Distinguishing between Acceleration and GravityThe Equivalence principle tells us that gravity and acceleration are indistinguishable. This principle follows from the consideration fo the experiences of a person sealed in a opaque box.
In 1907, Einstein imagined two thought experiments:
- a) A person in a completely sealed box feels a force pushing them down into the boxes floor. There are two possible (but not mutually exclusive) explanations:
- i. The force is due to gravity, the box is moving with constant velocity near the surface of a planet
ii. The box is in outer space, with rockets attached to it that are accelerating it “upwards”
- i. The box is in outer space and not accelerating.
ii. The box is in free fall in a gravitational field.
Here Einstein used a bit of “classic physics reasoning” – if there is no experiment that can be done to distinguish between reasons i and ii (in either a or b), then, to a physicist, the two cases are “the same”
More generally: if two situations are experimentally indistinguishable, they are the same.
Einstein claims he came by this idea one day sitting at his desk in the patent office. Through his window, he watched a painter fall from a scaffold. The painter was briefly in free fall, leading Einstein to ponder whether there was a difference between free fall and simply being in the absence of gravity. His conclusion, expanded into the equivalence principle, was that there is not.
Strictly speaking, the thought experiments above only work for a person who is a point. If they have any height at all, and sufficiently sensitive equipment, they could measure the variation of gravity with height and tell the difference between i and ii. The difference between point and extended measurements will be discussed later in this course.
There are many ways to write “laws of physics” that fail to satisfy the equivalence principle. For example, look at Newton’s laws of motion and gravity near the surface of the Earth:
- F=mia and F=mgg
However, many, many observations have been made, and it turns out, up to an accuracy of 1 part in 1018 that these masses are the same (or at least have a constant ratio, that could be hidden in scaling g by a constant factor).This fact is required a priori by the equivalence principle. If the inertial and gravitational masses of objects varied, cases i and ii could be easily distinguished experimentally.