April 21, 2018 U: Uncertainty (What it can mean in everyday life).
What is really meant by Uncertainty with a capital U? Uncertainty, aka Heisenberg’s Uncertainty Principle, was suggested in order to understand the quantum nature or reality of the behaviors of subatomic particles.
Here we’re going to show you how Uncertainty doesn’t just apply to the subatomic world, but our world as well, because it all has to do with perspective. We said before there are times when scientists design an experimental setup, they mistakenly think they can merge runs at different perspectives, call them controlled, and miss the point entirely. Uncertainty is all about perspective. When we observe from one point of view, that doesn’t mean we can always observe the same thing from another point of view and combine results.
POV 1: If we approach a house from above we may take an image of a tile roof.
POV 2: If we approach a house from the front, we see a door and two windows.
So, is a roof a house? So, is a front door a house? Can we tell everything about the house by just looking from above or in front? The answer is no. The roof and front door are only aspects of a house (they lead to the understanding of what a house might be. They are virtual condensations of the meaning of the house from different perspectives, but they are not the real house (we may never know what that is).
Uncertainty says if we look from above, we can’t see anything out front. If we look out front, we can’t see anything from above. This is a way to see how perspective can both help us know the aspects of things, and this is a way that trips us up experimentally, because if we don’t note the unique setup and view of our experiment, we really don’t know what aspects we’re observing (The branch of science called thermodynamics is excellent in its inventory of all possible changes in perspective across boundaries).
POV 1: a small packet of energy when it goes through a slit toward a screen, will hit the screen at a point. We look at that lighted image (at a point) and say, that’s a particle.
POV 2: a small packet of energy when it goes through two slits (a given small distance apart) will hit the screen at many points in a wave or interference pattern.
The above example is from a double slit experiment which has two experimental setups. Can we combine results and say there are two aspects of an energy packet? You bet we can. However, we cannot be certain that what we saw from one perspective (an explicit virtuality) was the exact same thing that we saw at another (implicit reality).
Classic Uncertainty says that you can know the position (particle image) of anything (energy packet) but if you know the location or position, you cannot know the velocity, or anything having to do with the energy packet in time.
In the Double Slit Experiment, researchers tried to combine both position and velocity from the two perspectives. When they did, they saw that the particles seemed to change their positions faster than light. An easy mistake to make if one does not thoroughly understand the nature of perspective. It is the perspective that can change (that they made to change in their experiment) faster than light, not the energy packet whose speed is limited by the speed of light as all small energy packets are in our universe (in normal space-time).
Evidence of Uncertainty can exist in many observations. So what does Uncertainty mean and what is the evidence for this meaning?
In the double slit experiment when we look from the perspective of one datapoint (one slit), we know location, but two or more slits give us the aspect of time (velocity or momentum). We cannot see both, meaning we cannot attribute both to the same energy packet, only to all energy packets in general.
An example of the difference between observing for location and speed can be seen when observing a train. When we look from one datapoint (the train at a stations from the center of the tracks) then we see its position on the tracks. But when we want to see its velocity, that takes time, and that takes more than one datapoint. And what perspective must we take to see the train move? The best way to view the speed of the train is to look perpendicular to the tracks.
So we see that two or more data points must allows us to see a movement of the train in time (speed), but when we measure the speed, we don’t know the train’s instantaneous position (the train doesn’t have a position, only velocity from that perpendicular perspective).
In The General Energy Equation used by scientists and physicists (and in our fluids experiment), solutions are found by inserting complex numbers into the equation. A complex number gives what is called a REAL component and an IMAGINARY one. The components represent aspects that cannot both be applied simultaneously to any aspect other than itself.
For fluids we can find the fluid’s energy potential (the REAL component) and its flux or flow (its kinetic energy in time, the IMAGINARY component). But those two aspects though they apply to fluid behavior, they do not apply to the same molecule or grouping of molecules, because of Uncertainty you can’t look at a position of a system of particles and the motion of that system of particles at the same time.) And now you know how Uncertainty limits what you can know about something through perspective (the experimental setup of your observation).
And the two different perspectives can be from two different systems. Notice in our experiment with the offset mode of the expanding droplet, when it still looks like a circle to us humans (System Perspective 1), it looks like a sine wave as seen with reference to the droplet’s center (System Perspective 2). So, is the radius constant for the circular droplet, or is it not? It’s one or the other, depending on perspective. To say anything about the droplet’s change in shape, we need to observe what the droplet, its boundary, might see, and not what we see, or we will miss the moment the droplet’s boundary goes unstable.
There is a solution to the expanding droplet saying it goes unstable (the offset growth begins at a point in time related to it viscosity (the inverse of the Atwood Ratio (viscosity contrast over the boundary in time). But for higher flow rates and viscosity contrasts (greater than in our experiment: air into water/see THE EXPERIMENT page for videos of high flow rates), the initiation of the growth of the first offset trough differed from the initiation point of instability of the droplet (when fingers/crests began to grow) by a certain amount.
The time until an expanding droplet goes wonky (the waves on its surface begin to grow) would be a great problem to research. Why is that? Because equations for interfacial tension are almost identical to equations for gravitational attraction between two bodies in normal space. Gravitational attraction is different at higher energy levels (Mercury is seen to be at a different distance from the sun than predicted: called General Relativity) just like the first trough in the unstable expanding droplet at high energies/flows is thought to initiate at a different position than predicted for normal space. Could the different initiation of the droplets instability be modeled by the Lorentz Transformation just like Newton’s Gravitational Equation can, or did the researchers miss that the offset mode, that looks like a perfect circle is really offset from its center or injection point (and the beginning of its growth is the beginning of instability)?