History of the Alps

From Wikipedia, the free encyclopedia

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

View of the Matterhorn within the Alps

The valleys of the Alps have been inhabited since prehistoric times. The Alpine culture, which developed there, centers on transhumance.

Currently the Alps are divided among eight states: France, Monaco, Italy, Switzerland, Liechtenstein, Austria, Germany and Slovenia. In 1991 the Alpine Convention was established to regulate this transnational area, whose area measures about 190,000 square kilometres (73,000 sq mi).

Early history (before 1200)

The Wildkirchli caves in the Appenzell Alps show traces of Neanderthal habitation (about 40,000 BCE). During the Würm glaciation (up to c. 11700 BP), the entire Alps were covered in ice. Anatomically modern humans reach the Alpine region by c. 30,000 years ago. MtDNA Haplogroup K (believed to have originated in the mid-Upper Paleolithic, between about 30,000 and 22,000 years ago, with an estimated age here of c. 12,000 years BP), is a genetic marker associated with southeastern Alpine region.

Traces of transhumance appear in the neolithic. In the Bronze Age, the Alps formed the boundary of the Urnfield and Terramare cultures. The mummy found on the Ötztaler Alps, known as "Ötzi the Iceman," lived c. 3200 BC. At that stage the population in its majority had already changed from an economy based on hunting and gathering to one based on agriculture and animal husbandry. It is still an open question whether forms of pastoral mobility, such as transhumance (alpiculture), already existed in prehistory.

The earliest historical accounts date to the Roman period, mostly due to Greco-Roman ethnography, with some epigraphic evidence due to the Raetians, Lepontii and Gauls, with Ligurians and Venetii occupying the fringes in the southwest and southeast, respectively (Cisalpine Gaul) during the 4th and 3rd centuries BC. The Rock Drawings in Valcamonica date to this period. A few details have come down to modern scholars of the conquest of many of the Alpine tribes by Augustus, as well as Hannibal's battles across the Alps. Most of the local Gallic tribes allied themselves with the Carthaginians in the Second Punic War, for the duration of which Rome lost control over most of Northern Italy. The Roman conquest of Italy was only complete after the Roman victory over Carthage, by the 190s BC.

Satellite photo showing the Alps in winter, at the top of the Italian peninsula.

Between 35 and 6 BC, the Alpine region was gradually integrated into the expanding Roman Empire. The contemporary monument Tropaeum Alpium in La Turbie celebrates the victory won by the Romans over 46 tribes in these mountains. The subsequent construction of roads over the Alpine passes first permitted southern and northern Roman settlements in the Alps to be connected, and eventually integrated the inhabitants of the Alps into the culture of the Empire. The upper Rhône valley or Vallis Poenina fell to the Romans after a battle at Octodurus (Martigny) in 57 BC. Aosta was founded in 25 BC as Augusta Praetoria Salassorum in the former territory of the Salassi. Raetia was conquered in 15 BC.

With the division of the Roman Empire and the collapse of its Western part in the fourth and fifth centuries, power relations in the Alpine region reverted to their local dimensions. Often dioceses became important centres. While in Italy and Southern France, dioceses in the Western Alps were established early (beginning in the fourth century) and resulted in numerous small sees, in the Eastern Alps such foundations continued into the thirteenth century and the dioceses were usually larger. New monasteries in the mountain valleys also promoted the Christianisation of the population. In that period the core area of supra-regional political powers was mainly situated north of the Alps, first in the Carolingian Empire and later, after its division, in France and the Holy Roman Empire. The German emperors, who received the imperial investiture from the Pope in Rome between the ninth and the fifteenth centuries, had to cross the Alps along with their entourages.

In the 7th century, much of the Eastern Alps were settled by Slavs. Between the 7th and 9th century, the Slavic principality of Carantania existed as one of the few non-Germanic polities in the Alps. The Alpine Slavs, who inhabited the majority of present-day Austria and Slovenia, were gradually Germanized from the 9th to the 14th century. The modern Slovenes are their southernmost descendants.

The successive emigration and occupation of the Alpine region by the Alemanni from the 6th to the 8th centuries are, too, known only in outline. For "mainstream" history, the Frankish and later the Habsburg empire, the Alps had strategic importance as an obstacle, not as a landscape, and the Alpine passes have consequently had great significance militarily.

Between 889 and 973, a Muslim community existed at Fraxinetum in the Western Alps. These "Saracens", as they were known, blocked the Alpine passes to Christian travelers until their expulsion by Christian forces led by Arduin Glaber in 973, at which point transalpine trade was able to resume.

Not until the final breakup of the Carolingian Empire in the 10th and 11th centuries is it possible to trace out the local history of different parts of the Alps, notably with the High Medieval Walser migrations.

Later Medieval to Early Modern Era (1200 to 1900)

The French historian Fernand Braudel, in his famous volume on Mediterranean civilisation, describes the Alps as “an exceptional range of mountains from the point of view of resources, collective disciplines, the quality of its human population and the number of good roads.” This remarkable human presence in the Alpine region came into being with the population growth and agrarian expansion of the High Middle Ages. At first a mixed form of agriculture and animal husbandry dominated the economy. Then, from the Late Middle Ages onwards, cattle tended to replace sheep as the dominant animals. In a few regions of the northern slope of the Alps, cattle farming became increasingly oriented toward long-range markets and substituted agriculture completely. At the same time other types of interregional and transalpine exchange were growing in significance. The most important pass was the Brenner, which could accommodate cart traffic beginning in the fifteenth century. In the Western and Central Alps, the passes were practicable only by pack animals up to the period around 1800.

The process of state formation in the Alps was driven by the proximity to focal areas of European conflicts such as in the Italian wars of 1494–1559. In that period the socio-political structures of Alpine regions drifted apart. One can identify three different developmental models: one of princely centralization (Western Alps), a local-communal one (Switzerland) and an intermediate one, characterised by a powerful nobility (Eastern Alps).

Until the late nineteenth century many Alpine valleys remained mainly shaped by agrarian and pastoral activities. Population growth favoured the intensification of land use and the spread of corn, potato and cheese production. The shorter growing season at higher altitudes did not seem to be an impediment until around 1700. Later, however, it became a major obstacle to the further intensification of agriculture, especially in comparison to the surrounding lowlands where land productivity increased rapidly. Inside the Alpine region there was a striking difference between the western and central parts, which were dominated by small farming establishments, and the eastern part, which were characterised by medium or big farms. Migration to the urbanised zones of the surrounding areas was already apparent before 1500 and was often temporary. In the Alps themselves, urbanisation was slow.

Central Alps

Further information: Old Swiss Confederacy and Highest Alemannic

In the Central Alps the chief event, on the northern side of the chain, is the gradual formation from 1291 to 1516 of the Swiss Confederacy, at least so far as regards the mountain Cantons, and with especial reference to the independent confederations of the Grisons and the Valais, which only became full members of the Confederation in 1803 and 1815 respectively. The attraction of the south was too strong for both the Forest Cantons and the Grisons, so that both tried to secure, and actually did secure, various bits of the Milanese.

The Gotthard Pass was known in antiquity as Adula Mons, but it was not one of the important Alpine passes due to the impassability of the Schöllenen Gorge north of the pass. This changed dramatically with the construction of the so-called Devil's Bridge by the year 1230. Almost immediately, in 1231, the formerly unimportant valley of Uri was granted imperial immediacy and became the main route connecting Germany and Italy. Also in 1230, a hospice dedicated to Gotthard of Hildesheim was built on the pass to accommodate the pilgrims to Rome which now took this route. The sudden strategical importance for the European powers gained by what is now Central Switzerland was an important factor in the formation of the Old Swiss Confederacy beginning in the late 13th century.

In the 15th century, the Forest Cantons won the Val Leventina as well as Bellinzona and the Val Blenio (though the Ossola Valley was held for a time only). Blenio was added to the Val Bregaglia (which had been given to the bishop of Coire in 960 by the emperor Otto I), along with the valleys of Mesocco and of Poschiavo.

Western Alps

Further information: County of Savoy and Duchy of Savoy

In the case of the Western Alps (excluding the part from the chain of Mont Blanc to the Simplon Pass, which followed the fortunes of the Valais), a prolonged struggle for control took place between the feudal lords of Savoy, the Dauphiné and Provence. In 1349 the Dauphiné fell to France, while in 1388 the county of Nice passed from Provence to the house of Savoy, which also then held Piedmont as well as other lands on the Italian side of the Alps. The struggle henceforth was limited to France and the house of Savoy, but little by little France succeeded in pushing back the house of Savoy across the Alps, forcing it to become a purely Italian power.

One turning-point in the rivalry was the Treaty of Utrecht (1713), by which France ceded to Savoy the Alpine districts of Exilles, Bardonnèche (Bardonecchia), Oulx, Fenestrelles, and Châtean Dauphin, while Savoy handed over to France the valley of Barcelonnette, situated on the western slope of the Alps and forming part of the county of Nice. The final act in this long-continued struggle took place in 1860, when France obtained by cession the rest of the county of Nice and also Savoy, thus remaining sole ruler on the western slope of the Alps.

Eastern Alps

The Eastern Alps had been included in the Frankish Empire since the 9th century. From the High Middle Ages and throughout the Early Modern era, the political history of the Eastern Alps can be considered almost totally in terms of the advance or retreat of the house of Habsburg. The Habsburgers' original home was in the lower valley of the Aar, at Habsburg castle. They lost that district to the Swiss in 1415, as they had previously lost various other sections of what is now Switzerland. But they built an impressive empire in the Eastern Alps, where they defeated numerous minor dynasties. They won the duchy of Austria with Styria in 1282, Carinthia and Carniola in 1335, Tirol in 1363, and the Vorarlberg in bits from 1375 to 1523, not to speak of minor "rectifications" of frontiers on the northern slope of the Alps. But on the other slope their progress was slower, and finally less successful. It is true that they won Primiero quite early (1373), as well as (1517) the Ampezzo Valley and several towns to the south of Trento. In 1797 they obtained Venetia proper, in 1803 the secularized bishoprics of Trento and Brixen (as well as that of Salzburg, more to the north), besides the Valtellina region, and in 1815 the Bergamasque valleys, while the Milanese had belonged to them since 1535. But in 1859 they lost to the house of Savoy both the Milanese and the Bergamasca, and in 1866 Venetia proper also, so that the Trentino was then their chief possession on the southern slope of the Alps. The gain of the Milanese in 1859 by the future king of Italy (1861) meant that Italy then won the valley of Livigno (between the Upper Engadine and Bormio), which is the only important bit it holds on the non-Italian slope of the Alps, besides the county of Tenda (obtained in 1575, and not lost in 1860), with the heads of certain glens in the Maritime Alps, reserved in 1860 for reasons connected with hunting. Following World War I and the demise of Austria-Hungary, there were important territorial changes in the Eastern Alps.

Modern history (1900 to present)

Population

For the modern era it is possible to offer a quantitative estimate of the population of the Alpine region. Within the area delimited by the Alpine Convention, there were about 3.1 million inhabitants in 1500, 5.8 in 1800, 8.5 in 1900 and 13.9 in 2000.

Sixteenth-century scholars, especially those from cities near the Alps, began to show a greater interest for the mountain phenomena. Their curiosity was also aroused by important questions of the genesis of the earth and the interpretation of the Bible. By the eighteenth century, a distinctive enthusiasm for nature and the Alps spread in European society. An example thereof is the famous multi-volume work “Voyages dans les Alpes” (1779–1796) by Horace-Bénédict de Saussure. In his work the naturalist from Geneva described, among other things, his 1787 ascent of Mont Blanc at 4800 metres above sea level. This new interest is also reflected in literature, most notably by Jean-Jacques Rousseau’s best-selling romantic novel “Julie, ou la nouvelle Heloise” (1761). These cultural developments resulted in a growth of interest in the Alps as a travel destination and laid the foundation for modern tourism. As Europe was getting increasingly more urbanised, the Alps distinguished themselves as a place of nature. During the colonial expansion many mountains in Asia, Australia and America were now named after the Alps as well.

During the nineteenth and twentieth centuries several important changes occurred. First, the Alpine population was now characterised by a particular growth rate, which was increasingly differentiated from that of the more dynamic non-mountain areas. Second, the migratory fluxes became ever more important and ever more directed toward extra-European destinations. Beginning in the early twentieth century, several regions were affected by depopulation. This process amplified the imbalanced distribution of the population within the Alps, because the urban centres at lower altitudes experienced strong growth and clearly became the most important dynamic localities during the twentieth century.

Economy

The economy showed many signs of change too. First of all, the agriculture sector started to lose importance, and sought to survive by introducing specialised crops in valley bottoms and reinforcing cattle-raising at higher altitudes. This profound transformation was obviously due to the spread of industrialisation in Europe during the nineteenth century, which had its impact on the Alps, directly or indirectly. On the one hand, activities such as iron manufacturing, which had become prominent during the early modern era, reached their limits due to transportation costs and the increasing scale of business operations. On the other hand, at the turn of the twentieth century, new opportunities emerged for the manufacturing sector, due largely to electric power, one among the main innovations of the second industrial revolution. Abundant water and steep slopes made the Alps an ideal environment for the production of hydroelectric power. Hence many industrial sites appeared there.

However, it was undoubtedly the service sector that experienced the most important new development within the Alpine economy: the rapid rise of tourism. The first phase was dominated by summertime visits and, by about 1850, the expansion of Alpine health resorts and spas. Later, tourism started to shift to the winter season, particularly after the introduction of ski-lifts in early twentieth century. For a long time, transit traffic and trade had been an essential part of the service sector in the Alps. The traditional routes and activities began to face strong competition from the construction of railway lines and tunnels such as the Semmering (1854), the Brenner (1867), the Fréjus/Mont-Cenis (1871), the Gotthard (1882), the Simplon (1906) and the Tauern (1909). In 2016 opened the 57 km long Gotthard Base Tunnel. With a maximum elevation of only 549 metres above sea level, it is the first flat direct route through the Alpine barrier.

In general, it is noteworthy that even if modern industry – tourism, the railway and later the highway system – represented opportunities for the Alps, complementing its traditional openness to new challenges, it also produced negative consequences, such as the human impact on the environment.

Milestones of railway transit across the Alps

• 

  Brenner Pass Railway (1867), maximum elevation: 1,371 m

• 

  Fréjus Rail Tunnel (1871), maximum elevation: 1,338 m

• 

  Gotthard Rail Tunnel (1882), maximum elevation: 1,151 m

• 

  Simplon Tunnel (1906), maximum elevation: 705 m

• 

  Gotthard Base Tunnel (2016), maximum elevation: 549 m

Political history

Like other parts of Europe, the Alpine region was affected by the formation of the nation states that produced tensions between various groups and had consequences for border areas. In these regions, the coercive power of the state was felt much more strongly that it had been before. Borders lost their permeability and now bisected areas formerly characterised by a shared sense of community and ongoing exchanges. During World War I the eastern Alpine region was one of the epicentres of the conflict.

After World War II, the Alps entered a new phase. At one and the same time, regional identities were reinforced and a common Alpine identity was constructed. A remarkable step was made in 1991 with the signing of the Alpine Convention between all Alpine countries and the European Union. This process was strengthened by the appearance of a new set of cultural values for the Alps. In the nineteenth century, there had been a tension between the romantic advocates of the “sacredness” of the Alpine peaks (such as John Ruskin), and modern mountain climbers (such as Leslie Stephen), who promoted the notion of the Alps as the “playground of Europe.” In the twentieth century, the mountains acquired a clearly positive, iconic, status as places unsullied by undesirable urban influences such as pollution, noise and so on.

Tourism and alpinism

Further information: Exploration of the High Alps and Tourism in Switzerland § History

 

Chamonix, The Monument of Horace-Bénédict de Saussure and Jacques Balmat, in honor of their climb of Mont Blanc

The fascination that the Alps exerted on the British has to be related to the general increase in charm and appeal of this mountain range during the eighteenth century. Yet British particularities were involved as well. Traditionally, many Englishmen felt the attraction of the Mediterranean, which was associated with the practice of the Grand Tour, and thus had to cross Europe and the Alps to reach it. From a place of transit, the Alps turned into a tourist destination as the flow of people and means of transport increased. Moreover, with the invention of new sports the Alps became an area of experimental training. The Alps offered many mountain climbers a degree of difficulty that fit their expectations.

The convergence of these phenomena granted to Alpine tourism a central position. It intensified from the middle of the nineteenth century onwards and, in spite of fluctuations, would never lose its importance. Railway companies, travel guides, travelogues and travel agents joined forces to make the Alps a prestigious tourist destination. With Thomas Cook in particular, the Alps appeared, as early as 1861, in the catalog of tourist offers and were instrumental in the establishment of a “truly international industry” of tourism. This industry developed the infrastructure: railway lines, hotels and other services such as casinos, promenades, improvements, and funiculars.

The conquest of the Alps by British tourists was achieved along with their domestication and with the passionate participation of local, regional and national élites, be they political, economic or cultural. Leslie Stephen, in a best-selling book first published in 1871, defined the Alps as “the Playground of Europe.” The book highlights the incredible success of the mountains but it also reflects the tensions that emerged among their visitors. There was a clash between the “real enthusiasts,” sensitive to beauty, and the “flock of ordinary tourists” sticking to their customs and comforts.

During the twentieth century, then, the Alps were involved in the globalisation of tourism, a process that caused the multiplication of its destinations. However, in the British population these mountains retained an undeniable attraction. In fact, the British continued to view winter sports in particular (such as skiing, skating, bobsleigh, curling) as significant grounds for justifying their travel and their perpetuation of a unique culture. The personalities of Gavin de Beer and Arnold Lunn represent this attitude through a prolific interpretation of this mountain range from every possible perspective. Indeed, the British have never ceased to love and be attracted to the Alps. This is not likely to end soon, if the advertisements and presentations of the major Alpine resorts that intersperse the Sunday editions of the major newspapers are any indicator.

Linguistic history

Further information: Linguistic geography of Switzerland

The Alps are at the crossroads of the French, Italian, German and South Slavic linguistic sprachraums. They also act as a linguistic refugium, preserving archaic dialects such as Romansh, Walser German or Romance Lombardic. Extinct languages known to have been spoken in the Alpine region include Rhaetic, Lepontic, Ligurian and Langobardic.

As a result of the complicated history of the Alpine region, the native language and the national feelings of the inhabitants do not always correspond to the current international borders. The Trentino-Alto Adige/Südtirol region, which was annexed by Italy after World War I, has a German-speaking majority in the northern province of South Tyrol. There are Walser German speakers to found in northern Italy near the Swiss border. There are some French and Franco-Provencal-speaking districts in the Italian Aosta Valley, while there are clusters of Slovene-speakers in the Italian portion of the Julian Alps, in the Resia Valley (where the archaic Resian dialect of Slovene is still spoken) and in the mountain district known as Venetian Slovenia.

Common good (economics)

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Common_good_(economics) 

Wild fish are an example of common goods. They are non-excludable, as it is impossible to prevent people from catching fish. They are, however, rivalrous, as the same fish cannot be caught more than once.

Common goods (also called common-pool resources) are defined in economics as goods that are rivalrous and non-excludable. Thus, they constitute one of the four main types based on the criteria:

• whether the consumption of a good by one person precludes its consumption by another person (rivalrousness)
• whether it is possible to prevent people (consumers) who have not paid for it from having access to it (excludability)

As common goods are accessible by everybody, they are at risk of being subject to overexploitation which leads to diminished availability if people act to serve their own self-interests.

Characteristics of common goods

Common-pool resources are sufficiently large that it is difficult, but not impossible, to define recognized users and exclude other users altogether. Based on the criteria, common goods are:

• rivalrous: When one person consumes a good, another person is unable to subsequently consume that good and the overall stock of the good decreases. For example, when a fisherman catches a fish, no other fisherman is able to catch that fish.
• non-excludable: There is no possibility to exclude anybody from consumption of this good.

Common goods can be institutions, facilities, constructions or nature itself. As long as it can be used by all members of society and not privately consumed by specific individuals or not all parts of society as private goods.

For common goods to be able to exist, in most cases payment of taxes is needed, as common goods are socially beneficial and everyone is interested in satisfy some considered basic necessities. As the government is commonly the agent who drives expenses to create common goods, the community pays an amount in exchange.

A society requires to have certain elements in order to succeed in the creation of common goods. Developed countries normally share those elements such as being a democracy and having basic rights and freedoms, a transportation system, cultural institutions, police and public safety, a judicial system, an electoral system, public education, clean air and water, safe and ample food supply, and national defense.

A common problem with the common goods today is that its existence affects society as a whole, so we must all make a sacrifice to create a common good. Society then have to choose between the interest of a few or the sacrifice of all.

Accomplishing a common good has consistently required a level of individual penance. Today, the compromises and forfeits important for the benefit of everyone regularly include paying taxes, tolerating individual bother, or surrendering certain advantages and cultural beliefs. While infrequently offered intentionally, these penances and compromises are generally joined into laws and public policy. Some cutting-edge instances of the benefit of all and the penances associated with accomplishing them are:

• Public Infrastructure Improvement: Usually the improvement of highways, water, sewer and power lines require the addition or increase of taxes, as well as the use of eminent domain.
• Civil Rights and Racial Equality: Even though inequality and racial disparities must move in the way to seize to exist, vestiges of privileges for a fraction of the society still exist and had been progressively eliminated by new laws.
• Environmental Quality: New laws and movements increase regarding the global environmental problem as a healthy environment benefit the common good and now it isn't going to be only a matter of a few.

History

Despite its growing importance in modern society, the concept of the common good was first mentioned more than two thousand years ago in the writings of Plato, Aristotle, and Cicero. Regardless the time period Aristotle described the problem with common goods accurately: “What is common to many is taken least care of, for all men have greater regard for what is their own than for what they possess in common with others.” As early as the second century AD, the Catholic religious tradition defined the common good as “the sum of those conditions of social life which allow social groups and their individual members relatively thorough and ready access to their own fulfilment.”

In later centuries, philosophers, politicians and economists have referred to the concept of common good such as Jean-Jacques Rousseau, in his 1762 book "The Social Contract". The Swiss philosopher, writer, and political theorist argues that in successful societies, the “general will” of the people will always be directed toward achieving the collectively agreed common good. Rousseau contrasts the will of all—the total of the desires of each individual—with the general will—the “one will which is directed towards their common preservation and general well-being.” Rousseau further contends that political authority, in the form of laws, will be viewed as legitimate and enforceable only if it is applied according to the general will of the people and directed toward their common good.

Adam Smith also referred to common goods in his book “The Wealth of Nations”, as individuals moved by an “invisible hand” to satisfy their own interests serve the purpose of the common good. He advocated that in order to realize common interests, society should shoulder common responsibilities to ensure that the welfare of the most economically disadvantaged class is maintained.

This view was later shared by the American philosopher John Rawls, who in his book “Theory of Justice” believes that public good is the core of a healthy moral, economic and political system. Rawls defined the common interest as “certain general conditions that are … equally to everyone's advantage.”

In this case, Rawls equates the common interest with the combination of social conditions for the equal sharing of citizenship, such as basic freedom and fair economic opportunities.

Examples

Congested roads - Roads may be considered either public or common resources. Road is public good whenever there is no congestion, thus the use of the road does not affect the use of someone else. However, if the road is congested, one more person driving the car makes the road more crowded which causes slower passage. In other words, it creates a negative externality and road becomes common good.

Clean water and air - Climate stability belongs to classic modern examples. Water and air pollution is caused by market negative externality. Water flows can be tapped beyond sustainability, and air is often used in combustion, whether by motor vehicles, smokers, factories, wood fires. In the production process these resources and others are changed into finished products such as food, shoes, toys, furniture, cars, houses and televisions.

Fish stocks in international waters - Oceans remain one of the least regulated common resources. When fish are withdrawn from the water without any limits being imposed just because of their commercial value, living stocks of fish are likely to be depleted for any later fishermen. This phenomenon is caused by no incentives to let fish for others. To describe situations in which economic users withdraw resources to secure short-term gains without regard for the long-term consequences, the term tragedy of the commons was coined. For example, forest exploitation leads to barren lands, and overfishing leads to a reduction of overall fish stocks, both of which eventually result in diminishing yields to be withdrawn periodically.

Other natural resources - Another example of a private exploitation treated as a renewable resource and commonly cited have been trees or timber at critical stages, oil, mined metals, crops, or freely accessible grazing.

Debates about sustainability can be both philosophical and scientific. However, wise-use advocates consider common goods that are an exploitable form of a renewable resource, such as fish stocks, grazing land, etc., to be sustainable in the following two cases:

• As long as demand for the goods withdrawn from the common good does not exceed a certain level, future yields are not diminished and the common good as such is being preserved as a 'sustainable' level.
• If access to the common good is regulated at the community level by restricting exploitation to community members and by imposing limits to the quantity of goods being withdrawn from the common good, the tragedy of the commons may be avoided. Common goods that are sustained through an institutional arrangement of this kind are referred to as common-pool resources.

Tragedy of the commons

Tragedy of commons is a problem in economics in which everybody has an incentive to use a resource at the expense of everyone else who uses it, with no way of preventing anyone from consuming it. Generally, the resource in question is without barriers to entry and is demanded in excess of its supply, leading to depletion of the resource.

Example

For example, imagine there are several shepherds, each with their own flock of sheep, who have access to a communal field which they all use for grazing. As the sheep graze unhindered, they deplete the overall stock of grass in the field and there is less for other sheep to consume. The tragedy is that eventually the field will become barren and will be no use to any of the shepherds.

Possible solutions

Assigning property rights is one possible solution to the problem. This involves essentially converting what was a common-pool resource into a private good. This would prevent that over-consumption of the good as the owner(s) of the good would have an incentive to regulate their consumption in order to keep the stock of that good at a healthy level.

Next solution is government intervention. Right to use the land can be allocated, the number of sheep in every herd can be regulated or externality made by sheep can be internalized by taxing sheep.

Collective solutions can also be reached to solve the problem. Before English enclosure laws were enacted, there were agreements in place between lords and rural villagers to overcome this problem. Practices such as seasonal grazing and crop rotation regulated land use. Over-using the land resulted in enforcebale sanctions.

Common goods and normal goods

Normal goods are goods that experience an increase in demand as the income of consumers increases.. The demand function of a normal good is downward sloping, which means there is an inverse relationship between the price and quantity demanded. In other words, price elasticity of demand is negative for normal goods. Common goods mean that demand and price change in the opposite direction. If something is a normal goods, then the consumer's demand for the goods and the consumer's income level change in the same direction. At this time, the substitution effect and income effect will strengthen each other, so the price change will lead to the opposite direction of demand change. Then the goods must be a common goods, so the normal goods must be a common goods.

Other goods

Main article: Goods § Goods classified by exclusivity and competitiveness

 

	Excludable	Non-excludable
Rivalrous	Private goods food, clothing, cars, parking spaces	Common-pool resources fish stocks, timber, coal, free public transport
Non-rivalrous	Club goods cinemas, private parks, satellite television, public transport	Public goods free-to-air television, air, national defense, free and open-source software

In addition to common goods, there are three other kinds of economic goods, including public goods, private goods, and club goods. Common goods that a businessman gives a thumbs up can include international fish stocks and other goods. Most international fishing areas have no limit on the number of fish that can be caught. Therefore, anyone can fish as he likes, which makes the good things not excluded. However, if there are no restrictions, fish stocks may be depleted when other fishermen arrive later. This means that fish populations are competitive. Other common commodities include water and game animals.

Tragedy of the commons

The tragedy of the commons was originally mentioned in 1833 by the Victorian economist William Forster Lloyd, who was a member of the Royal Society . He offered the example of a hypothetical tract of shared grazing land, in which all of the villagers brought their cows to this common grazing space, resulting in overgrazing and the depletion of the resource(Lloyd, 1833). Individuals may theoretically limit their use in order to avoid depleting a shared resource, if they so chose. However, there is a problem with free riders. In situations where people rely on others to reduce their productivity. The result of everyone taking advantage of the system and making the most of it is a scenario of over-consumption.

Lorentz factor

From Wikipedia, the free encyclopedia

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

The Lorentz factor or Lorentz term is a quantity expressing how much the measurements of time, length, and other physical properties change for an object while that object is moving. The expression appears in several equations in special relativity, and it arises in derivations of the Lorentz transformations. The name originates from its earlier appearance in Lorentzian electrodynamics – named after the Dutch physicist Hendrik Lorentz.

It is generally denoted γ (the Greek lowercase letter gamma). Sometimes (especially in discussion of superluminal motion) the factor is written as Γ (Greek uppercase-gamma) rather than γ.

Definition

The Lorentz factor γ is defined as

${\displaystyle \gamma ={\frac {1}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}={\frac {1}{\sqrt {1-\beta ^{2}}}}={\frac {dt}{d\tau }}}$,

where:

• v is the relative velocity between inertial reference frames,
• c is the speed of light in a vacuum,
• β is the ratio of v to c,
• t is coordinate time,
• τ is the proper time for an observer (measuring time intervals in the observer's own frame).

This is the most frequently used form in practice, though not the only one (see below for alternative forms).

To complement the definition, some authors define the reciprocal

${\displaystyle \alpha ={\frac {1}{\gamma }}={\sqrt {1-{\frac {v^{2}}{c^{2}}}}}\ ={\sqrt {1-{\beta }^{2}}};}$

see velocity addition formula.

Occurrence

Following is a list of formulae from Special relativity which use γ as a shorthand:

• The Lorentz transformation: The simplest case is a boost in the x-direction (more general forms including arbitrary directions and rotations not listed here), which describes how spacetime coordinates change from one inertial frame using coordinates (x, y, z, t) to another (x′, y′, z′, t′) with relative velocity v:
  $${\displaystyle {\begin{aligned}t'&=\gamma \left(t-{\frac {vx}{c^{2}}}\right),\\[2pt]x'&=\gamma \left(x-vt\right).\end{aligned}}}$$

  

Corollaries of the above transformations are the results:

• Time dilation: The time (∆t′) between two ticks as measured in the frame in which the clock is moving, is longer than the time (∆t) between these ticks as measured in the rest frame of the clock:
  $${\displaystyle \Delta t'=\gamma \Delta t.}$$

  
• Length contraction: The length (∆x′) of an object as measured in the frame in which it is moving, is shorter than its length (∆x) in its own rest frame:
  $${\displaystyle \Delta x'=\Delta x/\gamma .}$$

  

Applying conservation of momentum and energy leads to these results:

• Relativistic mass: The mass m of an object in motion is dependent on ${\displaystyle \gamma }$ and the rest mass m₀:
  $${\displaystyle m=\gamma m_{0}.}$$

  
• Relativistic momentum: The relativistic momentum relation takes the same form as for classical momentum, but using the above relativistic mass:
  $${\displaystyle {\vec {p}}=m{\vec {v}}=\gamma m_{0}{\vec {v}}.}$$

  
• Relativistic kinetic energy: The relativistic kinetic energy relation takes the slightly modified form:
  $${\displaystyle E_{k}=E-E_{0}=(\gamma -1)m_{0}c^{2}}$$

  
  As ${\displaystyle \gamma }$ is a function of ${\displaystyle {\tfrac {v}{c}}}$, the non-relativistic limit gives ${\textstyle \lim _{c\to \infty }E_{k}={\tfrac {1}{2}}m_{0}v^{2}}$, as expected from Newtonian considerations.

Numerical values

Lorentz factor γ as a function of velocity. Its initial value is 1 (when v = 0); and as velocity approaches the speed of light (v → c) γ increases without bound (γ → ∞).

 

α (Lorentz factor inverse) as a function of velocity - a circular arc.

In the table below, the left-hand column shows speeds as different fractions of the speed of light (i.e. in units of c). The middle column shows the corresponding Lorentz factor, the final is the reciprocal. Values in bold are exact.

Speed (units of c), β = v/c	Lorentz factor, γ	Reciprocal, 1/γ
0	1	1
0.050	1.001	0.999
0.100	1.005	0.995
0.150	1.011	0.989
0.200	1.021	0.980
0.250	1.033	0.968
0.300	1.048	0.954
0.400	1.091	0.917
0.500	1.155	0.866
0.600	1.25	0.8
0.700	1.400	0.714
0.750	1.512	0.661
0.800	1.667	0.6
0.866	2	0.5
0.900	2.294	0.436
0.990	7.089	0.141
0.999	22.366	0.045
0.99995	100.00	0.010

Alternative representations

Main articles: Momentum and Rapidity

There are other ways to write the factor. Above, velocity v was used, but related variables such as momentum and rapidity may also be convenient.

Momentum

Solving the previous relativistic momentum equation for γ leads to

${\displaystyle \gamma ={\sqrt {1+\left({\frac {p}{m_{0}c}}\right)^{2}}}}$.

This form is rarely used, although it does appear in the Maxwell–Jüttner distribution.

Rapidity

Applying the definition of rapidity as the hyperbolic angle ${\displaystyle \varphi }$:

${\displaystyle \tanh \varphi =\beta }$

also leads to γ (by use of hyperbolic identities):

${\displaystyle \gamma =\cosh \varphi ={\frac {1}{\sqrt {1-\tanh ^{2}\varphi }}}={\frac {1}{\sqrt {1-\beta ^{2}}}}.}$

Using the property of Lorentz transformation, it can be shown that rapidity is additive, a useful property that velocity does not have. Thus the rapidity parameter forms a one-parameter group, a foundation for physical models.

Series expansion (velocity)

The Lorentz factor has the Maclaurin series:

${\displaystyle {\begin{aligned}\gamma &={\dfrac {1}{\sqrt {1-\beta ^{2}}}}\\&=\sum _{n=0}^{\infty }\beta ^{2n}\prod _{k=1}^{n}\left({\dfrac {2k-1}{2k}}\right)\\&=1+{\tfrac {1}{2}}\beta ^{2}+{\tfrac {3}{8}}\beta ^{4}+{\tfrac {5}{16}}\beta ^{6}+{\tfrac {35}{128}}\beta ^{8}+{\tfrac {63}{256}}\beta ^{10}+\cdots ,\\\end{aligned}}}$

which is a special case of a binomial series.

The approximation γ ≈ 1 + 1/2 β² may be used to calculate relativistic effects at low speeds. It holds to within 1% error for v < 0.4 c (v < 120,000 km/s), and to within 0.1% error for v < 0.22 c (v < 66,000 km/s).

The truncated versions of this series also allow physicists to prove that special relativity reduces to Newtonian mechanics at low speeds. For example, in special relativity, the following two equations hold:

${\displaystyle {\begin{aligned}{\vec {p}}&=\gamma m{\vec {v}},\\E&=\gamma mc^{2}.\end{aligned}}}$

For γ ≈ 1 and γ ≈ 1 + 1/2 β², respectively, these reduce to their Newtonian equivalents:

${\displaystyle {\begin{aligned}\mathbf {p} &=m\mathbf {v} ,\\E&=mc^{2}+{\tfrac {1}{2}}mv^{2}.\end{aligned}}}$

The Lorentz factor equation can also be inverted to yield

${\displaystyle \beta ={\sqrt {1-{\frac {1}{\gamma ^{2}}}}}.}$

This has an asymptotic form

${\displaystyle \beta =1-{\tfrac {1}{2}}\gamma ^{-2}-{\tfrac {1}{8}}\gamma ^{-4}-{\tfrac {1}{16}}\gamma ^{-6}-{\tfrac {5}{128}}\gamma ^{-8}+\cdots }$.

The first two terms are occasionally used to quickly calculate velocities from large γ values. The approximation β ≈ 1 − 1/2 γ⁻² holds to within 1% tolerance for γ > 2, and to within 0.1% tolerance for γ > 3.5.

Applications in astronomy

The standard model of long-duration gamma-ray bursts (GRBs) holds that these explosions are ultra-relativistic (initial ${\displaystyle \gamma }$ greater than approximately 100), which is invoked to explain the so-called "compactness" problem: absent this ultra-relativistic expansion, the ejecta would be optically thick to pair production at typical peak spectral energies of a few 100 keV, whereas the prompt emission is observed to be non-thermal.

Subatomic particles called muons travel at a speed such that they have a relatively high Lorentz factor and therefore experience extreme time dilation. As an example, muons generally have a mean lifetime of about 2.2 μs which means muons generated from cosmic ray collisions at about 10 km up in the atmosphere should be non-detectable on the ground due to their decay rate. However, it has been found that ~10% of muons are still detected on the surface, thereby proving that to be detectable they have had their decay rates slow down relative to our inertial frame of reference.