@ACuriousMind In GR and SR, isn't force given by $\mathbf{F} = \gamma(\mathbf{v})^3 m_0 \, \mathbf{a}_\parallel + \gamma(\mathbf{v}) m_0 \, \mathbf{a}_\perp$?
Doesn't make $F=ma$ correct. It may be near correct, but it's not how the Universe works.
Then again, we might find something more precise than $\mathbf{F} = \gamma(\mathbf{v})^3 m_0 \, \mathbf{a}_\parallel + \gamma(\mathbf{v}) m_0 \, \mathbf{a}_\perp$
Again, Newtonian physics can be misleading. For example, why be taught that gravity is a force when it's actually just a consequence of the curvature of spacetime?
It's so much easier to just explain what's more accurate.
@SirCumference Yes, but learning what? You're not learning "more accurate stuff" most of the time, you're spending most of the time learning purely mathematical techniques
@SirCumference There are two different issue here. I agree with you that it should be made more clearer that this is not the way the world "actually" works, that there are better, but more complicated theories. I disagree that this means we shouldn't teach the easier theories first to make for a gradual learning curve.
Yeah, don't get me started about the Bohr atom. That one's a "simpler" theory that doesn't actually contribute to understanding because most people just start poking holes in it as soon as they hear it
Many people will end up using non-relativistic classical mechanics. In applied realms, it can be incredibly important. Why teach general relativity to an aerospace engineer when Newtonian gravity will give a great approximation in their applications?
@SirCumference You seem to have strange idea of what scientific theories are. They are not "truth". They are predictive models of certain subsets of the universe around us. There is no value in teaching a very complicated general model when a simple, more limited model will momentarily suffice. Not all scientific theories are meant to be theories of everything, they don't need to be to be useful.
@SirCumference When I teach Newtonian mechanics, I teach with sufficient accuracy about the behaviour of slow-moving bodies. I don't see what is so terrible about that, especially given that no one will ever use GR to compute non-relativistic behaviours.
Imagine teaching the earth was flat. Some people would learn it's round. This wouldn't be important to everyone, but it should be made known to everyone
@SirCumference That is a different case because there is no use to assuming the earth is flat. It doesn't lead to a simpler, nicer description fo the system you are describing.
Because these are some well-known things. Half of the people on earth have heard of "spacetime" but maybe 5% actually know how space and time are related
The only other option is to teach the advanced stuff, which is unnecessary. Hell, most people don't even need to know what the structure of an atom is. So there's no reason to sit them through even more stuff, especially if they don't want to know them.
As an example, what's one subject you don't care about?
user54412
Consider this: My college classmates were exclusively valedictorians of their high school, and they aced every test given to them up until college. A large fraction of them -- perhaps even a majority -- would not be able to understand the differential geometry at the heart of GR.
@SirCumference Okay. Why don't you care about economics?
user54412
12:40 AM
What then would the rest of the world do when you declare that the only physics they're allowed to know is that incomprehensible pinnacle of modern understanding?
@SirCumference, can you actually do GR calculations, or do you only have a conceptual view? Because if it's the latter, I'd say your understanding of physics is more false than one of your classmates who knows nothing about GR, but can calculate in newtonian mechanics well.
@SirCumference Stop being so damn poetic and think about actual people and their actual lives. Of what importance is it that everyone know what spacetime is?
@SirCumference I'm not talking about why you think science is more important. You care about loads of other things that don't explain why we're here, right?
@SirCumference or take QFT for an example. I calculated cross sections for QED interactions. But before doing any full calculation, I would get intuition and partial results from classical mechanics, classical E&M, and semiclassical QM! a hundred times faster, and really the only way to check your final result.
@SirCumference without the more basic, 'less true' theories to back me up, it would've been impossible. Also, 'more true' theories are often made by standing on top of less true ones and guessing the next level.
@knzhou It's also important to have the right equations. I can technically get a more precise answer if I use $\mathbf{F} = \gamma(\mathbf{v})^3 m_0 \, \mathbf{a}_\parallel + \gamma(\mathbf{v}) m_0 \, \mathbf{a}_\perp$ instead of $F=ma$
@SirCumference yeah, but once you're staring at your gigantic final answer, how do you tell it's right? 99% of the time, it's by taking a limit and confirming it reduces to what F=ma says.
@SirCumference I know people who can't even count and live theirs lives ''fine'', I could do my bidding of life without knowing the earth isn't the center of the universe
Firstly I think shades of this question have appeared elsewhere (like here, or here). Hopefully mine is a slightly different take on it. If I'm just being thick please correct me.
We always hear about the force of gravity being the odd-one-out of the four forces. And this argument, whenever i...
I have studied some of Einstein's Theory of General Relativity, and I understand that it states that gravity isn't a force but rather the effects of objects curving space-time. If this is true, then why are we instructed in middle school that it is a force?
1. Look at the number of upvotes for those questions. That means many people are asking themselves your question. 2. Look at the top answers. They say: We need to because it is useful. Who are you to unilaterally declare that people should care more about your precious "true" theory than about useful theories?
user54412
@SirCumference No. It is not a simplification.
user54412
Your philosophical position is that there is some absolute truth that we have progressively dumbed down.
But GR hasn't really failed us yet, has it? Our equations still work with extreme precision in even more cases than those of Newtonian physics. Is that not more accurate?
@SirCumference The assertion that GR is the "clear better method" is just wrong. Please derive the trajectory of a simple pendulum for me with GR.
user54412
Again, what do you do with the billions of people who could have understood some basic physics, but who will understand nothing if you only teach advanced stuff?
Then do the same thing with Newtonian mechanics, and with the small-angle approximation. Then do the experiment, compare the results, and tell me again that GR is the "clear better method".
@SirCumference Efficience is the word for 90% of the cases
user54412
Welcome to Physics.SE! This is hilarious but it doesn't answer the question. Furthermore it is quantitatively incorrect: for reasonable estimates of the number of medieval witches and the number of boiling kettles, there's much more diabolical energy released by boiling kettles than established by the witches. Your theory predicts that witch-drowning predates medieval times. Perhaps the screams of extinct dinosaurs are involved as well. — rob4 mins ago
@SirCumference oh jeez, I don't think so. it's hard enough to analyze a really symmetric black hole in GR, and you'd have to work for weeks to do a two-loop diagram in QFT.
meanwhile, I know high schoolers that can calculate what happens if a block is attached to a pulley on a ramp with friction. that's way more complicated.
we already have an issue with most people hating physics at high school, do you really want to foist upon the averag student to apply GR to everything?
I would still maintain that even in a world where everyone is capable of and interested in learning GR, teaching Newtonian mechanics would still be worthwhile.
Firstly I think shades of this question have appeared elsewhere (like here, or here). Hopefully mine is a slightly different take on it. If I'm just being thick please correct me.
We always hear about the force of gravity being the odd-one-out of the four forces. And this argument, whenever i...
I have studied some of Einstein's Theory of General Relativity, and I understand that it states that gravity isn't a force but rather the effects of objects curving space-time. If this is true, then why are we instructed in middle school that it is a force?
