by Tim James
Suppose you shot an arrow away from you at 20 m/s and your friend was riding a bicycle alongside it at 15 m/s (presumably she had her hand repaired from when you blasted it off with a cannonball earlier).
You would say the arrow is moving at 20 m/s but if you were to ask her, she will naturally say the arrow is travelling at 5 m/s relative to her and the bicycle. Both your numbers are true because all speeds are equally valid. Apart from the speed of light. That is 299,792,458 m/s for everyone. Everywhere. All the time.
You may have learned in school that light slows down as it moves through glass but this is a tiny bit misleading. The photons are getting absorbed and re-emitted by atoms within the glass, which delays the overall travel time, but the speed of photons in between each atom is still 299,792,458 m/s. It is a constant value of the universe.
If you shine a torch beam away from you, the beam speed is 299,792,458 m/s. Your friend is once again pedalling her bicycle parallel to the beam at, let’s say, 100 m/s (she is very physically fit). If you were to ask her how fast the beam was going now, she would also say 299,792,458 m/s. The same as you. But that seems wrong. If she is moving next to the beam at 100 m/s, surely she should measure it as slower than your answer, like she did with the arrow? Special relativity says otherwise. The speed of light is the same for everyone.
Even if she was moving at 99 per cent of the speed of light, her speedometer would still measure the beam at 299,792,458 m/s. You would expect her to get a different answer but she gets the same every time.
Or suppose she cycles towards you, and the beam advances in her direction, head on. Should she not perceive the beam faster because she is approaching it as it approaches her? No, says Einstein. She sees the beam at the same speed.
There is an easy way to prove that the speed of light is always the same for every observer (see Appendix III) but if we take it as a given for now, the implications are truly bizarre.
If two people are moving at different speeds yet measure light at the same speed, something must be distorting between their reference frames. If they are measuring two different scenarios but getting the same answer then something is off and the culprit, said Einstein, is time itself.
If we accept the two postulates of special relativity, time must be passing at different rates for two moving observers. As a person travels faster, their clock slows down and, as a result, a beam of light seems just as fast, since they are moving through time slower. Time is running slower for your friend on her bike, and therefore when she measures the speed of the beam going past it seems just as fast.
She would not sense this time dilation, however. If she were to look at her watch she would not see the second hands ticking any differently. All the particles inside her brain are experiencing time at a stretched rate, too. From her perspective, you are the one whose timeline is being warped. She sees you being sped up like a movie played on fast-forward and neither of you gets to say your time is ‘correct’ because all measurements are equally valid.
Sounds made up, right? Well, in 1971 Richard Keating and Joseph Hafele put special relativity to the test by synchronising two atomic clocks and separating them at different velocities. One was placed on board a commercial jet-plane (with a ticket made out to Mr Clock) and flown around the world eight times, while the other remained on the ground.
When the flight was over Hafele and Keating compared Mr Clock’s reading with his brother and found he was lagging by exactly the amount of time Einstein predicted.
It is a small effect to be sure (Mr Clock lost a few nanoseconds only) but as you move faster you really do age a little slower. Up to a point.
The time dilation effect cannot go on forever because there is a slowest rate time can pass – it can stop altogether. Guess which speed causes that to happen? It’s 299,792,458 m/s. The speed of light is really the speed at which time stops, so this is as fast as anything can ever go.
When we talk about the speed of light and say it is the fastest anything can travel, we are not phrasing it correctly. It would be better to say the faster you go, the slower time goes until you hit 299,792,458 m/s at which point time stops for you.
There is nothing special about light per se; what is special is that the universe has a maximum speed and light happens to move at it. Time distortion sets a speed limit on how fast anything can go, which makes quantum entanglement impossible.
In special relativity nothing can travel between two particles faster than 299,792,458 m/s, but information between entangled particles has to do precisely that. The particle that chooses up-spin has to send a communiqué faster than light to its partner, telling it to collapse. A phenomenon Einstein called ‘spooky action at a distance’.
SPOOKY CAT
Einstein, Podolsky and Rosen highlighted this mismatch between quantum mechanics and special relativity but also offered a solution. Quantum mechanics was at fault and Einstein was correct. Big surprise there.
Entangled particles have to be deciding ahead of time which way to spin if measured. They make this agreement as they are being generated in the entangler (the casual name I’ve given to a device that creates entangled pairs) and then they follow their prearranged flight path.
They have a conversation that goes something like:
Electron: Hey dude, if we come across a Stern–Gerlach spin detector you should go up-spin and I’ll go down-spin, OK?
Other Electron: Wait, why do I have to go up-spin?
Electron: (Sigh) You always have to be like this, don’t you?
Other Electron: Like what?
Electron: Difficult.
Other Electron: I’m not being difficult, bro, I just think we should be fair about spin-states.
That wording is exactly how Einstein phrased it.
In Einstein’s view of entanglement, the particles are not deciding at the point of detection what they are going to be, they have a predetermined answer which we are discovering. Superpositions do not really exist. Only ignorance.
Suppose we had a red cat and a green cat, which both get put into boxes and sent off to opposite ends of the solar system. If we open one of the boxes at our end we might find the red cat and thus instantly know what the other box contains. The information ‘green cat’ has metaphorically crossed the universe towards us but there is no violation of relativity here because nothing has to literally cover that distance.
The quantum view is that the cats have not picked properties yet and decide at random, communicating telepathically with each other at the point of measurement, faster than light. Einstein’s view was that the cat’s properties were always there; we just cannot see them until we measure.
After publishing this paper, Einstein and Rosen continued to work closely and enjoyed a lasting friendship. Podolsky, on the other hand, faded into moderate obscurity, although it has been claimed by some historians that he worked as a spy for the KGB during the cold war, operating under the insanely cool code name: Quantum.3
Oh, and by the way, I know every analogy in quantum mechanics seems to involve opening or closing a box of some sort. I will go a different way for the next one. I promise.
EINSTEIN, THE BELL TOLLS FOR THEE
Einstein’s theory was ready to do some well-deserved laurel resting, but along came a Northern Irish scientist named John Stewart Bell who threw a monkey in the mechanics in the 1960s. A passionate scientist all his life, Bell disliked pomposity and went to great lengths explaining physics to the general public and, in the process of trying to find a way of describing the EPR paradox, he came up with something rather curious.
Bell’s theorem, the idea which got him shortlisted for the Nobel Prize,4 was a game-changing way of putting the EPR paradox to an experimental test. Tragically, Bell never received the Nobel Prize because he died before the committee made their decision, and the prize is never awarded posthumously. His theorem, however, lives on.
Let’s entangle two particles, call them Alice and Bob, and send them both through separate
Stern–Gerlach gateways on opposite sides of a room. We can have our gates aligned vertically, horizontally or diagonally for each measurement we take and, for now, let us say Einstein was right: both particles pre-determine which spin they are going to adopt upon measurement.
Vertical gateways yield up/down spin results, horizontal gateways yield left/right spin results and diagonal gateways yield… umm… north-east/south-west results?
The horizontal and vertical spins of a particle are independent, but the diagonal spin is not. Whatever vertical or horizontal spin a particle has will influence which way it chooses to go if measured diagonally.
Think of it like this. If we set both our detectors vertically then if Alice is up, there is a 100 per cent chance Bob will be down. If we set Bob’s detector at right angles, however, we do not know what the outcome will be. Alice will be up but there is a 50 per cent chance of Bob picking left or right.
But if Bob’s detector is at a forty-five-degree angle, that makes it halfway between the two extremes, meaning we can predict its spin with an accuracy halfway between 50 per cent and 100 per cent. We can predict which diagonal outcome Bob will pick 75 per cent of the time.
If a particle is up vertically, its diagonal spin is 75 per cent likely to be north-east (i.e. pointing slightly upward) and if it is down its diagonal measurement is 75 per cent likely to be south-west (pointing slightly downward).
According to Einstein, both Alice and Bob have already chosen whether they are going to be up or down, which Bell pointed out means they have a slight preference for making one diagonal decision over another.
We cannot measure an electron’s diagonal and vertical spin at the same time (curse you, Heisenberg) but we can measure their entangled partner. If we measure the vertical spin of Alice and find it to be up, Bob should have the opposite spin pre-determined (down), which will therefore influence what it does diagonally. If Alice is up, Bob is 75 per cent likely to point south-west in a diagonal gateway.
Now say we do the experiment a hundred times. If we set the Alice detector vertically, then 75 per cent of the time she picks up, Bob will be south-west and vice versa.
If, on the other hand, Bob and Alice genuinely have not made their minds up until detection, the results of the experiment should violate the 75 per cent value and we will get a different number. This would possibly answer whether superpositions really exist.
In 1982, the French physicist Alain Aspect managed to build a real working entangler machine according to Bell’s specifications and ran an EPR experiment in the hopes of validating Einstein and dooming Bohr’s Copenhagen interpretation for good.5
Bell hoped it would reveal a 75 per cent match for Alice and Bob, proving there were hidden properties decided in advance by the particles. But the numbers were off. Completely off. Bell’s 75 per cent number was not observed, which means Einstein’s classical pre-determined explanation for the EPR paradox is wrong.
Particles are not deciding in advance what to be when measured. Somehow, they are truly deciding their state at the point of measurement, even when separated by distances forbidden by special relativity. Quantum weirdness prevails.
This does not necessarily prove that particles are sending messages faster than light, but in all honesty nobody is sure what it does prove.
Something going faster than light between particles is one explanation. Another is that the particles are linked via tiny wormholes transcending the dimensions of our universe. Another is that entangled particles are not separated at all and there is a spatial illusion that makes us humans think they are apart when really they are together.
We cannot make sense of it but somehow two entangled particles stay in communication no matter how far apart. What you do to a particle on Earth will instantly affect its twin on the moon without time for a message to pass between. Your guess for what is going on is as good as anyone else’s. Personally, I’m going to say it’s goblins.
CHAPTER NINE Teleportation, Time Machines and Twirling
INSTANT INSTAGRAM
If we have two electrons which we entangle on Earth and send to opposite ends of space, the entanglement link allows them to communicate instantly. Could we use this to send signals faster than light then? Sadly, the answer appears to be no.
Let us suppose we have two entangled particles with undetermined spins and we seal them inside two boxes… wait, no, I said we would avoid boxes in the next analogy… we seal them inside two chickens. One chicken is sent to Mars and the other is sent to Neptune.
When our Martian colonist opens up her chicken and looks inside, the particle adopts an up state. This is interesting, she thinks. She knows immediately that the other experimenter on Neptune has a down-spin particle inside her chicken. But she has no way of telling her friend about this result, other than sending a message via ordinary channels.
There would be no way to send a signal via the entanglement link because all the link does is communicate which eigenstate a particle has adopted. We have no control over that (it is random) so we have no control over what messages get sent between entangled particles.
If our experimenter could somehow convince a particle to take the up state or the down, she could use a series of chickens to encode binary information, which her friend could uncover on Neptune, but this is not possible.
A superposition cannot be influenced without measuring it and measuring it collapses it, defeating the whole purpose. The only information you could ever find out through entanglement would be the results of another scientist’s lab book. Faster than light communication is not on the cards. Teleportation though…
BEAM ME UP
On 4 July 2017 a group of physicists working in China published their new world record – the longest distance teleportation ever executed.1 The previous record had been set in 2012 when a group of researchers managed to teleport something a distance of 143 kilometres between mountains on the Canary Islands2 but this new record beat it by a factor of ten.
The team, led by Pan Jianwei, performed a quantum teleportation from their laboratory in Tibet to the satellite Micus, orbiting 1400 km above the Earth. This is Earth-to-space instant transportation and the Trekkie in me is beginning to tingle.
Quantum teleportation was outlined in 1993 by Asher Peres, William Wootters and Charles Bennett while working at the University of Montreal.3 We already know particles going faster than light is forbidden by special relativity but, thanks to entanglement, information about a particle’s state can sneak around the problem.
Consider, once more, Alice and Bob. After being created by the entangler, they are sent to different locations we want to teleport between. Bob is sent to a satellite and Alice is kept in our laboratory on Earth. We do not know any of Alice or Bob’s individual properties yet (that is what makes them entangled) but we know their overall state.
Now we introduce a third particle, the one we want to teleport. We will call it Cathy. Cathy is in a known state but if we bring her into contact with Alice, we can entangle the two of them in a superposition of their own.
We have to make sure we do not accidentally measure Alice in the process because that will collapse the entanglement bridge she has with Bob, but if we are careful (using devices called CNOT and Hadamard gates) we can get Cathy to shed her eigenstate and entangle with Alice.
Effectively, we open a room we know Alice is inside but do not look as we hold the door for Cathy to be ushered in. Cathy and Alice’s state is now in a superposition so we’ve lost information about each one, but Cathy’s original identity is in there somewhere, being shared among both.
Since we have entangled Alice with Cathy without breaking the original entanglement to Bob, the Cathy information is now shared with him also, even though he is in space. We have formed a triple entanglement scenario Schrödinger would no doubt have approved of.
If we do things just right, we can now take a measurement that tells us some of Cathy and Alice’s information but not all of it, keeping the re
st entangled with Bob still.
Suppose we do a measurement on Cathy and Alice that reveals their hair colour, but not eye colour. The hair-colour information is collapsed but eye colour is still up for grabs. If we now radio up to the satellite where Bob is and tell them to do an eye-colour measurement on Bob, we have a good chance of finding that Bob now has Cathy’s eyes.
Cathy herself has not been physically transferred through space, but part of her identity has. It is as if Bob is a blank canvas and Cathy’s image is peeled off and stuck to him.
Peres and Wootters wanted to call this phenomenon quantum tele-pheresis, but Bennett insisted ‘teleportation’ sounded cooler4 and he was not wrong.
There are a few limitations we have to be clear on though. First, Cathy will hang on to her properties until she is put into superposition with Alice. That means we cannot turn Bob into Cathy and still have the original Cathy preserved. If we want to transfer Cathy’s properties we have to detach them from her. This is called the ‘no cloning principle’ and says that quantum information can be transferred but never duplicated.
Second, we cannot transfer information without a measurement apparatus at the other end to detect it. Once we have done a measurement on Cathy and Alice, we still have to send a regular signal telling the person with the Bob particle which property to measure. If eye colour is the one that was sent (and we do not have control over this), then it is no good measuring Bob’s hair colour, which will have already collapsed.
Obviously the real teleportation process is not measuring things such as eye colour, it is measuring things such as spin state and energy, but these properties are how a particle identifies itself so it might as well be the same thing.
