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What is the etymology of the term "Quantum Leap / Quantum Jump"? Doesn't 'Quantum' mean small and discrete?

Dictionary.com: says:

  • A dramatic advance, especially in knowledge or method, as in Establishing a central bank represents a quantum leap in this small country's development. This term originated as quantum jump in the mid-1900s in physics, where it denotes a sudden change from one energy state to another within an atom. Within a decade it was transferred to other advances, not necessarily sudden but very important ones.

But how came Quantum Leap to mean sudden and conspicuous change?

  • I'll note that the term was popularized by a 1989 TV show. – Hot Licks May 30 '17 at 11:09
  • There is no such thing as the etymology of a phrase. Etymology is for single words. The origin of phrases is a different thing. – Lambie May 31 '17 at 12:17
  • @HotLicks: I dispute your fact.  Google Ngram Viewer confirms my personal memory that “quantum leap” was at the height of its popularity when Quantum Leap debuted, and, if anything, has leveled off since then. – Scott Jul 24 '17 at 18:47
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You ask:

how did quantum leap come to mean a sudden and conspicuous change?

In physics, a quantum jump is an instantaneous1 change of a quantum system from one state to an entirely different2 state. So the meaning of "sudden and conspicuous" is not very much of a leap at all from the scientific definition.

The meaning of "large" really isn't justified by the scientific meaning, but it's easy to see how "sudden and conspicuous" could acquire the implication of "large".

1 If you're a philosopher of quantum mechanics, you can argue over whether a quantum jump is really instantaneous, or whether it just appears to be so.
2 Here, the technical term in quantum mechanics for entirely different is orthogonal.

  • "Large" could be justified by quantum entanglement and non-locality, where an effect can occur instantaneously across an arbitrarily large distance. – dangph May 31 '17 at 13:55
  • @dangph: It could. But that's kind of an ex post facto justification. Historically, quantum leap acquired the possible implication "large" well before most physicists were worried about quantum entanglement and non-locality. – Peter Shor May 31 '17 at 15:36
  • Einstein, Podolsky, and Rosen pointed out the problem of non-locality in 1935, which Einstein described as "spooky action at a distance". But you are most probably right that this action at a distance has nothing to do with the "leap" in question. Come to think of it, the leap probably has nothing to do with physics at all as such. Maybe the leap has more to do with a the mental leap needed to think about this new kind of physics. – dangph Jun 1 '17 at 1:14
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As suggested by the following source, it refers to the connotation of quantum meaning a "sudden large increase".

Quantum leap:

  • This is a transferred or figurative use of the concept of the same name in particle physics or quantum mechanics. From the OED: "quantum increase, a sudden large increase; cf. quantum jump; quantum jump, an abrupt transition between one stationary state of a quantized system and another, with the absorption or emission of a quantum; also transf., a sudden large increase or advance; quantum leap, a sudden large advance.

(The Phrase Finder)

The following source illustrates the evolution of "quantum" meaning "something big":

  • The first use of “quantum leap” to mean “really big” was in 1956, the OED says, in a discussion of the US-Soviet balance of power in a nuclear postwar world, where a writer described “The enormous multiplication of power, the ‘quantum leap’ to a new order of magnitude of destruction.”

But note that:

  • Though using “quantum leap” to mean “big jump” is fully idiomatic, it’s best to avoid using just plain “quantum” to mean “huge” (especially if addressing a physicist). Most dictionaries still define it as simply “an amount.” It’s only the hyperbole that gives it mass quantity.

(archives.cjr.org)

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Quantum does not mean "small and discrete", it only means "discrete", as in "quantisation" - fitting values into a discrete defined set. For instance in mathematics the operation of "rounding" quantises fractions into the set of integers.

Similarly in electronics, sampling signals quantises them into a discrete digital value.

You have the connotation of "small" because quantum physics coincidentally mostly deals with very small things - the smallest divisions (or quanta) of matter.

A quantum leap, however, has the connotation of large, because a leap covers a large distance. However it is quantum, so cannot be further divided within the context that it is used.

For instance the United States could have all its coordinates quantised to within the individual states. A step from the center of one state to the center of a neighbouring state is quite a large distance, but it is only a change of one quanta.

So a quantum leap is a discrete change from one state (not a US state now) to the next state, with the connotation that the states involved are big and cover a large "area".

Another good way of thinking about it is a staircase. Each step is a quanta. The bigger the steps the bigger the leap to get to the next one.

A good synonym is also "step change".

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In the standard model of an atom a Quanta means discreet steps or values.An Electron can only be in any one discreet size of orbit. If it is made to move out of this orbit it will leap to the next discreet orbit.

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    This is actually a better explanation than the others. A "quantum leap" is a jump between two states where there is no gradual movement and no intermediate step -- it's not simply that the jump covers several steps at once, but that there often is no intermediate step that could be taken. – Hot Licks Dec 23 '17 at 21:28
  • Riiight ... a quantum leap is the smallest possible change in a system — so this answer totally fails to explain how the term "quantum leap" has come in non-scientific contexts to mean a large change. – Scott Dec 30 '17 at 8:37

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