http://upload.wikimedia.org/wikiped...simir_plates.svg/300px-Casimir_plates.svg.png
Relative to the sides of the plates, which way are the little blue arrows pointing, and why are there bigger blue arrows on the outside of the plates and smaller blue arrows on the insides? Where in the diagram do you see blue arrows pointing away from any sides of any plates?
Since MM has not been able to understand the simple concept of negative pressure explained many times in this thread (and in the many other threads and forums that he has participated in), it is obviously futile to explain this again.
But miracles happen so:
MM's obsession with pretty pictures has lead him to be deluded that this diagram is significant in some way. This is wrong:
- The diagram is wrong as already noted (the waves should be zero at the plates).
- The diagram has nothing to do with the calculation of the pressure exerted by the Casimir effect. That calculation results in values of pressure that are negative. Scientists call this negative pressure.
- The diagram has nothing to do with the measurement of the pressure exerted by the Casimir effect in experiments. Those measurement measure negative pressure.
There are bigger blue arrows on the outside of the plates because the author of the diagram wanted to
illustrate that the force (not the pressure MM) exerted on the plate by vacuum flutuations (the wavy green lines) is greater on the outside of the plates than the force (not the pressure MM) exerted on the plate by vacuum flutuations on the inside of the plates.
MM: A high school physics assignment for you:
First asked 3 February 2010
Calculate the pressure caused by the big blue arrows on the left hand plate. Assume that the force is F1.
Calculate the pressure caused by the small blue arrows on the left hand plate. Assume that the force is F2.
Calculate the pressure caused by the big blue arrows on the right hand plate. Assume that the force is F1.
Calculate the pressure caused by the small blue arrows on the right hand plate. Assume that the force is F2.
Remember that a force that points in the opposite direction to another has an opposite magnitude, e.g. if the first force has a positive value then the second force has a negative value. So you will have to set a convention about how to determine this, e.g. forces pointing to the right are positive.
N.B. Apply the same convention to both plates.
High school students know that when you have 2 forces acting on an object then you can always replace them with their sum to get the force on that object. Do that with the diagram and you get "blue arrows", i.e. forces (not the pressures MM), pointing away from the plates.
A
really simple explanation suitable for high school students for negative pressure has already been presented to MM.
Here it is again:
Using the definiton of pressure as equal to the magnitude of the force (F)normal to that surface divided by the area of the surface:
- A force F1 pushes on a surface of area A. The pressure p = F1/A.
This is positive (e.g. atmospheric pressure).
- A force F2 pulls on a surface of area A. The pressure p = -F2/A.
This is negative (e.g. the Casimir effect).
(
F is the force vector, F is the magnitude of
F)
Why is the force that pulls have a negative magnitude?
Consider if both forces were present and equal, e.g. the Casimir effect in a low pressure environment. Then the forces add up to zero. That means that the magnitude of one force must be the negative of the other force. It is convenient to have a pushing force positive so that the pressure is positive and we do not have to deal with negative signs in everyday situations, e.g. weather maps.
There are no surfaces when we are talking about cosmology as in this thread. In that case we have to use the more technical definition of pressure as p as a change of energy per volume (p=-dE/dV if I remember correctly).