What Distance Makes the Casimir Effect Negligible?

Click For Summary
SUMMARY

The Casimir Effect becomes negligible at distances where the balance between internal and external pressures results in no net change in plate positions over time. The relevant formula for parallel plates of ideal conductivity is given by ##\displaystyle {F_c \over A} = -\frac {\hbar c \pi^2} {240 a^4}##, where 'a' represents the distance between the plates. The discussion also touches on the gradual decrease of gravitational attraction with distance, emphasizing that there is no sharp boundary for its effects. Overall, the equilibrium point for the Casimir Effect is determined by the specific distance at which the forces balance out.

PREREQUISITES
  • Understanding of the Casimir Effect and its implications in quantum physics.
  • Familiarity with the formula for force per area between parallel plates of ideal conductivity.
  • Basic knowledge of gravitational forces and their variation with distance.
  • Concept of pressure balance in physical systems.
NEXT STEPS
  • Research the mathematical derivation of the Casimir Effect formula for parallel plates.
  • Explore the implications of quantum foam and its relationship with the Casimir Effect.
  • Investigate the concept of capillary action in small spaces and its analogies with quantum effects.
  • Study gravitational forces and their diminishing effects at varying distances from Earth.
USEFUL FOR

Physicists, researchers in quantum mechanics, and anyone interested in the implications of the Casimir Effect and gravitational forces in theoretical physics.

_PJ_
Messages
229
Reaction score
15
I was thinking recently about the Casimir Effect and at what distance does the effect become negligible?

Is there any relevance on the surface area (or difference in areas) between the plates (I personally held the opposite, that any point can be considered to have equivalent pressure as any other approximated over time).

Naturally, this distance would entail the point at which there is a balance between the internal (i.e. between plates) and external pressures is when the plates are no longer 'pushed' together as result, but at what length does this occur? Presumably there will always be a very slight imbalance one way or the other due to continuous fluctuation, although at the given length there will be an overall equilibrium so as there is no net change in the plate positions over time.

----

ALMOST related, and perhaps worthy of its own thread, but it is relevant enough to be here I felt, is there any evidence or possibility for "capillary action" or suitable equivalent analogue with Casimir effect type small spaces and quantum foam 'fluidity'?
 
Physics news on Phys.org
At what distance does the gravitational attraction of Earth become negligible? There is no sharp border, it just gets weaker and weaker.

For parallel plates of ideal conductivity, it is ##\displaystyle {F_c \over A} = -\frac {\hbar c \pi^2} {240 a^4}## with the distance a.
 
  • Like
Likes bhobba
Negligible only has meaning with respect to some kind of comparison.
 
  • Like
Likes vanhees71
mfb said:
At what distance does the gravitational attraction of Earth become negligible? There is no sharp border, it just gets weaker and weaker.

For parallel plates of ideal conductivity, it is ##\displaystyle {F_c \over A} = -\frac {\hbar c \pi^2} {240 a^4}## with the distance a.
Thank you so much!

As is usually the case with such questions, with hindsight it seems remarkably obvious!
 

Similar threads

  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 46 ·
2
Replies
46
Views
5K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 17 ·
Replies
17
Views
3K
  • · Replies 49 ·
2
Replies
49
Views
5K
Replies
10
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 1 ·
Replies
1
Views
1K