psychophysicists , the value we ’re look for is promise the “ just - noticeable dispute ” , or JND : the amount a economic value must be change in guild for a difference to be detectable at least half the clip .
While it is n’t capital at super - low or -high frequencies , for most forcible quantities there ’s a pretty good principle of thumb for figuring out the JND : it ’s called the Weber – Fechner law , andit statesthat “ the ratio of the increase threshold to the background signal loudness is a constant . ”
It cook good sense : it ’s sound out that if you have two small quantities , you need less of a remainder for it to be noticeable than if you have two larger quantity . Think about talking in a quiet library versus a tacky natal day political party – it ’s right smart comfortable to tell a loud audio from a quieter one in the first office than the second .
When applied to weighting , the law reveals something very commodious : to be “ obtrusive ” , the difference between two object must beat least five percentof one of their weights .
The fresh iPhone 14 , according to official specs , weighs 172 grams – intend that it would take a weight growth of 8.6 grams before you ’d notice that it had been made heavier . If 512 gigabytes weigh about 10 - 16grams , that would intend you ’d require – cryptical breath here folks – about 44,000,000,000,000,000,000 gigabyte , or 44 million extra zettabytes of entropy stored on your earphone .
How long would that take to download ? Well , quite apart from the fact that your phone would never be able-bodied to hold in such a wodge of selective information – in fact , you ’d needover 30 billion human brainsjust to contain it all – it would be quite the foresightful - condition commitment . Even with optimal 5 G speeds of around 200 megabits per second , it would take around 56,000 years to download that amount of data point onto your phone – and you ’d probably need that extra clip , since theentire internetis currently estimated to containless than 100 zettabyte .
So , does your phone weigh more when it ’s full of data point ? Yes , technically – but not so much that you’devernotice it . you’re able to carry on snapping those photos and videos without having to hit the gym afterwards – you ’ll probably ladder out of interesting thing to document before your phone becomes grueling by even a mcg .
