Time reversal, in Physics, refers to when the expression for the time in any equation or formula is replaced with its negative value. This is done so that the event described using the formula or equation can be described such that it runs the same when in past to present mode as well as future to present mode, i.e., both ways in time. Essentially, this is called time-reversal and it goes to show that there is no particular preferred direction that time is required to go in for it to make sense - it is as simple as knowing that in reverse, an event can occur exactly the same way.
Time-reversal invariance refers to this exact idea in a more formalized manner. Time-reversal invariance implies the following three ideas:
The same laws of Physics apply to either equation or formula whether it is or isn’t in reverse.
The second event, i.e., the version of the same event that has been reversed, cannot be distinguished from the original event.
The flow of time does not necessarily have a preferred direction, and events remain the same (or indistinguishable, as mentioned before) no matter which direction that time goes in.
This is, though, based on the idea that any formula or equation that has been reversed in time using a negative sign, and it remains unchanged, is time-reversal invariant.
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Quantum Time Reversal
Let’s understand quantum time reversal or how time reversal works with quantum Physics. In order to understand this, let’s first go through what the arrow of time or time arrow is. An arrow implies pointing towards a single direction, and similarly, with time, a time arrow points to a single direction saying that time only moves in one direction. It speaks to the asymmetry of time, which, incidentally, time-reversal does away with. Quantum time reversal is based on the difficulty coming with the practicality of time reversibility. The proponents of quantum physics, in relation to time reversal, state that it cannot be carried out without creating an artificial setup to artificially reverse a time arrow or partake in time reversing an equation or formula. This artificial creation can be compared to pressing the rewind button on any device.
Space Inversion and Time Reversal
Space inversion is also called parity or space reflection. It refers to when one of three spatial coordinates are reversed to denote a time reversal. To explain this further, we must understand that space is three-dimensional, meaning that it has three spatial coordinates. You can understand this by picturing cartesian planes which have 3 axes rather than 2. All of these three coordinates exist in the positive, meaning that they truly exist and move in one single direction, which may or may not be the direction in which the arrow of time points. Imagine that one of these coordinates has been reversed, i.e. made to be in the negative - this is what we call space inversion. It relates to the idea of space reflection or parity, as mentioned before, meaning that if time is reversed, both images or events must be identical as if they are an image and its reflection. Parity, in its definition, refers to equality, which again relates to the same point of an equal reflection.
Electromagnetic Time Reversal
Electromagnetic time reversal refers to when electromagnetic waves are taken in reverse. Anything can be put in time-reversal by simply adding a negative sign. When doing this with electromagnetic waves, it refers to sending back the same wave on the same frequency to where it originally came from. By this, it means that when a wave is passed from an antenna and then sent back to the same antenna, there has been a time reversal of that electromagnetic wave that has taken place there. Electromagnetic time reversal communications may be one of the most important functions of the idea of reversal in physics. This is because it facilitates all kinds of radio communications carried out amongst common people, by armed forces (especially the naval and air forces), and even in research for time and space.