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Why Einstein was Right

October 20, 2011

Ever since the recent neutrino experiments that hint at faster-than-light travel, everyone (especially the media) is in a frenzy about Why Einstein Was Wrong, or in more extreme cases, Why Science Is Wrong. There are better bloggers than I covering the neutrino experiments and relativity in general, but I wanted to add my meagre weight to the consensus that the Theory of Special Relativity is in no danger of being disproven, regardless of the final outcome of the neutrino experiment. Just as Newtonian mechanics and Galileo’s original Theory of Relativity are still valid in most circumstances, Einstein’s Theory of Special Relativity has been proven over and over to hold for many circumstances, and if it proves not to hold for faster-than-light particles it is still valid for everything else.

Having established that, I would now like to put forward some ideas of my own about Special Relativity that seem to have been (in my opinion) unfairly dismissed or not really considered. I will try and keep this simple, but it is complex physics, so I can’t guarantee it will be easy reading.1 – What if faster-than-light particles do not follow the rules of Special Relativity?

At university I had the honour of being taught by a leading professor in the field of quantum entanglement, and after lectures I would chat to him about various science fiction concepts like faster-than-light travel, time travel and the possible uses of quantum entanglement. I enjoy reading and writing, especially science fiction, but I can’t stand it when authors get the science completely wrong, so what better way to make sure I get it right than by asking the experts? One thing that always bugged me, though, was that he kept saying FTL travel and communication would break causality, which didn’t make sense to me. My view was that the cause happens before the effect, regardless of which order you saw them in, so causality wasn’t affected.

It turns out that this is all due to Special Relativity. If you have a particle travelling faster than light, putting it into the equations for relativistic motion gives you a particle with an imaginary mass and negative time.* Since nobody knows what on earth imaginary mass could be, this makes things awkward, but they also travel back in time. You can remove the imaginary mass component, but only if you remove any interactions with slower-than-light particles. Basically, if faster-than-light particles exist, we cannot see them or interact with them in any way, so they effectively can’t exist in any useful way. Also, using time dilation you can directly prove causality breaks using faster-than-light communication, via the amazingly-named thought experiment of the tachyonic antitelephone.

But, all of this hinges on one assumption that may or may not be true: that faster-than-light particles use the same relativistic equations of motion that slower-than-light particles do. Given that we don’t have anything else to use it’s not a bad assumption, but that kind of assumption lead to embarrassments like the ultraviolet catastrophe, and ruling out any other possibilities without any evidence at all is not good science. If these neutrinos did travel faster than light, then clearly FTL particles do not use relativistic laws of motion, and we then get on with figuring out what they use instead. If the experimenters made a mistake and they didn’t travel faster than light, then nothing has changed, but we still don’t know what laws (if any) FTL particles use. For now though, we will just have to wait and see.

2 – Does instantaneous travel or communication count as faster-than-light?

My next issue is that all of the above doesn’t seem to apply to instantaneous travel and communication like quantum teleportation and entanglement, but they are also ruled out. There is the no-communication theorem, which I will look at in a minute, but most people don’t even go this far. I’ve seen some people try to argue that instant communication isn’t possible from the assumption that it breaks causality, which is about as useful as saying things fall down because they fall down. If you start from the assumption that instant communication isn’t possible, of course you will conclude that instant communication isn’t possible!

The only argument I have seen that actually appears to make sense is based on the no-communication theorem, which is so mathematically dense I can’t even begin to follow it. However, there seem to be some criticisms levelled at it that it too assumes FTL communication isn’t possible as its starting point, and experiments which seem to disprove supraluminal communication completely. With nothing actually travelling faster than light, then the laws of relativistic motion don’t break as they are not required – there isn’t any motion – so there is nothing I can see that would prevent instantaneous travel and communication from happening. In fact, since we already know teleportation happens on a tiny scale (like quantum tunnelling), I think it looks quite likely that this would be possible.

3 – A extension of Einstein’s postulates

Finally, this is something slightly different that I’ve been wondering about. Galileo originally came up with the original Theory of Relativity (also known as the Galilean Invariance): the idea that you cannot tell how fast something is travelling without an outside reference. For example, without watching the scenery go by outside, you don’t know how fast a car is going.** Everything inside the car is the same, and if it had no windows you just wouldn’t be able to tell. You can feel it speed up and slow down, but at a constant speed it feels exactly the same as if you weren’t moving at all.

This is what caused Einstein to come up with the Special Theory of Relativity in the first place: if you were travelling at exactly the speed of light, you would know immediately how fast you were travelling without an outside reference, as everything would suddenly go black. This is because as you approached the speed of light, there would be a bigger and bigger gap between photons reaching your eye, until you got to exactly the speed of light, when the photons that were just about to hit your retina suddenly can’t – your retina is travelling at the same speed, so they can’t catch up! This also does not count as an outside reference, as you won’t be able to see anything, inside or outside.

Bizarrely, even though his theory has been proven right (time dilation and stuff does actually happen), I suspect his original basis may have been wrong. Well, not actually wrong, just not quite thought out far enough. His theory shows than you cannot reach c – the speed of light in a perfect vacuum – but wouldn’t the situation I described above happen if you were travelling at the speed of light in air? Assuming you are stood in an atmosphere identical to Earth’s in your spaceship, wouldn’t you know when you reached the speed of light through that atmosphere, because the photons wouldn’t be able to reach your eye? The Special Theory of Relativity says nothing about this, and we know particles will sometimes travel faster than light can in a given medium, because it happens in the cooling fluid of nuclear reactors.

So, what’s the deal with this? Was Galileo wrong about needing an outside reference, or is there another part to relativistic motion that we haven’t discovered yet? I’d really like to know, but I cannot find anything or anyone at all that has mentioned this – I can’t be the first or the only person to consider this, can I?


*Also, using the equations from Special Relativity FTL particles have less energy the faster they go, until they reach zero energy at a speed of infinity. This just can’t happen, they must have an infinite amount of kinetic energy at an infinite speed (unless it is something to do with that pesky imaginary mass they have), which also means if FTL particles exist they just can’t use Special Relativity.

**The speedometer does not work for this purpose, as it only measures your speed relative to the ground – a car on a treadmill might say 30mph but not actually be moving. It also doesn’t take into account the 67,000 mph we are travelling at around the Sun!

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