### Why today's time machines don't disappear

I love giving talks about the science of time travel as a result of Build Your Own Time Machine - and I can't help but feel there will be a few more as we lead up to the 50th anniversary of Doctor Who in November. I usually start by pointing out that there is nothing in the laws of physics that prevents time travel. In fact it's happening all the time. The best manmade examples? Voyager 1 has travelled 1.1 seconds into the future, while the GPS satellites constantly slip into the past. Often people don't believe me - and they have a good, if invalid, reason for this disbelief.

The thing is, when a time machine moves into the future or the past it disappears, doesn't it? The Tardis does, and so did H. G. Wells' time machine. But Voyager and the GPS satellites stubbornly insist on still being there. This is because it's something fiction gets wrong. Most time machines don't disappear as they travel through time. Let's take a look at those two examples, but exaggerate the effect to see what's going on.

We'll start with the simpler one, travelling into the future. Anything that moves has a time stream that slows down compared with the place it is moving with respect to. So when, for instance Voyager 1 flies away from the Earth, its time runs slower. This is a well tested and inevitable effect of special relativity. So let's imagine that Voyager 1 travels much closer to the speed of light than it actually does. And now we use a magic telescope that allows us to see from the Earth into Voyager 1, so we can watch its clock. We would see the clock running incredibly slowly. When a year has passed by on the Earth, perhaps just a second has ticked past on the clock. So after 10 years, just 10 seconds has passed by on the probe. If Voyager 1 arrived back at the Earth at this point, it would have moved 10 years into Earth's future.

Now here's the thing. For that whole 10 years we still see Voyager 1 - we just see its clock ticking past very slowly indeed. It doesn't disappear, we continue to see it. But hang on, you might say, this is cheating. Voyager isn't really moving into the future, it just looks like that because its clock seems to be running slowly. But this isn't a 'seems to be' (as it is sometimes described even in popular science books). From the Earth's viewpoint that clock really is running slowly. As is everything else on board. If Voyager was much bigger and had a crew then the people on the ship will only have aged 10 seconds and experienced 10 seconds passing by. They really have travelled into the future.

(If you are wondering why time only slows on the ship, you are a clever person. Special relativity works both ways. From the ship's viewpoint, the Earth is moving away at high speed, and to anyone on Voyager, time on the Earth seems to run slowly. But the situation isn't symmetrical. The ship undergoes acceleration at both ends of its trip that the Earth doesn't, and it is this acceleration that means the ship experiences something different to the Earth.)

So to the more unlikely aspect of time travel. Because heading off to the future doesn't risk any strange paradoxes, but should you travel into the past, surely all those funny things like killing your parents before you are born can happen? Let's take a look at the GPS satellite.

The satellite is moving, so seen from the Earth, just like Voyager 1, the satellite's time runs a bit slower because of special relativity. But there is a second effect here which operates in the opposite direction and is more significant. General relativity shows us that gravity slows time down. The stronger the gravitational field, the slower time runs. So time runs faster on the GPS satellite than it does on the Earth. The opposite effect to Voyager 1, so the satellite moves into the future. Again, let's imagine the (tiny) effect is hugely exaggerated and every second that passes on Earth, a year passes on the satellite. So after 10 seconds passes on the Earth, the satellite is pretty well 10 years ahead. Once more, if we watch the satellite travel through time, we don't see it disappear. We just see its clocks run really quickly.

So let's finish the time voyage. On the satellite, say, it is 2023, while it is 2013 on the Earth. So the satellite pops down to Earth and moves ten years into the past. Whizzo magico. Only here's the thing - it can't move back before it was first set up, because time doesn't go backwards on the Earth, it just runs very slowly from the satellite's viewpoint. So it can't go back into the past (or peer down at Earth and discover next week's lottery results) or do something that will effect the future, because the Earth's future hasn't happened yet. The future it has moved from is its own. Like Voyager, it might seem that this cheating, but it really isn't. For instance, if people lived on that GPS satellite, in the 10 seconds that elapsed on Earth, they could do 10 years of work and bring back with them newly written novels etc., bringing them from the future to the past. They just couldn't get up to any tricksy paradoxes.

If you find this all rather disappointing, there is a third class of time machine where you would disappear, and where paradoxes are possible. These are the ones depending on wormholes, neutron star cylinders and the like which won't be around for millions of years and may never be possible to construct. But you shouldn't be disappointed by what is possible now, because we still have the amazing fact that both backward and forward travelling time machines exist today.

### Why I hate opera

If I'm honest, the title of this post is an exaggeration to make a point. I don't really hate opera. There are a couple of operas - notably Monteverdi's Incoranazione di Poppea and Purcell's Dido & Aeneas - that I quite like. But what I do find truly sickening is the reverence with which opera is treated, as if it were some particularly great art form. Nowhere was this more obvious than in ITV's recent gut-wrenchingly awful series Pop Star to Opera Star , where the likes of Alan Tichmarsh treated the real opera singers as if they were fragile pieces on Antiques Roadshow, and the music as if it were a gift of the gods. In my opinion - and I know not everyone agrees - opera is: Mediocre music Melodramatic plots Amateurishly hammy acting A forced and unpleasant singing style Ridiculously over-supported by public funds I won't even bother to go into any detail on the plots and the acting - this is just self-evident. But the other aspects need some ex

### Is 5x3 the same as 3x5?

The Internet has gone mildly bonkers over a child in America who was marked down in a test because when asked to work out 5x3 by repeated addition he/she used 5+5+5 instead of 3+3+3+3+3. Those who support the teacher say that 5x3 means 'five lots of 3' where the complainants say that 'times' is commutative (reversible) so the distinction is meaningless as 5x3 and 3x5 are indistinguishable. It's certainly true that not all mathematical operations are commutative. I think we are all comfortable that 5-3 is not the same as 3-5.  However. This not true of multiplication (of numbers). And so if there is to be any distinction, it has to be in the use of English to interpret the 'x' sign. Unfortunately, even here there is no logical way of coming up with a definitive answer. I suspect most primary school teachers would expands 'times' as 'lots of' as mentioned above. So we get 5 x 3 as '5 lots of 3'. Unfortunately that only wor

### Which idiot came up with percentage-based gradient signs

Rant warning: the contents of this post could sound like something produced by UKIP. I wish to make it clear that I do not in any way support or endorse that political party. In fact it gives me the creeps. Once upon a time, the signs for a steep hill on British roads displayed the gradient in a simple, easy-to-understand form. If the hill went up, say, one yard for every three yards forward it said '1 in 3'. Then some bureaucrat came along and decided that it would be a good idea to state the slope as a percentage. So now the sign for (say) a 1 in 10 slope says 10% (I think). That 'I think' is because the percentage-based slope is so unnatural. There are two ways we conventionally measure slopes. Either on X/Y coordiates (as in 1 in 4) or using degrees - say at a 15° angle. We don't measure them in percentages. It's easy to visualize a 1 in 3 slope, or a 30 degree angle. Much less obvious what a 33.333 recurring percent slope is. And what's a 100% slope