In the book What is life? by Erwin Schrodinger, he says that the laws of physics are statistical in nature.

Today, thanks to the ingenious work of biologists, mainly of geneticists, during the last thirty or forty years, enough is known about the actual material structure of organisms and about their functioning to state that, and to tell precisely why present day physics and chemistry could not possibly account for what happens in space and time within a living organism.

The arrangements of the atoms in the most vital parts of an organism and the interplay of these arrangements differ in a fundamental way from all those arrangements of atoms which physicists and chemists have hitherto made the object of their experimental and theoretical research. Yet the difference which I have just termed fundamental is of such a kind that it might easily appear slight to anyone except a physicist who is thoroughly imbued with the knowledge that the laws of physics and chemistry are statistical throughout.

For it is in relation to the statistical point of view that the structure of thevital parts of living organisms differs so entirely from that of any piece of matter that we physicists and chemists have ever handled physically in our laboratories or mentally at ourwriting desks. The non physicist cannot be expected even to grasp let alone to appreciate the relevance of the difference in ‘statistical structure’ stated in terms so abstract as I have just used.

Could you please explain this to a non physics student?

  • $\begingroup$ As some of the answers explain, QM can be interpreted statistically (look up the 'ensemble interpretation' for more on this), but when it comes to the 'fundamental differences' with living organisms, I suspect Schrodinger was probably talking nonsense... $\endgroup$
    – Mark A
    Feb 20 '17 at 2:55
  • $\begingroup$ @MarkA When predicting the behavior of a mass of mostly similar material with little micro-structure, statistical laws of chemistry and physics are sufficient. For example, we can approximate planets and stars as mostly uniform balls of stuff, and apply gravity, and get a pretty decent description of how planets orbit stars. We can refine this with further approximations. Organisms, in contrast, are ridiculously complex in their structure, and similar "start with a spherical cow" doesn't get far? $\endgroup$
    – Yakk
    Feb 20 '17 at 13:42
  • $\begingroup$ @Yakk It sounded to me like he was implying that the functioning of living organisms cannot be explained by the laws of physics, but I haven't read the book so I may have misinterpreted the quote. Even if his point was about the levels of organization present in biology I'm still not sure where he's going with the focus on the statistical nature of physical laws, particularly as statistical physics is essential in understanding many biological processes as well. Oh well, to comment further I guess I'd have to read the book ;-) $\endgroup$
    – Mark A
    Feb 21 '17 at 5:51
  • $\begingroup$ @Qmechanic When schrodinger talks about physical laws being statistical in nature. i assume he is not talking about Classical mechanics. is that correct? $\endgroup$ Feb 22 '17 at 11:26

Up until just after the turn of the 20th century scientists, physicists believed that nature was very deterministic, predictable. Schrodinger was however of a new generation of scientists along with Bohr, Heisenberg and Planck that developed a theory of the very small, quantum physics (aka quantum mechanics).

The very core of quantum mechanics is wrapped in uncertainty; Schrodinger discovered the wave equation and Heisenberg the uncertainty principle. Both were equivalent and both did not predict with certainty but rather probability.

Although Einstein also contributed to the new physics with his papers on Brownian motion and the photoelectric effect, he held fast to determinism even up to his death in 1955. At the 5th Solvay Conference he debated with Bohr and Einstein's famous quote: "God doesn't play dice with the world"

But the success of quantum mechanics has played out and uncertainty indeed appears to be the rule in physics.

  • $\begingroup$ Schrodinger discovered the wave equation and Heisenberg the uncertainty principle. Both were equivalent I d/v because I think this is wrong. What d'you reckon? $\endgroup$
    – user140606
    Feb 19 '17 at 19:00
  • 1
    $\begingroup$ @Countto10 nipne.ro/rjp/2011_56_9-10/1053_1056.pdf . And Schrodinger indeed 'discovered' his wave equation. It was a 'lucky' guess. $\endgroup$
    – docscience
    Feb 19 '17 at 19:06
  • $\begingroup$ @Countto10 and before you decide to downvote, please check the facts. Thanks $\endgroup$
    – docscience
    Feb 19 '17 at 19:07
  • $\begingroup$ @Countto10 and "Schr¨odinger succeeded in showing the mathematical equivalence of matrix and wave mechanics" in arxiv.org/pdf/physics/0610121.pdf . The historical background, that the development was a 'synthesis' . Today we can derive the wave equation, similarly as Feynman did in the 50's using other known principles. $\endgroup$
    – docscience
    Feb 19 '17 at 19:18
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    $\begingroup$ @docscience They are not equivalent. Schrodinger's equation cannot imply the uncertainty relation since the latter is a property on self-adjoint non-commuting operators, not solutions of the Schrodinger equation. $\endgroup$ Feb 19 '17 at 19:35

Some phenomena in nature are not deterministic to great extent. Specially in quantum physics. Many of quantum mechanics experiments can not be explained at individual event level but they can be very accurately predicted at an average level. That gives the impression that the laws of physics are statistical in nature. But the reason for this is our inability to measure and determine outcomes at individual event level.

As one example, if we align an electron's spin along horizontal axis, and then try to measure its spin along vertical axis, it will be either up, or down. We can not say about such a specific electron whether the spin will be up for sure, or down for that matter. But QM laws tell us that on an average, 50% of such electrons will measure up spin and 50% of them will measure down spin. When we conduct the experiments on a very large number of such electrons, 50/50 outcome is found to be true to six sigma levels. So, the averages work as predicted. Average is a statistical value. Statistics brings probability into picture.

This makes some people think the laws are statistical in nature. But they actually are not necessarily that way. We do not have tools sensitive enough to predict the outcomes at individual electron level.

This happens due to randomness in nature, which is way too complex to calculate.

As a classical example, we can predict how much water evaporate from a pool on daily basis and so can predict how long it will take for the pool to dry up. But, there is no way for us to predict - what day/time, a specific water molecule will evaporate from the pool. We probably do not even have a way to tell one molecule from another, so it even becomes a moot point to ask to make that prediction in the first place.

What makes QM phenomena very strange is - when we try to explain, how the statistical results are framed by nature. Again, this strangeness exists and survives due to our inability to explain the physical mechanism behind the outcomes.

Taking a crude example, if we keep pouring dirt at one place, it always takes the shape of a heap. We can say, the heap is formed due to probability of how many particles land where. But we can also say that, wherever individual particles land, the heap is actually shaped up by gravity to keep things in balance on overall basis.

While we can predict the shape will be a heap, we can not tell where a specific particle of dirt will be stabilized in the heap. There is so much randomness involved that it is just not possible for us to tell it.

But on the other hand, there are numerous examples where we can accurately predict at individual event level. For example, if we know the speed and angle of a projectile, we can accurately calculate where it will land (ignoring wind effects etc.) And all such projectiles will land exactly as predicted. So, there is no probability involved here, or we can say, the probability is 100%, which basically is a deterministic law, not a statistical law.

  • $\begingroup$ You are implying hidden variables: that if we knew more, QM would be deterministic; or specifically, we could predict the spin an electron would have when we measure it. But, we know enough that this implies non-locality. That seems like a big thing to just assume is the case. Or did I misread you? $\endgroup$
    – Yakk
    Feb 20 '17 at 2:05
  • $\begingroup$ @Yakk: What I mean is that nature knows more than we do. And that is to be the case more and more likely as we go smaller and smaller. Therefore, at quantum levels, we do not have tools to measure without impacting what is being measured. Actually, it is not measurement, it is alignment. If I ask you to align an electron along X axis, I guess you would do that by measuring it along X axis. Is there any other way? If so, measurement and alignment are no different at quantum levels. I am not implying hidden variables. Will describe in next comment. $\endgroup$
    – kpv
    Feb 20 '17 at 2:26
  • $\begingroup$ @Yakk: Local Hidden Variables (LHV) usually refer to the static information stored within the particle, or pair (in case of entanglement). That is not sufficient to give the statistical results. What I refer to is nature - including, source, detector, and vicinity of experiment. They all together know what is going to happen. "Note vicinity of experiment" also covers randomness in nature. "Randomness" which falls in place over a large sample. In case of my heap example, there are no hidden variables, It is just act of balancing over time. Gravity does the balancing, not random statistics. $\endgroup$
    – kpv
    Feb 20 '17 at 2:35
  • $\begingroup$ @Yakk: I do not believe non-locality has been proved beyond doubts. Actually I have experienced huge resistance from most everyone (who knows QM) towards attempts even to scrutinize non-locality. But this question does not seem to be about non-locality. $\endgroup$
    – kpv
    Feb 20 '17 at 2:50
  • $\begingroup$ So, superdeterminsim? There are stark constraints on any hidden variables theory to match experiment. I do not see where you are talking explicitly about those constraints. $\endgroup$
    – Yakk
    Feb 20 '17 at 3:35

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