The law of attraction states that conscious and unconscious thoughts shape a person's reality. The more our thoughts are drawn toward a desired or feared event, the more likely it is to come to pass.
Various versions of the law of attraction have been floating around for most of humanity's history. It lies at the heart of virtually all magical systems: As I will, so mote it be. It has echoes in Hindu and Buddhist reincarnation, where our own wants and needs dictate who our next parents will be. In modern times, the law of attraction was named and popularised by the 2006 film and book "The Secret".
The law of attraction is not a mathematical part of quantum physics. Although it cannot be tested or otherwise examined using the scientific method, its proponents point to Schroedinger's equation and the observer effect of quantum physics, suggesting that the law of attraction is a logical extrapolation.
The observer effect means that no introduced element can be fully independent of a system. To measure, observe, or evaluate a system is to interact with it and thus to influence it. In physics as in many other sciences, it has long been established that the method of measuring affects what will be seen. If a beam of light is aimed at a pair of double slits used for observing wave patterns, it produces a classic wave pattern. If the same beam of light is aimed at a sheet of paper where the effect of individual photons could be seen as speckles, those speckles will appear. This is why the law of attraction holds that we find what we seek.
Even to detect an electron, a photon must have encountered that electron first. The interaction of photon and electron alters the electron, however: so it can't be known what the electron would have done without that interaction.
The effect is even more basic than that. To measure the temperature of a glass of water, a thermometer is inserted: which itself alters the temperature of the water.
Quantum physicists resolve the observer effect through Bell's Theorum, which argues that no system can exist independently of its observers, even if those 'observers' have no consciousness. When extrapolated to non-isolated systems, the terms 'observer' and 'observed' become entirely meaningless. Everything interacts with everything else. The entire universe is just one entangled quantum system.
Schroedinger's equations are best known through the paradox of Schroedinger's cat. This thought experiment imagines a simple situation: a cat hidden in a box. A beam is fired in such a way that the resulting nuclear reaction has a 50% chance of a lethal outcome for the cat. This is a wave function with two eigenstates: (1) the cat is alive, and (2) the cat is dead. Until the box is opened and the cat can be observed, both eigenstates co-exist. When the box is opened and the cat is observed, the wave function collapses into a single occurrence: either the cat is alive or the cat is dead.
The law of attraction claims that the links inherent in the observer effect can be used consciously to achieve a desired end, solely by the power of focused observation. In the language (but not the mathematics) of quantum physics, the law of attraction means that when a wave function with multiple eigenstates collapses into a single occurrence, the end result is influenced by the conscious will.
Within the current level of quantum physics research, conscious awareness seems to make no difference to there being an interaction. Quantum physics cannot, however, measure whether consciousness might have resulted in a different type of interaction, or whether focused will played a role in why a wave function collapsed into one particular occurrence and not another. In most standard interpretations of quantum physics, the very question is meaningless.
In the many-world interpretation of quantum physics, there is no need even for possibility to resolve into a certainty: every possibility creates a new world where that possibility happened. It is the ultimate negation of the power of personal will.
Maybe science will never be able to fully explain the interrelationship of consciousness and its environment. In the meantime, it may be pleasant to believe that our focused will, in and of itself, can influence the universe around us.