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Waves would spread outward from each point, eventually overlapping to form a more complex pattern. This is a superposition of waves. Similarly, in quantum science, objects such as electrons and photons have wavelike properties that can combine and become what is called superposed.  Credit: Shutterstock Image Lightbox  Credit: Shutterstock [Download Full Image](https://caltechsites-prod-assets.resources.caltech.edu/scienceexchange/images/tworipples.original.jpg) While waves on the surface of a pond are formed by the movement of water, quantum waves are mathematical. They are expressed as equations that describe the probabilities of an object existing in a given state or having a particular property. The equations might provide information on the probability of an electron moving at a specific speed or residing in a certain location. When an electron is in superposition, its different states can be thought of as separate outcomes, each with a particular probability of being observed. An electron might be said to be in a superposition of two different velocities or in two places at once. Understanding superposition may help to advance quantum technology such as [quantum computers](https://scienceexchange.caltech.edu/topics/quantum-science-explained/quantum-computing-computers). The concept of quantum superposition might be difficult to visualize. Traditional descriptions have used the analogy of a coin that is heads up and tails up at the same time, or the famous Schrödinger's cat thought experiment, in which physicist Erwin Schrödinger imagined placing a cat in a sealed box along with a poisonous substance that has an equal chance of killing the cat—or not—within an hour. Schrödinger proposed that, at the end of the hour, the cat could be said to be both alive *and* dead, in a superposition of states until the box is opened, and that the act of observation randomly determines whether the cat is alive *or* dead. Schrödinger intended the example to demonstrate what he saw as the absurdity of quantum science. In mathematical terms, superposition can be thought of as an equation that has more than one solution. When we solve *x*2 = 4, *x* can either be 2 or –2. Both answers are correct. Superposed wave functions will be more complicated to solve, but they can be approached with the same mindset. ### How can scientists observe superposition? Many experiments have been conducted that definitively prove the existence of superposition. One example recruits the help of light filters: screens that selectively block light, such as those found in polarized sunglasses or camera lenses. Most of the light we see around us is a combination of many different waves coming from the sun and other sources. The peaks and valleys of these waves are rotated in different directions at once. In other words, the light is in a superposition of these different polarized states.  Polarization of light Credit: Lance Hayashida for Caltech Science Exchange Image Lightbox  Polarization of light Credit: Lance Hayashida for Caltech Science Exchange [Download Full Image](https://caltechsites-prod-assets.resources.caltech.edu/scienceexchange/images/Superposition-Waves-Monochrome-B.original.jpg) As light waves interact with their surroundings, their properties change. Light that reflects off of the surface of a lake or snow-covered ground will be more likely to be polarized horizontally. If this light then encounters a filter that permits only vertically polarized light to pass through, the reflection will be blocked. This is how polarized sunglasses filter out the glare from reflective surfaces on a bright day. Superposition becomes apparent when we arrange more than one filter in different ways to tease out additional properties of light. Light that passes through a horizontal filter will have a 100 percent chance of passing through a second horizontal filter, i.e., all of it will pass through. If this second filter is gradually rotated toward a vertical orientation, the chance of the light passing through both filters steadily decreases. Half of the light will pass through when the filter reaches the diagonal (45 degrees), and no light will pass through when the filter is vertical. If superposition did not exist, light would be completely blocked as soon as the second filter was rotated by even a fraction of a degree because all of the light that went through the first filter would be strictly horizontally polarized.  No light passes through a horizontal filter followed by a vertical filter. Credit: Lance Hayashida for Caltech Science Exchange Image Lightbox  No light passes through a horizontal filter followed by a vertical filter. Credit: Lance Hayashida for Caltech Science Exchange [Download Full Image](https://caltechsites-prod-assets.resources.caltech.edu/scienceexchange/images/Superposition-Polarized-Filters-Part1-D_g2JrxWN.original.jpg) Surprisingly, adding a diagonal filter between the horizontal and vertical filters allows some light to go all the way through the system. This is also a result of superposition. The new filter will permit 50 percent of the light coming through the horizontal filter to pass. Then, because the new filter is also diagonal relative to the vertical filter, the vertical filter will permit 50 percent of the light to pass through.  Some light passes through a horizontal filter followed consecutively by a diagonal filter and a vertical filter. Credit: Lance Hayashida for Caltech Science Exchange Image Lightbox  Some light passes through a horizontal filter followed consecutively by a diagonal filter and a vertical filter. Credit: Lance Hayashida for Caltech Science Exchange [Download Full Image](https://caltechsites-prod-assets.resources.caltech.edu/scienceexchange/images/Superposition-Polarized-Filters-Part2-D.original.jpg) The diagonal filter acts to "reset" the superposition of the light by making it more likely to be vertically polarized. ## Dive Deeper [A Molecular Approach to Quantum Computing](https://www.caltech.edu/about/news/molecular-approach-quantum-computing?utm_medium=web&utm_campaign=csequantum&utm_source=caltech-science-exchange&utm_content=&utm_term=) [The Two-Slit Experiment and "One Mystery" of Quantum Mechanics](https://www.informationphilosopher.com/quantum/two-slit/) [Giant Molecules Exist in Two Places at Once in Unprecedented Quantum Experiment](https://www.scientificamerican.com/article/quantum-time-twist-offers-a-way-to-create-schroedingers-clock/)   California Institute of Technology  1200 East California Boulevard Pasadena, California 91125 [Content Use Policy](https://scienceexchange.caltech.edu/about/content-use-policy) \| [Digital Accessibility](https://digitalaccessibility.caltech.edu/) \| Cookie Consent \| [Privacy Notice](https://www.caltech.edu/privacy-notice) \| Site Content Copyright © 2026

Imagine touching the surface of a pond at two different points at the same time. Waves would spread outward from each point, eventually overlapping to form a more complex pattern. This is a superposition of waves. Similarly, in quantum science, objects such as electrons and photons have wavelike properties that can combine and become what is called superposed.  Credit: Shutterstock While waves on the surface of a pond are formed by the movement of water, quantum waves are mathematical. They are expressed as equations that describe the probabilities of an object existing in a given state or having a particular property. The equations might provide information on the probability of an electron moving at a specific speed or residing in a certain location. When an electron is in superposition, its different states can be thought of as separate outcomes, each with a particular probability of being observed. An electron might be said to be in a superposition of two different velocities or in two places at once. Understanding superposition may help to advance quantum technology such as [quantum computers](https://scienceexchange.caltech.edu/topics/quantum-science-explained/quantum-computing-computers). The concept of quantum superposition might be difficult to visualize. Traditional descriptions have used the analogy of a coin that is heads up and tails up at the same time, or the famous Schrödinger's cat thought experiment, in which physicist Erwin Schrödinger imagined placing a cat in a sealed box along with a poisonous substance that has an equal chance of killing the cat—or not—within an hour. Schrödinger proposed that, at the end of the hour, the cat could be said to be both alive *and* dead, in a superposition of states until the box is opened, and that the act of observation randomly determines whether the cat is alive *or* dead. Schrödinger intended the example to demonstrate what he saw as the absurdity of quantum science. In mathematical terms, superposition can be thought of as an equation that has more than one solution. When we solve *x*2 = 4, *x* can either be 2 or –2. Both answers are correct. Superposed wave functions will be more complicated to solve, but they can be approached with the same mindset. ### How can scientists observe superposition? Many experiments have been conducted that definitively prove the existence of superposition. One example recruits the help of light filters: screens that selectively block light, such as those found in polarized sunglasses or camera lenses. Most of the light we see around us is a combination of many different waves coming from the sun and other sources. The peaks and valleys of these waves are rotated in different directions at once. In other words, the light is in a superposition of these different polarized states.  Polarization of light Credit: Lance Hayashida for Caltech Science Exchange As light waves interact with their surroundings, their properties change. Light that reflects off of the surface of a lake or snow-covered ground will be more likely to be polarized horizontally. If this light then encounters a filter that permits only vertically polarized light to pass through, the reflection will be blocked. This is how polarized sunglasses filter out the glare from reflective surfaces on a bright day. Superposition becomes apparent when we arrange more than one filter in different ways to tease out additional properties of light. Light that passes through a horizontal filter will have a 100 percent chance of passing through a second horizontal filter, i.e., all of it will pass through. If this second filter is gradually rotated toward a vertical orientation, the chance of the light passing through both filters steadily decreases. Half of the light will pass through when the filter reaches the diagonal (45 degrees), and no light will pass through when the filter is vertical. If superposition did not exist, light would be completely blocked as soon as the second filter was rotated by even a fraction of a degree because all of the light that went through the first filter would be strictly horizontally polarized.  No light passes through a horizontal filter followed by a vertical filter. Credit: Lance Hayashida for Caltech Science Exchange Surprisingly, adding a diagonal filter between the horizontal and vertical filters allows some light to go all the way through the system. This is also a result of superposition. The new filter will permit 50 percent of the light coming through the horizontal filter to pass. Then, because the new filter is also diagonal relative to the vertical filter, the vertical filter will permit 50 percent of the light to pass through.  Some light passes through a horizontal filter followed consecutively by a diagonal filter and a vertical filter. Credit: Lance Hayashida for Caltech Science Exchange The diagonal filter acts to "reset" the superposition of the light by making it more likely to be vertically polarized.