What do we mean by “Local Physics”. We mean this…
From the cover of GRAVITATION, an off-beat view of Newton’s Apple. Here is illustrated just one aspect of it, through the “magnifying glass.” A Local View.
While the apple before us in three-dimensions of space is curved or round, from the point of view of an ant, it looks flat. Like it looks “through the magnifying glass.” The ant’s paths – to the ant – are straight lines. Where to our trained eye, we see curves on the apple’s surface far from the ant, the ant – not having our perspective – see straight lines. Which is what the ant should see in two-dimensions.
What can we learn from this?
(1) That geometry and physics (concomitantly) look simple locally. To be honest, this was Einstein’s and Schrödinger’s idea.
Now, why isn’t it simple globally? If ants could talk, they would explain that parallel paths start to fuse and diverge in very un-parallel ways. In fact if the ant travels “in a straight line” around the stem region of the apple, the ant comes back on his own path like an ellipse! Wha? How is that possible?
The physicist among these ants accommodates this phenomena through a physical law they might term, “centro-apple force,” of course! There is a force directed towards the center of the apple stem pulling the poor ant-travelers off-course.
You’ve heard the rest of this story, or stories, but for a four-dimensional apple, a Spacetime Apple. Those forces we call centripetal force in rotation and gravity – centerpointing forces. Both forces for us are real in 3D space; do not doubt their reality! And humans are made out to be ants! In this way, we can explain our world.
So Spacetime is our universe, with space united with time. We not only have space, but Spacetime as one thing. From this 4D Apple, we would find out three more things:
(2) Time is defined in terms of the other three dimensions, the space dimensions. (Einstein; Schrödinger) through velocity or speed. There is a proportionality constant, “c”, between space and time that has the same value as the speed of light (Einstein). The same “c” as in, E = mc² which for a physicist is called the energy-mass equivalency.
(3) Good “Clocks” would make free particles travel in simple straight lines, or on their natural “world-lines”, in Spacetime. (Misner, Thorne, Wilson; Einstein, Noether, and Hilbert, among others).
(4) Time is simple only locally. This was my idea and formulation. No biggie, but still important. Just taking (1) to its logical and local conclusion.
So my warning is this: anyone going out to spend ‘a billion dollars per launch’ on a “Space Clock” better have some idea of what they are trying to measure, who’s clock they want to control, and if it makes sense locally?
Photo credit: Solar System Exploration, NASA
One engineer who worked “locally” and designed two Cube-sats for Mars, known as MarCoA and MarCoB as part of the InSight Mission was Farah Alibay, a young JPL engineer from Montreal, Québec Canada. Her team and understanding led to Cube-sats, like college students send into low-Earth orbit (LEO).
The MarCos travelled with InSight and were released prior to InSight launching for the Martian surface. Their job was to relay in real-time the videos and communications of InSight as it landed safely to begin its mission. Since those Cube-sats were timing events far from Earth on the Martian surface, they were equipped with small Cs- and Rh-atomic clocks on-board the mission like these….
These Cube-sats acted like a small, temporary GPS system, as well, until they hurtled away into the asteroid belt.