The Arrow Of Time: Physics' One-Way Street

The laws of physics are not time-reversal invariant. While most laws of physics, like gravity and quantum mechanics, are symmetric with respect to time, the Second Law of Thermodynamics implies a direction. This law states that everything moves from an ordered state to a disordered state over time, and it is the only physical law that cannot go backward. For example, scrambled eggs never uncook and unscramble themselves, and shattered glass never reassembles itself. In 2012, scientists from the BaBar collaboration at SLAC experimentally proved that the laws of physics are different depending on the direction of time.

The laws of physics are not time-reversal invariant

This corresponds to a certain symmetry of nature: T-symmetry, or time-reversal invariance. Our everyday experience indicates to us that the laws of physics must violate this symmetry, but for decades, we couldn't demonstrate it. However, a few years ago, we experimentally proved the laws of physics are different depending on which direction time runs.

There are two very good reasons to believe that T-symmetry must be broken at a fundamental level. The first is the CPT theorem, which tells us that the combination of three symmetries (C-symmetry, P-symmetry, and T-symmetry) must always be preserved. As CP-symmetry violation has already been observed, we know that T-symmetry must be violated as well. The second reason is that we live in a universe where there is more matter than antimatter, but the laws of physics we know are completely symmetric between matter and antimatter.

In order to directly confirm the existence of T-violation, scientists had to design clever experiments. They leveraged the properties of quantum entanglement and decay through weak interactions to create particles where T-violation occurs. By creating and studying the decay of these particles, scientists were able to directly test for time-reversal violation. The results confirmed that the laws of physics are not identical whether time runs forwards or backwards.

T-symmetry, or time-reversal invariance, is broken

T-symmetry, or time-reversal invariance, is a theoretical symmetry of physical laws under the transformation of time reversal. In other words, the rules of physics are exactly the same whether time runs forwards or backwards.

However, T-symmetry is broken. Our everyday experiences indicate that the laws of physics violate this symmetry, and this has been experimentally proven. For example, clocks never run backwards, and scrambled eggs never uncook and unscramble themselves.

The CPT theorem, a proven theorem, also indicates that T-symmetry must be broken. If a quantum field theory obeys the rules of relativity, it must exhibit CPT-symmetry. CPT-symmetry states that a spinning particle moving forwards in time must obey the same rules as its antiparticle spinning in the opposite direction when moving backwards in time. As CP-symmetry violation has been observed, T-symmetry must be violated as well.

Additionally, the second law of thermodynamics, which states that entropy increases as time flows into the future, indicates that the macroscopic universe does not show symmetry under time reversal.

In particle physics, T-symmetry was directly tested and proven to be broken by the BaBar collaboration in 2012. This experiment involved creating over 400 million ϒ(4s) particles, which decay into B-mesons and anti-B-mesons. By measuring the decay of these particles, the scientists were able to demonstrate that the laws of physics are not identical whether time runs forwards or backwards.

The second law of thermodynamics, which talks about the statistics of large collections of particles, is broken

The second law of thermodynamics is not symmetric to the reversal of the time direction. While the laws of physics that govern the way the universe works are the same whether time runs forward or backward, the second law of thermodynamics is an exception. This is because the second law of thermodynamics is concerned with the direction of natural processes. It asserts that a natural process runs only in one sense and is not reversible. That is, the state of a natural system can be reversed, but not without increasing the entropy of the system's surroundings.

The second law of thermodynamics can be precisely stated in the following two forms:

> A cyclic transformation whose only final result is to transform heat extracted from a source that is at the same temperature throughout into work is impossible.

> A cyclic transformation whose only final result is to transfer heat from a body at a given temperature to a body at a higher temperature is impossible.

The second law of thermodynamics also states that the state of entropy of the entire universe, as an isolated system, will always increase over time. The changes in the entropy in the universe can never be negative. This is also known as the "arrow of time".

The CPT theorem, which combines C-symmetry, P-symmetry, and T-symmetry, is preserved

The CPT theorem first appeared in the work of Julian Schwinger in 1951, though it was not proven until 1954 by Gerhart Lüders and Wolfgang Pauli, and so it is sometimes known as the Lüders-Pauli theorem. At around the same time, John Stewart Bell also independently proved the theorem. The CPT theorem can be proved using the principle of Lorentz invariance and the principle of locality in the interaction of quantum fields.

The CPT theorem can be defined by considering a Lorentz boost in a fixed direction z, which can be interpreted as a rotation of the time axis into the z-axis. This defines a CPT transformation if we adopt the Feynman-Stueckelberg interpretation of antiparticles as particles traveling backward in time. This interpretation requires a slight analytic continuation, which is well-defined only under the following assumptions:

• The theory is Lorentz invariant
• The vacuum is Lorentz invariant
• The energy is bounded below

The CPT theorem has been further generalized to take into account pin groups, and it has been proven that CPT violation implies the breaking of Lorentz symmetry.

The laws of nature are not the same forwards and backwards in time

The laws of nature are not the same when time is run forwards and backwards. While Newton's laws of motion are the same whether time runs forwards or backwards, not all rules of physics are identical in both directions.

In our everyday experiences, clocks never run backwards, and scrambled eggs never uncook and unscramble themselves. However, if we were to look at the laws of physics that govern the universe, we would find something peculiar: the rules are exactly the same whether time runs forwards or backwards. This is known as T-symmetry or time-reversal invariance.

Our everyday experiences indicate that the laws of physics must violate this symmetry, but for decades, we couldn't demonstrate it. However, a few years ago, we experimentally proved that the laws of physics are different depending on which direction time runs.

Imagine you and a friend are in Pisa, with one of you standing at the top of the Leaning Tower of Pisa and the other at the bottom. If the person at the top drops a ball, the person at the bottom can easily predict where it will land. Now, if the person at the bottom were to throw the ball upwards with an equal and opposite velocity, it would arrive exactly at the location where the person at the top dropped the ball from. This is a situation where time-reversal invariance holds: the T-symmetry is unbroken.

There are two very good reasons to believe that T-symmetry must be broken at a fundamental level. The first is the CPT theorem, which states that if a quantum field theory obeys the rules of relativity, it must exhibit CPT-symmetry. The second reason is that we live in a universe where there is more matter than antimatter, but the laws of physics we know are completely symmetric between matter and antimatter.

In order to directly confirm the existence of T-violation, scientists had to design clever experiments. They leveraged the properties of quantum entanglement and the weak nuclear interaction, which is the only type of physics process where CP-violation is known to occur.

The results of these experiments proved that the laws of physics are not identical whether time runs forwards or backwards.

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