On the Continuum Fallacy: Is Temperature a Continuous Function?

IF 1.2 3区 物理与天体物理 Q3 PHYSICS, MULTIDISCIPLINARY
Aditya Jha, Douglas Campbell, Clemency Montelle, Phillip L. Wilson
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Abstract

It is often argued that the indispensability of continuum models comes from their empirical adequacy despite their decoupling from the microscopic details of the modelled physical system. There is thus a commonly held misconception that temperature varying across a region of space or time can always be accurately represented as a continuous function. We discuss three inter-related cases of temperature modelling — in phase transitions, thermal boundary resistance and slip flows — and show that the continuum view is fallacious on the ground that the microscopic details of a physical system are not necessarily decoupled from continuum models. We show how temperature discontinuities are present in both data (experiments and simulations) and phenomena (theory and models) and how discontinuum models of temperature variation may have greater empirical adequacy and explanatory power. The conclusions of our paper are: a) continuum idealisations are not indispensable to modelling physical phenomena and both continuous and discontinuous representations of phenomena work depending on the context; b) temperature is not necessarily a continuously defined function in our best scientific representations of the world; and c) that its continuity, where applicable, is a contingent matter. We also raise a question as to whether discontinuous representations should be considered truly de-idealised descriptions of physical phenomena.

Abstract Image

关于连续性谬误:温度是连续函数吗?
人们经常认为,连续统模型的不可或缺性来自于它们的经验充分性,尽管它们与模拟物理系统的微观细节脱钩。因此,有一种普遍的误解,认为温度在一个空间或时间区域内的变化总是可以精确地表示为连续函数。我们讨论了三个相互关联的温度模拟案例——相变、热边界阻力和滑动流动——并表明连续体观点是错误的,因为物理系统的微观细节不一定与连续体模型解耦。我们展示了温度不连续如何存在于数据(实验和模拟)和现象(理论和模型)中,以及温度变化的不连续模型如何具有更大的经验充分性和解释力。我们论文的结论是:a)连续体理想化对于物理现象建模并不是必不可少的,现象的连续和不连续表示都取决于上下文;B)在我们对世界最好的科学表述中,温度不一定是一个连续定义的函数;c)在适用的情况下,其连续性是一个偶然事项。我们还提出了一个问题,即不连续表征是否应被视为物理现象的真正去理想化描述。
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来源期刊
Foundations of Physics
Foundations of Physics 物理-物理:综合
CiteScore
2.70
自引率
6.70%
发文量
104
审稿时长
6-12 weeks
期刊介绍: The conceptual foundations of physics have been under constant revision from the outset, and remain so today. Discussion of foundational issues has always been a major source of progress in science, on a par with empirical knowledge and mathematics. Examples include the debates on the nature of space and time involving Newton and later Einstein; on the nature of heat and of energy; on irreversibility and probability due to Boltzmann; on the nature of matter and observation measurement during the early days of quantum theory; on the meaning of renormalisation, and many others. Today, insightful reflection on the conceptual structure utilised in our efforts to understand the physical world is of particular value, given the serious unsolved problems that are likely to demand, once again, modifications of the grammar of our scientific description of the physical world. The quantum properties of gravity, the nature of measurement in quantum mechanics, the primary source of irreversibility, the role of information in physics – all these are examples of questions about which science is still confused and whose solution may well demand more than skilled mathematics and new experiments. Foundations of Physics is a privileged forum for discussing such foundational issues, open to physicists, cosmologists, philosophers and mathematicians. It is devoted to the conceptual bases of the fundamental theories of physics and cosmology, to their logical, methodological, and philosophical premises. The journal welcomes papers on issues such as the foundations of special and general relativity, quantum theory, classical and quantum field theory, quantum gravity, unified theories, thermodynamics, statistical mechanics, cosmology, and similar.
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