Relativity and your smartphone

Einstein’s theory of general relativity has dramatically changed life on our planet. It’s used in a lot of different technologies, but perhaps the most surprising place to find the theory of relativity is in your smartphone. Smartphones account for general relativity in two different ways.

The place that it’s most commonly pointed out is in GPS. Your phone figures out where it is by calculating the distance to a number of satellites. It does this by measuring the time of flight of a signal broadcast by each satellite. Once the phone knows how far away different satellites are, it can do triangulation on the known positions of the satellites to figure out where you are. This location measurement can be pretty precise (on the order of a meter).

The precision of GPS is possible because your phone takes into account special relativity in the form of time dilation. Satellites are travelling very fast with respect to a stationary smartphone. That high speed means that time goes slower for the satellite, and the clock it uses to calculate time of flight is off. Your phone takes that into account when calculating how long it took the signal broadcast by the satellite to get to wherever you are.

General relativity comes into play because satellites are so much higher than your phone, which means that they experience less of Earth’s gravity than you do (note that this is different fromĀ microgravity). Since satellites experience less gravity than you do, time travels faster for them. So there are really two relativistic effects that need to be taken into account to actually figure out how fast time is travelling for the satellite, which can help tell how long it takes for a radio signal to travel from the satellite to your phone.

The second way that a smartphone takes general relativity into account is far simpler. Your phone has an accelerometer in it that measures acceleration on the phone. This is how your phone knows which way you’re holding it. It’s also how it makes those cool light-saber sounds when you swing your phone around.

When you’re having a light-saber duel, your phone is measuring the acceleration applied by your wild jabs and lunges. No relativity there. However, when the phone is stationary and it detects which way it’s oriented, it’s measuring gravity. Gravity isn’t acceleration, but it is indistinguishable under the theory of general relativity. It’s only through the effects described by general relativity that your phone works the way that it does.

Science! It’s closer than you think!