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It is said that almost all phenomena are dependent on cause and effect. There is assumed to be a chain of cause and effect ,leading the philosophers and scientist to believe that there must have been a first cause.

However spontaneous phenomena do not require any previous cause and scientifically we say that such a phenomena is driven by the laws of probability. For example - radioactivity

My question is : What are some examples of spontaneous phenomena other than radioactivity?

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Also quantum fluctuations are examples of random events. They happen spontaneously: Out of the vacuum arises a pair of particle and antiparticle, which both live for a short time period and then annihilate again. Vacuum fluctuations are ubiquitous.

Vacuum fluctuations violate the often quoted philosophical principle

ex nihilo nihil = nothing comes from nothing.

From the viewpoint of quantum theory: Contrary to all apperances, according to Heisenberg’s uncertainty the corresponding violation of energy conservation is admissible. Because for such pair of virtual particles the product of the indeterminacy of the lifetime ”Delta t” and the indeterminacy of the energy “Delta E” satisfies the uncertainty

Delta t x Delta E >= ½ ħ

Vacuum fluctuations play a fundamental role in Quantum Field Theory (QFT). Each field in QFT undergoes permanently quantum fluctuations.

For an introduction see https://en.wikipedia.org/wiki/Quantum_fluctuation, https://en.wikipedia.org/wiki/Vacuum_polarization

Phenomena like quantum fluctuations support the validity of

All that's not forbidden happens

as a principle for philosophy of nature.

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  • It's worth noting that while virtual particles characterize processes allowed in perturbative quantum field theory, and perturbative QFT is extraordinarily accurate (at least in the case where it works, namely quantum electrodynamics), it is not clear that virtual particles actually exist in a meaningful sense anywhere outside the Feynman diagrams they're used in.
    – elutionary
    Oct 31, 2023 at 19:30
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    I agree. The ontology of virtual particles is an outgoing discussion: Are they only a mathematical tool?
    – Jo Wehler
    Oct 31, 2023 at 19:41
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Radioactivity is not spontaneous, it does have a cause. Probabilistic does not mean the same as spontaneous.

Voluntary actions by living beings are spontaneous, they are not caused by any prior events, they are caused by the being's decision to act.

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  • +1 for "voluntary actions". Asking and aswering on this site are good examples of "spontaneous". Oct 31, 2023 at 6:57
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    I do not think spontaneous means "does not have a cause" or anything like "voluntary". Physicists do call a form of decay spontaneous fission, they also have spontaneous emission, spontaneous symmetry breaking, etc. And voluntary actions are not entirely uncaused either, there are physical constraints and motives involved. There isn't much difference with partial causes of quantum events, collapse is an analog of "decision".
    – Conifold
    Oct 31, 2023 at 7:11
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    @Futilitarian Both reduce a list of possibilities to the one actualized.
    – Conifold
    Oct 31, 2023 at 9:55
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    Radioactivity has a cause but no trigger. In that sense it is spontaneous. It happening does not depend on any prior event.
    – kutschkem
    Oct 31, 2023 at 11:22
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    Surely it's the opposite. Even when we are being impulsive, our actions arise with accounts by us why we are doing them, not sponteneously. Whereas with nuclear decay what you call 'cause' is just being the thing, eg an atom of an unstable isotope.
    – CriglCragl
    Oct 31, 2023 at 12:37
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I'm going to post from the perspective of a natural scientist, so please forgive any misuses of philosophical terminology.

In thermodynamics, we define a spontaneous process as one that occurs without an external input to a system—that input is associated with energy, but isn't exactly the same (the technical term is free energy, but exactly what that looks like depends on the environment around your system in question).

This is important because it suggests a subtle frame challenge to the premise of your question: Spontaneous events have a cause, it's just internal to the system rather than external. Your example of radioactive decay is certainly spontaneous, but the cause is easy to identify: the configuration of such and such a nucleus has more energy than a different configuration, which can be accessed by emitting some particle (the decay event). Other answerers have also clarified that such an event is probabilistic: we cannot say with certainty when it will occur, merely that it can do so (and spontaneously: by itself).

All kinds of chemical reactions occur spontaneously, assuming the conditions are set up correctly beforehand. For instance, the conversion of organic polymers such as hydrocarbons and proteins into water and carbon monoxide is spontaneous in a sufficiently concentrated bath of oxygen gas and above some temperature known as the autoignition point. (This reaction is known as fire.) Iron spontaneously—but rather slowly—reacts with oxygen in the air, even at ambient temperature, to form iron oxide (that is rust).

Now, you might argue that setting up the conditions for a spontaneous process counts as an external input! You can probably expand the definition of "process" to find where the whole setup is spontaneous again, but the problem persists. Ultimately, of course, we reach a question beyond physics: what caused the universe to come into existence? After that, the Second Law of Thermodynamics suggests that every* process in the universe is spontaneous, slowly using up the available free energy. But this is only an (ironclad) empirical law, not a mathematical theorem.

One might say that a freely chosen action by a person is spontaneous because was internal to that person. But this is only an analogy, of course. Ultimately, even causality cannot be explained by the laws of physics.

* Or, at least, so close to every that it doesn't make a difference

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There are also phenomena which have a cause, but that cause is diffuse enough to be practically indeterminate.

For example, there is a landslide after a rainstorm. Which drop caused the slide? Or even, how much less rain could there have been before the slide did not happen? Would the slide have occurred if there hadn't been that other storm last week, last year?

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