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Mormonism and Physics, Astronomy, Quantum Mechanics, String Theory, M-theory, etc.

This article attempts to accumulate general Mormon views regarding physics, astronomy, quantum mechanics, string theory, m-theory, the omniverse, as well as philosophy.

Mormon Apologetics and Studies

• Neal A. Maxwell Institute for Religious Scholarship
• Neal A. Maxwell Institute for Religious Scholarship
• Maxwell Institute Blog

Heisenberg's Uncertainty Principle

In quantum mechanics, the uncertainty principle, also known as Heisenberg's uncertainty principle, is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle known as complementary variables, such as position x and momentum p, can be known simultaneously. Introduced first in 1927, by the German physicist Werner Heisenberg, it states that the more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice versa. The formal inequality relating the standard deviation of position σ_x and the standard deviation of momentum σ_p was derived by Earle Hesse Kennard later that year and by Hermann Weyl in 1928:

$\sigma _{x}\sigma _{p}\geq {\frac {\hbar }{2}}~~$

(ħ is the reduced Planck constant).

Historically, the uncertainty principle has been confused with a somewhat similar effect in physics, called the observer effect, which notes that measurements of certain systems cannot be made without affecting the systems. Heisenberg offered such an observer effect at the quantum level (see below) as a physical "explanation" of quantum uncertainty. It has since become clear, however, that the uncertainty principle is inherent in the properties of all wave-like systems, and that it arises in quantum mechanics simply due to the matter wave nature of all quantum objects. Thus, the uncertainty principle actually states a fundamental property of quantum systems, and is not a statement about the observational success of current technology. It must be emphasized that measurement does not mean only a process in which a physicist-observer takes part, but rather any interaction between classical and quantum objects regardless of any observer.

Since the uncertainty principle is such a basic result in quantum mechanics, typical experiments in quantum mechanics routinely observe aspects of it. Certain experiments, however, may deliberately test a particular form of the uncertainty principle as part of their main research program. These include, for example, tests of number–phase uncertainty relations in superconducting or quantum optics systems. Applications dependent on the uncertainty principle for their operation include extremely low noise technology such as that required in gravitational-wave interferometers.

Introduction

Main article: Introduction to quantum mechanics

Click to see animation. The evolution of an initially very localized gaussian wave function of a free particle in two-dimensional space, with colour and intensity indicating phase and amplitude. The spreading of the wave function in all directions shows that the initial momentum has a spread of values, unmodified in time; while the spread in position increases in time: as a result, the uncertainty Δx Δp increases in time.

The superposition of several plane waves to form a wave packet. This wave packet becomes increasingly localized with the addition of many waves. The Fourier transform is a mathematical operation that separates a wave packet into its individual plane waves. Note that the waves shown here are real for illustrative purposes only, whereas in quantum mechanics the wave function is generally complex.

As a fundamental constraint, higher level descriptions of the universe must supervene on quantum mechanical descriptions which includes Heisenberg's uncertainty relationship. However, humans do not form an intuitive understanding of this uncertainty principle in everyday life. This is because the constraint is not readily apparent on the macroscopic scales of everyday experience. So it may be helpful to demonstrate how it is integral to more easily understood physical situations. Two alternative conceptualizations of quantum physics can be examined with the goal of demonstrating the key role the uncertainty principle plays. A wave mechanics picture of the uncertainty principle provides for a more visually intuitive demonstration, and the somewhat more abstract matrix mechanics picture provides for a demonstration of the uncertainty principle that is more easily generalized to cover a multitude of physical contexts.

Mathematically, in wave mechanics, the uncertainty relation between position and momentum arises because the expressions of the wavefunction in the two corresponding orthonormal bases in Hilbert space are Fourier transforms of one another (i.e., position and momentum are conjugate variables). A nonzero function and its Fourier transform cannot both be sharply localized. A similar tradeoff between the variances of Fourier conjugates arises in all systems underlain by Fourier analysis, for example in sound waves: A pure tone is a sharp spike at a single frequency, while its Fourier transform gives the shape of the sound wave in the time domain, which is a completely delocalized sine wave. In quantum mechanics, the two key points are that the position of the particle takes the form of a matter wave, and momentum is its Fourier conjugate, assured by the de Broglie relation p = ħk, where k is the wavenumber.

In matrix mechanics, the mathematical formulation of quantum mechanics, any pair of non-commuting self-adjoint operators representing observables are subject to similar uncertainty limits. An eigenstate of an observable represents the state of the wavefunction for a certain measurement value (the eigenvalue). For example, if a measurement of an observable A is performed, then the system is in a particular eigenstate Ψ of that observable. However, the particular eigenstate of the observable A need not be an eigenstate of another observable B: If so, then it does not have a unique associated measurement for it, as the system is not in an eigenstate of that observable.

Wave mechanics interpretation

Plane wave

Wave packet

Propagation of de Broglie waves in 1d—real part of the complex amplitude is blue, imaginary part is green. The probability (shown as the colour opacity) of finding the particle at a given point x is spread out like a waveform, there is no definite position of the particle. As the amplitude increases above zero the curvature reverses sign, so the amplitude begins to decrease again, and vice versa—the result is an alternating amplitude: a wave.

Main article: Wave packet

Main article: Schrödinger equation

According to the de Broglie hypothesis, every object in the universe is a wave, a situation which gives rise to this phenomenon. The position of the particle is described by a wave function $\Psi (x,t)$. The time-independent wave function of a single-moded plane wave of wavenumber k₀ or momentum p₀ is

$\psi (x)\propto e^{ik_{0}x}=e^{ip_{0}x/\hbar }~.$

The Born rule states that this should be interpreted as a probability density function in the sense that the probability of finding the particle between a and b is

$\operatorname {P} [a\leq X\leq b]=\int _{a}^{b}|\psi (x)|^{2}\,\mathrm {d} x~.$

In the case of the single-moded plane wave, $|\psi (x)|^{2}$ is a uniform distribution. In other words, the particle position is extremely uncertain in the sense that it could be essentially anywhere along the wave packet. Consider a wave function that is a sum of many waves, however, we may write this as

$\psi (x)\propto \sum _{n}A_{n}e^{ip_{n}x/\hbar }~,$

where A_n represents the relative contribution of the mode p_n to the overall total. The figures to the right show how with the addition of many plane waves, the wave packet can become more localized. We may take this a step further to the continuum limit, where the wave function is an integral over all possible modes

$\psi (x)={\frac {1}{\sqrt {2\pi \hbar }}}\int _{-\infty }^{\infty }\phi (p)\cdot e^{ipx/\hbar }\,dp~,$

with $\phi (p)$ representing the amplitude of these modes and is called the wave function in momentum space. In mathematical terms, we say that $\phi (p)$ is the Fourier transform of $\psi (x)$ and that x and p are conjugate variables. Adding together all of these plane waves comes at a cost, namely the momentum has become less precise, having become a mixture of waves of many different momenta.

One way to quantify the precision of the position and momentum is the standard deviation σ. Since $|\psi (x)|^{2}$ is a probability density function for position, we calculate its standard deviation.

The precision of the position is improved, i.e. reduced σ_x, by using many plane waves, thereby weakening the precision of the momentum, i.e. increased σ_p. Another way of stating this is that σ_x and σ_p have an inverse relationship or are at least bounded from below. This is the uncertainty principle, the exact limit of which is the Kennard bound. Click the show button below to see a semi-formal derivation of the Kennard inequality using wave mechanics.

Proof of the Kennard inequality using wave mechanics

We are interested in the variances of position and momentum, defined as $\sigma _{x}^{2}=\int _{-\infty }^{\infty }x^{2}\cdot |\psi (x)|^{2}\,dx-\left(\int _{-\infty }^{\infty }x\cdot |\psi (x)|^{2}\,dx\right)^{2}$ $\sigma _{p}^{2}=\int _{-\infty }^{\infty }p^{2}\cdot |\phi (p)|^{2}\,dp-\left(\int _{-\infty }^{\infty }p\cdot |\phi (p)|^{2}\,dp\right)^{2}~.$ Without loss of generality, we will assume that the means vanish, which just amounts to a shift of the origin of our coordinates. (A more general proof that does not make this assumption is given below.) This gives us the simpler form $\sigma _{x}^{2}=\int _{-\infty }^{\infty }x^{2}\cdot |\psi (x)|^{2}\,dx$ $\sigma _{p}^{2}=\int _{-\infty }^{\infty }p^{2}\cdot |\phi (p)|^{2}\,dp~.$ The function $f(x)=x\cdot \psi (x)$ can be interpreted as a vector in a function space. We can define an inner product for a pair of functions u(x) and v(x) in this vector space: $\langle u|v\rangle =\int _{-\infty }^{\infty }u^{*}(x)\cdot v(x)\,dx,$ where the asterisk denotes the complex conjugate. With this inner product defined, we note that the variance for position can be written as $\sigma _{x}^{2}=\int _{-\infty }^{\infty }|f(x)|^{2}\,dx=\langle f|f\rangle ~.$ We can repeat this for momentum by interpreting the function ${\tilde {g}}(p)=p\cdot \phi (p)$ as a vector, but we can also take advantage of the fact that $\psi (x)$ and $\phi (p)$ are Fourier transforms of each other. We evaluate the inverse Fourier transform through integration by parts: ${\begin{aligned}g(x)&={\frac {1}{\sqrt {2\pi \hbar }}}\cdot \int _{-\infty }^{\infty }{\tilde {g}}(p)\cdot e^{ipx/\hbar }\,dp\\&={\frac {1}{\sqrt {2\pi \hbar }}}\int _{-\infty }^{\infty }p\cdot \phi (p)\cdot e^{ipx/\hbar }\,dp\\&={\frac {1}{2\pi \hbar }}\int _{-\infty }^{\infty }\left[p\cdot \int _{-\infty }^{\infty }\psi (\chi )e^{-ip\chi /\hbar }\,d\chi \right]\cdot e^{ipx/\hbar }\,dp\\&={\frac {i}{2\pi }}\int _{-\infty }^{\infty }\left[{\cancel {\left.\psi (\chi )e^{-ip\chi /\hbar }\right|_{-\infty }^{\infty }}}-\int _{-\infty }^{\infty }{\frac {d\psi (\chi )}{d\chi }}e^{-ip\chi /\hbar }\,d\chi \right]\cdot e^{ipx/\hbar }\,dp\\&={\frac {-i}{2\pi }}\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }{\frac {d\psi (\chi )}{d\chi }}e^{-ip\chi /\hbar }\,dx\,e^{ipx/\hbar }\,dp\\&=\left(-i\hbar {\frac {d}{dx}}\right)\cdot \psi (x),\end{aligned}}$ where the canceled term vanishes because the wave function vanishes at infinity. Often the term $-i\hbar {\frac {d}{dx}}$ is called the momentum operator in position space. Applying Parseval's theorem, we see that the variance for momentum can be written as $\sigma _{p}^{2}=\int _{-\infty }^{\infty }|{\tilde {g}}(p)|^{2}\,dp=\int _{-\infty }^{\infty }|g(x)|^{2}\,dx=\langle g|g\rangle .$ The Cauchy–Schwarz inequality asserts that $\sigma _{x}^{2}\sigma _{p}^{2}=\langle f|f\rangle \cdot \langle g|g\rangle \geq |\langle f|g\rangle |^{2}~.$ The modulus squared of any complex number z can be expressed as $|z|^{2}={\Big (}{\text{Re}}(z){\Big )}^{2}+{\Big (}{\text{Im}}(z){\Big )}^{2}\geq {\Big (}{\text{Im}}(z){\Big )}^{2}={\Big (}{\frac {z-z^{\ast }}{2i}}{\Big )}^{2}.$ we let $z=\langle f|g\rangle$ and $z^{*}=\langle g|f\rangle$ and substitute these into the equation above to get $|\langle f|g\rangle |^{2}\geq {\bigg (}{\frac {\langle f|g\rangle -\langle g|f\rangle }{2i}}{\bigg )}^{2}~.$ All that remains is to evaluate these inner products. ${\begin{aligned}\langle f|g\rangle -\langle g|f\rangle &=\int _{-\infty }^{\infty }\psi ^{*}(x)\,x\cdot \left(-i\hbar {\frac {d}{dx}}\right)\,\psi (x)\,dx\\&{}\,\,\,\,\,-\int _{-\infty }^{\infty }\psi ^{*}(x)\,\left(-i\hbar {\frac {d}{dx}}\right)\cdot x\,\psi (x)dx\\&=i\hbar \cdot \int _{-\infty }^{\infty }\psi ^{*}(x)\left[\left(-x\cdot {\frac {d\psi (x)}{dx}}\right)+{\frac {d(x\psi (x))}{dx}}\right]\,dx\\&=i\hbar \cdot \int _{-\infty }^{\infty }\psi ^{*}(x)\left[\left(-x\cdot {\frac {d\psi (x)}{dx}}\right)+\psi (x)+\left(x\cdot {\frac {d\psi (x)}{dx}}\right)\right]\,dx\\&=i\hbar \cdot \int _{-\infty }^{\infty }\psi ^{*}(x)\psi (x)\,dx\\&=i\hbar \cdot \int _{-\infty }^{\infty }|\psi (x)|^{2}\,dx\\&=i\hbar \end{aligned}}$ Plugging this into the above inequalities, we get $\sigma _{x}^{2}\sigma _{p}^{2}\geq |\langle f|g\rangle |^{2}\geq \left({\frac {\langle f|g\rangle -\langle g|f\rangle }{2i}}\right)^{2}=\left({\frac {i\hbar }{2i}}\right)^{2}={\frac {\hbar ^{2}}{4}}$ or taking the square root $\sigma _{x}\sigma _{p}\geq {\frac {\hbar }{2}}~.$ Note that the only physics involved in this proof was that $\psi (x)$ and $\phi (p)$ are wave functions for position and momentum, which are Fourier transforms of each other. A similar result would hold for any pair of conjugate variables.

North America

The Church of Jesus Christ of Latter-day Saints membership in North America as of January 1, 2011.

The Church of Jesus Christ of Latter-day Saints membership in North America as a percentage of total population for year 2011.

Country	Membership	Population	% LDS	Stakes	Districts	Wards	Branches	Total Congregations	Missions	Temples	Family History Centers
Belize	4,502	349,728	1.29%		2		11	11
Canada	190,265	35,344,962	0.54%	47	3	333	146	479	7	8	165
Costa Rica	42,943	4,667,096	0.92%	6	4	43	30	73	1	1
El Salvador	117,234	6,340,000	1.85%	18	2	123	41	164	3	1
Greenland	15	56,370	0.03%				1	1
Guatemala	247,708	15,806,675	1.57%	42	18	243	174	417	6	2
Honduras	160,437	8,555,072	1.88%	23	7	149	77	226	4	1
Mexico	1,344,239	119,713,203	1.12%	230	37	1,535	450	1,980	34	12	266
Nicaragua	84,405	6,071,045	1.39%	9	6	61	40	101	2
Panama	50,062	3,661,868	1.37%	7	4	39	33	72	1	1
United States	6,398,889	317,831,000	2.01%	1,520	9	11,928	1,938	13,866	120	70	1,847

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United States

For a breakdown of membership statistics by state in the United States, see The Church of Jesus Christ of Latter-day Saints membership statistics (United States)

This page shows membership statistics of The Church of Jesus Christ of Latter-day Saints within the United States.

• Official LDS Membership - Membership count on record provided by the Church of Jesus Christ of Latter-day Saints. These records include adults and children, and also include both active and less active members.
• From religious surveys - General religious surveys conducted within the United States. These surveyed U.S. adults about their religious beliefs.

Official LDS Membership

Membership reported by The Church of Jesus Christ of Latter-day Saints on January 1, 2012 was used to determine the number of members in each state. The United States Census Bureau 2012 Census population estimates was used as the basis for the general population.

Maps

• 
  Official Latter-day Saint membership by state as of January 1, 2012
• 
  Percent of general population that are Latter-day Saints as of January 1, 2012
• 
  LDS Membership as Percentage of Population in 2000

Table

Each state link gives a brief history and additional membership information for that state.

State	Membership	Population	% LDS	Stakes	Districts	Wards	Branches	Total Congregations	Missions	Temples	Family History Centers
Alabama	36,255	4,822,023	0.75%	7		42	33	78	1	1	36
Alaska	33,204	731,449	4.54%	7		55	28	84	1	1	15
Arizona	410,263	6,626,624	6.19%	98		719	86	836	6	5	66
Arkansas	29,345	2,949,131	0.97%	7		38	26	66	1		21
California	780,200	38,340,000	2.03%	157		1,184	164	1,368	19	7	184
Colorado	149,876	5,187,582	2.89%	33		272	31	306	4	1	52
Connecticut	15,352	3,590,347	0.43%	3		28	5	34			9
Delaware	5,192	917,092	0.57%	2		9	3	12			3
District of Columbia	2,488	632,323	0.39%			2	1	3
Florida	146,509	19,317,568	0.76%	28		186	50	238	5	2	69
Georgia	81,563	9,919,945	0.82%	16		111	40	150	3	1	42
Hawaii	73,471	1,404,054	5.23%	16		124	11	138	1	2	25
Idaho	425,739	1,595,728	26.68%	127		999	82	1,102	4	4	63
Illinois	56,932	12,875,255	0.44%	12		93	34	127	3	2	36
Indiana	42,856	6,537,334	0.66%	11		68	31	99	1		29
Iowa	26,547	3,074,186	0.86%	7		41	28	69	1		29
Kansas	35,902	2,885,905	1.24%	7		55	20	75	1		25
Kentucky	33,757	4,380,415	0.77%	7		44	33	77	1	1	23
Louisiana	29,682	4,601,893	0.64%	6		36	19	55	1	1	13
Maine	10,845	1,329,192	0.82%	2		17	10	27			11
Maryland	43,459	5,884,563	0.74%	8		67	14	81	2	1	13
Massachusetts	26,423	6,646,144	0.40%	4		39	13	52	1	1	12
Michigan	43,579	9,883,360	0.44%	8	1	62	33	95	2	1	42
Minnesota	31,871	5,379,139	0.59%	8		56	24	75	1	1	23
Mississippi	21,699	2,984,926	0.73%	4		28	16	44	1		16
Missouri	68,962	6,021,988	1.15%	16		111	37	151	2	2	45
Montana	48,344	1,005,141	4.76%	11		78	42	124	1	1	46
Nebraska	24,140	1,855,525	1.30%	4		41	20	60	1	1	18
Nevada	180,600	2,788,931	6.48%	34		295	29	327	3	2	29
New Hampshire	8,298	1,320,718	0.63%	3		15	5	19	1		6
New Jersey	33,066	8,864,590	0.37%	5	1	37	23	61	1		18
New Mexico	69,703	2,085,538	3.34%	13		95	47	142	2	1	31
New York	80,535	19,570,261	0.41%	16	1	88	64	149	4	2	53
North Carolina	81,189	9,752,073	0.83%	16		115	39	154	2	1	46
North Dakota	9,994	699,628	1.43%	3		8	9	21		1	7
Ohio	60,364	11,544,225	0.52%	13		99	30	125	3	1	43
Oklahoma	45,734	3,814,820	1.20%	8		59	25	86	2	1	24
Oregon	152,011	3,899,353	3.90%	36		253	50	306	3	2	66
Pennsylvania	51,527	12,763,536	0.40%	12		80	26	106	2		41
Rhode Island	4,133	1,050,292	0.39%			6	2	8			1
South Carolina	39,473	4,723,723	0.84%	6		49	14	68	1	1	19
South Dakota	10,644	833,354	1.28%	2	1	10	23	33	1		11
Tennessee	48,612	6,456,243	0.75%	11		74	28	102	2	2	30
Texas	325,946	26,059,203	1.25%	64	3	488	132	620	8	4	112
Utah	1,975,939	2,900,872	68.12%	575	1	4,481	334	4,816	9	14	148
Vermont	4,600	626,011	0.73%	1		8	4	12			6
Virginia	93,395	8,185,867	1.14%	20		157	40	197	3		35
Washington	279,492	6,897,012	4.05%	57		463	65	543	7	3	78
West Virginia	17,227	1,855,413	0.93%	4		25	12	37	1		14
Wisconsin	25,693	5,726,398	0.45%	6		42	26	68	1		24
Wyoming	66,259	582,658	11.37%	17		137	18	155			38

Territories

State	Membership	Population	% LDS	Stakes	Districts	Wards	Branches	Total Congregations	Missions	Temples
American Samoa	15,411	54,947	28.1%	4		31	5	36
Guam	2,252	185,674	1.41%	1		4		4	1
Northern Mariana Islands	753	51,395	1.47%			1		1
Puerto Rico	20,940	3,667,084	0.56%	5		27	14	41	1
Virgin Islands (US)	570	105,275	0.54%				2	2

From religious surveys

The American Religious Identification Survey (ARIS) 2001 was based on a random digit-dialed telephone survey of 50,281 American adults in the continental U.S. Its findings are found on the map below on the left.

The Pew Forum on Religion & Public Life published a survey of 35,556 adults living in the United States that was conducted in 2007. These results are found on the map below on the right. Note: some less populated states were combined in this survey. These include:Montana-Wyoming,D.C.-Maryland, North & South Dakota, New Hampshire-Vermont, and Connecticut-Rhode Island.

Maps

Percentage of US adult population by state claiming membership in the LDS church in the 2001 ARIS survey. Click image for map legend.

Percentage of US adult population, by state, claiming Mormon as religious preference in the 2007 survey by the Pew Forum on Religion & Public Life.

2007 Pew Forum on Religion & Public Life

The 2007 Pew Forum on Religion & Public Life survey, conducted by Princeton Survey Research Associates International (PSRAI), found 1.7% of the U.S. adult population self identified themselves as Mormon. The table below lists a few significant findings, from the survey, about Mormons.

Demographic	Mormons (U.S.)	U.S. Avg.
Married	71%	54%
Divorced or separated	9%	12%
3 or more children at home	21%	9%
Weekly (or more) Attendance at Religious Services	76%	39%

See also

• LDS membership statistics (worldwide)
• LDS membership statistics (Canada)

Canada

For a breakdown of membership statistics by province in Canada, see The Church of Jesus Christ of Latter-day Saints membership statistics (Canada)

The general population was taken from Statistics Canada using the first quarter 2011 population estimates. The official membership statistics as of Jan 1, 2012 by The Church of Jesus Christ of Latter-day Saints was used for all other data.

This table is sortable. The link under the names of each province corresponds to brief LDS history and other information for that particular area.

The Church of Jesus Christ of Latter-day Saints membership in North America as of January 1, 2011.

The Church of Jesus Christ of Latter-day Saints membership in North America as a percentage of total population for year 2011.

Table

Province	Membership	Population	% LDS	Stakes	Districts	Wards	Branches	Total Congregations	Missions	Temples
Alberta	79,023	3,645,257	2.17%	22		174	32	212	2	3
British Columbia	29,296	4,400,057	0.67%	8	1	49	28	79	1	1
Manitoba	4,452	1,208,268	0.37%	1		7	5	12	1
New Brunswick	2,302	751,171	0.31%	1		5	1	6
Newfoundland	748	514,536	0.15%				3	3
Northwest Territories & Nunavut	141	73,368	0.19%				1	1
Nova Scotia	4,912	921,727	0.53%	1		6	11	14	1	1
Ontario	51,902	12,851,821	0.40%	9	2	59	40	98	1	1
Prince Edward Island	490	140,204	0.35%				3	3
Quebec	11,306	7,903,001	0.14%	3		19	16	35	1	1
Saskatchewan	5,406	1,033,381	0.52%	2		8	9	15		1
Yukon	287	33,897	0.85%				1	1
TOTAL	190,265	33,476,688	0.57%	47	3	327	150	479	7	8

See also

• The Church of Jesus Christ of Latter-day Saints in Canada
• LDS membership statistics (World)
• LDS membership statistics (United States)

Caribbean

Country	Membership	Population	% LDS	Stakes	Districts	Wards	Branches	Total Congregations	Missions	Temples	Family History Centers
Antigua and Barbuda	209	90,156	0.23%				1	1
Aruba	507	109,153	0.46%				2	2			1
Bahamas	962	351,461	0.27%		1		2	2			1
Barbados	869	288,725	0.30%		1		3	3			1
Bermuda	156	69,467	0.22%				1	1
Bonaire	78	16,541	0.47%				1	1
British Virgin Islands	150	31,912	0.47%				1	1
Cayman Islands	204	55,456	0.37%				1	1
Cuba	44	11,477,459	0.0009%				2	2
Curaçao	548	150,563	0.36%				1	1			1
Dominica	173	73,286	0.24%				1	1
Dominican Republic	126,413	10,219,630	1.24%	20	9	124	81	205	3	1	29
Grenada	336	109,590	0.31%				1	1
Guadeloupe	488	405,739	0.12%		1		3	3			1
Haiti	19,216	10,413,211	0.18%	4	3	22	21	43	1		6
Jamaica	5,712	2,909,714	0.20%	1	1		19	19	1		2
Martinique	197	392,291	0.05%				1	1			1
Puerto Rico	21,363	3,674,209	0.58%	5		29	12	41	1		8
Saint Kitts and Nevis	194	51,134	0.38%				1	1			1
Saint Lucia	263	162,781	0.16%				2	2
Sint Maarten	232	39,689	0.58%				1	1
Saint Vincent	578	103,220	0.56%				2	2
Trinidad and Tobago	3,179	1,328,019	0.24%	1		5	5	10	1		1
Turks and Caicos Islands	92	47,754	0.19%				1	1
Virgin Islands (US)	585	106,405	0.55%				2	2