## Wormholes and quantum entanglement

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Been a while…

There is a fascinating article in this week’s New Scientist about the idea that quantum mechanics and general relatively could be linked via the idea of the “wormhole” – a fold in spacetime that links what appears to be two very distant parts of the universe.

The article – as is generally the case in a popular science magazine – is more hand wavy than scientific, but the concepts involved don’t seem to be difficult to grasp and they might answer some of the more mysterious aspects of quantum mechanics – especially the problem “spooky action at a distance“: quantum entanglement.

Quantum entanglement is the seeming evidence that two particles separated by distance appear to exchange information instantaneously: for when one particle changes state (or rather when its state is observed), the other does too. The suggestion is that, actually, these two particles are not separated by distance by are linked by a wormhole.

Sounds like a piece of Hollywood science, for sure, but it is an idea based on our understanding of black holes – a prediction of Einstein’s general relativity that we have lots of (indirect) evidence for: these would seem to be surrounded by entangled particles – the so-called quantum firewall.

## Why we’ll never meet aliens

Well, the answer is pretty plain: Einstein‘s theory of general relativity – which even in the last month has added to it’s already impressive list of predictive successes – tells us that to travel at the speed of light a massive body  would require an infinite amount of propulsive energy. In other words, things are too far away and travel too slow for us to ever hope to meet aliens.

But what if – and it’s a very big if – we could communicate with them, instantaneously? GR tells us massive bodies cannot travel fast, or rather along a null time line – which is what really matters if you want to be alive when you arrive at your destination – but information has no mass as such.

Intriguingly, an article in the current edition of the New Scientist looks at ways in which quantum entanglement could be used to pass information – instantaneously – across any distance at all. Quantum entanglement is one of the stranger things we can see and measure today – Einstein dismissed it as “spooky interaction at a distance” – and essentially means that we can take two similar paired particles and by measuring the state of one can instantaneously see the other part of the pair fall into a particular state (e.g., if the paired particles are electrons and we measure one’s quantum spin, the other instantly is seen to have the other spin – no matter how far away it is at the time).

Entanglement does not allow us to transmit information though, because of what the cosmologist Antony Valentini calls, in an analogy with thermodynamic “heat death”, the “quantum death” of the universe – in essence, he says that in the instants following the Big Bang physical particles dropped into a state in which – say – all electron spins were completely evenly distributed, meaning that we cannot find electrons with which to send information – just random noise.

But – he also suggests – inflation – the super-rapid expansion of the very early universe may also have left us with a very small proportion of particles that escaped “quantum death” – just as inflation meant that the universe is not completely smooth because it pushed things apart at such a rate that random quantum fluctuations were left as a permanent imprint.

If we could find such particles we could use them to send messages across the universe at infinite speed.

Perhaps we are already surrounded by such “messages”: those who theorise about intelligent life elsewhere in the universe are puzzled that we have not yet detected any signs of it, despite now knowing that planets are extremely common. That might suggest either intelligent life is very rare, or very short-lived or that – by looking at the electromagnetic spectrum – we are simply barking up the wrong tree.

Before we get too excited I have to add a few caveats:

• While Valentini is a serious and credible scientist and has published papers which show, he says, the predictive power of his theory (NB he’s not the one speculating about alien communication – that’s just me) – such as the observed characteristics of the cosmic microwave background (an “echo” of the big bang) – his views are far from the scientific consensus.
• To test the theories we would have to either be incredibly lucky or detect the decay products of a particle – the gravitino – we have little evidence for beyond a pleasing theoretical symmetry between what we know about “standard” particle physics and theories of quantum gravity.
• Even if we did detect and capture such particles they alone would not allow us to escape the confines of general relativity – as they are massive and so while they could allow two parties to theoretically communicate instantly, the parties themselves would still be confined by GR’s spacetime – communicating with aliens would require us and them in someway to use such particles that were already out there, and perhaps have been whizzing about since the big bang itself.

But we can dream!

Update; You may want to read Andy Lutomirski’s comment which, I think it’s fair to say, is a one paragraph statement of the consensus physics. I am not qualified to say he’s wrong and I’m not trying to – merely looking at an interesting theory. And I have tracked down Anthony Valentini’s 2001 paper on this too.

## Lorentz and Einstein

When I was at York University earlier this week I took a break from computer science to remind myself of some of the basics of (special) relativity and was struck, while reading the opening few pages of Rindler’s Essential Relativity: Special, General, and Cosmological (which would appear to be the set text at York), just how simple the basic maths of one of the core concepts of relativity is.This is the idea that observers in one inertial frame see objects moving at high speed foreshortened (and time dilated). This insight is not Einstein’s, but Lorentz‘s (though Lorentz did not see the importance of time dilation and it was Einstein who understood the fundamental nature of the result and so built a whole new dynamics on top of it).

The maths of this are such that any good GCSE student should get it – and it might suit teaching physics better if that was emphasised rather than the supposedly counter-intuitive nature of the relativity principle it leads on to – because I am sure that puts people off.

I am going to use the example used in the book – someone swimming up and down and back and across a river – to explain it. If you are happy with Pythagoras’s theorem then you will have no problem with this.

But first a little historical background – James Clerk Maxwell formulated the theory of the electromagnetic field and from that came the idea that light travelled as a wave. But in what medium? After all, you drop a stone in the water and you see waves, but they are waves of water.

It was speculated that the equivalent of water was ‘the luminiferous ether’ – an all pervading medium through which the waves of light undulated.

But as the Earth moved through the universe – solar rotation being the biggest factor – that should mean we would see light move faster when it was travelling in the same direction as the Earth’s motion (just as you can swim faster down stream with the current pushing you along). Except that there was no sign of this.

A famous and sophisticated experiment – the Michelson-Morley experiment – and many others – sought to measure the difference in the speed of light when it travelled in the direction of, and orthogonal to, the Earth’s motion. None was seen.

To see the size of the effect that was expected – imagine that you are a swimmer who travels at speed $V$ in a river with a current that moves with speed $v$. To swim downstream to a fixed point at a distance $P$ away would take $\frac{P}{V+v}$ seconds, while to swim back to our starting point would take  $\frac{P}{V-v}$ (as now the current is against us) – the total time then is $\frac{P}{V+v} + \frac{P}{V-v} = \frac{2PV}{V^2-v^2}$.

Now let us assume the river is wide, of width $P$ and we decide to swim straight across and back. Here too we have to fight the current, as it tends to make us drift downstream – so we have a classic right angled triangle of forces, with the effective distance we swim being the hypotenuse of the triangle.

So to get across takes $\frac{P}{\sqrt{V^2-v^2}}$ and across and back takes $\frac{2P}{\sqrt{V^2-v^2}}$.

Plainly these two times (downstream and across) are not the same – but the Michelson-Morley experiment suggests that for light, they are. So Lorentz suggested that objects travelling in the direction of motion were contracted – substituting $c$ for $V$ and $L$ for the length of an object in the direction of travel and $W$ for the length of the object when orthogonal to the direction of travel we get (remember the light is our swimmer here):

$\frac{2W}{\sqrt{c^2 -v^2}} = \frac{2Lc}{c^2-v^2}$

So $\frac{W}{\sqrt{c^2-v^2}} = \frac{Lc}{c^2-v^2}$

And $\frac{L}{W} = \frac{c^2-v^2}{c\sqrt{c^2-v^2}} = \frac{\sqrt{c^2-v^2}}{c}$

Or, as it is more conventionally written $\sqrt{1-\frac{v^2}{c^2}}$ (square both sides, divide by $c^2$ – then take the square root).

In other words as an object approaches the speed of light then an observer at rest will see it contract. For jet travelling at 700 km/h, the contraction is somewhat less than of the order of one part in a trillion, nothing you would notice! (In fact it is so small I cannot get the calculator on my computer to give me a useful answer).

## How random is random?

What is a truly random event?

We are used to the idea that flipping a coin is likely to generate a random sequence of heads or tails but, of course, it is perfectly possible to predict, using the rules of classical mechanics, the outcome of a series of coin tosses if we know the values of a not very long list of parameters. In other words, the outcome of flipping a coin is entirely deterministic, it is just that humans are unlikely to be able to faithfully replicate the same flick over and over again.

Quantum events – such as the $\alpha$particle decay are, as far as our knowledge today tells us, truly random – in the sense they have a probability of occurring in a given time period but we have no way of knowing if a given nucleus will decay at any given time.

This is really a very profound finding – it implies that two physical objects, in this case atomic nuclei, behave in completely different ways despite all the physical parameters describing their existence being the same. That sounds like the exact opposite of everything that science has taught us about the nature of the universe.

Thinking about this, one can quickly come to agree with Einstein that it must be based on a flawed understanding of physical reality as “God does not play dice”. But it is also the best explanation we have for that physical reality.

But why would a nucleus decay in one time period and not another? Can this really be an event without specific cause? Just a ‘randomly‘ chosen moment? But chosen by what?

Of course, some will say by “God” but that really is metaphysics – a completely untestable and unverifiable proposition that merely kicks the physical puzzle in a domain beyond physics.

## If it wasn’t for those pesky neutrinos

Neutrinos have proved to be nothing but trouble for scientists over the years.

They could not detect them from the Sun (where they are produced as a by-product of fusion), then they did or did not have mass. Now, it seems, they travel faster than light and are threatening to overturn the apple cart of relativistic space-time. If my dimly recalled understanding of relativity is correct, this would imply that, from the netrino’s point of view, it travels in the opposite direction to the way we see it moving in our reference frame: plainly, either the experiment is giving the wrong results or our theory of space-time is very seriously flawed.

Of course, what these troubles mean is that neutrinos have been huge allies in our search for a better understanding of physical reality. Though this new finding – which has plainly caused consternation amongst those who have been conducting the experiment – would be truly shocking if confirmed.