IIRC, Sir Isaac Newton formulated his new physics by observing objects as they moved, measuring space, time, and mass, and mathematically manipulating those measurements with his other discovery, calculus.
Suppose we filmed a cube, 1 cubic centimeter, one gram, and dropped it from a height of one meter…but filmed it in slo motion. We tell Newton to formulate another set of physics by observing this film, and not telling him just what slo-mo is.
He may very well state that the cube is falling in a less-than-one-G environment.
But how would he encounter such things as mass, force, the gravitational constant, etc.?
I don’t see where he would have any trouble with any of the other concepts. G is clearly distinguishable from g[sub]e[/sub], where g[sub]e[/sub] is earth’s gravity. He was applying his work to the movements of the planets, after all, and that g[sub]sun[/sub] is very different.
Unless I’m missing what you’re asking, the answer is that he would have proceded exactly as he did.
As one measurement is shortened or lengthened, at least one if not many more measurements would in turn enlarge or contract in proportion to the “film” being slowed down or speeded up.
Would all the equasions and formulae still remain identical, or would even some constants, like c, change?
If you slow down time, do you also slow down light?
If all of your physics experiments were viewed via film which was unbeknownst to you slowed down, then yes, you would measure a correspondingly slower value for the speed of light. But all of the relationships between things would still be the same, and the structure of physics as a whole would be no different.
For comparison, let’s look at the analogous question for lengths: Suppose that, unbeknownst to Newton, he was using a mismarked ruler, with all of the tick marks uniformly stretched too far apart. He would measure different values, of course, but would the actual physical results be any different? The answer to this one is easy: Of course not. He did, in fact, use a ruler marked differently than the ones modern physicists use: Each increment on his ruler was 2.54 times as long as the increments we use.
Little known facts. Prior to 1959 the English to metric conversion was 39.37 "/meter. This works out to 2.5400050800102 cm/in. In that year the inch was redefined as exactly 2.54 cm. It’s commonly known as the “international inch.”
except
For survey purposes the old inch is still used. When the conversion factor is 39.37 in./m a note is added to the measurement that it is “US Survey.” This was done to avoid all sorts of legal problems in trying to adjust boundries in places like Manhattan where land value is out of sight.
Take a bodyless car going about 5 miles per hour the passenger is not strapped in to the seat. After about a minute the driver hits the brakes. The passenger leans forward a bit but not much else.
Speed the film up 10x and Newton would wonder what happened to all that momentum; surely the passenger should be flung out his seat.
There’s still some things missing from the OP. Do you tell Isaac what a movie is? Do you tell him the movie is of things happening on Earth? Do you tell him that you have changed something as-yet undisclosed relative to what he would see live?
If your “slo motion” is not slowed down by a constant factor, for example, all sorts of things might have been derived.
You can measure the constant G by various methods. Some use time and others (like making a pendulum rest in a different location by importing a huge weight into the lab) do not. Isaac could find your film breaks some symmetries.
Not if all his experiments were done via slow-motion film. All experiments to measure any given quantity will ultimately have the same time dependance. You might, for instance, measure a force by seeing what acceleration it puts on a known mass (which is time-dependant), or you might do it by seeing how much a spring is stretched (which doesn’t seem like it’d be time-dependant). But how do you measure the strength of your spring? Well, you could put a known mass on the end of it and measure the period of oscillation… But that’s time-dependant again.
Both of those cases should throw the passenger out of his seat, if there’s nothing to prevent it. Since the passenger, at 5 mph, isn’t thrown out of his seat, something must have prevented it. This might, for instance, be the passenger holding onto something. In this case, viewing the film at high speed, Newton might have concluded that the person was holding on with superhuman strength. But that wouldn’t be anything special; if there was another person running along beside the car, Newton would also think that person to be superhuman, for running that fast. The force that holds the person back might be friction, but friction would also be correspondingly larger in the sped-up case: A sped-up film would appear to correspond to a world with a higher value of g (since things fall faster), and friction between your butt and the seat is going to be proportional to (among other things) g.