Comment by Lerc
10 months ago
While I'm interested in the topic of the post and have seen plenty of visualisations of balls rolling around hills, I was a little disappointed that it didn't cover the thing that has bugging me for years.
Momentum, or specifically inertia, in physics, what the hell is it? There's a Feynman tale where he asked his father why the ball rolled to the back of a trolly when he pulled the trolley. The answer he received was the usual description of inertia, but also the rarely given insight that describing something and giving it a name is completely different from knowing why it happens.
It's one of those things that I lie in bed thinking about. The other one is position, I can grasp the notion of spacetime and the idea of movement and speed as changes in position in space relative to position in time. I really don't have a grasp of what position is though. I know the name, I can attach the numbers to it, but that doesn't really cover what the numbers are of though.
A rough idea and simplification:
Suppose you have a bunch of 2D points, without coordinates, they exist because you say so, they can represent anything you want.
But you can't do a lot with those points, you may be interested in knowing their distances. To do that, you create some reference system, i.e. 2 non parallel axis and you set a unit on each, for example one could have one centimeter and the other one meter.
Now by placing the reference system on one particular point for example, you can 'identify' each other point on that scale.
With this correspondance, you can uniquely map each point to a coordinate and each coordinate to a point in space, this allows you to measure distances for example.
Notice that the choosen coordinates didn't really matter nor the direction of the axis. But as the rest of the 2D world can be mapped to them, everything is coherent.
Now if you create a novel axis system with another initial point and both axis with 1cm on each, you can find a transformation that transform your first system into the second, this transformation allows you to transform any other point in the new coordinates system.
So what is a position exactly? I would say it's the identification of some objects by an arbitrarly chosen referential system. What are the numbers? They corresponds to an arbitrary chosen unit of measure.
I hope this will give you more tought matter :)
What specifically do you feel you don't grok about inertia? I'll admit the use of "inertia" for explaining phenomena historically bothered me as it seemed like it was just an extra word that was already covered. Inertia/momentum describes what an object will do in the next instant if nothing else "happens" to the object. Force describes deviation from this according to dp/dt = F. Of course this is in the classical sense.
I'm not sure about position. It's a hard one to think about. What's important is that position's numbers (coordinates ) are defined according to a coordinate system. But the actual physical "position" doesn't care about the coordinate system. So things like distance or the time it takes to get from one point to the other (in some units) are invariant under coordinate changes.
>What specifically do you feel you don't grok about inertia?
It's the why of it. Why do objects stay in motion? Why does it take force to change that? It's hard to imagine a universe where this is not so.
Observation has given us a description that makes good predictions, but that's the what happens. Not the why.
I think it might be similar to the position problem in the sense of what does it mean to say a property is a property of something.
In a more philosophical matter, why there need to be a why? Does the full universe need to be causal? Are we biased to think that there always must be a why?
In Feynman lectures there is a very nice way of describing what is energy, if you like this kind of things it's also a big question ;)
Note:I think the why is important to explore, but I'm unsure there is always something more complex than 'otherwise the universe would collapse or be completely different' it may be that some more fundamental axiom, that I'm unaware of, leads to inertia in such a way that the universe is coherent
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What’s hard to understand about position? Isn’t it just a specific coordinate in some space?
Apart from the issue of relativity mentioned in the sibling comment.
I can easily imagine a bunch of perpendicular lines to describe a volume and I can use coordinates to indicate a point within that volume. Those are just abstract concepts though. How does something that exists have a position.
If you go further and think of the interactions of particles as expressions of perterberances of a field I guess it comes down to what is the amplitude comprised of and ultimately why is it meaningful that there is a relationship between one field and another in a way that you can say that you are talking about the same place.
Maybe that's what both questions devolve down to. Why do fields interact? Or perhaps, why would a fundamental property have a relationship to anything at all if it is fundamental?
Except there is no absolute coordinate system. Position is relative to something, and it’s not space. Likewise movement is only meaningful if defined with respect to something else.
Momentum is simply established movement with respect to something else. Acceleration is the only really meaningful thing, as it involves force and a transfer of energy. Momentum is a measure of how much acceleration it would require to change relative speeds with respect to something else. If you removed the something else from the system or substituted it for something with the same “momentum,” everything would cease to have momentum and would not be moving.
The insight that there is no global coordinate system in space is a key insight of relativity. Momentum is a measurement of the state of a system in an inertial frame and can be seen as a measure of the energy required to effectively get all the mass to have that velocity, or the energy required to bring the entire frame to relative rest. It’s a conserved measure, and a bunch of other useful things - but it itself isn’t “a thing,” it’s a measure.
"Except there is no absolute coordinate system. Position is relative to something"
Yes, just pick something. I think I get what you're saying, but I'm unclear why its not straightforward. I must be missing something.
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