Question

please explain the arrow method clearly

Answer 1

In our universe the time moves only in one direction that is forward and the movement of the time in forward direction is called an arrow of time.The arrow of time refers to the way we always progressing in particular direction most of the events we experience are irreversible e.g eggs may break but they never spontaneously reform.The arrow of time always moves in the direction of increase in entropy increase in disorder.There are three types of arrow of time.Thermodynamical arrow of time:The thermodynamical arrow of time is related to entropy (second law of thermodynamic)The second law of thermodynamic shows that the arrow of time point in the direction of increase in entropy.Entropy can be thought of, in most cases, as meaning that things (matter, energy, etc) have tendency to dispare e.g hot water always cools downThe past is low entropy state and and the future is high entropy state.

2. Cosmological arrow of time:

The cosmological arrow of time is related to gravityThe cosmological arrow of time predict that space indeed expanding and galexies are moving further apartThe arrow of time point in the direction of universe expansion as the universe continue to grow bigger and biggerIn everyday life we are not physically conscious about the expansion of universe so it is difficult to see how we can perceive the expansion of universe as an arrow of timeWhat remain major unknown in modern physics through is why the universe had very low entropy at its origin big bangRecently some physicist have suggested that perhaps when the universe we know began another paealler universe simultaneously created in which the time flows in the other direction.

3. Quantum mechanical arrow of time:

The whole mechanism of quantum mechanics is baised on on Schrödinger's equation and the collapse of wave function and this appears to be time asymmetric phenomenonFor e.g the location of particle is described by the wave function which essentially gives various probabilities that the particle is in many different possible position or superposition and the wave function only collapse only when the particle is actually observed at that point the particle can finally be said to be in particular position and all the information from the wave function is lost and cannot be recreated. In this respect, the process is time irreversible and arrow of time is createdBut it is not clear how the quantum arrow of time if indeed exist at all is related to the other arrowIt is possible that it is linked to the thermodynamic arrow, in that nature shows a bias for collapsing wave functions into higher entropy state versus lower ones.

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Answer 2

Question:-

1. Explain the arrow method clearly

Answer:-

• In general this method is used to solve the problems based on unitary method.

Best examples:-

 Example 1 :- (Based on inverse proportion)

1. A certain sum is divided equally among 50 boys and each boy gets ₹ 75. If the same sum is divided equally among 60 boys; how much will each get?

Solution:-

   Let each boy gets ₹ x

1. Form two columns, on heading no. of boys and other heading each gets.

       Since we are to find the share of each boy; column heading each gets must be on the extreme right. Now write the different quantities

2. Mark an arrow in the downward direction for the column on the extreme right.

3. Since it is case of inverse proportion, mark an arrow in the first column in the upward direction (i.e. direction opposite to the arrow on the extreme right column)

4. Now according to the arrow taken:

$\rm \dfrac{Value \: on \: head}{Value \: on \: tail}$ for one arrow = $\rm \dfrac{Value \: on \: head}{Value \: on \: tail}$ for another arrow

⇒ $\rm \dfrac{x}{75}=\dfrac{50}{60} i.e. x=\dfrac{50 \times 75}{60}=62.5$

⁂ Each boy gets ₹ 62.50