Intelligent Design Mathematics

Absolute zero proven mathematically impossible?

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rubidium atoms a few billionths of a degree above absolute zero/NIST/JILA/CU-Boulder

From Leah Crane at New Scientist:

It’s an absolute. Mathematics has put speed limits on cooling, finally proving a century-old law – that unless you have infinite time and resources, you can’t get to the absolute zero of temperature.

Now Jonathan Oppenheim and Lluís Masanes at University College London have mathematically derived the unattainability principle and placed limits on how fast a system can cool, creating a general proof of the third law.

By applying mathematical techniques from quantum information theory, they proved that no real system will ever reach 0 kelvin: it would take an infinite number of steps. More.

Paper is open access.

Abstract: The most accepted version of the third law of thermodynamics, the unattainability principle, states that any process cannot reach absolute zero temperature in a finite number of steps and within a finite time. Here, we provide a derivation of the principle that applies to arbitrary cooling processes, even those exploiting the laws of quantum mechanics or involving an infinite-dimensional reservoir. We quantify the resources needed to cool a system to any temperature, and translate these resources into the minimal time or number of steps, by considering the notion of a thermal machine that obeys similar restrictions to universal computers. We generally find that the obtainable temperature can scale as an inverse power of the cooling time. Our results also clarify the connection between two versions of the third law (the unattainability principle and the heat theorem), and place ultimate bounds on the speed at which information can be erased

Curious indeed, the difference that exists between something and nothing. Consider, for example, Physics and the contemplation of nothing.

Note: We are told that the current coldest spot in the universe is planned for the International Space Station:

This August, NASA plans to launch to the ISS an experiment that will freeze atoms to less than 1 billionth of a degree above absolute zero — more than 100 million times colder than the far reaches of deep space, agency officials said. (Earlier NASA statements put the experiment temperature at one ten billionth of a degree.)

The instrument suite, which is about the size of an ice chest, is called the Cold Atom Laboratory (CAL). It consists of lasers, a vacuum chamber and an electromagnetic “knife” that together will slow down gas particles until they are almost motionless. (Remember that temperature is just a measurement of how fast atoms and molecules are moving.)

See also: Is celeb number pi a “normal” number? Not normal. And things get worse. Surely this oddity is related in some way to the unreasonable effectiveness of mathematics.

Here’s some zero fun: Is zero even?

and

Must we understand “nothing” to understand physics?

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3 Replies to “Absolute zero proven mathematically impossible?

  1. 1
    Armand Jacks says:

    I am embarrassed to admit that I very seldom watch the videos posted at UD. But this Nova video was amazing and thought provoking.

  2. 2
    kairosfocus says:

    It has been generally accepted for a century or more, that no finite number of refrigeration cycles can reduce a body to absolute zero. Last I checked, years ago now, lasers were being used to get closer and closer, I stopped tracking just how close. BTW, maybe the most impressive linked phenom is Liquid Helium II, a superfluid. Try https://www.youtube.com/watch?v=sKOlfR5OcB4&ytbChannel=AntiProtonBoy

  3. 3
    PaV says:

    How much money was spent to ‘prove’ that we can’t lift ourselves up by our bootstraps—IOW, the ‘obvious’?

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