Gravity and Me. My BBC4 doc and the problem with the app

Every now and then (OK, once a year at best these days) I’ll write a blog to accompany a TV documentary I’ve made. Usually this is because I want to explain something subtle that I didn’t have time to do in the programme and for which Twitter simply cannot do justice. This one is to accompany my new documentary on BBC4 (aired on 28 March) entitled “Gravity and Me: the force that shapes our lives”.

Now, because I don’t want this blog to get too long, I am going to assume that you’ve watched the programme itself. If not, and assuming you’re reading this blog during the month following transmission – oh, and living in the UK - then you can catch it on BBC iPlayer here.

Right, ready? Good…

In the programme I start, and finish, with a simple (age-old) question: why do things fall? If the answer is just ‘because of gravity’ it would have been a rather short film. Luckily, the subject of gravity, how we came to understand what it is and where it comes from, provides for a rich, intellectual journey.

The reason for this blog is to explore and clarify in a little more depth the issue of the smartphone app I discuss in the film and the mistake I made in the relativity formulae that it uses to calculate how much your time slowing down. On first discovering my mistake, it was clear that the only course of action – indeed the most interesting, honest and informative course of action – was not only to come clean, but to present my mistake in all its glory in the programme. After all, that’s how science works and make progress – how would we ever discover anything new about the world if we cannot make mistakes and learn from them.

In 1905, Albert Einstein published his famous papers on Special Relativity (SR) in which he explained that time and space are not absolute and separate, but two aspects of the same thing: four-dimensional spacetime. This means that distance and time intervals between events (hence the rate at which clocks tick) will be depend on your state of motion. The faster a clock moves, the slower it will tick. If you have not come across this idea of time dilation and want to know more then I recommend you read a good popular science book on the subject (like mine, for example!) This effect is very noticeable once things move at a significant fraction of the speed of light. But even at the more sedate speeds that we humans move relative to each other, like every time you drive your car or get on a bus or train, or even run or walk, there is still an effect. And, the faster you move and the longer you move at that speed, the slower your clock ticks, including your own internal biological clock, and so the slower you age - by tiny, tiny fractions of a second of course.

This is called SR time dilation. Now, a decade after his work on SR, Einstein published an even grander idea, called his general theory of Relativity (or GR) where he showed that there is another way to slow time down: using gravity. You see, Einstein explained that, unlike what Newton had thought, gravity is not some invisible force that pulls objects towards the ground or keeps the moon in orbit around the earth, instead Einstein described it as the curvature of spacetime itself. This means that gravity – basically wherever there is matter (stuff) – warps space and… drum roll please… slows down time. This is GR time dilation: the stronger the gravity, the slower clocks tick. If you’ve seen the film Interstellar (the science of which, by the way, is 100% accurate as far as obeying our currently understood laws of physics, particularly Einstein’s GR) then you’ll recall (spoiler alert if you haven’t seen the film) that Matthew McConaughey’s character spends time in the very strong gravitational field near a black hole and so his time runs so slowly compared with time on earth that when he returns home his young daughter is now an old lady!

While we don’t yet have that sort of access to black holes to do this at the moment, we can still measure this effect in earth’s gravity.  The bottom line is: the closer you are to the centre of the earth, the stronger the gravitational field you will be in and the slower your time will run. So you will age ever so slightly more slowly at sea level than you would up a mountain.

So, we have these two competing effects and I therefore decided it would be cool to develop a phone app to measure the tiny different rates at which we are all ageing. Now I know my relativity (or so I thought). It’s not my research specialism, but I had taught it to undergraduates for many years. So, I provided the formulae for the phone app. Basically, it records your GPS location (latitude, longitude and altitude above sea level) and it takes measurements at regular intervals so can even calculate how fast you’ve moved between two locations.

Now, here’s the crucial part. The earth is not a perfect sphere; it bulges at the equator, so someone standing at the equator is further from the centre of the earth than someone at the north pole and so they feel a slightly weaker gravitational pull. Therefore, clocks at the pole should be ticking slightly slower than those at the equator due to GR time dilation. But the earth is also spinning and clocks at the equator are moving faster than clocks at the pole (as seen by some adjudicating astronaut floating out in space) so equator clocks should tick slower than pole clocks (SR time dilation). But effect one wins? Calculating the two effects separately I found that the GR effect was much bigger, so a clock at the pole ticks, over all, more slowly because it feels stronger gravity, despite the clock on the equator moving faster. Even in the UK, where most people had downloaded the app, this was measurable: the further north you went, the slower your clock ticked and the slower you aged.

So far so good. Or so I thought.

My very smart exec producer Paul Sen called me one evening in mid-December last year, a week before the editing of the programme was due to finish and when I would record the voiceover - for a hoped-for transmission in the new year. He said he’d been reading some physics forum online that seemed to suggest I had screwed something up. I dropped everything and went to read up about the subject. I also quickly emailed half a dozen colleagues around the world who are world experts on Einstein’s relativity – including, I should say, Kip Thorne, a world renown authority and indeed the man behind the science of the movie Interstellar.

Yes, I had made a mistake. In fact, the two effects: the slowdown of time at the pole because it feels stronger gravity than the equator and slowdown of time at the equator because it is moving faster… EXACTLY CANCEL OUT!  Indeed, all stationary clocks at sea-level on earth tick at the same rate. This is called International Atomic Time (IAT) as it is used to synchronise atomic clocks (our most accurate time keepers) and to ensure for example that global positional satellites are measuring time accurately (after all they really are feeling weaker gravity and are moving fast).  In technical terms, all points on the surface of the earth are called points on the geoid, an equipotential gravitational surface (in case you were wondering).

So, cue panicking Jim, stop the doc edit, halt BBC4 plans for transmission, back to the drawing board to fix the app. It certainly made for a nice dramatic turn in the film. My new formulae still took into account how high above sea-level you were (so your time speeds up a little) and how fast you were moving relative to the ground (how fast your time slows down), but now all times were compared with IAT clocks at rest at sea-level rather than with a hypothetical clock floating in space far from earth’s gravity. Another technical aside is that there’s a rather subtle idea called the Sagnac effect, which basically means your clock would tick at different rates if you travel east (with the spin of the earth) or west (against the spin).

Are you confused yet? If so, welcome to my world – and I’m supposed to know this stuff.

Anyway, I hope this extra information helps ‘clarify’ a few things. What it does show is that gravity is not just a boring force that keeps us stuck to the ground. It’s a subtle phenomenon that the world’s greatest minds (and me) have grappled with. If it makes your head hurt then my work here is done.

Feel free to use this information to show off your intellectual superiority to family and friends.

Oh, and download the app. It’s called Timewarper and runs on iPhones and Androids.

And it’s correct now. 

I think.