Bell's spaceship paradox

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https://en.wikipedia.org/wiki/Bell%27s_spaceship_paradox 

Above: In S the distance between the spaceships stays the same, while the string contracts. Below: In S′ the distance between the spaceships increases, while the string length stays the same.

Bell's spaceship paradox is a thought experiment in special relativity. It was first described by E. Dewan and M. Beran in 1959 but became more widely known after John Stewart Bell elaborated the idea further in 1976. A delicate thread hangs between two spaceships headed in the same direction. They start accelerating simultaneously and equally as measured in the inertial frame S, thus having the same velocity at all times as viewed from S. Therefore, they are all subject to the same Lorentz contraction, so the entire assembly seems to be equally contracted in the S frame with respect to the length at the start. At first sight, it might appear that the thread will not break during acceleration.

This argument, however, is incorrect as shown by Dewan and Beran, and later Bell. The distance between the spaceships does not undergo Lorentz contraction with respect to the distance at the start, because in S, it is effectively defined to remain the same, due to the equal and simultaneous acceleration of both spaceships in S. It also turns out that the rest length between the two has increased in the frames in which they are momentarily at rest (S′), because the accelerations of the spaceships are not simultaneous here due to relativity of simultaneity. The thread, on the other hand, being a physical object held together by electrostatic forces, maintains the same rest length. Thus, in frame S, it must be Lorentz contracted, which result can also be derived when the electromagnetic fields of bodies in motion are considered. So, calculations made in both frames show that the thread will break; in S′ due to the non-simultaneous acceleration and the increasing distance between the spaceships, and in S due to length contraction of the thread.

In the following, the rest length or proper length of an object is its length measured in the object's rest frame. (This length corresponds to the proper distance between two events in the special case, when these events are measured simultaneously at the endpoints in the object's rest frame.)

Dewan and Beran

Dewan and Beran stated the thought experiment by writing:

"Consider two identically constructed rockets at rest in an inertial frame S. Let them face the same direction and be situated one behind the other. If we suppose that at a prearranged time both rockets are simultaneously (with respect to S) fired up, then their velocities with respect to S are always equal throughout the remainder of the experiment (even though they are functions of time). This means, by definition, that with respect to S the distance between the two rockets does not change even when they speed up to relativistic velocities."

Then this setup is repeated again, but this time the back of the first rocket is connected with the front of the second rocket by a silk thread. They concluded:

"According to the special theory the thread must contract with respect to S because it has a velocity with respect to S. However, since the rockets maintain a constant distance apart with respect to S, the thread (which we have assumed to be taut at the start) cannot contract: therefore a stress must form until for high enough velocities the thread finally reaches its elastic limit and breaks."

Dewan and Beran also discussed the result from the viewpoint of inertial frames momentarily comoving with the first rocket, by applying a Lorentz transformation:

"Since ${\displaystyle t^{\prime }=(t-vx/c^2)/\sqrt{1-v^2/c^2}}$, (..) each frame used here has a different synchronization scheme because of the ${\displaystyle vx/c^2}$ factor. It can be shown that as ${\displaystyle v}$ increases, the front rocket will not only appear to be a larger distance from the back rocket with respect to an instantaneous inertial frame, but also to have started at an earlier time."

They concluded:

"One may conclude that whenever a body is constrained to move in such a way that all parts of it have the same acceleration with respect to an inertial frame (or, alternatively, in such a way that with respect to an inertial frame its dimensions are fixed, and there is no rotation), then such a body must in general experience relativistic stresses."

Then they discussed the objection, that there should be no difference between a) the distance between two ends of a connected rod, and b) the distance between two unconnected objects which move with the same velocity with respect to an inertial frame. Dewan and Beran removed those objections by arguing:

• Since the rockets are constructed exactly the same way, and starting at the same moment in S with the same acceleration, they must have the same velocity all of the time in S. Thus, they are traveling the same distances in S, so their mutual distance cannot change in this frame. Otherwise, if the distance were to contract in S, then this would imply different velocities of the rockets in this frame as well, which contradicts the initial assumption of equal construction and acceleration.
• They also argued that there indeed is a difference between a) and b): Case a) is the ordinary case of length contraction, based on the concept of the rod's rest length l₀ in S₀, which always stays the same as long as the rod can be seen as rigid. Under those circumstances, the rod is contracted in S. But the distance cannot be seen as rigid in case b) because it is increasing due to unequal accelerations in S₀, and the rockets would have to exchange information with each other and adjust their velocities in order to compensate for this – all of those complications don't arise in case a).

Bell

Vertical arrangement as suggested by Bell.

In Bell's version of the thought experiment, three spaceships A, B and C are initially at rest in a common inertial reference frame, B and C being equidistant to A. Then, a signal is sent from A to reach B and C simultaneously, causing B and C starting to accelerate in the vertical direction (having been pre-programmed with identical acceleration profiles), while A stays at rest in its original reference frame. According to Bell, this implies that B and C (as seen in A's rest frame) "will have at every moment the same velocity, and so remain displaced one from the other by a fixed distance." Now, if a fragile thread is tied between B and C, it's not long enough anymore due to length contractions, thus it will break. He concluded that "the artificial prevention of the natural contraction imposes intolerable stress".

Bell reported that he encountered much skepticism from "a distinguished experimentalist" when he presented the paradox. To attempt to resolve the dispute, an informal and non-systematic survey of opinion at CERN was held. According to Bell, there was "clear consensus" which asserted, incorrectly, that the string would not break. Bell goes on to add,

"Of course, many people who get the wrong answer at first get the right answer on further reflection. Usually they feel obliged to work out how things look to observers B or C. They find that B, for example, sees C drifting further and further behind, so that a given piece of thread can no longer span the distance. It is only after working this out, and perhaps only with a residual feeling of unease, that such people finally accept a conclusion which is perfectly trivial in terms of A's account of things, including the Fitzgerald contraction."

Importance of length contraction

In general, it was concluded by Dewan & Beran and Bell, that relativistic stresses arise when all parts of an object are accelerated the same way with respect to an inertial frame, and that length contraction has real physical consequences. For instance, Bell argued that the length contraction of objects as well as the lack of length contraction between objects in frame S can be explained using relativistic electromagnetism. The distorted electromagnetic intermolecular fields cause moving objects to contract, or to become stressed if hindered from doing so. In contrast, no such forces act on the space between objects. (Generally, Richard Feynman demonstrated how the Lorentz transformation can be derived from the case of the potential of a charge moving with constant velocity (as represented by the Liénard–Wiechert potential). As to the historical aspect, Feynman alluded to the circumstance that Hendrik Lorentz arrived essentially the same way at the Lorentz transformation, see also History of Lorentz transformations.)

However, Petkov (2009) and Franklin (2009) interpret this paradox differently. They agreed with the result that the string will break due to unequal accelerations in the rocket frames, which causes the rest length between them to increase (see the Minkowski diagram in the analysis section). However, they denied the idea that those stresses are caused by length contraction in S. This is because, in their opinion, length contraction has no "physical reality", but is merely the result of a Lorentz transformation, i.e. a rotation in four-dimensional space which by itself can never cause any stress at all. Thus the occurrence of such stresses in all reference frames including S and the breaking of the string is supposed to be the effect of relativistic acceleration alone.

Discussions and publications

Paul Nawrocki (1962) gives three arguments why the string should not break, while Edmond Dewan (1963) showed in a reply that his original analysis still remains valid. Many years later and after Bell's book, Matsuda and Kinoshita reported receiving much criticism after publishing an article on their independently rediscovered version of the paradox in a Japanese journal. Matsuda and Kinoshita do not cite specific papers, however, stating only that these objections were written in Japanese.

However, in most publications it is agreed that the string will break, with some reformulations, modifications and different scenarios, such as by Evett & Wangsness (1960), Dewan (1963), Romain (1963), Evett (1972), Gershtein & Logunov (1998), Tartaglia & Ruggiero (2003), Cornwell (2005), Flores (2005), Semay (2006), Styer (2007), Freund (2008), Redzic (2008), Peregoudov (2009), Redžić (2009), Gu (2009), Petkov (2009), Franklin (2009), Miller (2010), Fernflores (2011), Kassner (2012), Natario (2014), Lewis, Barnes & Sticka (2018), Bokor (2018). A similar problem was also discussed in relation to angular accelerations: Grøn (1979), MacGregor (1981), Grøn (1982, 2003).

Immediate acceleration

Minkowski diagram: Length ${\displaystyle L^{\prime }}$ between the ships in S′ after acceleration is longer than the previous length ${\displaystyle L_{old}^{\prime }}$ in S′, and longer than the unchanged length ${\displaystyle L}$ in S. The thin lines are "lines of simultaneity".

 

Loedel diagram of the same scenario

Similarly, in the case of Bell's spaceship paradox the relation between the initial rest length ${\displaystyle L}$ between the ships (identical to the moving length in S after acceleration) and the new rest length ${\displaystyle L^{\prime }}$ in S′ after acceleration, is:

${\displaystyle L^{\prime }=\gamma L}$.

This length increase can be calculated in different ways. For instance, if the acceleration is finished the ships will constantly remain at the same location in the final rest frame S′, so it's only necessary to compute the distance between the x-coordinates transformed from S to S′. If ${\displaystyle x_A}$ and ${\displaystyle x_B=x_A+L}$ are the ships' positions in S, the positions in their new rest frame S′ are:

${\displaystyle \begin{array}{rl}{x}_A^{\prime }& =\gamma \left(x_A-vt\right)\\ x_B^{\prime }& =\gamma \left(x_A+L-vt\right)\\ L^{\prime }& =x_B^{\prime }-x_A^{\prime }\\ & =\gamma L\end{array}}$

Another method was shown by Dewan (1963) who demonstrated the importance of relativity of simultaneity. The perspective of frame S′ is described, in which both ships will be at rest after the acceleration is finished. The ships are accelerating simultaneously at ${\displaystyle t_A=t_B}$ in S (assuming acceleration in infinitesimal small time), though B is accelerating and stopping in S′ before A due to relativity of simultaneity, with the time difference:

${\displaystyle \begin{array}{rl}\mathrm{\Delta }{t}^{\prime }& =t_B^{\prime }-t_A^{\prime }=\gamma \left(t_B-\frac{v{x}_B}{c^2}\right)-\gamma \left(t_A-\frac{v{x}_A}{c^2}\right)\\ & =\frac{\gamma vL}{c^2}\end{array}}$

Since the ships are moving with the same velocity in S′ before acceleration, the initial rest length ${\displaystyle L}$ in S is shortened in S′ by ${\displaystyle L_{old}^{\prime }=L/\gamma }$ due to length contraction. From the frame of S′, B starts accelerating before A and also stops accelerating before A. Due to this B will always have higher velocity than A up until the moment A is finished accelerating too, and both of them are at rest with respect to S′. The distance between B and A keeps on increasing till A stops accelerating. Although A's acceleration timeline is delayed by an offset of ${\displaystyle \mathrm{\Delta }{t}^{\prime }}$, both A and B cover the same distance in their respective accelerations. But B's timeline contains acceleration and also being at rest in S` for ${\displaystyle \mathrm{\Delta }{t}^{\prime }}$ till A stops accelerating. Hence the extra distance covered by B during the entire course can be calculated by measuring the distance traveled by B during this phase. Dewan arrived at the relation (in different notation):

${\displaystyle \begin{array}{rl}{L}^{\prime }& =L_{old}^{\prime }+v\mathrm{\Delta }{t}^{\prime }=\frac{L}{\gamma }+\frac{\gamma v^{2}L}{c^2}\\ & =\gamma L\end{array}}$

It was also noted by several authors that the constant length in S and the increased length in S′ is consistent with the length contraction formula ${\displaystyle L=L^{\prime }/\gamma }$, because the initial rest length ${\displaystyle L}$ is increased by ${\displaystyle \gamma }$ in S′, which is contracted in S by the same factor, so it stays the same in S:

${\displaystyle L_{contr.}=L^{\prime }/\gamma =\gamma L/\gamma =L}$

Summarizing: While the rest distance between the ships increases to ${\displaystyle \gamma L}$ in S′, the relativity principle requires that the string (whose physical constitution is unaltered) maintains its rest length ${\displaystyle L}$ in its new rest system S′. Therefore, it breaks in S′ due to the increasing distance between the ships. As explained above, the same is also obtained by only considering the start frame S using length contraction of the string (or the contraction of its moving molecular fields) while the distance between the ships stays the same due to equal acceleration.

Constant proper acceleration

The world lines (navy blue curves) of two observers A and B who accelerate in the same direction with the same constant magnitude proper acceleration (hyperbolic motion). At A′ and B′, the observers stop accelerating.

 

Two observers in Born rigid acceleration, having the same Rindler horizon. They can choose the proper time of one of them as the coordinate time of the Rindler frame.

 

Two observers having the same proper acceleration (Bell's spaceships). They are not at rest in the same Rindler frame, and therefore have different Rindler horizons

 

Main articles: Hyperbolic motion (relativity), Rindler coordinates, and Born rigidity

Instead of instantaneous changes of direction, special relativity also allows to describe the more realistic scenario of constant proper acceleration, i.e. the acceleration indicated by a comoving accelerometer. This leads to hyperbolic motion, in which the observer continuously changes momentary inertial frames

${\displaystyle \begin{array}{rl}x& =\frac{c^2}{\alpha }\left(\sqrt{1+{\left(\frac{\alpha t}{c}\right)}^2}-1\right)=\frac{c^2}{\alpha }\left(\cosh \frac{\alpha \tau }{c}-1\right)\\ c\tau & =\frac{c^2}{\alpha }\mathrm{asinh}\frac{\alpha t}{c},ct=\frac{c^2}{\alpha }\sinh \frac{\alpha \tau }{c}\end{array}}$

where ${\displaystyle t}$ is the coordinate time in the external inertial frame, and ${\displaystyle \tau }$ the proper time in the momentary frame, and the momentary velocity is given by

${\displaystyle v=\frac{\alpha t}{\sqrt{1+{\left(\frac{\alpha t}{c}\right)}^2}}=c\tanh \frac{\alpha \tau }{c}}$

The mathematical treatment of this paradox is similar to the treatment of Born rigid motion. However, rather than ask about the separation of spaceships with the same acceleration in an inertial frame, the problem of Born rigid motion asks, "What acceleration profile is required by the second spaceship so that the distance between the spaceships remains constant in their proper frame?" In order for the two spaceships, initially at rest in an inertial frame, to maintain a constant proper distance, the lead spaceship must have a lower proper acceleration.

This Born rigid frame can be described by using Rindler coordinates (Kottler-Møller coordinates)

${\displaystyle \begin{array}{rlrl}ct& =\left(x^{\prime }+\frac{c^2}{\alpha }\right)\sinh \frac{\alpha t^{\prime }}{c},& y& =y^{\prime },\\ x& =\left(x^{\prime }+\frac{c^2}{\alpha }\right)\cosh \frac{\alpha t^{\prime }}{c}-\frac{c^2}{\alpha },& z& =z^{\prime }.\end{array}(t^{\prime }=\tau )}$

The condition of Born rigidity requires that the proper acceleration of the spaceships differs by

${\displaystyle {\alpha }_2=\frac{{\alpha }_1}{1+\frac{{\alpha }_1{L}^{\prime }}{c^2}}}$

and the length ${\displaystyle L^{\prime }=x_2^{\mathrm{\prime }}-x_1^{\mathrm{\prime }}}$ measured in the Rindler frame (or momentary inertial frame) by one of the observers is Lorentz contracted to ${\displaystyle L=x_2-x_1}$ in the external inertial frame by

${\displaystyle L=\frac{L^{\prime }}{\cosh \frac{\alpha t^{\prime }}{c}}=L^{\prime }\sqrt{1-\frac{v^2}{c^2}}}$

which is the same result as above. Consequently, in the case of Born rigidity, the constancy of length L' in the momentary frame implies that L in the external frame decreases constantly, the thread doesn't break. However, in the case of Bell's spaceship paradox the condition of Born rigidity is broken, because the constancy of length L in the external frame implies that L' in the momentary frame increases, the thread breaks (in addition, the expression for the distance increase between two observers having the same proper acceleration becomes also more complicated in the momentary frame).

Prosody (linguistics)

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Prosody_(linguistics)

In linguistics, prosody (/ˈprɒsədi, ˈprɒzədi/) is the study of elements of speech that are not individual phonetic segments (vowels and consonants) but which are properties of syllables and larger units of speech, including linguistic functions such as intonation, stress, and rhythm. Such elements are known as suprasegmentals.

Prosody may reflect features of the speaker or the utterance: their emotional state; the form of utterance (statement, question, or command); the presence of irony or sarcasm; emphasis, contrast, and focus. It may reflect elements of language not encoded by grammar, punctuation or choice of vocabulary.

Attributes of prosody

In the study of prosodic aspects of speech, it is usual to distinguish between auditory measures (subjective impressions produced in the mind of the listener) and objective measures (physical properties of the sound wave and physiological characteristics of articulation that may be measured objectively). Auditory (subjective) and objective (acoustic and articulatory) measures of prosody do not correspond in a linear way. Most studies of prosody have been based on auditory analysis using auditory scales.

There is no agreed number of prosodic variables. In auditory terms, the major variables are:

• the pitch of the voice (varying between low and high)
• length of sounds (varying between short and long)
• loudness, or prominence (varying between soft and loud)
• timbre or phonatory quality (quality of sound)

In acoustic terms, these correspond reasonably closely to:

• fundamental frequency (measured in hertz, or cycles per second)
• duration (measured in time units such as milliseconds or seconds)
• intensity, or sound pressure level (measured in decibels)
• spectral characteristics (distribution of energy at different parts of the audible frequency range)

Different combinations of these variables are exploited in the linguistic functions of intonation and stress, as well as other prosodic features such as rhythm and tempo. Additional prosodic variables have been studied, including voice quality and pausing. The behavior of the prosodic variables can be studied either as contours across the prosodic unit or by the behavior of boundaries.

Phonology

Prosodic features are suprasegmental, since they are properties of units of speech that are defined over groups of sounds rather than single segments. When talking about prosodic features, it is important to distinguish between the personal characteristics that belong to an individual's voice (for example, their habitual pitch range, intonation patterns, etc.) and the independently variable prosodic features that are used contrastively to communicate meaning (for example, the use of changes in pitch to indicate the difference between statements and questions). Personal characteristics that belong to an individual are not linguistically significant while prosodic features are. It is not clear which aspects of prosody are found in all languages and which are specific to particular languages and dialects.

Intonation

Main article: Intonation (linguistics)

Some writers (e.g., O'Connor and Arnold)  have described intonation entirely in terms of pitch, while others (e.g., Crystal)  propose that "intonation" is a combination of several prosodic variables. English intonation is often said to be based on three aspects:

• The division of speech into units
• The highlighting of particular words and syllables
• The choice of pitch movement (e.g., fall or rise)

The choice of pitch movement and the highlighting of particular words to create different intonation patterns can be seen in the following English examples:

"That's a cat?"

"Yup. That's a cat."

"A cat? I thought it was a mountain lion!"

The example above is an example of using intonation to highlight particular words and to employ rising and falling of pitch to change meaning. If read out-loud, the pitch of your voice moves in different directions on word "cat." In the first line, the pitch goes up indicating a question. In the second line, pitch falls indicating a statement or confirmation. Finally, in the third line, a complicated rise-fall pattern indicates incredulity. Each pitch/intonation pattern communicates a different meaning.

An additional pitch-related variation is pitch range; speakers are capable of speaking with a wide range of pitch (this is usually associated with excitement), while at other times with a narrow range. English makes use of changes in key; shifting one's intonation into the higher or lower part of one's pitch range is believed to be meaningful in certain contexts.

Stress

Stress functions as the means of making a syllable prominent. Stress may be studied in relation to individual words (named "word stress" or lexical stress) or in relation to larger units of speech (traditionally referred to as "sentence stress" but more appropriately named "prosodic stress"). Stressed syllables are made prominent by several variables. Stress is typically associated with the following:

• pitch prominence (a pitch level that is different from that of neighboring syllables, or a pitch movement)
• increased length (duration)
• increased loudness (dynamics)
• differences in timbre: in English and some other languages, stress is associated with aspects of vowel quality (whose acoustic correlate is the formant frequencies or spectrum of the vowel). Unstressed vowels tend to be centralized relative to stressed vowels, which are normally more peripheral in quality.

Some of these cues are more powerful or prominent than others. Alan Cruttenden, for example, writes "Perceptual experiments have clearly shown that, in English at any rate, the three features (pitch, length and loudness) form a scale of importance in bringing syllables into prominence, pitch being the most efficacious, and loudness the least so".

When pitch prominence is the major factor, the resulting prominence is often called accent rather than stress.

There is considerable variation from language to language concerning the role of stress in identifying words or in interpreting grammar and syntax.

Tempo

Main article: Speech tempo

Rhythm

Although rhythm is not a prosodic variable in the way that pitch or loudness are, it is usual to treat a language's characteristic rhythm as a part of its prosodic phonology. It has often been asserted that languages exhibit regularity in the timing of successive units of speech, a regularity referred to as isochrony, and that every language may be assigned one of three rhythmical types: stress-timed (where the durations of the intervals between stressed syllables is relatively constant), syllable-timed (where the durations of successive syllables are relatively constant) and mora-timed (where the durations of successive morae are relatively constant). As explained in the isochrony article, this claim has not been supported by scientific evidence.

Pause

See also: Pausa

Voiced or unvoiced, the pause is a form of interruption to articulatory continuity such as an open or terminal juncture. Conversation analysis commonly notes pause length. Distinguishing auditory hesitation from silent pauses is one challenge. Contrasting junctures within and without word chunks can aid in identifying pauses.

There are a variety of "filled" pause types. Formulaic language pause fillers include "Like", "Er" and "Uhm", and paralinguistic expressive respiratory pauses include the sigh and gasp.

Although related to breathing, pauses may contain contrastive linguistic content, as in the periods between individual words in English advertising voice-over copy sometimes placed to denote high information content, e.g. "Quality. Service. Value."

Chunking

Pausing or its lack contributes to the perception of word groups, or chunks. Examples include the phrase, phraseme, constituent or interjection. Chunks commonly highlight lexical items or fixed expression idioms. Chunking prosody is present on any complete utterance and may correspond to a syntactic category, but not necessarily. The well-known English chunk "Know what I mean?" in common usage sounds like a single word ("No-wada-MEEN?") due to blurring or rushing the articulation of adjacent word syllables, thereby changing the potential open junctures between words into closed junctures.

Cognitive aspects

Intonation is said to have a number of perceptually significant functions in English and other languages, contributing to the recognition and comprehension of speech.

Grammar

It is believed that prosody assists listeners in parsing continuous speech and in the recognition of words, providing cues to syntactic structure, grammatical boundaries and sentence type. Boundaries between intonation units are often associated with grammatical or syntactic boundaries; these are marked by such prosodic features as pauses and slowing of tempo, as well as "pitch reset" where the speaker's pitch level returns to the level typical of the onset of a new intonation unit. In this way potential ambiguities may be resolved. For example, the sentence "They invited Bob and Bill and Al got rejected" is ambiguous when written, although addition of a written comma after either "Bob" or "Bill" will remove the sentence's ambiguity. But when the sentence is read aloud, prosodic cues like pauses (dividing the sentence into chunks) and changes in intonation will reduce or remove the ambiguity. Moving the intonational boundary in cases such as the above example will tend to change the interpretation of the sentence. This result has been found in studies performed in both English and Bulgarian. Research in English word recognition has demonstrated an important role for prosody.

Focus

Intonation and stress work together to highlight important words or syllables for contrast and focus. This is sometimes referred to as the accentual function of prosody. A well-known example is the ambiguous sentence "I never said she stole my money", where there are seven meaning changes depending on which of the seven words is vocally highlighted. However, there is a longer example, "I messaged you because it's been bothering me", which has eight different meaning depending on which word is stressed.

Discourse

Prosody plays a role in the regulation of conversational interaction and in signaling discourse structure. David Brazil and his associates studied how intonation can indicate whether information is new or already established; whether a speaker is dominant or not in a conversation; and when a speaker is inviting the listener to make a contribution to the conversation.

Emotion

Main article: Emotional prosody

Prosody is also important in signalling emotions and attitudes. When this is involuntary (as when the voice is affected by anxiety or fear), the prosodic information is not linguistically significant. However, when the speaker varies his speech intentionally, for example to indicate sarcasm, this usually involves the use of prosodic features. The most useful prosodic feature in detecting sarcasm is a reduction in the mean fundamental frequency relative to other speech for humor, neutrality, or sincerity. While prosodic cues are important in indicating sarcasm, context clues and shared knowledge are also important.

Emotional prosody was considered by Charles Darwin in The Descent of Man to predate the evolution of human language: "Even monkeys express strong feelings in different tones – anger and impatience by low, – fear and pain by high notes." Native speakers listening to actors reading emotionally neutral text while projecting emotions correctly recognized happiness 62% of the time, anger 95%, surprise 91%, sadness 81%, and neutral tone 76%. When a database of this speech was processed by computer, segmental features allowed better than 90% recognition of happiness and anger, while suprasegmental prosodic features allowed only 44%–49% recognition. The reverse was true for surprise, which was recognized only 69% of the time by segmental features and 96% of the time by suprasegmental prosody. In typical conversation (no actor voice involved), the recognition of emotion may be quite low, of the order of 50%, hampering the complex interrelationship function of speech advocated by some authors. However, even if emotional expression through prosody cannot always be consciously recognized, tone of voice may continue to have subconscious effects in conversation. This sort of expression stems not from linguistic or semantic effects, and can thus be isolated from traditional linguistic content. Aptitude of the average person to decode conversational implicature of emotional prosody has been found to be slightly less accurate than traditional facial expression discrimination ability; however, specific ability to decode varies by emotion. These emotional have been determined to be ubiquitous across cultures, as they are utilized and understood across cultures. Various emotions, and their general experimental identification rates, are as follows:

• Anger and sadness: High rate of accurate identification
• Fear and happiness: Medium rate of accurate identification
• Disgust: Poor rate of accurate identification

The prosody of an utterance is used by listeners to guide decisions about the emotional affect of the situation. Whether a person decodes the prosody as positive, negative, or neutral plays a role in the way a person decodes a facial expression accompanying an utterance. As the facial expression becomes closer to neutral, the prosodic interpretation influences the interpretation of the facial expression. A study by Marc D. Pell revealed that 600 ms of prosodic information is necessary for listeners to be able to identify the affective tone of the utterance. At lengths below this, there was not enough information for listeners to process the emotional context of the utterance.

Child language

Unique prosodic features have been noted in infant-directed speech (IDS) - also known as baby talk, child-directed speech (CDS), or "motherese". Adults, especially caregivers, speaking to young children tend to imitate childlike speech by using higher and more variable pitch, as well as an exaggerated stress. These prosodic characteristics are thought to assist children in acquiring phonemes, segmenting words, and recognizing phrasal boundaries. And though there is no evidence to indicate that infant-directed speech is necessary for language acquisition, these specific prosodic features have been observed in many different languages.

Aprosodia

An aprosodia is an acquired or developmental impairment in comprehending or generating the emotion conveyed in spoken language. Aprosody is often accompanied by the inability to properly utilize variations in speech, particularly with deficits in ability to accurately modulate pitch, loudness, intonation, and rhythm of word formation. This is seen sometimes in persons with Asperger syndrome.

Brain regions involved

Producing these nonverbal elements requires intact motor areas of the face, mouth, tongue, and throat. This area is associated with Brodmann areas 44 and 45 (Broca's area) of the left frontal lobe. Damage to areas 44/45, specifically on the right hemisphere, produces motor aprosodia, with the nonverbal elements of speech being disturbed (facial expression, tone, rhythm of voice).

Understanding these nonverbal elements requires an intact and properly functioning right-hemisphere perisylvian area, particularly Brodmann area 22 (not to be confused with the corresponding area in the left hemisphere, which contains Wernicke's area). Damage to the right inferior frontal gyrus causes a diminished ability to convey emotion or emphasis by voice or gesture, and damage to right superior temporal gyrus causes problems comprehending emotion or emphasis in the voice or gestures of others. The right Brodmann area 22 aids in the interpretation of prosody, and damage causes sensory aprosodia, with the patient unable to comprehend changes in voice and body language.

Cerebral hemisphere

From Wikipedia, the free encyclopedia

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

Cerebral hemisphere
Human brain seen from front.
Right cerebral hemisphere   Left cerebral hemisphere

The vertebrate cerebrum (brain) is formed by two cerebral hemispheres that are separated by a groove, the longitudinal fissure. The brain can thus be described as being divided into left and right cerebral hemispheres. Each of these hemispheres has an outer layer of grey matter, the cerebral cortex, that is supported by an inner layer of white matter. In eutherian (placental) mammals, the hemispheres are linked by the corpus callosum, a very large bundle of nerve fibers. Smaller commissures, including the anterior commissure, the posterior commissure and the fornix, also join the hemispheres and these are also present in other vertebrates. These commissures transfer information between the two hemispheres to coordinate localized functions.

There are three known poles of the cerebral hemispheres: the occipital pole, the frontal pole, and the temporal pole.

The central sulcus is a prominent fissure which separates the parietal lobe from the frontal lobe and the primary motor cortex from the primary somatosensory cortex.

Macroscopically the hemispheres are roughly mirror images of each other, with only subtle differences, such as the Yakovlevian torque seen in the human brain, which is a slight warping of the right side, bringing it just forward of the left side. On a microscopic level, the cytoarchitecture of the cerebral cortex, shows the functions of cells, quantities of neurotransmitter levels and receptor subtypes to be markedly asymmetrical between the hemispheres. However, while some of these hemispheric distribution differences are consistent across human beings, or even across some species, many observable distribution differences vary from individual to individual within a given species.

Structure

Each cerebral hemisphere has an outer layer of cerebral cortex which is of grey matter and in the interior of the cerebral hemispheres is an inner layer or core of white matter known as the centrum semiovale. The interior portion of the hemispheres of the cerebrum includes the lateral ventricles, the basal ganglia, and the white matter.

Poles

Poles of cerebral hemispheres

There are three poles of the cerebrum, the occipital pole, the frontal pole, and the temporal pole. The occipital pole is the posterior end of each occipital lobe in each hemisphere. It is more pointed than the rounder frontal pole. The frontal pole is at the frontmost part of the frontal lobe in each hemisphere, and is more rounded than the occipital pole. The temporal pole is located between the frontal and occipital poles, and sits in the anterior part of middle cranial fossa in each temporal lobe.

Composition

If the upper part of either hemisphere is removed, at a level about 1.25 cm above the corpus callosum, the central white matter will be exposed as an oval-shaped area, the centrum semiovale, surrounded by a narrow convoluted margin of gray substance, and studded with numerous minute red dots (puncta vasculosa), produced by the escape of blood from divided blood vessels.

If the remaining portions of the hemispheres be slightly drawn apart a broad band of white substance, the corpus callosum, will be observed, connecting them at the bottom of the longitudinal fissure; the margins of the hemispheres which overlap the corpus callosum are called the labia cerebri.

Each labium is part of the cingulate gyrus already described; and the groove between it and the upper surface of the corpus callosum is termed the callosal sulcus.

If the hemispheres are sliced off to a level with the upper surface of the corpus callosum, the white substance of that structure will be seen connecting the two hemispheres.

The large expanse of medullary matter now exposed, surrounded by the convoluted margin of gray substance, is called the centrum semiovale. The blood supply to the centrum semiovale is from the superficial middle cerebral artery. The cortical branches of this artery descend to provide blood to the centrum semiovale.

Development

The cerebral hemispheres are derived from the telencephalon. They arise five weeks after conception as bilateral invaginations of the walls. The hemispheres grow round in a C-shape and then back again, pulling all structures internal to the hemispheres (such as the ventricles) with them. The intraventricular foramina (also called the foramina of Monro) allows communication with the lateral ventricles. The choroid plexus is formed from ependymal cells and vascular mesenchyme.

Function

Hemisphere lateralization

Main article: Lateralization of brain function

Broad generalizations are often made in popular psychology about certain functions (e.g. logic, creativity) being lateralized, that is, located in the right or left side of the brain. These claims are often inaccurate, as most brain functions are actually distributed across both hemispheres. Most scientific evidence for asymmetry relates to low-level perceptual functions rather than the higher-level functions popularly discussed (e.g. subconscious processing of grammar, not "logical thinking" in general). In addition to this lateralization of some functions, the low-level representations also tend to represent the contralateral side of the body.

The best example of an established lateralization is that of Broca's and Wernicke's Areas (language) where both are often found exclusively on the left hemisphere. These areas frequently correspond to handedness however, meaning the localization of these areas is regularly found on the hemisphere opposite to the dominant hand. Function lateralization, such as semantics, intonation, accentuation, and prosody, has since been called into question and largely been found to have a neuronal basis in both hemispheres.

Cerebral hemispheres of a human embryo at 8 weeks.

Perceptual information is processed in both hemispheres, but is laterally partitioned: information from each side of the body is sent to the opposite hemisphere (visual information is partitioned somewhat differently, but still lateralized). Similarly, motor control signals sent out to the body also come from the hemisphere on the opposite side. Thus, hand preference (which hand someone prefers to use) is also related to hemisphere lateralization.

In some aspects, the hemispheres are asymmetrical; the right side is slightly bigger. There are higher levels of the neurotransmitter norepinephrine on the right and higher levels of dopamine on the left. There is more white matter (longer axons) on the right and more grey matter (cell bodies) on the left.

Linear reasoning functions of language such as grammar and word production are often lateralized to the left hemisphere of the brain. In contrast, holistic reasoning functions of language such as intonation and emphasis are often lateralized to the right hemisphere of the brain. Other integrative functions such as intuitive or heuristic arithmetic, binaural sound localization, etc. seem to be more bilaterally controlled.

Clinical significance

Infarcts of the centrum ovale can occur.

As a treatment for epilepsy the corpus callosum may be severed to cut the major connection between the hemispheres in a procedure known as a corpus callosotomy.

A hemispherectomy is the removal or disabling of one of the hemispheres of the brain. This is a rare procedure used in some extreme cases of seizures which are unresponsive to other treatments.