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First encounter with relativity

Pierre Binétruy focuses on the notion of inertia, measured by mass, frame of reference and Galileo's principle of relativity
The notion of inertia is quite interesting. And it’s important to identify it fully. Inertia is resistance to the changes of motion. And the quantity that characterises inertia is the mass– mass of the object, which measures the quantity of matter inside the object. Now, quite often, one makes a confusion between weight and mass. And so let me illustrate this on an example. Let us consider a mine cart full of ore which is standing on a rail track. And let me ask you whether you prefer to set it in motion when it’s empty or when it’s full. Of course, most of you will prefer to push the cart to start it, to set it in motion, when it’s empty.
And if I ask you why, probably you’ll tell me that if it’s full then the weight of the ore inside the mine cart is pushing on the railway tracks and prevents you from pushing the cart. Now if that is so, then let me ask you a different question. Imagine that the mine cart is in motion, and then you stop it. Now, if your thinking was right, then you prefer to stop the mine cart which is full, because it presses more on the railway tracks, and so it helps you in stopping the cart. Of course, you know that you prefer to stop the mine cart when it’s empty.
Again, because it has got less mass, less inertia, so it resists less to the changes in motion. And so you see, on that example, that what measures the inertia of a material body is the quantity of matter which is measured by the mass. And, as we will see, this is very different from the notion of weight.
So let us pronounce, for the first time in this course, and certainly not the last time, the word “relativity.” Not Einstein relativity yet, but Galilean relativity. And so, before doing that, let me get back to Aristotle. Aristotle was claiming that the Earth is motionless. And why is that? Well, there’s an easy proof, he was saying. If you take this ball and throw it up, it falls back into your hands. And so that means that the Earth cannot be moving, because otherwise it would be falling a little further down the way. Now Galileo claimed that this was a clear misunderstanding. And he took the example of a ship cabin. So let’s imagine that we’re in this cabin.
Everything is closed. All the windows are closed. We don’t know whether we are moving or not moving– whether the boat– the ship– is moving. And so let us make some experiments about the falling objects, like dropping this ball, for example. Now what Galileo claims is that there is no way we could tell whether the boat is moving at constant velocity, as a uniform motion, or is at standstill, by doing experiments like experiments with falling objects. And so, if that is true, then it’s the same thing with the earth. We cannot tell by the falling objects whether the Earth is moving or is motionless.
And so that led him to identify what are known as “inertial reference frames” or “Galilean reference frames,” which are frames of reference– like the cabin of a ship, like, we’ll see later, a train, which are moving with respect to one another at constant velocity. For example, this boat, here, is moving a certain velocity. That’s a Galilean frame of reference. Another boat is not moving. It’s in the harbour, and that’s another frame of reference. And if we do experiments in these different frames of reference, then we should not be able to make a distinction.
And so he even turned this into a principle– the Galilean principle of relativity– which says that the laws of physics are universal in all inertial frames of reference. So that means that the laws of physics are identical in all frames of reference which are moving with respect to one another at constant velocity.
To conclude this first sequence, let us recall the concept that we have introduced so far. We have seen that there is a universality of the fall of material objects. And inertia is a concept that characterises the resistance to motion. The mass of an object is a quantity that characterises this inertia, and it measures the amount of matter in the object. The weight, on the other hand, is a force exerted on a body in the gravitational field of the Earth. And mass and weight are different. We have already identified different kinds of motion– uniform motion, motion with constant velocity; accelerated motion, when the velocity increases– this is, for example, the motion of a falling body in the vacuum.
We have identified the notion of frame of reference, which is the frame in which one performs an experiment. And there is a class of particular reference frames– so-called “inertial reference frames”– which are frames in uniform motion with respect to one another. And this allows us to give the Galilean principle of relativity, which tells us that the laws of physics are identical in all inertial reference frames.
Continue with Galileo, focusing on the notions of inertia and mass. And discover the principle of relativity, as expressed by the same Galileo. This will lead us smoothly to Einstein’s version of relativity, later this week. (6:46)
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