Physicists Rewrite a Quantum Rule That Clashes with Our Universe

Modern physics is cleaved by a split. On the other side is quantum theory, which claims that particles are not real. Einstein believed that space and time can bend and cause gravity. Physicists have been trying to reconcile quantum mechanics and gravity for 90 years. The quest has run into problems.

A principle at the center of quantum mechanics, an assumption about how the world works that seems obvious, is mounting hints that at least part of the problem.

Something always happens according to the principle of unitarity. The probability of all possible outcomes must be summed up to 100%. Unitarity makes it hard for atoms and particles to change from moment to moment. Change is a two-way street and can be undone on paper. Physicists have long been guided by these requirements. An assistant professor at the University of Illinois said that it was a very restrictive condition.

Physicists can't reconcile quantum mechanics and gravity because of a straitjacket. Bianca Dittrich said that unification in quantum gravity is a very open question.

The problem is that the universe is getting bigger. General relativity describes this expansion. Unitarity demands a neat symmetry between past and future on the quantum level, but it means that the future of the universe looks completely different from its past. Steve Giddings is a quantum gravity theorist at the University of California Santa Barbara.

For a long time, concern over this conflict has been present. Two quantum gravity theorists may have found a way to better fit our growing universe. According to Andrew Strominger and Jordan Cotler of Harvard University, isometry can accommodate an expanding universe while still satisfying the strict requirements that first made unitary a guiding light.

Strominger stated that you don't need unitarity. There is too mucharity in a condition.

Many physicists are in favor of the isometry proposal, but some disagree as to whether the update is too radical or not.

A Fixed Sum

Events are played out in a unitary way in everyday life. A coin toss has a high chance of success.

The pioneers of quantum mechanics made a surprising discovery a century ago. It was surprising that the quantum world operates by more complicated numbers. The degree to which a particle is in a certain state is called an amplitude. Physicists square the amplitude to get rid of the imaginary and negative bits and come up with a positive probability. The squares of all the amplitudes must equal 1 in order for unitarity to be true.

Unitarity is given by the squaring of hidden amplitudes to calculate outcomes. When a particle flies through a magnetic field or collides with another particle, its amplitudes change as well. Physicists use the fact that amplitudes never change in a way that affects the fixed sum of their squares to work out how a particle is allowed to evolve. The British physicist Paul Dirac discovered an equation that implied the existence of antimatter in the 1920's. Dirac wrote that he was not interested in considering any theories that wouldn't fit with his darling.

The quantum state of a particle is tracked by physicists in order to keep probabilities and amplitudes in line. Physicists use mathematical objects called matrices to transform the coordinates of the particle. Unitarity dictates that a physically allowed change must correspond to a special "unitary" matrix that rotates the particle's state in Hilbert space without changing the sum of the squares of its coordinates.

It is a mathematical fact that if you know the specific unitary matrix corresponding to some change over time, your quantum state can be changed into the future or into the past. In the Hilbert space, it will always land on another viable state, which will never grow or shrink. The future and the past both determine the future. Information is neither created nor destroyed.

The universe that surrounds us seems to clash with the bedrock assumption.

A Cosmic Clash

The Galaxies are flying in opposite directions. Physicists have realized that our expanding universe poses a problem for quantum mechanics by presenting particles with many options for where to be and how to behave. The Hilbert space of possibilities can't grow with space. Nima Arkani-Hamed is a theoretical physicist at the Institute for Advanced Study in New Jersey.

Strominger said that it was the elephant in the room for a long time.

Giddings sets a thought experiment in a universe that is both unitary and expanding. Giddings said it would be possible to take the current state of the universe and add one innocuous photon to it. Unitarity wants us to be able to calculate what the universe looked like in the past.

A glitch can be created by adding an extra photon. Going into the past will cause the universe to get smaller. This isn't a problem in the real universe because a photon shrinks only until the moment of its creation through a process called a subatomic process. The extra photon wasn't created by that special process, so instead of disappearing when you turn back time, its wavelength will get impossibly small, concentrating its energy so much that the photon collapses into a black hole The implication is that in this fictional, expanding universe, black holes convert into light waves. According to the thought experiment, a nave combination of unitarity and expansion doesn't work.

Dittrich doesn't think unitarity smells right. The idea of changing from one moment to the next is complicated by general relativity and quantum mechanics. She said she never depended so much on unitarity.

Is there an alternative framework that could accommodate both quantum theory and Cosmic Expansion?

Unitarity 2.0

Strominger and Cotler split their time between quantum information theory and quantum gravity research. The quantum error correction scheme is similar to the expanding universe in that a small message from a quantum state is redundantly stored in a bigger system. They thought that the young universe might be similar to the modern one.

Strominger said that this is exactly what people have been doing.

The two homed in on a class of transformations that are known as isometries. Isometric changes are similar to unitary ones with more flexibility.

An electron can be found in two different places. The two locations have all possible combinations of amplitudes. The points on a circle have some value in both directions. Unitary changes do not affect the set of possibilities.

Let the universe swell just enough to allow a third position to be visualized. The electron has a special way of gaining anotherdimension. The circle becomes a sphere and the particle's quantum state can be changed to accommodate different places. Under the change, the distance between the two states on the circle remains the same. The options increase but not with physical consequences.

Giddings stated that working with isometries is a generalization of unitarity. Some of the essence is retained.

As real space expands, our universe would have a huge number of dimensions. Strominger and Cotler looked at the expansion of a toy universe with a line ending in a mirror. The universe is likely to grow from one length to another.

The Schrdinger equation is used for such calculations. The purpose of the Schrdinger equation is to enforce unitarity. The path integral is an alternative version of quantum mechanics that Strominger and Cotler used. The creation of new states, which appear as branching paths leading to multiple endpoints, can be accommodated by this method. The matrix Strominger and Cotler created was not a unitary one, but a matrix that encapsulated the growth of the toy universe.

The Schrdinger equation won't work if you want to describe an expanding universe It continues to work on its own volition. This alternative way of doing quantum mechanics will be more useful to us in understanding an expanding universe according to Cotler.

A Mirage of Possibilities

The thought experiment has caused problems for Giddings and others. Through a conceptual change, it would be possible to think about the relationship between the past and the future in a different way.

A toy universe, one born in one of two possible initial states, 0 or 1 is described by Cotler. Each 0 becomes 1 and each 1 becomes 10 at any given time. If the universe starts at 0, it will grow as follows: 0 1 2 3 4 It will become 10010110 if it begins at 1 Everything about the universe is captured by the strings. The string was made from 0s and 1s.

There are two states in the toy universe, one arising from 0 and the other from 1. The initial one-digit configuration has been changed into an eight-digit one. There are two possibilities at the beginning and two at the end. The framework for describing the expanding universe is provided by the Isidore evolution. It doesn't create the freedom to add an extra photon between here and Andromeda which would make it difficult to turn back the clock. There is a possibility that the universe is in the 0101 state. If you flip the first 0 to a 1 you will get a state with a seemingly valid set of coordinates in the larger space. You can see that the state has no parent state. The universe could not have existed.

Cotler said there are some configurations of the future that don't correspond to what happened in the past. There isn't anything in the past that would change them.

Giddings encountered a number of paradoxes while studying black holes. He believes that a given state of the universe is only physically possible if it can evolve backwards. He said that the puzzle was a long one. Strominger and Cotler are trying to inspire a new way of thinking about things.

Giddings thinks the approach needs to be further developed. Dittrich came to similar realizations a decade ago while trying to formulate a toy quantum theory with Philipp Hhn. One hope is that such work will eventually lead to a specific rule that governs our universe. The calculation of which specific patterns in the distribution of the matter in the sky are possible and which aren't could be used to test the predictions against observational data. He said you will find this if you look closer. It could be useful.

To Isometry and Beyond

Theory and thought experiments show that isometry helps combine the malleability of space-time with quantum theory.

Black holes, intense concentrations of matter that warp space-time into a dead end is one thought experiment. Black holes evaporate over time, meaning that the quantum state of anything that fell in is meaningless. Physicists may face a different puzzle if black holes have Hilbert spaces. Strominger thinks there can be a solution that takes this into account.

A detailed quantum theory that explained where everything came from would be another prize. We don't have a universe, but we have a universe. Is that kind of evolution?

Arkani-Hamed doesn't believe that swap in isometry for unitarity goes far enough. One of the leaders of a research program is trying to break free of many fundamental assumptions in quantum theory and general relativity.

He thinks that whatever theory comes next, it will be a completely novel form, just as quantum mechanics was a break from the laws of motion. An example of what a new form might look like is the research program he points to. The volume of a geometric object is known as the amplituhedron. It is much easier to calculate the object's volume than it is to reconstruct the ways a particle collision might play out.

The principle is not used to construct the shape itself. There aren't any assumptions about how particles move. There is a chance for a new perspective on reality, one free from the cherished principles that currently conflict, because of the success of this purely geometric formulation of particle physics. Geometric shapes related to different particles and quantum theories are being explored more and more by researchers.

It is possible that it is a different way to organize unitarity.