Tabula rasa

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https://en.wikipedia.org/wiki/Tabula_rasa

Roman tabula, or wax tablet, with stylus

Tabula rasa (/ˈtæb.(j)ə.lə ˈrɑː.sə, -.zə, ˈreɪ.-/; Latin for "blank slate") is the idea of individuals being born empty of any built-in mental content, so that all knowledge comes from later perceptions or sensory experiences. Proponents typically form the extreme "nurture" side of the nature versus nurture debate, arguing that humans are born without any "natural" psychological traits and that all aspects of one's personality, social and emotional behaviour, knowledge, or sapience are later imprinted by one's environment onto the mind as one would onto a wax tablet. This idea is the central view posited in the theory of knowledge known as empiricism. Empiricists disagree with the doctrines of innatism or rationalism, which hold that the mind is born already in the possession of specific knowledge or rational capacity.

Etymology

Tabula rasa is a Latin phrase often translated as clean slate in English and originates from the Roman tabula, a wax-covered tablet used for notes, which was blanked (rasa) by heating the wax and then smoothing it. This roughly equates to the English term "blank slate" (or, more literally, "erased slate") which refers to the emptiness of a slate prior to it being written on with chalk. Both may be renewed repeatedly, by melting the wax of the tablet or by erasing the chalk on the slate.

Philosophy

Ancient Greek philosophy

In Western philosophy, the concept of tabula rasa can be traced back to the writings of Aristotle who writes in his treatise De Anima (Περί Ψυχῆς, 'On the Soul') of the "unscribed tablet." In one of the more well-known passages of this treatise, he writes that:

Haven't we already disposed of the difficulty about interaction involving a common element, when we said that mind is in a sense potentially whatever is thinkable, though actually it is nothing until it has thought? What it thinks must be in it just as characters may be said to be on a writing tablet on which as yet nothing stands written: this is exactly what happens with mind.

This idea was further evolved in Ancient Greek philosophy by the Stoic school. Stoic epistemology emphasizes that the mind starts blank, but acquires knowledge as the outside world is impressed upon it. The doxographer Aetius summarizes this view as "When a man is born, the Stoics say, he has the commanding part of his soul like a sheet of paper ready for writing upon." Diogenes Laërtius attributes a similar belief to the Stoic Zeno of Citium when he writes in Lives and Opinions of Eminent Philosophers that:

Perception, again, is an impression produced on the mind, its name being appropriately borrowed from impressions on wax made by a seal; and perception they divide into comprehensible and incomprehensible: Comprehensible, which they call the criterion of facts, and which is produced by a real object, and is, therefore, at the same time conformable to that object; Incomprehensible, which has no relation to any real object, or else, if it has any such relation, does not correspond to it, being but a vague and indistinct representation.

Ibn Sina (11th century)

In the 11th century, the theory of tabula rasa was developed more clearly by Ibn Sina (Avicenna). The Internet Encyclopedia of Philosophy describes him arguing that "human intellect at birth resembled a tabula rasa, a pure potentiality that is actualized through education and comes to know". Thus, according to Ibn Sina, knowledge is attained through "empirical familiarity with objects in this world from which one abstracts universal concepts," which develops through a "syllogistic method of reasoning; observations lead to propositional statements, which when compounded lead to further abstract concepts." He further argued that the intellect itself "possesses levels of development from the static/material intellect, that potentiality can acquire knowledge to the active intellect, the state of the human intellect at conjunction with the perfect source of knowledge."

Ibn Tufail (12th century)

In the 12th century, the Andalusian-Islamic philosopher and novelist, Ibn Tufail (known as Abubacer or Ebn Tophail in the West) demonstrated the theory of tabula rasa as a thought experiment through his Arabic philosophical novel, Hayy ibn Yaqdhan, in which he depicts the development of the mind of a feral child "from a tabula rasa to that of an adult, in complete isolation from society" on a desert island, through experience alone.

The Latin translation of his philosophical novel, entitled Philosophus Autodidactus, published by Edward Pococke the Younger in 1671, had an influence on John Locke's formulation of tabula rasa in An Essay Concerning Human Understanding.

Aquinas (13th century)

Female Figure (Sibyl with Tabula Rasa) by Diego Velázquez, c. 1648

In the 13th century, St. Thomas Aquinas brought the Aristotelian and Avicennian notions to the forefront of Christian thought. These notions sharply contrasted with the previously-held Platonic notions of the human mind as an entity that pre-existed somewhere in the heavens, before being sent down to join a body here on Earth (cf. Plato's Phaedo and Apology, as well as others). St. Bonaventure (also 13th century) was one of the fiercest intellectual opponents of Aquinas, offering some of the strongest arguments toward the Platonic idea of the mind.

Descartes (17th century)

Descartes, in his work The Search for Truth by Natural Light, summarizes an empiricist view in which he uses the words table rase, in French; in the following English translation, this was rendered tabula rasa:

All that seems to me to explain itself very clearly if we compare children's imagination to a tabula rasa on which our ideas, which resemble portraits of each object taken from nature, should depict themselves. The senses, the inclinations, our masters and our intelligence, are the various painters who have the power to execute this work; and amongst them, those who are least adapted to succeed in it, i.e., the imperfect senses, blind instinct, and foolish nurses, are the first to mingle themselves with it. There finally comes the best of all, intelligence, and yet it is still requisite for it to have an apprenticeship of several years, and to follow the example of its masters for long, before daring to rectify a single one of their errors. In my opinion this is one of the principal causes of the difficulty we experience in attaining to true knowledge. For our senses really perceive that alone which is most coarse and common; our natural instinct is entirely corrupted; and as to our masters, although there may no doubt be very perfect ones found amongst them, they yet cannot force our minds to accept their reasoning before our understanding has examined it, for the accomplishment of this end pertains to it alone. But it is like a clever painter who might have been called upon to put the last touches on a bad picture sketched out by prentice hands, and who would probably have to employ all the rules of his art in correcting little by little first a trait here, then a trait there, and finally be required to add to it from his own hand all that was lacking, and who yet could not prevent great faults from remaining in it, because from the beginning the picture would have been badly conceived, the figures badly placed, and the proportions badly observed.

Locke (17th century)

The modern idea of the theory is attributed mostly to John Locke's expression of the idea in Essay Concerning Human Understanding, particularly using the term "white paper" in Book II, Chap. I, 2. In Locke's philosophy, tabula rasa was the theory that at birth the (human) mind is a "blank slate" without rules for processing data, and that data is added and rules for processing are formed solely by one's sensory experiences. The notion is central to Lockean empiricism; it serves as the starting point for Locke's subsequent explication (in Book II) of simple ideas and complex ideas.

As understood by Locke, tabula rasa meant that the mind of the individual was born blank, and it also emphasized the freedom of individuals to author their own soul. Individuals are free to define the content of their character—but basic identity as a member of the human species cannot be altered. This presumption of a free, self-authored mind combined with an immutable human nature leads to the Lockean doctrine of "natural" rights. Locke's idea of tabula rasa is frequently compared with Thomas Hobbes's viewpoint of human nature, in which humans are endowed with inherent mental content—particularly with selfishness.

Freud (19th century)

The concept of Tabula rasa can be constructed from Sigmund Freud's psychoanalysis. Freud argued that the psyche was largely formed by socialization, not biology or genealogy. (see Oedipus complex). In Freud's schema of psycho-sexual development, the conflicting drives imprinted by the parents (the id versus the superego) produce ego, and that in spite of his neuroses, the analysand would discuss matters in a non-adversarial manner. The clinician would simply pose questions to the patient about his neuroses. Exposure to such questions would inculcate the patient's secondary defenses against the neuroses, helping him shed 'substitutive satisfactions,' sadomasochism. Freud's theories implied that humans are largely products of their socialization. In Freudian psychoanalysis, ones' neuroses are agitated until transference neuroses are projected onto the psychoanalyst. Freud posited the individual as a blank slate with an imprint of regressive characteristics through socialization.

Science

Psychology and neurobiology

Main articles: Nature versus nurture and Sex differences in humans

Psychologists and neurobiologists have shown evidence that initially, the entire cerebral cortex is programmed and organized to process sensory input, control motor actions, regulate emotion, and respond reflexively (under predetermined conditions). These programmed mechanisms in the brain subsequently act to learn and refine the ability of the organism. Psychological research has shown that — in contrast to written language — the brain is "hard-wired" at birth to acquire spoken language, something argued by both psychologist Steven Pinker and by the universal grammar theory of Noam Chomsky.

There have been claims by a minority in psychology and neurobiology, however, that the brain is tabula rasa only for certain behaviours. For instance, with respect to one's ability to acquire both general and special types of knowledge or skills, Michael Howe argued against the existence of innate talent. There also have been neurological investigations into specific learning and memory functions, such as Karl Lashley's study on mass action and serial interaction mechanisms.

Important evidence against the tabula rasa model of the mind comes from behavioural genetics, especially twin and adoption studies (see below). These indicate strong genetic influences on personal characteristics such as IQ, alcoholism, gender identity, and other traits. Critically, multivariate studies show that the distinct faculties of the mind, such as memory and reason, fractionate along genetic boundaries. Cultural universals such as emotion and the relative resilience of psychological adaptation to accidental biological changes also support basic biological mechanisms in the mind.

Social pre-wiring hypothesis

Twin studies have resulted in important evidence against the tabula rasa model of the mind, specifically, of social behaviour. The social pre-wiring hypothesis (also informally known as "wired to be social") refers to the ontogeny of social interaction. The theory questions whether there is a propensity to socially oriented action already present before birth. Research in the theory concludes that newborns are born into the world with a unique genetic wiring to be social.

Circumstantial evidence supporting the social pre-wiring hypothesis can be revealed when examining newborns' behaviour. Newborns, not even hours after birth, have been found to display a preparedness for social interaction. This preparedness is expressed in ways such as their imitation of facial gestures. This observed behaviour cannot be attributed to any current form of socialization or social construction. Rather, newborns most likely inherit to some extent social behaviour and identity through genetics.

Principal evidence for this theory is uncovered by examining twin pregnancies. The main argument is, if there are social behaviours that are inherited and developed before birth, then one should expect twin fetuses to engage in some form of social interaction before they are born. Thus, ten fetuses were analyzed over a period of time using ultrasound techniques. Using kinematic analysis, the results of the experiment were that the twin fetuses would interact with each other for longer periods and more often as the pregnancies went on. Researchers were able to conclude that the performance of movements between the co-twins were not accidental but specifically aimed.

The social pre-wiring hypothesis was proven correct:

The central advance of this study is the demonstration that 'social actions' are already performed in the second trimester of gestation. Starting from the 14th week of gestation twin fetuses plan and execute movements specifically aimed at the co-twin. These findings force us to predate the emergence of social behaviour: when the context enables it, as in the case of twin fetuses, other-directed actions are not only possible but predominant over self-directed actions.

Computer science

In artificial intelligence, tabula rasa refers to the development of autonomous agents with a mechanism to reason and plan toward their goal, but no "built-in" knowledge-base of their environment. Thus, they truly are a blank slate.

In reality, autonomous agents possess an initial data-set or knowledge-base, but this cannot be immutable or it would hamper autonomy and heuristic ability. Even if the data-set is empty, it usually may be argued that there is a built-in bias in the reasoning and planning mechanisms. Either intentionally or unintentionally placed there by the human designer, it thus negates the true spirit of tabula rasa.

A synthetic (programming) language parser (LR(1), LALR(1) or SLR(1), for example) could be considered a special case of a tabula rasa, as it is designed to accept any of a possibly infinite set of source language programs, within a single programming language, and to output either a good parse of the program, or a good machine language translation of the program, either of which represents a success, or, alternately, a failure, and nothing else. The "initial data-set" is a set of tables which are generally produced mechanically by a parser table generator, usually from a BNF representation of the source language, and represents a "table representation" of that single programming language.

AlphaZero achieved superhuman performance in chess and shogi using self-play and tabula rasa reinforcement learning, meaning it had no access to human games or hard-coded human knowledge about either board game, only the rules of the games.

Stochastic

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Stochastic

Stochastic (/stəˈkæstɪk/; from Ancient Greek στόχος (stókhos) 'target, aim, guess') is the property of being well-described by a random probability distribution. Stochasticity and randomness are technically distinct concepts. Stochasticity refers to a modeling approach, while randomness describes phenomena. These terms are often used interchangeably. In probability theory, the formal concept of a stochastic process is also referred to as a random process.

Stochasticity is used in many different fields, including actuarial science, image processing, signal processing, computer science, information theory, telecommunications, chemistry, ecology, neuroscience, physics, and cryptography. It is also used in finance, medicine, linguistics, music, media, colour theory, botany, manufacturing and geomorphology.

Etymology

The word stochastic in English was originally used as an adjective with the definition "pertaining to conjecturing", and stemming from a Greek word meaning "to aim at a mark, guess", and the Oxford English Dictionary gives the year 1662 as its earliest occurrence. In his work on probability Ars Conjectandi, originally published in Latin in 1713, Jakob Bernoulli used the phrase "Ars Conjectandi sive Stochastice", which has been translated to "the art of conjecturing or stochastics". This phrase was used, with reference to Bernoulli, by Ladislaus Bortkiewicz, who in 1917 wrote in German the word Stochastik with a sense meaning random. The term stochastic process first appeared in English in a 1934 paper by Joseph L. Doob. For the term and a specific mathematical definition, Doob cited another 1934 paper, where the term stochastischer Prozeß was used in German by Aleksandr Khinchin, though the German term had been used earlier in 1931 by Andrey Kolmogorov.

Mathematics

In the early 1930s, Aleksandr Khinchin gave the first mathematical definition of a stochastic process as a family of random variables indexed by the real line. Further fundamental work on probability theory and stochastic processes was done by Khinchin as well as other mathematicians such as Andrey Kolmogorov, Joseph Doob, William Feller, Maurice Fréchet, Paul Lévy, Wolfgang Doeblin, and Harald Cramér. Decades later Cramér referred to the 1930s as the "heroic period of mathematical probability theory".

In mathematics, the theory of stochastic processes is an important contribution to probability theory, and continues to be an active topic of research for both theory and applications.

The word stochastic is used to describe other terms and objects in mathematics. Examples include a stochastic matrix, which describes a stochastic process known as a Markov process, and stochastic calculus, which involves differential equations and integrals based on stochastic processes such as the Wiener process, also called the Brownian motion process.

Natural science

One of the simplest continuous-time stochastic processes is Brownian motion. This was first observed by botanist Robert Brown while looking through a microscope at pollen grains in water.

Physics

The Monte Carlo method is a stochastic method popularized by physics researchers Stanisław Ulam, Enrico Fermi, John von Neumann, and Nicholas Metropolis. The use of randomness and the repetitive nature of the process are analogous to the activities conducted at a casino. Methods of simulation and statistical sampling generally did the opposite: using simulation to test a previously understood deterministic problem. Though examples of an "inverted" approach do exist historically, they were not considered a general method until the popularity of the Monte Carlo method spread.

Perhaps the most famous early use was by Enrico Fermi in the 1930s, when he used a random method to calculate the properties of the newly discovered neutron. Monte Carlo methods were central to the simulations required for the Manhattan Project, though they were severely limited by the computational tools of the time. Therefore, it was only after electronic computers were first built (from 1945 on) that Monte Carlo methods began to be studied in depth. In the 1950s they were used at Los Alamos for early work relating to the development of the hydrogen bomb, and became popularized in the fields of physics, physical chemistry, and operations research. The RAND Corporation and the U.S. Air Force were two of the major organizations responsible for funding and disseminating information on Monte Carlo methods during this time, and they began to find a wide application in many different fields.

Uses of Monte Carlo methods require large amounts of random numbers, and it was their use that spurred the development of pseudorandom number generators, which were far quicker to use than the tables of random numbers which had been previously used for statistical sampling.

Biology

In biological systems the technique of stochastic resonance—introducing stochastic "noise"—has been found to help improve the signal-strength of the internal feedback-loops for balance and other vestibular communication. The technique has helped diabetic and stroke patients with balance control.

Many biochemical events lend themselves to stochastic analysis. Gene expression, for example, has a stochastic component through the molecular collisions—e.g., during binding and unbinding of RNA polymerase to a gene promoter which contributes to bursts of transcription and super-Poissonian variability in cell-to-cell RNA distributions—via the solution's Brownian motion.

Creativity

Simonton (2003, Psych Bulletin) argues that creativity in science (of scientists) is a constrained stochastic behaviour such that new theories in all sciences are, at least in part, the product of a stochastic process.

Computer science

Stochastic ray tracing is the application of Monte Carlo simulation to the computer graphics ray tracing algorithm. "Distributed ray tracing samples the integrand at many randomly chosen points and averages the results to obtain a better approximation. It is essentially an application of the Monte Carlo method to 3D computer graphics, and for this reason is also called Stochastic ray tracing."

Stochastic forensics analyzes computer crime by viewing computers as stochastic steps.

In artificial intelligence, stochastic programs work by using probabilistic methods to solve problems, as in simulated annealing, stochastic neural networks, stochastic optimization, genetic algorithms, and genetic programming. A problem itself may be stochastic as well, as in planning under uncertainty. Large language models have been described as stochastic parrots.

Finance

The financial markets use stochastic models to represent the seemingly random behaviour of various financial assets, including the random behavior of the price of one currency compared to that of another (such as the price of US Dollar compared to that of the Euro), and also to represent random behaviour of interest rates. These models are then used by financial analysts to value options on stock prices, bond prices, and on interest rates, see Markov models. Moreover, it is at the heart of the insurance industry.

Geomorphology

Main article: Meander § Stochastic theory

The formation of river meanders has been analyzed as a stochastic process.

Language and linguistics

Non-deterministic approaches in language studies are largely inspired by the work of Ferdinand de Saussure, for example, in functionalist linguistic theory, which argues that competence is based on performance. This distinction in functional theories of grammar should be carefully distinguished from the langue and parole distinction. To the extent that linguistic knowledge is constituted by experience with language, grammar is argued to be probabilistic and variable rather than fixed and absolute. This conception of grammar as probabilistic and variable follows from the idea that one's competence changes in accordance with one's experience with language. Though this conception has been contested, it has also provided the foundation for modern statistical natural language processing and for theories of language learning and change.

Manufacturing

Manufacturing processes are assumed to be stochastic processes. This assumption is largely valid for either continuous or batch manufacturing processes. Testing and monitoring of the process is recorded using a process control chart which plots a given process control parameter over time. Typically a dozen or many more parameters will be tracked simultaneously. Statistical models are used to define limit lines which define when corrective actions must be taken to bring the process back to its intended operational window.

This same approach is used in the service industry where parameters are replaced by processes related to service level agreements.

Media

The marketing and the changing movement of audience tastes and preferences, as well as the solicitation of and the scientific appeal of certain film and television debuts (i.e., their opening weekends, word-of-mouth, top-of-mind knowledge among surveyed groups, star name recognition and other elements of social media outreach and advertising), are determined in part by stochastic modeling.

Medicine

See also: Stochastic theory of hematopoiesis

Stochastic effect, or "chance effect" is one classification of radiation effects that refers to the random, statistical nature of the damage. In contrast to the deterministic effect, severity is independent of dose. Only the probability of an effect increases with dose.

Music

In music, mathematical processes based on probability can generate stochastic elements.

Stochastic processes may be used in music to compose a fixed piece or may be produced in performance. Stochastic music was pioneered by Iannis Xenakis, who coined the term stochastic music. Specific examples of mathematics, statistics, and physics applied to music composition are the use of the statistical mechanics of gases in Pithoprakta, statistical distribution of points on a plane in Diamorphoses, minimal constraints in Achorripsis, the normal distribution in ST/10 and Atrées, Markov chains in Analogiques, game theory in Duel and Stratégie, group theory in Nomos Alpha (for Siegfried Palm), set theory in Herma and Eonta, and Brownian motion in N'Shima. Xenakis frequently used computers to produce his scores, such as the ST series including Morsima-Amorsima and Atrées, and founded CEMAMu. Earlier, John Cage and others had composed aleatoric or indeterminate music, which is created by chance processes but does not have the strict mathematical basis (Cage's Music of Changes, for example, uses a system of charts based on the I-Ching). Lejaren Hiller and Leonard Issacson used generative grammars and Markov chains in their 1957 Illiac Suite. Modern electronic music production techniques make these processes relatively simple to implement, and many hardware devices such as synthesizers and drum machines incorporate randomization features. Generative music techniques are therefore readily accessible to composers, performers, and producers.

Social sciences

Stochastic social science theory is similar to systems theory in that events are interactions of systems, although with a marked emphasis on unconscious processes. The event creates its own conditions of possibility, rendering it unpredictable if simply for the number of variables involved. Stochastic social science theory can be seen as an elaboration of a kind of 'third axis' in which to situate human behavior alongside the traditional 'nature vs. nurture' opposition. See Julia Kristeva on her usage of the 'semiotic', Luce Irigaray on reverse Heideggerian epistemology, and Pierre Bourdieu on polythetic space for examples of stochastic social science theory.

Subtractive color reproduction

When color reproductions are made, the image is separated into its component colors by taking multiple photographs filtered for each color. One resultant film or plate represents each of the cyan, magenta, yellow, and black data. Color printing is a binary system, where ink is either present or not present, so all color separations to be printed must be translated into dots at some stage of the work-flow. Traditional line screens which are amplitude modulated had problems with moiré but were used until stochastic screening became available. A stochastic (or frequency modulated) dot pattern creates a sharper image.

Cosmological constant problem

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Cosmological_constant_problem

 

Beyond the Standard Model
Simulated Large Hadron Collider CMS particle detector data depicting a Higgs boson produced by colliding protons decaying into hadron jets and electrons

Unsolved problem in physics

 

Why is the vacuum energy density much smaller than a zero-point energy suggested by quantum field theory?

In cosmology, the cosmological constant problem or vacuum catastrophe is the substantial disagreement between the observed values of vacuum energy density (the small value of the cosmological constant) and the much larger theoretical value of zero-point energy suggested by quantum field theory.

Depending on the cutoff of Planck energy and other factors, the quantum vacuum energy contribution to the effective cosmological constant is calculated to be between 50 and as many as 122 orders of magnitude greater than has actually been observed, a state of affairs described by physicists as "the largest discrepancy between theory and experiment in all of science" and "probably the worst theoretical prediction in the history of physics".

History

The idea that empty space might contain zero-point radiation energy was proposed by Walther Nernst in 1916. He predicted that the value had to be either zero or very small. In 1926, Wilhelm Lenz concluded that "If one allows waves of the shortest observed wavelengths λ ≈ 2 × 10⁻¹¹ cm, ... and if this radiation, converted to material density (u/c² ≈ 10⁶), contributed to the curvature of the observable universe – one would obtain a vacuum energy density of such a value that the radius of the observable universe would not reach even to the Moon." Wolfgang Pauli reached the same conclusion in 1933. The idea that the vacuum energy was related to the expansion of the universe was proposed by Georges Lemaître in 1934.

After the development of quantum field theory in the 1940s and the observation of the expansion of the universe in 1950s, the first to address contributions of quantum fluctuations to the cosmological constant was Yakov Zeldovich in the 1960s. In quantum mechanics, the vacuum itself should experience quantum fluctuations. In general relativity, those quantum fluctuations constitute energy that would add to the cosmological constant. However, Zeldovich calculated vacuum energy density was forty orders of magnitude bigger than the observed cosmological constant.

In the 1970s, due to the discovery of the electroweak interaction, another contribution was added to the cosmological constant due to spontaneous symmetry breaking, increasing the discrepancy. Later estimates of the degree of mismatch were as high as 120 to 122 orders of magnitude; Modern research suggests that, when Lorentz invariance is taken into account, the degree of mismatch is closer to 60 orders of magnitude. 

With the development of inflationary cosmology in the 1980s, the problem became much more important: as cosmic inflation is driven by vacuum energy, differences in modeling vacuum energy lead to huge differences in the resulting cosmologies. Were the vacuum energy precisely zero, as was once believed, then the expansion of the universe would not accelerate as observed, according to the standard Λ-CDM model.

In 1989, Steven Weinberg showed that the different contributions to the cosmological constant cannot, under general conditions, cancel without fine tuning their values, this result became known as Weinberg's no-go theorem. In the 2000s, Weinberg also proposed, what is sometimes called the new cosmological problem, which consist in finding a theory that matches its non-zero value. The new cosmological problem is often equated with the cosmic coincidence problem (the fact that energy density from dark matter and dark energy are of the same order of magnitude today).

Estimated values

The vacuum energy density of the Universe based on 2015 measurements by the Planck collaboration is ρ_vac = 5.96×10⁻²⁷ kg/m³ ≘ 5.3566×10⁻¹⁰ J/m³ = 3.35 GeV/m³ or about 2.5×10⁻⁴⁷ GeV⁴ in geometrized units.

One assessment, made by Jérôme Martin of the Institut d'Astrophysique de Paris in 2012, placed the expected theoretical vacuum energy scale around 10⁸ GeV⁴, for a difference of about 55 orders of magnitude.

Cutoff dependence and renormalization

The calculated vacuum energy is a positive, rather than negative, contribution to the cosmological constant because the existing vacuum has negative quantum-mechanical pressure, while in general relativity, the gravitational effect of negative pressure is a kind of repulsion. (Pressure here is defined as the flux of quantum-mechanical momentum across a surface.) Roughly, the vacuum energy is calculated by summing over all known quantum-mechanical fields, taking into account interactions and self-interactions between the ground states, and then removing all interactions below a minimum "cutoff" wavelength to reflect that existing theories break down and may fail to be applicable around the cutoff scale. Because the energy is dependent on how fields interact within the current vacuum state, the vacuum energy contribution would have been different in the early universe; for example, the vacuum energy would have been significantly different prior to electroweak symmetry breaking during the quark epoch.

The vacuum energy in quantum field theory can be set to any value by renormalization. This view treats the cosmological constant as simply another fundamental physical constant not predicted or explained by theory. Such a renormalization constant must be chosen very accurately because of the many-orders-of-magnitude discrepancy between theory and observation, and many theorists consider this ad-hoc constant as equivalent to ignoring the problem.

Using Planck mass as the cut-off for a cut-off regularization scheme provides a difference of 120 orders of magnitude between the vacuum energy and the cosmological constant. However this method violates Lorentz covariance. Using dimensional regularization instead, reduces this difference to about 56 orders of magnitude.

Proposed solutions

Some proposals involve modifying gravity to diverge from general relativity. These proposals face the hurdle that the results of observations and experiments so far have tended to be extremely consistent with general relativity and the ΛCDM model, and inconsistent with thus-far proposed modifications. In addition, some of the proposals are arguably incomplete, because they solve the "new" cosmological constant problem by proposing that the actual cosmological constant is exactly zero rather than a tiny number, but fail to solve the "old" cosmological constant problem of why quantum fluctuations seem to fail to produce substantial vacuum energy in the first place. Nevertheless, many physicists argue that, due in part to a lack of better alternatives, proposals to modify gravity should be considered "one of the most promising routes to tackling" the cosmological constant problem.

Bill Unruh and collaborators have argued that when the energy density of the quantum vacuum is modeled more accurately as a fluctuating quantum field, the cosmological constant problem does not arise. Going in a different direction, George F. R. Ellis and others have suggested that in unimodular gravity, the troublesome contributions simply do not gravitate. Recently, a fully diffeomorphism-invariant action principle that gives the equations of motion for trace-free Einstein gravity has been proposed, where the cosmological constant emerges as an integration constant.

Another argument, due to Stanley Brodsky and Robert Shrock, is that in light front quantization, the quantum field theory vacuum becomes essentially trivial. In the absence of vacuum expectation values, there is no contribution from quantum electrodynamics, weak interactions, and quantum chromodynamics to the cosmological constant. It is thus predicted to be zero in a flat spacetime. From light front quantization insight, the origin of the cosmological constant problem is traced back to unphysical non-causal terms in the standard calculation, which lead to an erroneously large value of the cosmological constant.

In 2018, a mechanism for cancelling Λ out has been proposed through the use of a symmetry breaking potential in a Lagrangian formalism in which matter shows a non-vanishing pressure. The model assumes that standard matter provides a pressure which counterbalances the action due to the cosmological constant. Luongo and Muccino have shown that this mechanism permits to take vacuum energy as quantum field theory predicts, but removing the huge magnitude through a counterbalance term due to baryons and cold dark matter only.

In 1999, Andrew Cohen, David B. Kaplan and Ann Nelson proposed that correlations between the UV and IR cutoffs in effective quantum field theory are enough to reduce the theoretical cosmological constant down to the measured cosmological constant due to the Cohen–Kaplan–Nelson (CKN) bound. In 2021, Nikita Blinov and Patrick Draper confirmed through the holographic principle that the CKN bound predicts the measured cosmological constant, all while maintaining the predictions of effective field theory in less extreme conditions.

Some propose an anthropic solution, and argue that we live in one region of a vast multiverse that has different regions with different vacuum energies. These anthropic arguments posit that only regions of small vacuum energy such as the one in which we live are reasonably capable of supporting intelligent life. Such arguments have existed in some form since at least 1981. Around 1987, Steven Weinberg estimated that the maximum allowable vacuum energy for gravitationally-bound structures to form is problematically large, even given the observational data available in 1987, and concluded the anthropic explanation appears to fail; however, more recent estimates by Weinberg and others, based on other considerations, find the bound to be closer to the actual observed level of dark energy. Anthropic arguments gradually gained credibility among many physicists after the discovery of dark energy and the development of the theoretical string theory landscape, but are still derided by a substantial skeptical portion of the scientific community as being problematic to verify. Proponents of anthropic solutions are themselves divided on multiple technical questions surrounding how to calculate the proportion of regions of the universe with various dark energy constants.