Units,Dimensions,Conversion and Significant digits in physics

Measurement:

The method of comparing any amount of a physical quantity with standard amount of same kind is called measurement. Measurement of a physical quantity consists of a numerical value (n) and a unit(u)

Therefore,

Measurement=Numerical Value(n)*Unit(u)

Unit:

There are 3 kinds of unit.

a) Fundamental unit :

    The units of fundamental quantities that cann't be derived from other units.

    Example:kg,meter,second etc.

    It is 7 in number.

b)Supplementary units:

    Example: Units of plane angle and solid angle.

c) Derived units:

    The units derived from fundamental and supplementary units.

    Example: Joule, Pascal, Newton etc.

 Systems of Units:

 There are four system of units.

 a) CGS System: In this system units for length , mass and time are centimeter(m),gram(m) and              seconds(s) respectively.

 b) FPS System: Units for length ,mass and time are Foot(ft), pound(lb) and second(s) respectively.

 c) MKS System: Units for length for length, mass and time are meter(m), Kilogram(kg) and                    second(s) respectively.

 d) SI System: In this system, there are seven fundamental quantities and fundamental units.

Fundamental Units (In SI System):

Physical Quantity	Units	Symbol
Length mass time temperature luminosity electric current amount of substance	Meter kilogram second kelvin candela ampere mole	M kg s k cd a mol

Supplementary Units:

Physical Quantity	Units	Symbol
Plane angle Solid angle	Radian steradian	r sr

Conversion Factor:

1litre       = 10^-3 m³

1 g/cm³    = 10³ kg/ m³
1 N           = 10⁵ dyne
1 atm       = 1.01*10⁵ N/M²
1hp           = 746w
1cal          = 4.2J
1Kwh        = 3.6*10⁶ J

Dimensions and Dimensional Formulae:

·         The dimensions of a derived unit may be defined as the powers to which the fundamental units of mass, length and time must be raised to represent it.

For example:

Velocity=displacement/time

·         Thus the dimensions of the unit of velocity are one in length and -1 in time. Its dimension in mass is zero.

·         Work, energy ,quantity of heat , quantity of light, internal energy, torque each has dimensional formula ML²T^-2 (kgm²/s²)

·         Velocity, Speed, distance covered in nth second have same dimensional formula m⁰LT^-1 (M/S).

·         Pure numbers are dimensions.

Dimensions of Some Physical Quantities:

S.N	Physical Quantity	Dimensions	SI units
1	Density (D=M/V)	[ML-3]	Kg m-3
2	Force (F=Ma)	[MLT-2]	Kgms-2
3	Linear momentum (P=MV)	[MLT-1]	Kgms-1
4	Work or Energy(W=F*D)	[ML2T-2]	Kgm2s-2
5	Power (P=w/t)	[ML2T-3]	Kgm2s-3
6	Pressure (P=F/A)	[ML-1T-2]	Kgm-1s-2(N/M2)
7	Impulse(=F*t)	[MLT-1]	Kgms-1
8	Strain	[M0L0T0]	No Unit
9	Frequency (f)	[T1]	Hz
10	Stress (F/A)	[ML-1T2]	Kgm-1s-2

LATEST CHALLENGE FOR QUANTUM THEORY SURVIVAL

Fig1: Leggett's inequality to the test.

Since the quantum mechanics was first formulated a string of physicists including Albert Einstein have been uncomfortable with the idea of entanglement whereby a group of quantum particles have nearest relationship than allowed by classical physics. As an outcomes, some physicists have proposed substitute theories that allow such close relationship without the necessity for the quantum mechanics. While it has been very difficult to test these theories, researchers those who were in the UK have used "twisted light" to build an quantum theory seems foreign that back up quantum theory. The quantum theory seems foreign to our everyday experience because its defined our idea of "realism", The expectation that objects have definite properties whether we are looking at them or not.The quantum theory also seems to call falling out elsewhere, apparently defying the principle of locality that forbids the communication faster than the speed of light.

These oddments were expressed mathematically by the physicist John Bell in his famous inequality. John Bell showed that a particular combination of measurement performed on identically prepared pairs of particles would produce a various numerical bound that is satisfied by all showed. However, this bound is violated by the prediction of quantum physics for entangled particles pairs. In John Bell experiments two distant observer measures, for example, polarization of entangled particles along different direction and calculate correlations between them. This was done in the year 1970s by Stuart Freedman and John Clauser and in the year 1980s by Alain Aspect, who used entangled photon to confirm the quantum theory.

SACRIFICING lOCALITY FOR NATURALISM

Physics has generally accepted that the quantum worlds flout "local realism", but in the year 2003, Anthony Leggett of the university of Illinois at Urbana Champaign tried to restore realism by giving locality. If two entities can arrange their correlations through instantaneous communication then perhaps it's still possible that they have definite properties. LeggeTt's real but non local scenario passes the John Bell test,But could it really describes the quantum world?

Four years later, Physicists in Switzerland, Austria and Singapore answered with data. Instead of measuring the linear polarization state used to violate Bell's inequality they appeared for correlations between elliptical polarization,combination of photon could respond to one another instantly, the correlation between polarization states still breached Leggett's inequality. The determination being that instantaneous communication is not enough to explain web and realism must also be abandoned.

This conclusion is now backup by Sonja Franke Arnold and colleges at the University of Glasgow and Stratchlyde who have performed another experiment showing that web photons exhibit entangled photons show stronger correlation than a allowed for particle with individually defined properties, even if they would be allowed to communicate constantly, But rather than polarization, they studied the properties of each and every photon's orbital angular momentum.

TWISTING LIGHT:

In photons, the orbital angular momentum can be understand by imagining that the wave twists around beam axis. It can draw a simple corkscrew pattern. A double helix or more clumsy helices with increasing angular momentum, Franke Arnold and her team focused on the double helix pattern.

The experiments done by firing an ultraviolet laser into an optical crystal designed to split the high energy photons into pairs of entangled infrared photons by Glasgow student jacquie Romero.These went on to computer controlled holograms. which were set to photons that passed the holograms were then counted by single photon detector.

Correlation between two entangled photons, one with a clockwise orbital angular momentum while the other twist anticlockwise is predicted by Leggett's and Bell's proposals as complementary states and measure the resulting detector occur too often to agree with Leggett's theory.

A PHILOSOPHICAL RESULT:

"The main results is really a philosophical outcomes", says Franke Arnold. Entangled particles can not be described as individual entity, not even with a telepathic connection to their partners. Simon Groblacher of the university of Vienna point out, These experiments theories still others are not described by Leggett's inequality. His team 1st showed violation of Leggett's inequality through photon polarization and he says, that it is photons. The experiment seems to be simpler, he adds, making superposition of more than two states.

Photo Electric Effect

The emission of electrons from the surface of metal when a beam of light with sufficiencly high frequency incident on it is called as photoelectric effect. Lenard studied the photo electric photometric phenomena in 1900 A.D its process and resuits described . It consists of an evacuated tube containing two electrodes and a window through light can be enter and incident on one electrodes varying potetial differnce can be applied between two electrodes by help ofrheostat and sheel. Beam of light of various frequency and intenties are allowed to incident an electrode on electrode and the enjection of electode is obserbed by nothing current in ammeter. 

LENARD FOUND THE THREE RESULTS BE WHICH ARE GIVEN BELOW:

1. Photometric effect occurs only when light of sufficient frequency whose value depends on nature of metal surface , incident on metal surface. The minimum frequency for which photometric effect frequewncy of metal surface.
2. The number of photoelectrons emitting per second depends on the intencity of incident light doesnot depends on frequency of incident light.
3. The kinetic energy of photoelectrons emitted from metal surface depends on the frequency of incident on intensity of incident light .