Ok readers (all 3 of you), I have a question about quantum entanglement.

Background:
For those of you who don't know what it quantum entanglement is, it is basically a state of existence where two quantum particles (just think of them as grains of sand), are bound in such a way that whatever "state" (think positive or negative charge) one of them is in, the other one will be the opposite. So if one grain is positive, the other one will be negative. This occurs no matter how far apart the two particles are. This is a gross oversimplification and the whole charge/grain of sand thing is a metaphor for particles and spin and things like that. Here is the link to the wikipedia article on quantum entanglement.

Also for the non-astronomer/physicists, the Lorentz transformation is equation for calcluating time when traveling at speeds relative to an observer (I think). Basically, it has been proven with high accuracy clocks and really fast planes that when you travel fast, time slows down for you. I think it goes something like, if you travel for a year at the speed of light, 50+ years will have passed on earth.

Here is the situation:
Take a pair of quantum particles that are entangled. One of them is on Earth and the other is on a ship traveling at near the speed of light. Assume that you have some way of discerning when you are communicating (changing the state) as opposed to the random noise. On earth, mission control intends to send a binary message of 0100 1100 to the ship by changing the state of its particle to corresponding 0 and 1 at 1 hertz (sending one bit per second).

Here is the question:
At what frequency will the ship receive the message? Will the Lorentz transformation apply? If they are traveling at a speed which time is half as fast as earth's time will they receive the message at 2 hertz? Will it be relative to the particle and remain 1 hertz?

I think we might need to involve Joleen on this one, Paul.

Update: Joleen has responded via email!


From Joleen:

First a clarification: the "lorentz transformation" is used when two observers are traveling relative to each other near the speed of light. If two such observers try make a measurement of mass, length, or time they will get different answers. Traveling at 10% the speed light makes only a .5% difference in the measurements so at slow speeds measurements will look the same. Whereas at 90% the speed of light you will be off by 2.3x (or 230%). So reader, in order to get 50 years to pass earth whereas only one year passes in the plane you have to travel at something like. 0.9998 times the speed of light.

One of the key things you are actually missing in your question is "as measured by which observer". So you on the ship might see the bits change at 1 HZ, but if you somehow measured the same frequency on the earth you would see that the ship receives the message at 2Hz. And, if you tried to measure how fast the Earth people switched their bits you would actually measure 2Hz. Tricky. :) I'm not entirely sure whether the fact the message is sent via quantum entanglement further complicates the issue or not.

Sadly, it took me like half an hour to come to that conclusion instead of working. My quantum and special relativity skills are very rusty.

Joleen :)

Addendum. I think the 2Hz might actually be 0.5 Hz. Because the time between bits changing would either be 1 sec. or 2sec which in frequency is either 1Hz or 0.5 Hz.