If measuring one entangled particle is linked to the result at the other, why not use that link to send messages faster than light? Imagine an engineer with a source of entangled pairs placed between Earth and Mars, hoping to beat a radio delay that can reach twenty minutes. It cannot be done.
Each side sees pure randomness
The key fact is simple. Whatever setting Ana chooses, the results on Ben's side, taken by themselves, look exactly the same: a random sequence with fixed odds. If Ben measures his photons with an upright filter, he gets passes and blocks at fifty fifty, whether Ana measured upright, at forty five degrees, at some other angle, or not at all. The correlation exists only in the pairing of results: which of Ben's photons passed alongside which of Ana's. To see the correlation, the two records must be brought together and compared, which requires ordinary communication no faster than light.
This is a theorem of quantum mechanics, often called the no-signaling or no-communication theorem. The no-signaling theorem says that the statistics of results at one location cannot be changed by the choice of measurement made at a distant location. Ana's choice affects what the joint pattern looks like, but nothing that Ben can see on his own.
Why Ana cannot choose her result
An eager inventor might reply: then let Ana force her photon to pass, and Ben's will pass too. But Ana cannot choose her result. She chooses only the setting. Each individual outcome is random, and nothing in quantum mechanics lets an experimenter pick which outcome occurs. The randomness of single outcomes is exactly what keeps entanglement from becoming a telephone.
Why Ben cannot copy his photon
Another scheme: let Ben make many copies of his photon and test the copies at different angles, building up a picture of its state and so learning which setting Ana used. This fails too. The no-cloning theorem, proved in 1982, shows that no device can make a perfect copy of an unknown quantum state. The proof, by William Wootters and Wojciech Zurek and independently by Dennis Dieks, was in fact prompted by a proposed faster than light signaling device that relied on copying. The device would have worked if cloning were possible. It is not, and the scheme collapsed.
Relativity and the order of events
In the best Bell tests, the two measurements are separated so that no light signal could connect them. Einstein's relativity has a striking consequence for such events: when two events are too far apart for light to connect them, observers moving in different ways can disagree about which happened first. For one observer, Ana measured first; for another, Ben did. If entanglement worked by a real signal from the first measurement to the second, nature would have to pick a preferred observer to decide which was first. Standard quantum mechanics does not need to, because its predictions about the joint pattern are the same in either order.
So quantum mechanics and relativity coexist without contradiction at the level of experiments. Many physicists, following the philosopher Abner Shimony, describe the relationship as a peaceful but uneasy truce: the correlations cannot be explained locally, yet they cannot be used to send signals. What Bell tests rule out is a local hidden variable explanation of the correlations, not the ban on faster than light messages. Whether something deeper, invisible to experiment, connects the partners is a question of interpretation, and QUAN 202 takes it up.
Common misreadings
Because of the no-signaling theorem, several popular claims are wrong. Entanglement does not let anyone send messages instantly to a spacecraft or across the galaxy. News stories about instant communication through entanglement are usually describing a scheme that also relies on ordinary signals, which set the real speed limit. The honest summary is that entanglement creates correlations that become useful once the parties communicate in the ordinary way. That usefulness is real: it underlies quantum cryptography and other technologies covered in QUAN 203.
Worked example: the quantum telegraph that fails
An engineer proposes a code. A source halfway between Earth and Mars sends entangled photon pairs, one photon to each planet. To send a 1, the Earth operator measures her photons with an upright filter. To send a 0, she uses a filter at forty five degrees. The Mars operator always measures upright and hopes to see a difference.
Follow what happens. When Earth sends a 1, each Mars result is random, fifty fifty, but it matches the Earth result for the same pair. When Earth sends a 0, each Mars result is still random, fifty fifty, and now it agrees with the Earth result only about half the time. The difference lies only in how the Mars list lines up with the Earth list, and the Mars operator does not have the Earth list.
When Earth radios its list over, the list arrives after the ordinary light delay. Then the Mars operator can decode the bit, but no sooner than if Earth had simply radioed the bit itself. The scheme sends nothing ahead of light.