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The career of a young theoretical physicist consists of treating the harmonic oscillator in ever-increasing levels of abstraction.
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1 2. Free Fields The career of a young theoretical physicist consists of treating the harmonic oscillator in ever-increasing levels of abstraction. Sidney Coleman 2.1 Canonical Quantization In quantum mechanics, canonical quantization is a recipe that takes us from the Hamiltonian formalism of classical dynamics to the quantum theory. The recipe tells us to take the generalized coordinates q a and their conjugate momenta p a and promote them to operators. The Poisson bracket structure of classical mechanics morphs into the structure of commutation relations between operators, so that, in units with = 1, [q a,q b ] = [p a,p b ] = 0 [q a,p b ] = iδ b a (2.1) In field theory we do the same, now for the field φ a ( x) and its momentum conjugate π b ( x). Thus a quantum field is an operator valued function of space obeying the commutation relations [φ a ( x),φ b ( y)] = [π a ( x),π b ( y)] = 0 [φ a ( x),π b ( y)] = iδ (3) ( x y)δ b a (2.2) Note that we ve lost all track of Lorentz invariance since we have separated space x and time t. We are working in the Schrödinger picture so that the operators φ a ( x) and π a ( x) do not depend on time at all only on space. All time dependence sits in the states ψ which evolve by the usual Schrödinger equation i d ψ dt = H ψ (2.3) We aren t doing anything different from usual quantum mechanics; we re merely applying the old formalism to fields. Be warned however that the notation ψ for the state is deceptively simple: if you were to write the wavefunction in quantum field theory, it would be a functional, that is a function of every possible configuration of the field φ. The typical information we want to know about a quantum theory is the spectrum of the Hamiltonian H. In quantum field theories, this is usually very hard. One reason for this is that we have an infinite number of degrees of freedom at least one for every point x in space. However, for certain theories known as free theories we can find a way to write the dynamics such that each degree of freedom evolves independently 21
2 from all the others. Free field theories typically have Lagrangians which are quadratic in the fields, so that the equations of motion are linear. For example, the simplest relativistic free theory is the classical Klein-Gordon (KG) equation for a real scalar field φ( x, t), µ µ φ+m 2 φ = 0 (2.4) To exhibit the coordinates in which the degrees of freedom decouple from each other, we need only take the Fourier transform, φ( x,t) = ei p x φ( p,t) (2.5) (2π) 3 Then φ( p, t) satisfies ( ) 2 t 2 +( p2 +m 2 ) φ( p,t) = 0 (2.6) Thus, for each value of p, φ( p, t) solves the equation of a harmonic oscillator vibrating at frequency ω p = + p 2 +m 2 (2.7) We learn that the most general solution to the KG equation is a linear superposition of simple harmonic oscillators, each vibrating at a different frequency with a different amplitude. To quantize φ( x, t) we must simply quantize this infinite number of harmonic oscillators. Let s recall how to do this The Simple Harmonic Oscillator Consider the quantum mechanical Hamiltonian H = 1 2 p ω2 q 2 (2.8) with the canonical commutation relations [q,p] = i. To find the spectrum we define the creation and annihilation operators (also known as raising/lowering operators, or sometimes ladder operators) a = ω 2 q + i 2ω p, a = ω 2 q i 2ω p (2.9) which can be easily inverted to give q = 1 ω (a+a ), p = i 2ω 2 (a a ) (2.10) 22
3 Substituting into the above expressions we find while the Hamiltonian is given by [a,a ] = 1 (2.11) H = 1 2 ω(aa +a a) = ω(a a+ 1 2 ) (2.12) One can easily confirm that the commutators between the Hamiltonian and the creation and annihilation operators are given by [H,a ] = ωa and [H,a] = ωa (2.13) These relations ensure that a and a take us between energy eigenstates. Let E be an eigenstate with energy E, so that H E = E E. Then we can construct more eigenstates by acting with a and a, Ha E = (E +ω)a E, Ha E = (E ω)a E (2.14) So we find that the system has a ladder of states with energies...,e ω,e,e +ω,e +2ω,... (2.15) Iftheenergyisboundedbelow, theremust beaground state 0 whichsatisfiesa 0 = 0. This has ground state energy (also known as zero point energy), Excited states then arise from repeated application of a, H 0 = 1 ω 0 (2.16) 2 n = (a ) n 0 with H n = (n+ 1 )ω n (2.17) 2 where I ve ignored the normalization of these states so, n n The Free Scalar Field We now apply the quantization of the harmonic oscillator to the free scalar field. We write φ and π as a linear sum of an infinite number of creation and annihilation operators a p and a p, indexed by the 3-momentum p, φ( x) = π( x) = 1 [ ] a (2π) 3 p e i p x +a e i p x p 2ω p (2π) 3( i) ω p 2 [a p e i p x a p e i p x ] (2.18) (2.19) 23
4 Claim: The commutation relations for φ and π are equivalent to the following commutation relations for a p and a p [φ( x),φ( y)] = [π( x),π( y)] = 0 [φ( x),π( y)] = iδ (3) ( x y) [a p,a q ] = [a p,a q ] = 0 [a p,a q ] = (2π)3 δ (3) ( p q) (2.20) Proof: We ll show this just one way. Assume that [a p,a q ] = (2π)3 δ (3) ( p q). Then d 3 q ( i) ω q ( ) [φ( x),π( y)] = [a (2π) 6 2 ω p,a ]ei p x i q y q +[a p,a q]e i p x+i q y p ( i) ( = e i p ( x y) e i p ( y x)) (2.21) (2π) 3 2 The Hamiltonian = iδ (3) ( x y) Let s now compute the Hamiltonian in terms of a p and a p. We have H = 1 d 3 x π 2 +( φ) 2 +m 2 φ 2 2 = 1 [ d 3 x d 3 q ω p ω q (a 2 (2π) 6 2 p e i p x a e i p x p )(a q e i q x a e i q x q ) (i pa ω p ω p e i p x i pa e i p x p ) (i qa q e i q x i qa e i q x q ) q ] + m2 2 (a ω p ω p e i p x +a e i p x p )(a q e i q x +a e i q x q ) q = 1 1 [ ] ( ω 4 (2π) 3 p 2 ω + p2 +m 2 )(a p a p +a p a p )+(ω2 p + p2 +m 2 )(a p a p +a p a p ) p where in the second line we ve used the expressions for φ and π given in (2.18) and (2.19); to get to thethird line we ve integrated over d 3 x to get delta-functions δ (3) ( p± q) which, in turn, allow us to perform the d 3 q integral. Now using the expression for the frequency ω 2 p = p2 +m 2, the first term vanishes and we re left with H = 1 2 = (2π) ω 3 p (2π) 3 ω p [ ] a p a p +a p a p [ ] a p a p (2π)3 δ (3) (0) (2.22) 24
5 Hmmmm. We ve found a delta-function, evaluated at zero where it has its infinite spike. Moreover, the integral over ω p diverges at large p. What to do? Let s start by looking at the ground state where this infinity first becomes apparent. 2.3 The Vacuum Following our procedure for the harmonic oscillator, let s define the vacuum 0 by insisting that it is annihilated by all a p, a p 0 = 0 p (2.23) With this definition, the energy E 0 of the ground state comes from the second term in (2.22), [ H 0 E 0 0 = 1 ] 2 ω pδ (3) (0) 0 = 0 (2.24) The subject of quantum field theory is rife with infinities. Each tells us something important, usually that we re doing something wrong, or asking the wrong question. Let s take some time to explore where this infinity comes from and how we should deal with it. In fact there are two different s lurking in the expression (2.24). The first arises because space is infinitely large. (Infinities of this type are often referred to as infra-red divergences although in this case the is so simple that it barely deserves this name). To extract out this infinity, let s consider putting the theory in a box with sides of length L. We impose periodic boundary conditions on the field. Then, taking the limit where L, we get L/2 (2π) 3 δ (3) (0) = lim d 3 x e i x p L/2 L p=0 = lim d 3 x = V (2.25) L/2 L L/2 wherev isthevolumeofthebox. Sotheδ(0)divergencearisesbecausewe recomputing the total energy, rather than the energy density E 0. To find E 0 we can simply divide by the volume, E 0 = E 0 V = (2π) ω p (2.26) which is still infinite. We recognize it as the sum of ground state energies for each harmonic oscillator. But E 0 due to the p limit of the integral. This is a high frequency or short distance infinity known as an ultra-violet divergence. This divergence arises because of our hubris. We ve assumed that our theory is valid to arbitrarily short distance scales, corresponding to arbitrarily high energies. This is clearly absurd. The integral should be cut-off at high momentum in order to reflect the fact that our theory is likely to break down in some way. 25
6 We can deal with the infinity in (2.24) in a more practical way. In physics we re only interested in energy differences. There s no way to measure E 0 directly, so we can simply redefine the Hamiltonian by subtracting off this infinity, H = (2π) 3 ω pa p a p (2.27) sothat,withthisnewdefinition, H 0 = 0. Infact,thedifferencebetweenthisHamiltonian and the previous one is merely an ordering ambiguity in moving from the classical theory to the quantum theory. For example, if we defined the Hamiltonian of the harmonic oscillator to be H = (1/2)(ωq ip)(ωq+ip), which is classically the same as our original choice, then upon quantization it would naturally give H = ωa a as in (2.27). Thistypeoforderingambiguityarisesalotinfieldtheories. We llcomeacrossanumber of ways of dealing with it. The method that we ve used above is called normal ordering. Definition: We write the normal ordered string of operators φ 1 ( x 1 )...φ n ( x n ) as : φ 1 ( x 1 )...φ n ( x n ) : (2.28) It is defined to be the usual product with all annihilation operators a p placed to the right. So, for the Hamiltonian, we could write (2.27) as : H := (2π) ω pa 3 p a p (2.29) In the remainder of this section, we will normal order all operators in this manner The Cosmological Constant Above I wrote there s no way to measure E 0 directly. There is a BIG caveat here: gravity is supposed to see everything! The sum of all the zero point energies should contribute to the stress-energy tensor that appears on the right-hand side of Einstein s equations. We expect them to appear as a cosmological constant Λ = E 0 /V, R µν 1 2 Rg µν = 8πGT µν +Λg µν (2.30) Current observation suggests that 70% of the energy density in the universe has the properties of a cosmological constant with Λ (10 3 ev) 4. This is much smaller than other scales in particle physics. In particular, the Standard Model is valid at least up to ev. Why don t the zero point energies of these fields contribute to Λ? Or, if they do, what cancels them to such high accuracy? This is the cosmological constant problem. No one knows the answer! 26
7 2.3.2 The Casimir Effect I mentioned my results to Niels Bohr, during a walk. That is nice, he said, that is something new... and he mumbled something about zero-point energy. Hendrik Casimir Using the normal ordering prescription we can happily set E 0 = 0, while chanting the mantra that only energy differences can be measured. But we should be careful, for there is a situation where differences in the energy of vacuum fluctuations themselves can be measured. To regulate the infra-red divergences, we ll make the x 1 direction periodic, with size L, and impose periodic boundary conditions such that φ( x) = φ( x + L n) (2.31) with n = (1,0,0). We ll leave y and z alone, but remember that we should compute all physical quantities per unit area A. We insert two reflecting plates, separated by a distance d L in the x 1 direction. The plates are such that they impose φ(x) = 0 at the position of the plates. The presence of these plates affects the Fourier decomposition of the field and, in particular, means that the momentum of the field inside the plates is quantized as ( nπ ) p = d,p y,p z n Z + (2.32) L Figure 3: d For a massless scalar field, the ground state energy between the plates is E(d) A = dpy dp z 1 (nπ ) 2 +p 2 (2π) 2 y +p 2 d 2 z (2.33) n=1 while the energy outside the plates is E(L d). The total energy is therefore E = E(d)+E(L d) (2.34) which at least naively depends on d. If this naive guess is true, it would mean that there is a force on the plates due to the fluctuations of the vacuum. This is the Casimir force, first predicted in 1948 and observed 10 years later. In the real world, the effect is due to the vacuum fluctuations of the electromagnetic field, with the boundary conditions imposed by conducting plates. Here we model this effect with a scalar. 27
8 But there s a problem. E is infinite! What to do? The problem comes from the arbitrarily high momentum modes. We could regulate this in a number of different ways. Physically one could argue that any real plate cannot reflect waves of arbitrarily high frequency: at some point, things begin to leak. Mathematically, we want to find a way to neglect modes of momentum p a 1 for some distance scale a d, known as the ultra-violet (UV) cut-off. One way to do this is to change the integral (2.33) to, E(d) A = n=1 dpy dp z (2π) ( (nπ d ) 2 +p 2 y +p 2 z ) e a ( nπ d ) 2 +p 2 y+p 2 z (2.35) which has the property that as a 0, we regain the full, infinite, expression (2.33). However (2.35) is finite, and gives us something we can easily work with. Of course, we made it finite in a rather ad-hoc manner and we better make sure that any physical quantity we calculate doesn t depend on the UV cut-off a, otherwise it s not something we can really trust. The integral (2.35) is do-able, but a little complicated. It s a lot simpler if we look at the problem in d = 1+1 dimensions, rather than d = 3+1 dimensions. We ll find that all the same physics is at play. Now the energy is given by E 1+1 (d) = π n (2.36) 2d We now regulate this sum by introducing the UV cutoff a introduced above. This renders the expression finite, allowing us to start manipulating it thus, E 1+1 (d) π ne anπ/d 2d n=1 = 1 2 a n=1 n=1 e anπ/d = a = π e aπ/d 2d (e aπ/d 1) 2 1 e aπ/d = d 2πa π 2 24d +O(a2 ) (2.37) where, in the last line, we ve used the fact that a d. We can now compute the full energy, E 1+1 = E 1+1 (d)+e 1+1 (L d) = L 2πa π ( d + 1 ) +O(a 2 ) (2.38) L d 28
9 This is still infinite in the limit a 0, which is to be expected. However, the force is given by E 1+1 d = π +... (2.39) 24d2 where the... include terms of size d/l and a/d. The key point is that as we remove both the regulators, and take a 0 and L, the force between the plates remains finite. This is the Casimir force 2. If we ploughed through the analogous calculation in d = dimensions, and performed the integral (2.35), we would find the result 1 E A d = π2 (2.40) 480d 4 The true Casimir force is twice as large as this, due to the two polarization states of the photon. 2.4 Particles Having dealt with the vacuum, we can now turn to the excitations of the field. It s easy to verify that [H,a p ] = ω pa p and [H,a p ] = ω p a p (2.41) which means that, just as for the harmonic oscillator, we can construct energy eigenstates by acting on the vacuum 0 with a p. Let This state has energy p = a p 0 (2.42) H p = ω p p with ω 2 p = p2 +m 2 (2.43) But we recognize this as the relativistic dispersion relation for a particle of mass m and 3-momentum p, E 2 p = p 2 +m 2 (2.44) 2 The number 24 that appears in the denominator ofthe one-dimensionalcasimir forceplays a more famous role in string theory: the same calculation in that context is the reason the bosonic string lives in 26 = 24+2 spacetime dimensions. (The +2 comes from the fact the string itself is extended in one space and one time dimension). You will need to attend next term s String Theory course to see what on earth this has to do with the Casimir force. 29
10 We interpret the state p as the momentum eigenstate of a single particle of mass m. To stress this, from now on we ll write E p everywhere instead of ω p. Let s check this particle interpretation by studying the other quantum numbers of p. We may take the classical total momentum P given in (1.46) and turn it into an operator. After normal ordering, it becomes P = d 3 x π φ = (2π) 3 pa p a p (2.45) Acting on our state p with P, we learn that it is indeed an eigenstate, P p = p p (2.46) telling us that the state p has momentum p. Another property of p that we can study is its angular momentum. Once again, we may take the classical expression for the total angular momentum of the field (1.55) and turn it into an operator, J i = ǫ ijk d 3 x (J 0 ) jk (2.47) It s not hard to show that acting on the one-particle state with zero momentum, J i p = 0 = 0, which we interpret as telling us that the particle carries no internal angular momentum. In other words, quantizing a scalar field gives rise to a spin 0 particle. Multi-Particle States, Bosonic Statistics and Fock Space We can create multi-particle states by acting multiple times with a s. We interpret the state in which n a s act on the vacuum as an n-particle state, p 1,..., p n = a p 1...a p n 0 (2.48) Because all the a s commute among themselves, the state is symmetric under exchange of any two particles. For example, This means that the particles are bosons. p, q = q, p (2.49) The full Hilbert space of our theory is spanned by acting on the vacuum with all possible combinations of a s, 0, a p 0, a p a q 0, a p a q a r 0... (2.50) 30
11 This space is known as a Fock space. The Fock space is simply the sum of the n-particle Hilbert spaces, for all n 0. There is a useful operator which counts the number of particles in a given state in the Fock space. It is called the number operator N N = (2π) 3 a p a p (2.51) and satisfies N p 1,..., p n = n p 1,..., p n. The number operator commutes with the Hamiltonian, [N, H] = 0, ensuring that particle number is conserved. This means that we can place ourselves in the n-particle sector, and stay there. This is a property of free theories, but will no longer be true when we consider interactions: interactions create and destroy particles, taking us between the different sectors in the Fock space. Operator Valued Distributions Although we re referring to the states p as particles, they re not localized in space in any way they are momentum eigenstates. Recall that in quantum mechanics the position and momentum eigenstates are not good elements of the Hilbert space since they are not normalizable (they normalize to delta-functions). Similarly, in quantum field theory neither the operators φ( x), nor a p are good operators acting on the Fock space. This is because they don t produce normalizable states. For example, 0 a p a p 0 = p p = (2π)3 δ(0) and 0 φ( x)φ( x) 0 = x x = δ(0) (2.52) They are operator valued distributions, rather than functions. This means that although φ( x) has a well defined vacuum expectation value, 0 φ( x) 0 = 0, the fluctuations of the operator at a fixed point are infinite, 0 φ( x)φ( x) 0 =. We can construct well defined operators by smearing these distributions over space. For example, we can create a wavepacket ϕ = (2π) 3 e i p x ϕ( p) p (2.53) which is partially localized in both position and momentum space. (A typical state might be described by the Gaussian ϕ( p) = exp( p 2 /2m 2 )) Relativistic Normalization We have defined the vacuum 0 which we normalize as 0 0 = 1. The one-particle states p = a p 0 then satisfy p q = (2π) 3 δ (3) ( p q) (2.54) 31
12 But is this Lorentz invariant? It s not obvious because we only have 3-vectors. What could go wrong? Suppose we have a Lorentz transformation p µ (p ) µ = Λ µ ν pν (2.55) such that the 3-vector transforms as p p. In the quantum theory, it would be preferable if the two states are related by a unitary transformation, p p = U(Λ) p (2.56) This would mean that the normalizations of p and p are the same whenever p and p are related by a Lorentz transformation. But we haven t been at all careful with normalizations. In general, we could get p λ( p, p ) p (2.57) for some unknown function λ( p, p ). How do we figure this out? The trick is to look at an object which we know is Lorentz invariant. One such object is the identity operator on one-particle states (which is really the projection operator onto one-particle states). With the normalization (2.54) we know this is given by 1 = p p (2.58) (2π) 3 This operator is Lorentz invariant, but it consists of two terms: the measure and the projector p p. Are these individually Lorentz invariant? In fact the answer is no. Claim The Lorentz invariant measure is, 2E p (2.59) Proof: d 4 p is obviously Lorentz invariant. And the relativistic dispersion relation for a massive particle, p µ p µ = m 2 p 2 0 = E2 p = p2 +m 2 (2.60) is also Lorentz invariant. Solving for p 0, there are two branches of solutions: p 0 = ±E p. But the choice of branch is another Lorentz invariant concept. So piecing everything together, the following combination must be Lorentz invariant, d 4 p δ(p 2 0 p 2 m 2 ) = p0 >0 2p 0 (2.61) p0 =E p which completes the proof. 32
13 From this result we can figure out everything else. For example, the Lorentz invariant δ-function for 3-vectors is which follows because 2E p δ (3) ( p q) (2.62) 2E p 2E p δ (3) ( p q) = 1 (2.63) So finally we learn that the relativistically normalized momentum states are given by p = 2E p p = 2E p a p 0 (2.64) Notice that our notation is rather subtle: the relativistically normalized momentum state p differs from p by the factor 2E p. These states now satisfy p q = (2π) 3 2E p δ (3) ( p q) (2.65) Finally, we can rewrite the identity on one-particle states as 1 1 = p p (2.66) (2π) 3 2E p Sometextsalsodefinerelativisticallynormalizedcreationoperatorsbya (p) = 2E p a p. We won t make use of this notation here. 2.5 Complex Scalar Fields Consider a complex scalar field ψ(x) with Lagrangian L = µ ψ µ ψ M 2 ψ ψ (2.67) Notice that, in contrast to the Lagrangian (1.7) for a real scalar field, there is no factor of 1/2 in front of the Lagrangian for a complex scalar field. If we write ψ in terms of real scalar fields by ψ = (φ 1 + iφ 2 )/ 2, we get the factor of 1/2 coming from the 1/ 2 s. The equations of motion are µ µ ψ +M 2 ψ = 0 µ µ ψ +M 2 ψ = 0 (2.68) where the second equation is the complex conjugate of the first. We expand the complex field operator as a sum of plane waves as 1 ( ) ψ = b (2π) 3 p e +i p x +c e i p x p 2E p ψ 1 ( ) = b e i p x (2π) 3 p +c p e +i p x (2.69) 2E p 33
14 Sincetheclassicalfieldψ isnotreal,thecorrespondingquantumfieldψ isnothermitian. This is the reason that we have different operators b and c appearing in the positive and negative frequency parts. The classical field momentum is π = L/ ψ = ψ. We also turn this into a quantum operator field which we write as, π = (2π) i E p ) (b p e i p x c 3 p e +i p x 2 π = (2π) ( i) E p ) (b 3 p e +i p x c p e i p x (2.70) 2 The commutation relations between fields and momenta are given by [ψ( x),π( y)] = iδ (3) ( x y) and [ψ( x),π ( y)] = 0 (2.71) together with others related by complex conjugation, as well as the usual [ψ( x), ψ( y)] = [ψ( x),ψ ( y)] = 0, etc. One can easily check that these field commutation relations are equivalent to the commutation relations for the operators b p and c p, and [b p,b q ] = (2π)3 δ (3) ( p q) [c p,c q ] = (2π)3 δ (3) ( p q) (2.72) [b p,b q ] = [c p,c q ] = [b p,c q ] = [b p,c q ] = 0 (2.73) In summary, quantizing a complex scalar field gives rise to two creation operators, b p and c p. These have the interpretation of creating two types of particle, both of mass M and both spin zero. They are interpreted as particles and anti-particles. In contrast, for a real scalar field there is only a single type of particle: for a real scalar field, the particle is its own antiparticle. Recall that the theory (2.67) has a classical conserved charge Q = i d 3 x ( ψ ψ ψ ψ) = i d 3 x (πψ ψ π ) (2.74) After normal ordering, this becomes the quantum operator Q = (2π) 3 (c p c p b p b p) = N c N b (2.75) so Q counts the number of anti-particles (created by c ) minus the number of particles (created by b ). We have [H,Q] = 0, ensuring that Q is conserved quantity in the quantum theory. Of course, in our free field theory this isn t such a big deal because both N c and N b are separately conserved. However, we ll soon see that in interacting theories Q survives as a conserved quantity, while N c and N b individually do not. 34
15 2.6 The Heisenberg Picture Although we started with a Lorentz invariant Lagrangian, we slowly butchered it as we quantized, introducing a preferred time coordinate t. It s not at all obvious that the theory is still Lorentz invariant after quantization. For example, the operators φ( x) depend on space, but not on time. Meanwhile, the one-particle states evolve in time by Schrödinger s equation, i d p(t) dt = H p(t) p(t) = e ie pt p (2.76) Things start to look better in the Heisenberg picture where time dependence is assigned to the operators O, so that O H = e iht O S e iht (2.77) do H dt = i[h,o H ] (2.78) where the subscripts S and H tell us whether the operator is in the Schrödinger or Heisenberg picture. In field theory, we drop these subscripts and we will denote the picture by specifying whether the fields depend on space φ( x) (the Schrödinger picture) or spacetime φ( x, t) = φ(x) (the Heisenberg picture). The operators in the two pictures agree at a fixed time, say, t = 0. The commutation relations (2.2) become equal time commutation relations in the Heisenberg picture, [φ( x,t),φ( y,t)] = [π( x,t),π( y,t)] = 0 [φ( x,t),π( y,t)] = iδ (3) ( x y) (2.79) Now that the operator φ(x) = φ( x,t) depends on time, we can start to study how it evolves. For example, we have φ = i[h,φ] = i 2 [ d 3 y π(y) 2 + φ(y) 2 +m 2 φ(y) 2, φ(x)] = i d 3 y π(y)( i)δ (3) ( y x) = π(x) (2.80) Meanwhile, the equation of motion for π reads, π = i[h,π] = i 2 [ d 3 y π(y) 2 + φ(y) 2 +m 2 φ(y) 2, π(x)] 35
16 = i 2 d 3 y ( y [φ(y),π(x)]) φ(y)+ φ(y) y [φ(y),π(x)] ( = +2im 2 φ(y)δ (3) ( x y) d 3 y ( y δ (3) ( x y) ) ) y φ(y) m 2 φ(x) = 2 φ m 2 φ (2.81) where we ve included the subscript y on y when there may be some confusion about which argument the derivative is acting on. To reach the last line, we ve simply integrated by parts. Putting (2.80) and (2.81) together we find that the field operator φ satisfies the Klein-Gordon equation µ µ φ+m 2 φ = 0 (2.82) Things are beginning to look more relativistic. We can write the Fourier expansion of φ(x) by using the definition (2.77) and noting, e iht a p e iht = e ie pt a p and e iht a p e iht = e +ie pt a p (2.83) which follows from the commutation relations [H,a p ] = E p a p and [H,a p ] = +E pa p. This then gives, φ( x,t) = (2π) 3 1 2E p ( a p e ip x +a p e+ip x ) (2.84) which looks very similar to the previous expansion (2.18) except that the exponent is now written in terms of 4- vectors, p x = E p t p x. (Note also that a sign has flipped in the exponent due to our Minkowski metric contraction). It s simple to check that (2.84) indeed satisfies the Klein-Gordon equation (2.82). t O1 O2 x Causality We re approaching something Lorentz invariant in the Figure 4: Heisenberg picture, where φ(x) now satisfies the Klein- Gordon equation. But there s still a hint of non-lorentz invariance because φ and π satisfy equal time commutation relations, [φ( x,t),π( y,t)] = iδ (3) ( x y) (2.85) 36
17 But what about arbitrary spacetime separations? In particular, for our theory to be causal, we must require that all spacelike separated operators commute, [O 1 (x),o 2 (y)] = 0 (x y) 2 < 0 (2.86) This ensures that a measurement at x cannot affect a measurement at y when x and y are not causally connected. Does our theory satisfy this crucial property? Let s define (x y) = [φ(x),φ(y)] (2.87) The objects on the right-hand side of this expression are operators. However, it s easy to check by direct substitution that the left-hand side is simply a c-number function with the integral expression (x y) = What do we know about this function? (2π) 3 1 2E p ( e ip (x y) e ip (x y)) (2.88) It s Lorentz invariant, thanks to the appearance of the Lorentz invariant measure /2E p that we introduced in (2.59). It doesn t vanish for timelike separation. For example, taking x y = (t,0,0,0) gives [φ( x,0),φ( x,t)] e imt e +imt. It vanishes for space-like separations. This follows by noting that (x y) = 0 at equal times for all (x y) 2 = ( x y) 2 < 0, which we can see explicitly by writing [φ( x,t),φ( y,t)] = ( e i p ( x y) e i p ( x y)) (2.89) (2π) 3 p2 +m 2 and noticing that we can flip the sign of p in the last exponent as it is an integration variable. But since (x y) Lorentz invariant, it can only depend on (x y) 2 and must therefore vanish for all (x y) 2 < 0. We therefore learn that our theory is indeed causal with commutators vanishing outside the lightcone. This property will continue to hold in interacting theories; indeed, it is usually given asone of the axioms of local quantum field theories. Ishould mention however that the fact that [φ(x), φ(y)] is a c-number function, rather than an operator, is a property of free fields only. 37
18 2.7 Propagators We could ask a different question to probe the causal structure of the theory. Prepare a particle at spacetime point y. What is the amplitude to find it at point x? We can calculate this: 1 0 φ(x)φ(y) 0 = 0 a (2π) 6 p a p 0 e ip x+ip y 4E p E p = 1 e ip (x y) D(x y) (2.90) (2π) 3 2E p The function D(x y) is called the propagator. For spacelike separations, (x y) 2 < 0, one can show that D(x y) decays like D(x y) e m x y (2.91) So it decays exponentially quickly outside the lightcone but, nonetheless, is non-vanishing! The quantum field appears to leak out of the lightcone. Yet we ve just seen that spacelike measurements commute and the theory is causal. How do we reconcile these two facts? We can rewrite the calculation (2.89) as [φ(x),φ(y)] = D(x y) D(y x) = 0 if (x y) 2 < 0 (2.92) There are words you can drape around this calculation. When (x y) 2 < 0, there is no Lorentz invariant way to order events. If a particle can travel in a spacelike direction from x y, it can just as easily travel from y x. In any measurement, the amplitudes for these two events cancel. With a complex scalar field, it is more interesting. We can look at the equation [ψ(x),ψ (y)] = 0 outside the lightcone. The interpretation now is that the amplitude for the particle to propagate from x y cancels the amplitude for the antiparticle to travel from y x. In fact, this interpretation is also there for a real scalar field because the particle is its own antiparticle The Feynman Propagator As we will see shortly, one of the most important quantities in interacting field theory is the Feynman propagator, F (x y) = 0 Tφ(x)φ(y) 0 = { D(x y) x 0 > y 0 D(y x) y 0 > x 0 (2.93) 38
19 where T stands for time ordering, placing all operators evaluated at later times to the left so, { φ(x)φ(y) x 0 > y 0 Tφ(x)φ(y) = (2.94) φ(y)φ(x) y 0 > x 0 Claim: There is a useful way of writing the Feynman propagator in terms of a 4- momentum integral. d 4 p i F (x y) = e ip (x y) (2.95) (2π) 4 p 2 m 2 Notice that this is the first time in this course that we ve integrated over 4-momentum. Until now, we integrated only over 3-momentum, with p 0 fixed by the mass-shell condition to be p 0 = E p. In the expression (2.95) for F, we have no such condition on p 0. However, as it stands this integral is ill-defined because, for each value of p, the denominator p 2 m 2 = (p 0 ) 2 p 2 m 2 produces a pole when p 0 = ±E p = ± p 2 +m 2. We need a prescription for avoiding these singularities in the p 0 integral. To get the Feynman propagator, we must choose the contour to be Im(p 0) E p + E p Re(p 0) Proof: Figure 5: The contour for the Feynman propagator. 1 p 2 m 2 = 1 (p 0 ) 2 E 2 p = 1 (p 0 E p )(p 0 +E p ) (2.96) so the residue of the pole at p 0 = ±E p is ±1/2E p. When x 0 > y 0, we close the contour in the lower half plane, where p 0 i, ensuring that the integrand vanishes since e ip0 (x 0 y 0) 0. The integral over p 0 then picks up the residue at p 0 = +E p which is 2πi/2E p where the minus sign arises because we took a clockwise contour. Hence when x 0 > y 0 we have F (x y) = (2π) 4 2πi 2E p ie ie p(x0 y0 )+i p ( x y) 39
20 = 1 e ip (x y) = D(x y) (2.97) (2π) 3 2E p which is indeed the Feynman propagator for x 0 > y 0. In contrast, when y 0 > x 0, we close the contour in an anti-clockwise direction in the upper half plane to get, 2πi F (x y) = (2π) 4 ( 2E p ) ie+ie p(x0 y0 )+i p ( x y) 1 = e ie p(y0 x0 ) i p ( y x) (2π) 3 2E p 1 = e ip (y x) = D(y x) (2.98) (2π) 3 2E p where to go to from the second line to the third, we have flipped the sign of p which is valid since we integrate over and all other quantities depend only on p 2. Once again we reproduce the Feynman propagator. Instead of specifying the contour, it is standard to write Im(p 0 ) the Feynman propagator as F (x y) = d 4 p (2π) 4 ie ip (x y) p 2 m 2 +iǫ (2.99) + iε Re(p 0 ) iε with ǫ > 0, and infinitesimal. This has the effect of shifting the poles slightly off the real axis, so the integral along the real p 0 axis is equivalent to the contour shown in Figure 5. This way of writing the propagator is, for obvious reasons, called the iǫ prescription. Figure 6: Green s Functions There is another avatar of the propagator: it is a Green s function for the Klein-Gordon operator. If we stay away from the singularities, we have ( t 2 2 +m 2 d 4 p i ) F (x y) = (2π) 4 p 2 m 2 ( p2 +m 2 )e ip (x y) d 4 p = i e ip (x y) (2π) 4 = iδ (4) (x y) (2.100) Note that we didn t make use of the contour anywhere in this derivation. For some purposes it is also useful to pick other contours which also give rise to Green s functions. 40
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Personalised Blue Bear Baby Comforter with Ribbon Tags
Home / Homewares / Shop by Room / Baby's Room / Baby Care / Personalised Blue Bear Baby Comforter with Ribbon Tags
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Ollin Morales is an Angel Translator and spiritual teacher.
"Life isn't about finding yourself. Life is about creating yourself."
– George Bernard Shaw
Hi, I'm Ollin Morales. I'm a writer.
I also speak to Angels, which, I know, sounds totally crazy, but it's true. You can learn more about that by going here. (You can learn about how I became an angel translator by going here.)
Now to explain how this blog came about:
Once upon a time, an idea for a story came to me.
After writing some rough sketches several years ago, a very colorful and eccentric story was starting to emerge. Every day, after tutoring (my job at the time), I would find myself typing more of the story at local coffee shops, just for fun. Writing notes in between tutoring appointments. Drawing sketches of the characters and making story maps when my students were on their breaks.
I began to love this story very much and it started to become the most exciting project that I had ever worked on. But at that time I told very few people about it, because I was afraid that people would think it was crazy that me, a twenty-two-year-old man at the time, was spending his free time writing a fantasy story.
Two years later, after I kept on delaying writing the book (and after a serious of unfortunate events landed me with pretty much zilch in life) my sister suggested I write a blog about the experience to motivate me.
On February 26, 2010, I decided to take her advice. I would finally start writing the novel I had been wanting to write and finish it. I would write this blog journaling my experience so that my readers could encourage me but also keep me accountable.
Over the past seven years, this blog has grown to become so much bigger than me, and so much deeper than just my individual effort to keep loyal to my writing schedule.
My private journey, now public, has become a lifeline for hundreds of people who have decided to finally pursue their passions. It has touched readers who are struggling to summon up the courage to follow their passions–and the courage to create their own lives from scratch.
Over the past seven years, I've had to overcome some pretty challenging obstacles to get my novel written. But, thankfully, I keep overcoming those obstacles and I keep acquiring new tools to help me pull through. Each time I overcome a new obstacle, I share what I've learned with you so that you, too, can overcome the challenges you face.
Finally: the most recent plot twist in my life–me learning that I speak to angels–has kind of thrown a great big wrench into everything and I'm still wrapping my head around this new revelation.
So there you have it. Welcome to Courage 2 Create. It's the story of me writing my first novel… and how life keeps getting in the way.
But, really, it's the story of all of us, and the lengths that we'll take to create the life we want and give birth to the ideas that we hope will leave our mark on this world.
(And maybe realizing that I'm not writing this story but that this story is writing me.)
"Woah! This is a lot to read, and I'm new here. Where do I start?"
Welcome! I recommend that you start here.
"You've been doing this for seven years! But I just got here. Is there anyway I can play catch-up on your journey?"
Certainly! Read this post to catch up on everything that's happened on Courage 2 Create these last seven years.
"I'm loving it! Where do I subscribe?"
Find the paper icon on the very top of my side bar (its next to the magnifying glass icon) and the side bar will open. In the box titled "Subscribe by E-mail," enter your e-mail address then click on the button to subscribe.
Your subscription is totally FREE.
much love,
For those curious about my work with the Angels:
Ollin Morales is an Angel Translator (some have also referred to it as Shaman, intuitive medium, channel).
He has been an Angel Translator for over two years now helping hundreds of folks connect with their guardian angels and recieve their healing.
He has worked with over 200 people so far locally in Los Angeles and also nationally in the USA, as well as internationally in places like Europe, Canada, New Zealand and Austrailia.
His work is non-denominational and he welcomes people of all faiths and no faith (for academic purposes).
If you have questions about his methods or wish to book a reading you can do so by emailing him at
firstname.lastname@example.com, with "Angel Reading" in the subject of the email.
Learn more about his services by going here.
Listen to a radio interview with him about his angel work by going here.
Courage 2 Create and all its content is Copyrighted © 2017


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Vogue 8050; ca. 1971; Misses' Cover-Up and Pants. High-fitted, A-line cover-up in two lengths has cutaway armholes with contrast banding and front band concealing zipper closing. Sleeveless or full length sleeves. With or without contrast hood and hem banding. Straight-legged pants without side seams have elasticized waistline. Top-stitch trim.
Featured in Vogue Pattern Book Summer 1971 and on the cover of Vogue International Pattern Book June/July 1971
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mbchills modern and vintage sewing patterns
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This is philosophy but not as you know it. Throw yourself into a free flowing evening of improvisation where two leading philosophers will riff on whatever you want to ask about, from anteaters to zabaglione, Kim Kardashian to the colour yellow.
Sometimes deadly serious, usually very funny, this evening is your chance to steer a unique course through the history of ideas. TSOL faculty members and professional philosophers Mark Vernon and Robert Rowland Smith will bring you unexpected discoveries from philosophy, psychology, literature and art that might just answer what you always wanted to know.
Look out for future dates and come back again. The Philosophy Slam is never the same twice.
In our classroom on Marchmont Street, leading writers, economists, historians, philosophers, psychologists, artists and other thinkers offer provocation, inspiration and consolation in the form of advice for living better.
Each special event is limited to 32 participants, allowing for intimate engagement with the great ideas of our time. Speakers for this strand have been invited by The School of Life to present their own material. Session formats will vary depending on the subject.
The School of Life70 Marchmont StreetLondon WC1N 1AB
Concessions: we offer a 10% standard ticket price reduction on events under £50 for Students with valid ID, over-65's, un-waged and people with disabilities. To claim your discount please click here. Please note that we will check your ID for proof of eligibility on arrival at event.
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You are here
Omnibus Survey Household Survey Summary Report September 2000
Omnibus Survey
Household Survey
Summary Report
September 2000
The Bureau of Transportation Statistics - the federal statistical agency for the Department of Transportation charged with improving the knowledge base for public decision making - is coordinating the Omnibus Survey program. The survey is a ONEDOT effort to collect information about the transportation system, how it is used, and how it is viewed by the users.
BTS is gathering data each month on a random basis from 1,000 households to determine the general public's satisfaction with the nation's transportation system and to prioritize improvements to the transportation system. Each month the survey contains a set of core questions about transportation system use, as well as questions posed by the various operating administrations within the Department. Finally, each month the survey asks questions relating to one of the following DOT strategic goals: safety, mobility, human and natural environment, or national security.
These monthly surveys are designed to measure Americans' satisfaction with the transportation system and the Department of Transportation. They are not intended nor designed to measure characteristics of the transportation system. The data concerning characteristics of transportation are collected to enhance understanding of the customer satisfaction measures and the concerns respondents express regarding the transportation system.
Estimates such as the number of Americans traveling by air, the availability of public transportation, use of car pools, and the like may not match data from other sources because of sampling variability and methodological limitations of the survey. For example, the survey covers only people in households with a telephone. Characteristics related to the lack of a telephone will be estimated with imperfect accuracy. For example, estimates of households having no licensed motor vehicles are likely understated because the sample does not include households without telephones.
Another source of possible disagreement with other estimates occurs because the Omnibus survey does not use official definitions of transportation concepts in the interview. Due to time constraints, the survey often provides no definitions, but allows the respondent to interpret terminology in the question. Estimates based on respondent reports from the Omnibus Survey could differ from estimates obtained through different methods. For example, when the Omnibus asks respondents about the availability of public transportation, it does not specify, "within a quarter mile." Nor does it define "public transportation." Without precise definitions, respondents may consider charter buses, for example, to be "public transportation."
The findings provided by the Omnibus Survey program will provide a valuable framework for the Secretary and senior officials in DOT operating administrations to make measurable improvements in our transportation system, the security of our nation, and the quality of American life.
For More Information
Omnibus Survey Program
Office of Statistical Programs
Bureau of Transportation Statistics
US Department of Transportation
Sharon Durant
(202) 366-0649
John Bushery
(202) 493-0360
Elizabeth Grossman
(202) 366-2087
Major Findings
The strategic goals focused on in the September survey were mobility and economic growth, while the mode-specific questions concern rail grade crossings, travel by persons with disabilities, tire pressure, terrorism threats, airplane luggage restrictions, and truck safety. This report summarizes the major findings of the survey. More detailed results and the data are available on the BTS Omnibus website at www.bts.gov/omnibus.
Transportation System Use
More than 98 percent of the September survey respondents have used the transportation system in the past 30 days. The most common mode of transportation was a private vehicle which was used by more than 96 percent of the respondents. Almost 90 percent of the respondents had driven alone in the past 30 days while more than half had driven or ridden with someone else.
The proportion of respondents who have used each of the modes of transportation has remained relatively constant since the August Household Survey. Airplane usage and taxi, limo, and shuttle usage have both declined, while recreational boat usage has increased.
Approximately 207 million Americans drove or rode in a private vehicle in the past thirty days. One hundred and eighty-five million Americans drove alone in a private vehicle at least once, while the vast majority, 83.5 percent, did so more than 10 times. One hundred and seven million Americans drove or rode with others at least once. Commercial boats, intercity buses, intercity trains, and private or charter airplanes were the modes of transportation used least.
Frequency of Transportation Use in Last 30 Days - September
|Mode of transportation
|Total number (millions)
|Percent who used mode in last 30 days by number of times used
|1 or 2 times
|3 to 5 times
|6 to 10 times
|More than 10 times
|Drive alone in private vehicle
|Drive or ride with others
|Local bus, subway rail
|Recreational boat
|Taxi, limo or shuttle
|Commercial airliner
|Commercial boat
|Intercity bus
|Intercity train
|Private or charter airplane
The bicycle was also a popular mode of transportation; approximately 42 million American adults, 1 out of every 5, has ridden a bike in the past 30 days. Most adults used their bicycles for recreation or exercise. Only 7 percent report using their bicycles to commute to work.
Transportation System Use for Package Delivery
Internet and phone purchases that require delivery to homes have a major impact on transportation system use. Monitoring the flow of traffic on neighborhood streets and roads as a result of package delivery is important for DOT in order to assess the effects of congestion, delay, road conditions, and the like.
The number of adults who made purchases over the phone or Internet in the past 30 days that required delivery of a package declined from August to September. In the 30 days prior to the August Household survey, approximately 68.9 million Americans made at least one such purchase. In the 30 days prior to the September Household Survey, only 59.7 million Americans made at least one such purchase. In addition, the number of individuals making multiple purchases requiring package delivery declined.
The observed decline in purchases over the phone or Internet requiring package delivery may be a function of late summer vacation schedules. The Omnibus Survey program will continue to monitor trends in phone and Internet purchases among Americans.
Disability and Transportation Use
The September survey found that about one in ten (20 million) American adults have some kind of disability or health problem that makes it difficult for them to travel outside their homes. This number is the same as reported in the August Household Survey Report but lower then the number reported from the 1995 National Health Interview Survey (17 percent).
The September survey found that one in four of those with a disability or health problem which made it difficult to travel outside the home were age 65 or older. An additional 24 percent were in the 45 to 54 year age group. Despite the high proportion of respondents with disabilities or health problems in the latter age group, health problems increase with age. The growth in the number of people with disabilities can be expected to accelerate in the coming decades-resulting in larger and larger numbers of people who have difficulty traveling outside their homes.
Transportation service barriers impede the full social and labor-force participation of people with disabilities or health problems. Access to public buildings, including bus and transit stations and airports, may be a problem for them. Some modes of transportation, such as intercity buses and some subway systems, remain almost totally inaccessible to those with limited mobility. Air travel can be partially accessible or completely inaccessible, depending on the type of plane and the presence or absence of a jet way. Among the difficulties using public transportation cited by disabled persons, over 50 percent said they experienced problems with transportation as a driver of a private vehicle. Forty-six percent indicated they had difficulties traveling by bicycle, and 41 percent indicated they had difficulties traveling on public transportation.
Public Opinion About Transportation Issues
In the September Household Survey, respondents were asked again to rate their level of concern about eleven specific transportation issues. As in August, the September Household Survey shows that accidents evoke the greatest concern; an identical proportion of survey respondents, 59 percent, indicated they had "great concern" about accidents in August and September.
As found in August, the cost of transportation, the accessibility of transportation services for people with disabilities, and air pollution are the other areas of greatest concern to the American public. Interestingly, concern about crime while traveling has declined since August. In the August Household Survey, 40 percent of respondents expressed "great concern" about how safe they feel from crime while traveling. In September, that proportion dropped to 34 percent.
A new item in the September Household Survey, about which respondents were asked to rate their level of concern, was the availability of public transportation such as transit buses and trains in their area. More than one in four respondents, 27 percent, expressed "great concern" about this issue.
Respondents were also asked to rate their level of satisfaction or dissatisfaction with the same eleven specific transportation issues again. The proportions of respondents who said they were "very satisfied" or "very dissatisfied" with each issue are presented below.
Although the largest proportion of respondents expressed "great concern" about accidents, only a small proportion, 14 percent, were very dissatisfied about accident safety. In fact, for three of the five areas of greatest concern, accident safety, access for the disabled, and security from acts of terrorism, the proportion of respondents who were very satisfied was greater than the proportion of respondents who were very dissatisfied.
Respondents expressed the greatest dissatisfaction with transportation costs. Fifty percent, were dissatisfied or very dissatisfied with how much they spend on transportation. The other area of greatest dissatisfaction was travel delays. Thirty-nine percent of the respondents were dissatisfied or very dissatisfied with delays when they travel. An almost equal proportion of respondents, 38 percent, were dissatisfied or very dissatisfied with the availability of public transportation in their area.
|Delays and Congestion
This month Omnibus Survey focused on DOTs mobility strategic goals. Specifically, the September Household Survey sought to measure the impact of delays and congestion on the everyday lives of Americans.
Americans are bothered by traffic delays and congestion. For every two Americans who are not at all bothered, there are three Americans who are bothered a lot. Almost 50 percent are bothered a little bit.
One hundred and thirty-five million Americans commute to work or school on a regular basis. To assess the impact of congestion on their time, respondents were asked how long their commute between home and work or school was on average and how long it would be if there were no congestion.
Approximately 60 percent of Americans have commutes of 20 minutes or less. If there were no congestion, this proportion would rise to 75 percent. Without congestion, the proportion of Americans who commute for 30 minutes or more would decline from approximately 20 percent to only 10 percent.
An additional 65 million Americans travel from home to various places throughout the day. To assess the impact of congestion on their time, these respondents were asked how long it took them to get from home to their first stop on the most recent day on which they traveled and how long it would have taken had there been no delays or congestion.
On any given day, only 40 percent of Americans who make trips during the day can arrive at their first stop in 10 minutes or less. If there were no congestion, that proportion could increase by 25 percent.
The September Household Survey sought to assess the impact of congestion not only on people's time but also on their lives. To do this, respondents were asked how often delays and congestion had affected various aspects of their lives in the past week.
Delays and congestion affected the time of day traveled and the route taken frequently or occasionally for more than half the respondents. They seem to have had far less impact, however, on either the method of transportation used or attendance at meetings or appointments. Decisions about the method of transportation were never affected by delays or congestion for more than 75 percent of the respondents, and fully 85 percent of the respondents did not miss a meeting or appointment because of delays or congestion.
Tire Pressure
The recall of the Firestone tires on Ford Explorers has focused a lot of attention on the importance of tire pressure for vehicle safety. The September survey asked the American public about the number of licensed vehicles they own and how and when they check the air pressure in the tires of those vehicles.
There are approximately 193 million licensed vehicles in the U.S. More than half the households have two or three vehicles. Almost one in three has only one vehicle, while one in ten has four or more.
Almost half of all the survey respondents checked the air pressure in their tires themselves. Men, however, were almost three times as likely to check the air pressure in their tires themselves than were women. Seventy-two percent of the male respondents said they did it themselves compared with only 27 percent of the female respondents. Thirty-four percent of the female respondents said their spouse checked the air pressure in their tires.
Women were also twice as likely not to know who checked their tire air pressure or not to check it at all. The proportion of respondents who said "no one" or "don't know" was less than 2 percent.
Respondents were asked how often they checked or had someone else check the air pressure in their tires. An equal proportion, 29 percent, checked their tires either monthly or when they seemed low. Approximately five percent of the respondents reported that they checked their tires weekly.
Respondents who checked the air pressure in their own tires were asked what methods they used to determine the proper air pressure for their tires. The method cited by 45 percent of the respondents was relying on the information printed on the side of their tires. More than one in four, however, used their vehicle's owner's manual to determine the proper air pressure. Other methods respondents reported using include using air pressure or tire gauges or relying on others such as a relative, friend of mechanic.
Respondents who checked the air pressure in their own tires were also asked what methods they used to determine when the desired air pressure had been reached. Sixty-eight percent reported that they used a hand-held tire gauge. Another 27 percent relied upon the tire pump gauge or bell. Other methods mentioned for determining whether the desired air pressure had been reached were based on the vehicle's performance and the response of the tire after being pushed.
America's Perceptions of Truck Safety
Just under half of all Americans agree with the statement that most truck drivers drive safely, a decline from the findings in August. Although a large number of Americans agree most truck drivers drive safely, an even greater proportion (57 percent) feel very concerned about their own safety when traveling near large trucks. Over half of all drivers make a special effort to avoid driving near large trucks.
America's Understanding of Rail Crossing Safety
Every day, people attempt to beat a train to the railroad crossing, endangering their lives as well as those of the train crew and passengers. Although over 65 percent of the survey respondents, almost two out of every three, knew a motorist should "Stop, Look, and Listen" before proceeding across a railroad crossing, this proportion has declined from 69 percent in the August survey. The Household survey will continue to track this measure to provide a basis for DOT decision makers to assess the effectiveness of its public safety campaigns.
America's Understanding of Commercial Air Regulations
To assess America's understanding of commercial air regulations, respondents were asked whether ten items or groups of items were never allowed on commercial airline, allowed on commercial airlines with some restrictions, or always allowed on commercial airlines. The results from the September Household Survey are very similar to those from the August survey.
America's Perceptions of National Security
The proportion of Americans who agree that the U.S. is vulnerable to terrorism that threatens the safety of its transportation system declined slightly from 65 percent in August to 62 percent in September. Similarly, the proportion of Americans who agree that they are not concerned about terrorist acts threatening their own personal safety while traveling rose from 57 percent in August to 60 percent in September. Support for airport-type security measures at bus and rail stations to address the threat of terrorist acts remained virtually unchanged.


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A Tale of Two Cities: 3191 Miles Apart2013-01-04 11 Share Tweet
3191 miles is the approximate distance between Portland, Maine, and Portland Oregon. It's the title of a blog shared between two friends who live in the aforementioned cities. Their story is special and one we Lomographers may relate to.
Stephanie Congdon Barnes and Maria Alexandra Vettese met online in 2005 and became friends through their joint love of Arts and Crafts. They both live in Portland, however are 3191 miles apart owing to the fact they're in different States. They began their first year-long project together on January 1, 2007 titled "3191: A Year of Mornings" for which they snapped one photo each morning, over a 365-day period, which was subsequently published into a book.
Barnes (SCB) and Vettese (MAV)'s more recent projects include "A Year of Evenings" and "A Year of Sundays". Some photos from the latter are displayed above. SCB and MAV finally met up in 2008 after collaborating for two years and have exhibited in galleries, published books, and continue to tend their online magazine/blog and quarterly publications.
Does this sound familiar to you? Have you met an online friend through your shared passion of the analogue? Have you been swapping films for years and plan on meeting up in the near future, or have you already done so and are planning your next trip together? Share your stories and photos with us!
Follow the ongoing project on Facebook.
Information for this article was taken from 3191 Miles Apart.
written by soundfoodaround on 2013-01-04 #news #project #film-swap #maine #creative #portland #mornings #memory #oregon #friends #nights #sundays #3191


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"I have not failed. I've just found 10,000 ways that won't work."
~ Thomas A. Edison
"I have not failed. I've just found 10,000 ways that won't work."
~ Thomas A. Edison
Posted by Alexandria Sage on June 10, 2012
OMG, those flower photos are stunning. That's my favorite shade of purple!
They are a beautiful purple, aren't they? And guess what—for the life of me I do not know what variety they are! Their little ID card is sunken into the ground where I planted them. They are a sort of ground cover—not phlox, not thrift.
Any help in identifying them is appreciated!
Strong colour! Nice!
Amazing 😀
Thank you!
This brings a smile on my face….
For that I am very glad!
mirthful blossoms! so picturesque! 🙂
The mission statement and eight of the categories, with only slight alteration of the wording, are the original work of Stephen Deal, taken from his Senior Convocation speech "Things We Want You to Remember".
The "My Thoughts" category under the name of "Steve", are his original work as well.
Excerpts and links may be used but kindly ask permission. Then give credit where credit is due. Thank you!
Alexandria thanks Stephen Deal for his contribution as a guest author on this blog.


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3 Fire King? Mar Crest Currier and Ives Coffee Cups-Milk Glass
- Sold for: Start Free Trial or Sign In to see what it's worth.
- Item Category: -
- Source: eBay
- Sold Date: Jun 11, 2012
- Channel: Auction House Sell similar item on eBay
This listing is for three Fire King or Mar Crest white milk glass coffee cups in a Currier and Ives pattern. It shows children playing by a fence. All in very nice condition, no stains or chips. If you have any questions, please ask, and thanks for looking!


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Key Commitments
The 7 Key Commitments are principles which Members of Happy to Translate agree to incorporate into their business.
A Happy to Translate organisation will…
- Promote equal access to information and services for all people and communities by helping them to overcome language and communication barriers.
- Implement and maintain a high standard of customer service to improve access to information and services.
- Provide professional language and communication support to service users according to the Happy to Translate best practice guidance.
- Establish and maintain staff training and support on the use of Happy to Translate.
- Actively display and promote the Happy to Translate logo to the communities it serves and according to the Logo Design Guidelines.
- Monitor and evaluate the use of Happy to Translate and actively share and implement ideas for improvement.
- When possible, participate in a joined-up approach with other organisations to promote language and communication support.
All Happy to Translate member organisations are committed to upholding the Key Commitments.
The Commission joined HTT two years ago as a way of ensuring it was meeting the needs of all its applicants, irrespective of traditional language barriers. The logo has been successfully incorporated into all of our information literature and is on display throughout the office. We have found this approach to be extremely effective in contributing towards our equality commitments as well as general membership of HTT providing invaluable training, support and value for money.


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Hi companions in misfortune,
Why do you think about an indic that wouldn't run anymore when you re-start the plaform until you recompile it ?
This indic built under MT4 use simple init(), deinit(), start) & some includes .
All of these files are correctly placed in the new rooming V610 Folder.