Are high school physics teachers only allowed to teach physics that is strictly empirical?
Why would they be limited to that?
What do you consider to be "physics that is not strictly empirical"?
well... aren't they only supposed to teach real science and, isn't real science only empirical? How could something be science and not be empirical?
...for example, the vis viva equation, that an object's energy is equal to mass multiplied by the square of its velocity
If you are saying that vis viva is not empirically based you would be mistaken. Leibniz cited Galileo's experiments on the relationship between speed and height to formulate his notion of vis viva. Can you give a different example or explain yourself further?
In this sense vis viva is empirically based, since energy is proportional to mass multiplied by velocity squared, but not equal to it. KE = 1/2MV^2; here, an object set into motion with twice the velocity will move a distance four times as great, with three times the velocity, nine times as great. This is makes energy proportional to MV^2, not equal to it, although it is equal to 1/2 this.
High school physics teachers usually have fairly broad latitude, because at most high schools (at least in the US), there is no one else on the faculty who knows enough physics to delve into the distinctions you are trying to make.
If the students are doing well enough on the standardized tests, a physics teacher is unlikely to get any grief for throwing in a couple of non-standard topics unless they are religious or something.
The post I just wrote about the distinction between KE being proportional and not equal to MV^2 is valid and could actually have been included in the curriculum without any wrongdoing or inaccuracy on the part of the teacher. I wasn't clear on exactly what I meant on weather or not only empirical ideas are taught in the physics classroom. My example with vis viva was put forth because work = KE = 1/2MV^2. If the teacher said that work = 2 x the KE, then this would not be empirical? But forget about that. I just tried an example. Please answer my original question. Are only empirical ideas allowed to be taught in the physics classroom. The reason I brought up vis viva is because if it is taught that the work required to set a body in motion is equal to 2 x its KE, then this would not be empirical, because it cannot be tested.
On the other hand, it is indeed a small distinction regarding "proportional" or "equal to", but if the teacher stated that work was equal to MV^2, this would not be empirical, no?
Empirical means something that can be observed and tested and verified as fact. How can we experimentally verify that work is equal to MV^2? KE on the other hand can be verified, because we know that the resistance that can be overcome by a body in motion is = KE = 1/2MV^2
To be exact, it is not a small distinction regarding "proportional to" or "equal to".
non-standard doesn't make something empirical or not
But that choice is arbitrary and due to the units chosen for work. We could have defined kinetic energy to be equal to mv^2 and defined work as 2Fd. It was Coriolis' definition of work that added the factor of 1/2 to the vis viva term. It is perhaps important to keep in mind that the early pioneers of modern classical physics worked mostly with proportions and not with direct equations since algebra had not yet been fully developed.
But let's not get hung up on this example.
I'm sure there are topics broached by physics teachers at the high school level that do not meet this qualification. For example, I've had students give presentations on topics in modern physics. Any student that presents on string theory (if we want to call that physics) would be presenting a non-empirical theory by your definition (now, you could certainly argue that the teachers aren't 'teaching' string theory by doing this, but simply surveying the modern topics).
Interestingly, the 'atomic hypothesis' could have counted as a non-empirical theory before the technology was developed to 'see' atoms. Mach argued that the atomic hypothesis was not scientific because atoms could not be observed and thought that people shouldn't accept it.
Can we substitute 'metaphysical' for 'non-empirical' or do you think there is a distinction?
I think you meant 'non-empirical.' I would not draw a distinction. Something non-empirical, by your definition above, would be the same as something metaphysical according to my understanding. I just wanted to make sure that you didn't have any objection before I proceeded further.
what is the definition of metaphysical?
My teacher always taught us that KE or Work = 1/2MV^2, not MV^2
But there was a time, looking back when he seemed to be (just from a fragment of what he said, as this is all I remember) talking about MV^2, or twice the work. The fragment was exactly this: there was picture of a parabola on the board in lab or pre-lab in which he was marking off points and saying (and writing at the same time) "1/2"..."1/2"..."1/2", and crossing each one half off before he proceeded to writing the next one half. What was this. Do you remember your physics teacher doing something like this?
Well, metaphysics is a broad category of philosophy dealing with many different things. Like physics, metaphysics is concerned with the fundamental parts of nature and the rules (usually non-mathematical) that govern them. It is inherently non-testable. For example, a classic metaphysical principle is that the planets move in circular motions because circles are the most perfect shape. Another more modern metaphysical principle is Maupertuis' principle of least action which claims that nature is economical in its processes.
Sure, I'm not disputing that; it is the best way to define that quantity because it gets rid of many 'extra' factors of 2 that would appear if the units were chosen differently. My point was that this choice was arbitrary.
this was before the midterm
I'd need more information to interpret what he was doing.
I think it's arbitrary too.
I've been trying to figure it out for the longest time.
Did your physics teacher ever define work or KE as MV^2 as opposed to 1/2MV^2?
and how was the factor of "2" treated by men of science when thinking in terms of twice the KE or twice the work?
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