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## More on Cosmological constant

A constant introduced by Einstein (1917) into the equations of general relativity to allow a steady state cosmological solution to the Einstein field equations. The constant was introduced before the concept of the Big Bang had been conceived, so an expanding or contracting universe was regarded as physically implausible, leading Einstein to add as a "fudge factor." In theory, the constant can be derived from quantum field theory, but the derivation has not yet been performed. Einstein’s cosmological constant is equivalent to a vacuum energy density, which means it can be put on the left hand side of Einstein’s equations with the geometry (as Einstein did), or on the right hand side with the stress-energy, both forms being mathematically equivalent.

The value of in our present universe is not known, and may be zero, although there is some evidence for a nonzero value; a precise determination of this number will be one of the primary goals of observational cosmology in the near future.

The value of the cosmological constant is an empirical issue which will ultimately be settled by observation; meanwhile, physicists would like to develop an understanding of why the energy density of the vacuum has this value, whether it is zero or not. There are many effects which contribute to the total vacuum energy,

including the potential energy of scalar fields and the energy in “vacuum fluctuations” as predicted by quantum mechanics, as well as any fundamental cosmological constant.

If the recent observational suggestions of a nonzero are confirmed, we will be faced with the additional task of inventing a theory which sets the vacuum energy to a very small value without setting it precisely to zero. In this case we may distinguish between a “true” vacuum which would be the state of lowest possible energy which simply happens to be nonzero, and a “false” vacuum, which would be a metastable state different from the actual state of lowest energy (which might well have = 0). Such a state could eventually decay into the true vacuum, although its lifetime could be much larger than the current age of the universe. A

final possibility is that the vacuum energy is changing with time — a dynamical cosmological “constant”. This alternative, which is sometimes called “quintessence”, would also be compatible with a true vacuum energy which was ultimately zero, although it appears to require a certain amount of fine-tuning to make it work.

No matter which of these possibilities, if any, is true, the ramifications of an accelerating universe for fundamental physics would be truly profound.

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## Restoring force and Newton’s law

We know that whenever a body is deformed a restoring force originates and tries to restore the shape of the body and according to newtons third law of motion whenever a force acts on a body an equal and opposite force acts on the other body . So is the restoring force an opposite reacton to the deforming force and if it is not then why do we consider its direction equal and opposite to the deforming force while solving problems .

(Asked Akshat )

**Answer**: Restoring force comes into play only when a deforming force is exerted. When no external force acts on a body, the molecules are in equilibrium. No net force acts on it. If an external force is applied on it, it will try to increase or decrease the intermolecular distance giving rise to a state of inequilibrium to teh molecules and they will tend to go back to their original positions to retain their state of equilibrium. This gives rise to the** RESTORING FORCE**.

Restoring force the the **internal** force that comes into play whenever an external force tries to change the inter-molecular distance. The restoring force at any instant (within limits) is equal in magnitude and opposite in direction to the deforming force

## Can a body be said to be at rest as well as in motion at the same time?

“Can a body be said to be at rest as well as in motion at the same time?”

This question was asked by Anmol.

Motion and rest are relative concepts. There is no absolute rest. We can define the state of rest or motion only with respect to another object or a point in space taken as reference.

For example, a person inside a train considers himself to be at rest with respect to the fellow passengers or the walls of the train. But when he looks outside, he finds himself to be in motion with respect to the trees outside.

Hope the idea is clear.