The Arrow Of Time: Physics' One-Way Street

The laws of physics govern everything in the universe, from the motion of celestial bodies to the behaviour of subatomic particles. Interestingly, these laws are indifferent to the direction of time, implying that the rules are the same whether time runs forward or backward. This concept is known as T-symmetry or time-reversal invariance. However, our everyday experiences contradict this idea, as we never observe broken objects repairing themselves or time flowing backward. For decades, scientists struggled to reconcile this discrepancy between theory and observation. It was only recently that experiments provided compelling evidence that the laws of physics indeed behave differently depending on the direction of time. This discovery sheds light on the fundamental nature of time and the universe, challenging our understanding of cause and effect and raising intriguing questions about the underlying mechanisms that govern our world.

The Second Law of Thermodynamics

The law predicts whether processes are forbidden despite obeying the requirement of conservation of energy as expressed in the first law of thermodynamics. For example, the first law allows the process of a cup falling off a table and breaking, as well as allowing the reverse process of the cup fragments coming back together and 'jumping' back onto the table. However, the second law allows the former and denies the latter.

The second law may be formulated by the observation that the entropy of isolated systems left to spontaneous evolution cannot decrease, as they always tend toward a state of thermodynamic equilibrium where the entropy is highest at the given internal energy. An increase in the combined entropy of the system and its surroundings accounts for the irreversibility of natural processes, often referred to in the concept of the arrow of time.

The law states that there exists a useful state variable called entropy. The change in entropy (delta S, \(\Delta S\)) is equal to the heat transfer (delta Q, \(\Delta Q\)) divided by the temperature (T).

\(\LARGE Delta S=Delta Q/T\)

For a given physical process, the entropy of the system and the environment will remain constant if the process can be reversed. If we denote the initial and final states of the system by “i” and “f”, then:

\(\LARGE S_f=S_i(reversible process)\)

An example of a reversible process would be ideally forcing a flow through a constricted pipe. As the flow moves through the constriction, the pressure, temperature, and velocity would change, but these variables would return to their original values downstream of the constriction. The state of the gas would return to its original conditions and the change of entropy of the system would be zero.

The second law states that if the physical process is irreversible, the entropy of the system and the environment must increase; the final entropy must be greater than the initial entropy.

\(\LARGE S_f>S_i(reversible process)\)

An example of an irreversible process is where a hot object is put in contact with a cold object. Eventually, they both achieve the same equilibrium temperature. If we then separate the objects, they do not naturally return to their original (different) temperatures. The process of bringing them to the same temperature is irreversible.

T-symmetry

This is best understood through the concept of entropy. The second law of thermodynamics states that entropy increases as time flows forward. Therefore, the macroscopic universe does not show symmetry under time reversal. Time is said to be asymmetric, except for special equilibrium states when the second law of thermodynamics predicts time symmetry to hold.

However, quantum noninvasive measurements are predicted to violate time symmetry even in equilibrium, contrary to their classical counterparts, although this has not been experimentally confirmed.

In particle physics, the standard model has been formulated as a quantum field theory that has CPT symmetry (where C is the charge conjugation operation, P is parity, and T is time-reversal symmetry). However, time-reversal symmetry itself is not a symmetry, as has been observed through experiments.

Time-reversal symmetry is broken by the weak force, for example. In physical and chemical kinetics, T-symmetry of the mechanical microscopic equations implies two important laws: the principle of detailed balance and the Onsager reciprocal relations.

In quantum mechanics, T-symmetry is considered an anti-unitary operator. It also protects non-degenerate quantum states from having an electric dipole moment.

In conclusion, T-symmetry, or time-reversal symmetry, is a theoretical concept that states that the laws of physics would be the same if time ran backwards. However, this has been proven to be false through various observations and experiments.

Time-reversal invariance

Despite our everyday experiences indicating that the laws of physics violate T-symmetry, the rules of physics are exactly the same whether time runs forward or backward. For example, the laws of motion are the same whether you run the clock forward or backward in time. This is demonstrated by the legend of Galileo Galilei's experiment atop the Leaning Tower of Pisa, where two balls with the same trajectory are dropped from different points and land at the same time.

However, our universe does not show symmetry under time reversal due to the second law of thermodynamics, which states that entropy increases as time flows forward. This means that time is asymmetric, except for special equilibrium states when the second law of thermodynamics predicts time symmetry.

In quantum mechanics, there are different accounts of time-reversal transformations, leading to varying views on whether a given theory is time-reversal invariant. While Newton's laws of motion exhibit time-reversal invariance, not all rules of physics behave identically when time runs backward.

In recent years, scientists have experimentally proven that the laws of physics are different depending on the direction of time. For instance, the creation of over 400 million ϒ(4s) particles by the BaBar collaboration in 2012 directly detected time-reversal violation. This experiment demonstrated that the laws of nature are not identical when time runs forward or backward.

Macroscopic equations of motion

The two main descriptions of motion are dynamics and kinematics. Dynamics is the more general description, as it takes into account the momenta, forces, and energy of the particles. In this context, the term dynamics sometimes refers to the differential equations that the system satisfies (e.g. Newton's second law or Euler-Lagrange equations) or to the solutions to those equations.

Kinematics is simpler and only concerns variables derived from the positions of objects and time. In cases of constant acceleration, these simpler equations of motion are usually referred to as the SUVAT equations, which arise from the definitions of kinematic quantities: displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t).

In the case of uniform acceleration, there are three equations of motion, also known as the laws of constant acceleration. They can be used to derive components like displacement, velocity, time, and acceleration. They can only be applied when acceleration is constant and motion is in a straight line. The three equations are:

• V = u + at
• S = ut + 0.5at^2
• S = (u + v)t/2

Where:

• S = displacement
• U = initial velocity
• V = final velocity
• A = acceleration
• T = time of motion

These equations are also referred to as the SUVAT equations, where:

• S = displacement
• U = initial velocity
• V = final velocity
• A = acceleration
• T = time

The first general equation of motion developed was Newton's second law of motion, which states that the rate of change of momentum p of an object equals the force F acting on it:

F = dp/dt

Or, more famously:

F = ma

Since m (mass) is a constant in Newtonian mechanics.

Macroscopic Equations in Various Applications

Macroscopic equations are used in various fields and applications, including:

• Hybrid media
• Turbulent model solutions
• Plasma behaviour
• Battery performance modelling
• Exergy in continuous media
• Fluid behaviour
• Multiphase and multispecies transport in porous media
• MEMS device analysis

Microscopic physics of atoms

The study of microscopic physics at the atomic level falls within the realm of quantum mechanics. At this level, particles exhibit phenomena such as wave-particle duality, where particles can be described by both wave-like and particle-like properties. This duality is demonstrated in the particle-in-a-box model, where particles can exist in multiple states and exhibit behaviours like quantum parallelism.

The behaviour of individual atoms differs significantly from that of classical physics due to quantum effects. One phenomenon that explains this difference is decoherence in quantum mechanics. Decoherence occurs when the phases of the wavefunctions of different particles are randomised, resulting in a loss of the special correlation between particles. In a system with many atoms, the combined effect of decoherence and the law of large numbers leads to the emergence of classical physics behaviours.

Additionally, the high energy levels of atoms play a role in the transition from quantum to classical behaviour. At high energy levels, the difference in energy between states becomes negligible, and the energy spectrum becomes continuous rather than discrete. This results in the stabilisation of atoms at various energy levels, with most vibrating in valence bands below the band gap.

The study of mesoscopic physics, which deals with materials of intermediate size, ranging from the nanoscale to the microscopic, further illustrates the transition from quantum to classical behaviour. In mesoscopic physics, the average properties of constituent materials typically follow the laws of classical mechanics. However, mesoscopic objects are influenced by thermal fluctuations and may exhibit quantum mechanical properties, such as quantized conductance in wires.

The direct observation of T-symmetry violation, or time-reversal symmetry violation, provides experimental evidence that the laws of physics are not identical when time runs forward or backward. This violation was observed through the creation and study of particles containing bottom quarks, specifically the ϒ(4s) particle, which decays into a neutral B-meson and a neutral anti-B-meson. By measuring the decay of these particles and their anti-particles, scientists confirmed that the laws of physics exhibit different behaviours when time is reversed.

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