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Quantum theory is strange and counterintuitive, but it’s very precise. Lots of analogies and broad concepts are presented in popular science trying to give an accurate description of quantum behavior, but if you really want to understand how quantum theory (or any other theory) works, you need to look at the mathematical details. It’s only the mathematics that shows us what’s truly going on.

Mathematically, a quantum object is described by a function of complex numbers governed by the Schrödinger equation. This function is known as the wavefunction, and it allows you to determine quantum behavior. The wavefunction represents the state of the system, which tells you the probability of various outcomes to a particular experiment (observation). To find the probability, you simply multiply the wavefunction by its complex conjugate. This is how quantum objects can have wavelike properties (the wavefunction) and particle properties (the probable outcome).

No, wait. Actually a quantum object is described by a mathematical quantity known as a matrix. As Werner Heisenberg showed, each type of quantity you could observe (position, momentum, energy) is represented by a matrix as well (known as an operator). By multiplying the operator and the quantum state matrix in a particular way, you get the probability of a particular outcome. The wavelike behavior is a result of the multiple connections between states within the matrix.

SciWorks Radio is a production of 88.5 WFDD and SciWorks, the Science Center and Environmental Park of Forsyth County, located in Winston-Salem.

We’ve come a long way from stone tools. With great complexity, we manufacture things like jet airplanes, interplanetary probes, medical tools, and microprocessors. We build with a top-down approach, starting with a big picture concept which we then design and assemble in pieces.

Duke University professor of computer sciences, Dr. John Reif, notes that nature works from the bottom up to assemble complex structures in three dimensions.

In Brief:

• Scientists have formulated a mathematical theorem which shows that Newton’s Second Law may, at least, have a loophole.
• The finding may provide the foundation for future discoveries that may allow us to power devices remotely.

According to our best understanding of the Universe, if you travel back in time as far as you can, around 13.8 billion years or so, you’ll eventually reach a singularity — a super-dense, hot, and energetic point, where the laws that govern space-time breakdown.

Despite our best attempts, we can’t peer past that singularity to see what triggered the birth of our Universe — but we do know of only one other instance in the history of our Universe where a singularity exists, and that’s inside a black hole. And the two events might have more in common than you’ve ever considered, as physicist Ethan Siegel explains over at Forbes.

Continue reading “Physicist says our Universe could have spawned from a black hole” »

Researchers at the universities of Valencia and Florence propose an approach to the experimental data generated by the Large Hadron Collider that solves the infinity problem without breaching the four dimensions of space-time.

The theories currently used to interpret the data emerging from CERN’s Large Hadron Collider (LHC), which have so far most notably led to the discovery of the Higgs boson, are poorly defined within the four dimensions of space-time established by Einstein in his Theory of Special Relativity. In order to avoid the infinities resulting from the calculations that these theories inspire, new dimensions are added in a mathematical trick which, although effective, does not reflect what we now know about our Universe.

Now though, a group of researchers at the Institute of Corpuscular Physics (IFIC, CSIC-UV) in Valencia has devised a way to side-step the infinity issue and keep the theory within the bounds of the four standard dimensions of space-time.

Continue reading “Researchers solve the problem of the dimensions of space-time in theories relating to the LHC” »

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There are many scientific and non-scientific varieties of the answer about what came before Big Bang. Some say there was literally nothing and some say a black hole or a multiverse. But now a group of mathematicians from Canada and Egypt have analyzed some cutting edge scientific theory and a complex set of equations to find what preceded the universe in which we live. Their research paper has been published in Nature.

Continue reading “Scientists claim to have discover what existed BEFORE the beginning of the universe” »

A new mathematical model of memory could accelerate the quest to build super-powered, brain-inspired hardware systems.

Stockholm: The Nobel Physics prize was the second of the awards to be given away, on Tuesday, to a Birtish trio — scientists David Thouless, Duncan Haldane and Michael Kosterlitz for revealing the secrets of exotic matter.

Thouless, 82, is professor emeritus at the University of Washington in Seattle. Haldane, 65, is a professor at Princeton University, and Kosterlitz, born in 1942, teaches at Brown University in Providence, Rhode Island. The laureates will share the eight million Swedish kronor (around $931,000 or 834,000 euros) prize sum. Thouless won one-half of the prize, while Haldane and Hosterlitz share the other half.

“This year’s laureates opened the door on an unknown world where matter can assume strange states. They have used advanced mathematical methods to study unusual phases, or states, of matter, such as superconductors, superfluids or thin magnetic films. Thanks to their pioneering work, the hunt is now on for new and exotic phases of matter,” said the Nobel jury.

Continue reading “Nobel Physics Prize winners: All you need to know about mugs, donuts and quantum computing” »

When the project started, a “Red Team” of hackers could have taken over the helicopter almost as easily as it could break into your home Wi-Fi. But in the intervening months, engineers from the Defense Advanced Research Projects Agency (DARPA) had implemented a new kind of security mechanism — a software system that couldn’t be commandeered. Key parts of Little Bird’s computer system were unhackable with existing technology, its code as trustworthy as a mathematical proof. Even though the Red Team was given six weeks with the drone and more access to its computing network than genuine bad actors could ever expect to attain, they failed to crack Little Bird’s defenses.

“They were not able to break out and disrupt the operation in any way,” said Kathleen Fisher, a professor of computer science at Tufts University and the founding program manager of the High-Assurance Cyber Military Systems (HACMS) project. “That result made all of DARPA stand up and say, oh my goodness, we can actually use this technology in systems we care about.”

The technology that repelled the hackers was a style of software programming known as formal verification. Unlike most computer code, which is written informally and evaluated based mainly on whether it works, formally verified software reads like a mathematical proof: Each statement follows logically from the next. An entire program can be tested with the same certainty that mathematicians prove theorems.