Relativity - Aristotle, Galileo, Einstein, Einstein
Posted: Thu Jul 11, 2024 12:09 pm
So we all know about Galileo being banged up (placed under house arrest for purists) for arguing against the Vatican's Aristotelian stance that the Earth is the centre of the universe.
Aristotle's reasoning was based on the Greek theory of four elements, earth, water, air and fire, itself based on even older Mesopotamian and Egyptian ideas. (If you're into the really old stuff, you can read this: https://philosophynow.org/issues/104/Ph ... d_Branches) The theory being that all the elements have their natural layered place: earth at the centre, surrounded by water, air and fire all of which would eventually settle in that order; but there is also the aether above which spins around in concentric spheres, which rub against each other causing friction and thereby creating the illusion of heavenly bodies ‘particularly in that part where the sun is attached to it.’ Aristotle Metaphysics That movement is transferred down to Earth which is why everything is so mixed up.
Aristotle supported his view of a stationary Earth with the claim that if the Earth was moving, then if you dropped a stone, the stone would land as far from your feet as the Earth had moved in the time it took the stone to drop.
The idea of the Earth being at the centre of the universe, and hence the focus of God's attention, suited the Vatican and while a lot has been written about the details, the long and short of it is that the decision was made that Galileo, and his advocacy of the Copernican model of Earth in orbit around the Sun was too dangerous to be let out of the house. It didn't help that in his Dialogue Concerning the Two Chief World Systems, (Copernican and Aristotelian) the Aristotelian advocate is called Simplicio.
Anyway, in the same book Galileo countered Aristotle's claim about falling stones with this:
“Shut yourself up with some friend in the main cabin below decks on some large ship, and have with you there some flies, butterflies, and other small flying animals. Have a large bowl of water with some fish in it; hang up a bottle that empties drop by drop into a wide vessel beneath it. With the ship standing still, observe carefully how the little animals fly with equal speed to all sides of the cabin. The fish swim indifferently in all directions; the drops fall into the vessel beneath; and, in throwing something to your friend, you need to throw it no more strongly in one direction than another, the distances being equal; jumping with your feet together, you pass equal spaces in every direction. When you have observed all these things carefully (though doubtless when the ship is standing still everything must happen in this way), have the ship proceed with any speed you like, so long as the motion is uniform and not fluctuating this way and that. You will discover not the least change in all the effects named, nor could you tell from any of them whether the ship was moving or standing still.”
What he is describing is an inertial frame of reference, in which everything is moving at the same velocity relative to some external reference.
So Galilean relativity states that inside an inertial frame of reference, there is no way to know whether you are moving or not; it is only by looking out the window that you can tell you are moving relative to something else. Or it is moving relative to you - makes no difference.
The story goes that Einstein wondered what would happen if you could travel at the speed of light. Specifically he imagined looking at himself in a mirror in front of him, which, at the speed of light would go blank, because the light from his face couldn't go fast enough to reach the mirror to be reflected. This would break Galilean relativity, because there would be a way to know you are moving, albeit at the speed of light, in an inertial frame.
Einstein being Einstein decided to explore alternatives to a blank mirror and his solution was that, yeah, the mirror blanks out, but you wouldn't notice because for you, time stops. That's not some weird metaphysical spookiness, it is simply the fact that if in an inertial frame everything is moving as fast as anything can move, there can be no interaction between them - literally nothing happens. Outside the world keeps spinning and time moves on.
However, as Galileo noted, that is true only in the special case of motion that is "uniform and not fluctuating this way and that", hence special relativity. Assuming there are no flatearthers here by mistake, we all know that as we move across its surface, the Earth is spinning as it orbits the Sun, in a galaxy that is cartwheeling through a universe that is expanding. In other words, we are definitely not moving in a way that is uniform and not fluctuating this way and that, and yet relativity still holds.
General relativity deals with frames of reference which are either changing direction, changing speed or both, which is every frame of reference. Einstein claimed that being in a lift that is in free fall is equivalent to being in a lift in outer space, where there is no gravity. Here on Earth if you drop a stone, it accelerates at 9.8m per second per second. So after two seconds of falling a stone is going at 19.6m per second, after three seconds its 29.4m/s, about 100kph, 60mph. To experience the same 'gravity' a lift in outer space has to accelerate at 9.8 m/s2, or it has to change direction appropriately, which is the idea behind spinning big wheel space ships creating artificial gravity.
One of the key differences between special and general relativity is that in special relativity, there in no way to tell who is moving relative to what. Einstein illustrated this by imagining a 'light clock'. All clocks count periodic events, be that the swing of a pendulum or absorption and emission of photons in atoms. Einstein's light clock counts the bounces of a pulse of light between two mirrors facing each other stacked vertically.
According to special relativity, an observer in an inertial frame of reference (in the example Einstein used a train carriage) that includes a light clock, will see the pulse of light bouncing straight up and down. Someone else, watching the train go by, will see the light pulse take a diagonal route, because as the light leaves one mirror the other is moving and the light has to follow whatever path necessary to bounce off it. So because the speed of light is constant, the outside observer sees the clock on the train ticking slower than anyone in the carriage.
The confusing thing is that if the outside observer also has a light clock, people in the carriage see that as ticking slow. Since special relativity is about uniform velocity, the train and the outside observer will get further and further apart and never find out which clock was actually ticking slower. In general relativity, you can think of the train as being on a circular track, with the outside observer being in the middle watching the train go round and round. In that case, as I'm sure you have already realised, while the outside observer still sees the light on the train moving diagonally, anyone on the train sees the light in the middle bouncing straight up and down. In effect, that's what the Hafele-Keating experiment observed.
Anyway, as Einstein predicted, the effect on time of gravity is exactly the same as acceleration, ie, changing speed or direction. So Einstein came up with his idea of 'spacetime' being a 'fabric' that is warped by mass to account for this change of direction. But, as noted elsewhere, there are alternative explanations.
Aristotle's reasoning was based on the Greek theory of four elements, earth, water, air and fire, itself based on even older Mesopotamian and Egyptian ideas. (If you're into the really old stuff, you can read this: https://philosophynow.org/issues/104/Ph ... d_Branches) The theory being that all the elements have their natural layered place: earth at the centre, surrounded by water, air and fire all of which would eventually settle in that order; but there is also the aether above which spins around in concentric spheres, which rub against each other causing friction and thereby creating the illusion of heavenly bodies ‘particularly in that part where the sun is attached to it.’ Aristotle Metaphysics That movement is transferred down to Earth which is why everything is so mixed up.
Aristotle supported his view of a stationary Earth with the claim that if the Earth was moving, then if you dropped a stone, the stone would land as far from your feet as the Earth had moved in the time it took the stone to drop.
The idea of the Earth being at the centre of the universe, and hence the focus of God's attention, suited the Vatican and while a lot has been written about the details, the long and short of it is that the decision was made that Galileo, and his advocacy of the Copernican model of Earth in orbit around the Sun was too dangerous to be let out of the house. It didn't help that in his Dialogue Concerning the Two Chief World Systems, (Copernican and Aristotelian) the Aristotelian advocate is called Simplicio.
Anyway, in the same book Galileo countered Aristotle's claim about falling stones with this:
“Shut yourself up with some friend in the main cabin below decks on some large ship, and have with you there some flies, butterflies, and other small flying animals. Have a large bowl of water with some fish in it; hang up a bottle that empties drop by drop into a wide vessel beneath it. With the ship standing still, observe carefully how the little animals fly with equal speed to all sides of the cabin. The fish swim indifferently in all directions; the drops fall into the vessel beneath; and, in throwing something to your friend, you need to throw it no more strongly in one direction than another, the distances being equal; jumping with your feet together, you pass equal spaces in every direction. When you have observed all these things carefully (though doubtless when the ship is standing still everything must happen in this way), have the ship proceed with any speed you like, so long as the motion is uniform and not fluctuating this way and that. You will discover not the least change in all the effects named, nor could you tell from any of them whether the ship was moving or standing still.”
What he is describing is an inertial frame of reference, in which everything is moving at the same velocity relative to some external reference.
So Galilean relativity states that inside an inertial frame of reference, there is no way to know whether you are moving or not; it is only by looking out the window that you can tell you are moving relative to something else. Or it is moving relative to you - makes no difference.
The story goes that Einstein wondered what would happen if you could travel at the speed of light. Specifically he imagined looking at himself in a mirror in front of him, which, at the speed of light would go blank, because the light from his face couldn't go fast enough to reach the mirror to be reflected. This would break Galilean relativity, because there would be a way to know you are moving, albeit at the speed of light, in an inertial frame.
Einstein being Einstein decided to explore alternatives to a blank mirror and his solution was that, yeah, the mirror blanks out, but you wouldn't notice because for you, time stops. That's not some weird metaphysical spookiness, it is simply the fact that if in an inertial frame everything is moving as fast as anything can move, there can be no interaction between them - literally nothing happens. Outside the world keeps spinning and time moves on.
However, as Galileo noted, that is true only in the special case of motion that is "uniform and not fluctuating this way and that", hence special relativity. Assuming there are no flatearthers here by mistake, we all know that as we move across its surface, the Earth is spinning as it orbits the Sun, in a galaxy that is cartwheeling through a universe that is expanding. In other words, we are definitely not moving in a way that is uniform and not fluctuating this way and that, and yet relativity still holds.
General relativity deals with frames of reference which are either changing direction, changing speed or both, which is every frame of reference. Einstein claimed that being in a lift that is in free fall is equivalent to being in a lift in outer space, where there is no gravity. Here on Earth if you drop a stone, it accelerates at 9.8m per second per second. So after two seconds of falling a stone is going at 19.6m per second, after three seconds its 29.4m/s, about 100kph, 60mph. To experience the same 'gravity' a lift in outer space has to accelerate at 9.8 m/s2, or it has to change direction appropriately, which is the idea behind spinning big wheel space ships creating artificial gravity.
One of the key differences between special and general relativity is that in special relativity, there in no way to tell who is moving relative to what. Einstein illustrated this by imagining a 'light clock'. All clocks count periodic events, be that the swing of a pendulum or absorption and emission of photons in atoms. Einstein's light clock counts the bounces of a pulse of light between two mirrors facing each other stacked vertically.
According to special relativity, an observer in an inertial frame of reference (in the example Einstein used a train carriage) that includes a light clock, will see the pulse of light bouncing straight up and down. Someone else, watching the train go by, will see the light pulse take a diagonal route, because as the light leaves one mirror the other is moving and the light has to follow whatever path necessary to bounce off it. So because the speed of light is constant, the outside observer sees the clock on the train ticking slower than anyone in the carriage.
The confusing thing is that if the outside observer also has a light clock, people in the carriage see that as ticking slow. Since special relativity is about uniform velocity, the train and the outside observer will get further and further apart and never find out which clock was actually ticking slower. In general relativity, you can think of the train as being on a circular track, with the outside observer being in the middle watching the train go round and round. In that case, as I'm sure you have already realised, while the outside observer still sees the light on the train moving diagonally, anyone on the train sees the light in the middle bouncing straight up and down. In effect, that's what the Hafele-Keating experiment observed.
Anyway, as Einstein predicted, the effect on time of gravity is exactly the same as acceleration, ie, changing speed or direction. So Einstein came up with his idea of 'spacetime' being a 'fabric' that is warped by mass to account for this change of direction. But, as noted elsewhere, there are alternative explanations.