You most probably have read Newton's first law of motion also known as the law of inertia. The law states that a matter tends to stay in its initial state of rest or motion unless an external force is applied to it. It implies that anything with no energy can never start into motion and one in motion won't come into rest until it is stopped by an external force. However, in the universe, nothing is absolutely isolated. Every matter in the universe is subject to one or another influence. A matter in motion will always cease to the state of rest due to gravity or any frictional forces. For example, if we roll a ball in the ground, after traveling a small distance it will stop due to the friction with soil.
Perpetual Motion
Perpetual Motion is a motion that continues forever without any external influence. Perpetual motion is impossible since it violates the law of conservation of energy which states that the total energy of an isolated system. It implies that a matter without any external energy supply cannot deliver an unlimited amount of energy to its surrounding.
Even the celestial motions also fall within this boundary because they are subject to many cosmological effects which will dissipate their kinetic energy(though very much slowly). Processes like Solar wind, Interstellar medium resistance, gravitational radiation, thermal radiation constantly hinder the motion of the celestial bodies.
Perpetual Motion Machine
Perpetual Motion Machines are hypothetical machines which can run forever without any energy source. Such machines are impossible for the reason mentioned above.
Despite the constraint, creating a Perpetual Motion Machine has been a major interest of many investors since a long period of time. The earliest attempt to design such a machine was carried out by the Indian mathematician cum astronomer Bhaskara II during the 12th century. His design, the Bhaskara Wheel had tilted or curved spokes which contained a small amount of mercury. When set in motion, the mercury would flow from one side of the spoke to another thus moving running the machine forever. A much similar design is the overbalanced wheel as shown in the figure.
To really move the machine forever there should be a clockwise torque caused by the extended spokes, but it is canceled by the greater weight on other side providing a counter-clockwise torque. Thus both the forces are in equilibrium at all times and will stop the perpetual motion later.
Some other approaches include the Villard de Honnecourt's Perpetuum Mobile, The Brownian Ratchet, the Perpetual Motion Wheels designed by Leonardo Da Vinci and so on. Magnetic interactions have been a major key component of virtual perpetual motion e.g. Magnetic Levitation.
Time Translation Symmetry
Symmetry in physics is a mathematical or physical feature of a system which is unaltered under some transformations. Such transformations may be continuous( e.g. the rotation of a circle) or discrete( e.g. the rotation of a regular polygon). The most important example of symmetry in physics is that the speed of light has the same value in all frames of reference. Time Translation Symmetry is a kind of symmetry which says that laws of physics are invariant under such transformations. It means that the laws or equations that describe a system at moments 
For example, for the Newton's Equation:
the total energy of the system for the solution
is given by, 
which is independent of time . The conservation of total energy is due to the time translation invariance of the equation of motion.
Time Crystals: Breaking The Time Translation Symmetry
It was thought until recently that Time Translation Symmetry cannot be broken. However, the MIT professor Frank Wilczek in 2012 predicted a new state of matter known as Time Crystal which was first observed in 2017, which could break Time Translation Symmetry i.e. they can change in time without any external influence.
Just like a three-dimensional crystal repeats itself in space, a Time Crystal is a matter which repeats in both space and time. That is the time crystal keeps changing its shape in a periodic manner. It is a non-equilibrium matter in its ground state i.e. its perpetual motion does not require any external force.
However, Time Crystals do not violate the laws of thermodynamics as the total energy of the overall system is conserved, such a system does not spontaneously convert thermal energy to mechanical work and it cannot act as a perpetual store of work. But, the pattern changes perpetually from time to time as long as the system is maintained. However, the apparent motion of the system does not represent conventional kinetic energy.
Creating Time Crystals
A team at the Maryland University first created such a matter by using ten Ytterbium atoms in 2016. A LASER beam induced an electromagnetic field around these atoms which entangled various atoms in a repeating pattern. These atoms were then hit by another beam of LASER. The laser impulse created an instantaneous action and reaction on the entangled pairs of atoms much before the reaction propagates from one atom to another. It disturbed the system in a way that the system never stopped and later it started oscillating in a frequency which was not imparted by the laser in the first place. A Harvard team achieved a similar goal by using something called Nitrogen-Vacancy Centers which are actually flaws in the structure of diamonds.
Nature is full of exceptions and mysteries. There are always loopholes in laws of nature that breaks one or the other laws of physics. These exceptions lead to refinement or revision of the existing laws of physics or at least redefine these laws. Time Crystal is one of such exception which made the scientists make a revisit to the existing laws of physics. Time Crystals are assumed to find applications in designing Quantum Computers as Qubits can be stored in the entangled atoms of these crystals.
References
- Time Crystals Explained | Answers With Joe
- Nature: The Quest to Crystallize Time
- Berkeley News: Scientists Unveil New Form of Matter: Time Crystals
- Wikipedia: Perpetual Motion
- Wikipedia: History of Perpetual Motion Machine
- Wikipedia: Time Translation Symmetry
- Wikipedia: Time Crystals
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