Gravity can be described not as a force but a curvature of spacetime. I assume this can’t be done to the other 3 fundamental forces. If so, then we cannot treat gravity in a way similar to the other forces. Why then does QFT postulate the existence of gravitons? Why does it attempt to treat...
Electrons passing through a double slit is in a superposition of passing through the left slit and the right slit, thereby producing an interference pattern on the screen. But when a detector is placed to detect which slit the electrons pass through, the interference pattern is destroyed.
How...
In other words, does there exist, for an electron, a definite direction in physical space such that a measurement of its spin along that direction always give spin up, 100% of the time?
Suppose a wave function is a linear combination of 2 stationary states: ##\psi(x)=c_1\psi_1(x)+c_2\psi_2(x)##.
By [5.52] and [5.53], we have ##\psi(x+a)=e^{iK_1a}c_1\psi_1(x)+e^{iK_2a}c_2\psi_2(x)##. But to prove [5.49], we need ##K_1=K_2##. That means all the eigenvalues of the "displacement"...
Electrons are indistinguishable, but we may pretend that they are distinguishable if their wave functions do not overlap in space. For example, an electron "a" in Chicago and an electron "b" in Seattle would produce a zero integral in [5.20], and so their indistinguishablilty would not produce...
The book explains covalent bonding is due to exchange forces of attraction, which isn't a real force but the last term in [5.22]. This term arises due to electrons being indistinguishable particles.
If electrons were distinguishable, there would be no exchange forces. Then, would there still be...
Consider an ##N_2## molecule. Chemists say that the triple bond is due to one ##p_x - p_x## overlap, one ##p_y - p_y## overlap and one ##p_z - p_z## overlap. The x axis (the label is not important; I’m sure you know what I mean) is clear because it’s the longitudinal axis of the molecule. But...
Why can't the general state, in the presence of coupling, take the form $$\psi_-(r)\chi_++\psi_+(r)\chi_-$$ where ##\psi_+(r)## and ##\psi_-(r)## are respectively the symmetric and anti-symmetric part of the wave function, and ##\chi_+## and ##\chi_-## are respectively the spinors representing...
The book uses ladder operators ##L_+## and ##L_-## to find the eigenvalues ##m## of ##L_z##. By first deducing that these operators raise or lower the eigenvalue by ##\hbar##, and then deducing that the lowest eigenvalue is the negative of the highest eigenvalue ##l##, it proves that ##m = -l...
Why is there a preferred z axis even though the potential energy function is perfectly spherical? Shouldn't the electron be around the nucleus in a spherically symmetrical way?
Consider a gaussian wave packet whose wave function at a particular instant of time is
Its time dependence is implicit in the "constants" A, a, <x> and <p>, which may all be functions of time.
But regardless of what functions of time they may be, these constants will take on some values at...
For quantum mechanics to be internally consistent, the following must be true:
In other words, it is not alright for the solution space (to the Schrodinger equation) to span only a subspace of the Hilbert space. It has to span the entire Hilbert space. But why? What's inconsistent about it?
I...
Suppose the chance of winning and the chance of losing a game are both 0.5. You have $A at first, and the bet per game is $1. You stop playing when either you lose all your money (bad outcome) or when you reach $B, where B>A (good outcome). Then the chance of having the good outcome is...
Suppose ##X## ~ N(##\mu##,##\sigma^2##). Then ##\bar{X}## ~ N(##\mu##,##\frac{\sigma^2}{n}##), where ##\bar{X}## is the random variable for sample mean for samples of size ##n##.
But when the population variance ##\sigma^2## is unknown and the sample size ##n## is small, ##\bar{X}## no longer...
Suppose you are in a game with 4 rooms, A, B, C and D, with the rewards $30, $50, $70 and $100, respectively. There are 8 people in the game, and the reward in each room will be equally shared among those who choose the room. You will not know the choice of other players until you have made...
Suppose at the instant a gravitational wave passes through an interferometer, one of the interferometer's arm get stretched by 1%. Would the wavelength of the photon travelling in the arm also get stretched by 1%? If so, then would the frequency of the photon remain the same and hence increasing...
I don't fully understand the argument below used to derive the Lorentz transformation equation ##y'=y##.
Suppose we have a rod of unit length placed stationary in frame S. According to an observer in frame S' (which is moving at a velocity v relative to frame S), this rod is moving and its...
Since the universe's expansion is accelerating, let's suppose it will expands at a higher rate of 700 km per s per megaparsec (10 times the present value) in future. Then the Hubble radius would be 430 megaparsecs (0.1 times the present value). So shouldn't the Hubble sphere contract instead...
Suppose an object is moving away from you. Is there a way to determine, experimentally or otherwise, whether it is moving through space or whether it is sitting still but appears moving because the space between you and the object is expanding?
Galaxies that are sufficiently far away from us...
Nuclear binding energy is the energy that would be required to disassemble the nucleus of an atom into its component parts.
If book-binding cost is the cost required to bind a book, then shouldn't nuclear binding energy be the energy required to bind a nucleus?
Given the definition above...
Mentor Note: thread moved, therefore no template
A mass m is placed on a vertical spring and allowed to reach equilibrium, whose level is ##e_0## below the original level of the spring before placing the mass. It is then pushed downwards such that it is now a distance ##x_0## below the...
While it's true that it prevents successful penetration by unwanted males, but any unsuccessful fertilization by any males, unwanted or otherwise, results in fewer offsprings. This means lower genetic fitness for convoluted vaginas.
EDIT: Not in humans. But in other species in nature such as ducks.
The rays of light from a moving source are tilted towards the direction of the source's motion. It is as if light emitted by a moving object is concentrated conically, towards its direction of motion. This effect is called relativistic beaming.
For example, if a source is emitting light...
Suppose an observer in the earth frame set out to measure the length AB by measuring the time interval between the event "B coincides with D" (event BD) and the event "A coincides with D" (event AD), and then multiplying the time with ##v##. This observer argues that an observer in the train...
Emission theories propose that the velocity of light depends on the velocity of the light source. But the ordinary Doppler effect assumes the velocity of light remains as ##c## with respect to the ether medium, even when the light source is moving at speed ##v## with respect to the ether. They...
I find this question rather difficult!
Q1. I take Fig 1-11 to be the laboratory frame and ##v## to be the velocity of the ether wind. Since Lorentz length contraction occurs only horizontally, the right mirror should be further to the right horizontally in the ether frame. This makes the angle...
Consider two stationary masses, each 1 kg, placed a distance ##d_0## apart. Find the position ##x(t)## of each mass in terms of time ##t##. Consider only gravitation without relativistic effects.
Let the distance between the two masses at time ##t## be ##d(t)##. If we set the origin of our...
Is the attached solution complete? In particular, do we need to prove that ##V'(r_{12}')=V(r_{12})##, where ##V'(r_{12}')## is the potential energy function in the reference frame ##S'##, moving at a uniform velocity with respect to the reference frame ##S##, and ##r_{12}'## is the distance...