If denotes the quantum state of a particle ( n ) with momentum p, spin J whose component in the z-direction is σ, then one has

If the cord is twisted up tightly on itself and then the bucket is released, it begins to spin rapidly, not only with respect to the experimenter, but also in relation to the water it contains.

If light pressure were the cause of the rotation, then the better the vacuum in the bulb, the less air resistance to movement, and the faster the vanes should spin.

If multiple fermions have the same spatial probability distribution, then at least one property of each fermion, such as its spin, must be different.

If it exists, the graviton is expected to be massless ( because the gravitational force appears to have unlimited range ) and must be a spin 2 boson.

If a sample of cobalt-60 atoms is magnetized so that they spin counterclockwise around some axis, the beta radiation resulting from their nuclear decay will be preferentially directed opposite that axis.

Since counter-clockwise may be defined in terms of up, forward, and right, this experiment unambiguously differentiates left from right using only natural elements: If they were reversed, or the atoms spun clockwise, the radiation would follow the spin axis instead of being opposite to it.

If two quarks have unaligned spins, the spin vectors add up to make a vector of length S = 0 and only one spin projection ( S < sub > z </ sub > = 0 ), called the spin-0 singlet.

Alice could send bits to Bob in the following way: If Alice wishes to transmit a " 0 ", she measures the spin of her electron in the z direction, collapsing Bob's state to either or.

If the rotating body is symmetrical and its motion unconstrained, and, if the torque on the spin axis is at right angles to that axis, the axis of precession will be perpendicular to both the spin axis and torque axis.

If each of two hypothetical experimenters, Alice and Bob, has one of the particles that form an entangled pair, and Alice measures the spin of her particle, the measurement will be entirely unpredictable, with a 50 % probability of the spin being up or down.

If the objects are indeterminate until one of them is measured, then the question becomes, " How can one account for something that was at one point indefinite with regard to its spin ( or whatever is in this case the subject of investigation ) suddenly becoming definite in that regard even though no physical interaction with the second object occurred, and, if the two objects are sufficiently far separated, could not even have had the time needed for such an interaction to proceed from the first to the second object?

If the bucket's spinning is stopped then the surface of the water remains concave as it continues to spin.

:: If Alice wishes to transmit a ' 0 ', she measures the spin of her electron in the z direction, collapsing Bob's state to either | z +>< sub > B </ sub > or | z ->< sub > B </ sub >.

If Alice wishes to transmit a ' 1 ', she measures the spin of her electron in the x direction, collapsing Bob's state to either | x +>< sub > B </ sub > or | x ->< sub > B </ sub >.

If done correctly, a " Z " shot will apply spin to the ball as well on the final bounce, causing it to rebound perpendicular to the second wall and fall parallel to the back wall, the closer the better.

If the axis is within the body, and passes through its center of mass the body is said to rotate upon itself, or spin.

If one believes that spin measurements are indeed measuring the spin of a particle that existed prior to the measurement, then one does reach contradictions.

If the first 2 numbers or letters of the spin match up, the digital program will display many animations before the third reel stops spinning, to give the player added excitement.

If a bowler, usually a leg spin bowler, decides to attack the batsman's legs in an attempt to force a stumping, bowl him behind his legs, or induce a catch on the leg side, the field may stack 4-5 towards the leg side.

If a particle and antiparticle are in the appropriate quantum states, then they can annihilate each other and produce other particles.

If the path of the particle or centre of mass of the rigid body passes through the given origin, its angular momentum is zero.

If we define r < sub > i </ sub > as the displacement of particle i from the center of mass, and v < sub > i </ sub > as the velocity of particle i with respect to the center of mass, then we have

If a particle of the beam crosses this surface, there will be some kind of interaction.

If we think of the atoms as impenetrable steel discs and the impinging particle as a bullet of negligible diameter, this ratio is the probability that the bullet will strike a steel disc, i. e., that the atomic projectile will be stopped by the foil.

If this acceleration is multiplied by the particle mass, the leading term is the centripetal force and the negative of the second term related to angular acceleration is sometimes called the Euler force.

If the depletion layer is large enough to catch the whole shower or to stop a heavy particle, a fairly accurate measurement of the particle ’ s energy can be made, simply by measuring the charge conducted and without the complexity of a magnetic spectrometer, etc.

If an elementary particle truly has no substructure, then it is one of the basic building blocks of the universe from which all other particles are made.

If the entire volume of the observable universe ( taken to be 3 × 10 < sup > 80 </ sup > m < sup > 3 </ sup >) were packed solid with fine dust particles about 1. 5 micrometres in size, then the number of different ways of ordering these particles ( that is, assigning the number 1 to one particle, then the number 2 to another particle, and so on until all particles are numbered ) would be approximately one googolplex.

If the particles are indistinguishable, this is impossible by definition ; either particle can be in either state.

If the particles are bosons, they occupy a totally symmetric state, which is symmetric under the exchange of any two particle labels:

If a particle of charge q moves with velocity v in the presence of an electric field E and a magnetic field B, then it will experience a force

If a force is applied to a particle for a time interval, the momentum of the particle changes by an amount

If the particle is moving at speed in the first frame of reference, in the second it is moving at speed

If a charged particle moves in an electromagnetic field, its kinematic momentum is not conserved.

If, e. g., u is the speed of a particle, then the straightforward notation for its velocity is u, < u > u </ u >, or.

If the photon energy is absorbed, some of the energy liberates the electron from the atom, and the rest contributes to the electron's kinetic energy as a free particle.

If the particle is in an eigenstate of position, then its momentum is completely unknown.

If Alice has a particle which is entangled with a particle owned by Bob, and Bob teleports it to Carol, then afterwards, Alice's particle is entangled with Carol's.

`` If Blue Throat has his way he'll keep us all cooped up in here for days '', he said.

If Wilhelm Reich is the Moses who has led them out of the Egypt of sexual slavery, Dylan Thomas is the poet who offers them the Dionysian dialectic of justification for their indulgence in liquor, marijuana, sex, and jazz.

If the man on the sidewalk is surprised at this question, it has served as an exclamation.

If any one of them has any power to veto the Secretary General's decisions the nature of the organization will have changed.

If this new Bible does not increase in significance by repeated readings throughout the years, it will not survive the ages as has the King James Version.

If the case is thus determined by us to be domestic, the court has no jurisdiction.

If this capacity had not failed them, they would see that their enemy has made a disastrous miscalculation.

If the new Soviet series has followed the general pattern of previous Russian tests, the shots were roughly half fission and half fusion, meaning a fission yield of 30 to 40 megatons thus far.

If the superintendents do not receive more cooperation from Handlers, it has been suggested that licensed Judges also be qualified to judge this Class.

If your state has no provisions for the numbering of pleasure boats, you must apply for a number from the U.S. Coast Guard for any kind of boat with mechanical propulsion rated at more than 10 horsepower before it can be used on Federal waterways.

If design head has a deep cavity, clay lid will be quite thick at this point ; ;

If you run into excess plug fouling on one truck, check to be sure that the rig has a thermostat.

If we manage to keep track of a Bombus queen after she has left her feeding place, we may discover the snug little hideout which she has fixed up for herself when she woke up from her winter sleep.

If cell Af has not previously been assigned as the information cell of a form in the text-form list, it is now assigned as the information cell of Af.

If of the founders of glottochronology Swadesh has escaped our steady plodding, and Lees has repudiated his own share in the founding, that is no reason why we should swerve.

If the transferor has substantial assets other than the claim, it seems reasonable to assume no corporation would be willing to acquire all of its properties in the dim hope of collecting a claim for refund of taxes.

If the patient can perceive figure kinesthetically when he cannot perceive it visually, then, it would seem, the sense of touch has immediate contact with the spatial aspects of things in independence of visual representations, at least in regard to two dimensions, and, as we shall see, even this much spatial awareness on the part of unaided touch is denied by the authors.

If the distant patron of the suburban branch has been frightened away from downtown by traffic problems, however, the city store can only pressure the politicians to do something about the highways or await the completion of the federal highway program.

If a statement has been assigned an address in the index word area

If she has not had such experiences, the female's normal adolescent degree of indecision will be compounded.

If the change, at first sight, seems minor, we may recall that it took the Italian painters about two hundred years to make an analogous change, and the Italian painters, by universal consent, were the most brilliant group of geniuses any art has seen.

If Barnett doesn't call a special session in 1961, it will be the first year in the last decade that the Legislature has not met in regular or special session.

If the church has followed the plan of cultivation of prospects and carried through a program of membership preparation as outlined earlier in this book, the process of assimilation and growth will be well under way.