I read at a book this quote

"As the degrees of freedom of a particle are the product of all the degrees of freedom of its sub-particles, were a particle to have infinite subdivisions into lower-level particles, the degrees of freedom of the original particle would be infinite, violating the maximal limit of entropy density. The holographic principle thus implies that the subdivisions must stop at some level, and that the fundamental particle is a bit (1 or 0) of information."

I know like everybody else here that it´s wrong because fundamental particles are not Bits, because in they are not pure information nor are information itself, but what exactlly is wrong in the quote that makes it falacious?


1 Answer 1


The book in question is self-published, and a cursory glance through it and some of the author's other writings convinces me that he is almost certainly a crackpot (although perhaps self-educated enough to sound convincing to one who might not know better). If you have a true interest in topics about space and particle physics (and, if so, good for you!), I encourage you to obtain on of the many thousands of books on these subjects released by reputable publishers and authors.

To address this specific claim (and here I apologize for the use of technical jargon, but I don't presently have the time to break it down further), I will simply state that for a given physical macrostate of a statistical system, its entropy in terms of the possible corresponding microstates can be calculated as $$ S = \sum_{i \in \text{microstates}} p_i \log[p_i]$$ where $p_i$ is the probability of the system finding itself in microstate $i$. The sum would be replaced by an integral or multiple integral when the possible microstates are continuously distributed, but schematically, this shows what we want to see. That it that is completely possible to specify the entropy of a system made up of sub-parts, without reference to those subparts, so long as the probability of states in which those subparts are excited is sufficiently small. To give a completely practical example, one can compute the entropy of a gas of hydrogen molecules without considering that they are each made up of protons and electrons, so long as the temperature of the system is known to be low enough that the chance of any significant portion of the molecules being excited out of the ground state is small. Essentially, in this limit, we know that the state of a given molecule is completely specified by giving its position (and orientation, since molecular hydrogen is not a spherically symmetric), without having to consider internal degrees of freedom. It would certainly be onerous, and make all of statistical mechanics untenable, if we would need to know the ultimate, fundamental structure of matter before we could do any calculations. Rather, the concepts of classical statistical mechanics, including entropy, were formulated long before even the atomic theory of matter was accepted science!

Furthermore, and now I'm just piling on, I cannot find any evidence on the web of an accepted physical principle corresponding to the authors "maximal limit of entropy density". It's not even clear what claim he's making when he says that "the fundamental particle is a bit". Let's just suffice it to say that the quoted passage is little more than Deepak-Chopra-level bull poop.

  • $\begingroup$ Thank you for the explanation, I was sure it was wrong from the beginning I was interested because I´m a undergrad at physics but I´m on the first semester so I couldn´t say what was wrong according to the academic physics, but thank you very much for the answer!! $\endgroup$ Commented Apr 8, 2016 at 0:36
  • $\begingroup$ 'It from bit' is the idea information is fundamental en.m.wikipedia.org/wiki/…" $\endgroup$
    – CriglCragl
    Commented May 27, 2018 at 22:53

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