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*"Reversibility means that we never lose information, that at a fundamental level we can always retrodict the past as well as predict the future in the laws of physics".*

Susskind in his Theoretical minimum Lecture 2 describes about the laws which are true and which are not. He tells the law of Aristotle is wrong experimentally and if we see it logically. It predicts the future but can't the past. I have some difficulty in it. He writes

$$F(t)=m \dot x$$

$$F(t) \approx \frac{m(x(t+\Delta)-x(t))}{\Delta}$$

So, $$\frac{\Delta}m F(t) +x(t)= x(t+\Delta)$$

To predict the future we just have to know the current position which I assume would be some numerical value of x at time t, ##x(t)##. We can repeat the same thing over and over again to find new positions.

Take an example of spring force ##F(x)=-kx##.

$$x(t)\left[ 1-\frac{k \Delta}{m} \right]=x(t+\Delta)$$

I don't know how the spring here is behaving. He says the way spring behaves according to the law is the position decreases to zero point by a common factor ##\left[ 1-\frac{k \Delta}{m} \right]##. I am not sure how. Is it going to stop immediately after stretching and does not jiggle around?

The solution to the differential eqn ##-kx=m \dot x## is $$x=x(0)e^{-kt/m}$$ I am not sure but here is the position function with respect to time. Can't we now just put in time value and get the position to past and to the future?

Susskind says it sure can predict the future but not the past as we can't tell from where the spring came from since all stretchings end to the same point origin. I don't fully understand how we are unable to predict the past.

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