The Universe, as far as we can tell, only operates according to laws of physics. And just about all of the laws of physics that we know are completely time-reversible, meaning that the things they cause look exactly the same whether time runs forward or backward.
I am not sure I understand this, how can we reverse a law in time? So for example how does a time-reversible law and a time-irreversible law look like? What is the difference between them?
It is not really correct to call them " reversible laws of physics"
Laws of physics lead to mathematical models that describe observations. These models are usually differential equations of space and time. The solutions of these equations exist both for time going towards infinity as for time going towards minus infinity in most cases, for mechanics, electromagnetism, newton's gravitation. There exists a difference for thermodynamics, which is an emergent theory from the underlying statistical mechanics, where an arrow of time can be defined as explained in the answer by count_to_10 .
So in this sense the laws of mechanics and electromagnetism lead to time reversible solutions, whereas the laws of thermodynamics pick an arrow in time.
When one goes to quantum mechanics and the forces between elementary particles again time reversal is implied by some interactions , but there exists a CPT theorem where if CP is not conserved than again a time direction is chosen. But this is another story.
The standard reply is: get your video camera out, take a movie of dropping a (empty) coffee cup on the kitchen floor, then play the movie backwards. There is no physical way of telling which way time is running from your movie or the equations behind the event (Newtons Laws).
Rather than thinking of an absolute arrow of time, so the coffee cup will break apart and NEVER reassemble itself later, think in terms of probabilities. It's almost certain the cup will break up and in doing so, it will give you an indication of the direction of time, but there is a tiny, tiny probability that it may reassemble itself and give you an indication that time is running backwards. But because the coffee cup is composed of zillions of atoms, all of which would need to be restored to their former positions, this is very unlikely.
This is not a useful answer! 1. The statement: "There is no force/law that makes the cup rise" is completely misleading because it deals in likelihood (probability) not law. 2. The statement, "Even though, the mathematical formulas may allow the backward flow of events, there are no such forces that would cause it" is another irrelevant statement about probability. 3. The mathematical formulas are equivalent to the law, because the law NEVER violates the math. For purposes of explanation, the formula and law are the same.
The true issue in reversibility is, IF a series of events is run backwards (not will they run backwards), are laws violated or not? The answer is no there is no violation. Therefore physical law is time reversible.
Only the mathematical formulas are time reversible. That does not mean that the law itself is reversible. You can understand it this way - Every law/formula has an implicit condition that says - "time flows only forward".
Other way to understand can be that when the coffee cup falls, universe (gravity in this case) makes the cup fall. There is no force/law that makes the cup rise. It becomes even more complex when you consider the process of the cup breaking, and coffee spilling. i.e. there are natural forces/laws that cause the cup to break but there are no natural forces/laws that cause the broken cup to re-construct. Even though, the mathematical formulas may allow the backward flow of events, there are no such forces that would cause it.
