Month: May 2025

A question on Quora asks about speed of photons in a refractive medium.

Most of the answers given so far are correct – even when they contradict one another. This is because the path of a photon is something that is not well defined. In quantum theories particles with definite properties don’t really exist between observations, and what we call the path is just something that we infer after observations have been completed and depends on how closely we look. If we set up an experiment to detect single photons after passing from a source through a uniform medium like glass or air, then we find that no photons arrive when the straight line path is obstructed (so they appear to have followed a straight line) and the time delay between emission and detection corresponds to a speed slightly less than that of light in a vacuum. But on the other hand it seems that experiments designed to estimate the speed of photons between adjacent atoms show them travelling at the same speed as they would in a vacuum. One way of explaining this discrepancy is to realize that what quantum theory predicts is that the probability of detecting a photon is the squared magnitude of a sum (actually a generalized integral) of many complex-valued contributions corresponding to paths that a point particle could be imagined to have taken by going either directly in a straight line or by going on a (longer) polygonal path bouncing off electrons and protons in the medium. If there are many charged particles between source and detector the contributions from all these paths may interfere with one another in such a way that they cancel out almost completely everywhere except near events on the straight line path but at times slightly later than for direct travel in a vacuum.

Source: (1002) Alan Cooper’s answer to If photons don’t actually slow down in a medium like glass, how exactly does the path get ‘longer’ for them? – Quora

Travellers on the spaceship don’t actually see (or in any other way directly experience) the sudden ageing of those on earth when they turn around, but rather they just infer it from what they do see. Just before the turn-around, what the travellers see of Earth is actually not what they think is happening in their version of “now” but rather what was occurring at an earlier time when the light signal was emitted (and what for them is actually occurring “now” hasn’t been seen yet). After a quick turn-around what they see of the Earth is essentially the same as just before, but now the correction for light travel time is different and the result is that it now seems to them that the events occurring “now” on Earth (which they haven’t seen yet) correspond to a later Earth time than they did just before the turn. So even though they don’t see the jump it seems to the travellers as if the Earth’s clocks quickly jumped ahead. This solves the mystery of the age difference because the amount of the apparent jump in Earth’s time is exactly twice the amount of progress lost during the two periods where the Earth seems to be ageing slowly so at the end of the trip the tavellers and homies all agree that the Earth has aged more.

Source: (1002) Alan Cooper’s answer to In the twin paradox, why does the traveling twin experience a sudden jump in earth time during the frame switch, and how does this solve the mystery of the age difference? – Quora

Kronecker delta is not a tensor of any kind. It is just a fixed numerical matrix.

Tensors of order $#n#$ are linear functions from sets of $#n#$ vectors to the field of numbers and can be described in terms of any particular basis by arrays of numbers called components of the tensor with respect to that basis.

If the vector space has an inner product, then tensors of second order (ie ones involving two vectors) can be identified with linear operators on the vector space by requiring the matrix of the operator in basis $#\{ b_{i}\}#$ to be given by $#T_{ij}=\langle b_{i}|Tb_{j}\rangle=T(b_{i},b_{j})#$ .

In general, these components depend on the choice of basis, and the transformation rules for tensors tell us how they vary with changes in the basis that is being used to determine them.

For the special case where the tensor function $#T#$ is just the inner product, then for any orthonormal basis we get $#T_{ij}=T(b_{i},b_{j})=\langle b_{i}|b_{j}\rangle=\delta_{ij}#$, (and the corresponding operator is just the entity operator $#Tv=v#$ for all $#v#$). These components will be the same for any orthonormal basis, so the components are invariant under orthogonal transformations; but the same tensor may have a different matrix with respect to a basis that is either skew or not normalized. So what is true is that for a tensor whose components are given by the Kronecker delta, those components are invariant with respect to orthonormal changes of basis. (But, while the components will be changed by changes of scale or angle so that the new ones will not be given by$# \delta_{ij}#$, the Kronecker delta will still be what it was – just corresponding now to a different tensor.)

Source: (1002) Alan Cooper’s answer to Why doesn’t the transformation rule for pure covariant or contravariant tensors apply to the Kronecker delta? – Quora

The claim that “classical physics says magnetic fields shouldn’t do work” is false. What classical physics says is just that a magnetic field does no work on an isolated single-point charged particle (because a charge at a single point has no magnetic moment and the magnetic force on such a particle is always perpendicular to its direction of motion). But this does not preclude the doing of work on a wire loop carrying a current or on a rotating charge distribution. [To create such things though requires us to have some mechanism for confining or holding together the relevant charges, and although classical physics did not say these things were impossible it never got to the point of including a description of the required additional non-electromagnetic forces. Quantum mechanics, on the other hand, did provide a means (without even requiring non-electromagnetic forces) for describing situations in which charges could be confined in atoms or metallic solids (and even predicted that an isolated point charge would nonetheless have a nonzero magnetic moment).]

Source: (1002) Alan Cooper’s answer to What’s the role of quantum mechanics in explaining why magnets can lift iron if classical physics says magnetic fields shouldn’t do work? – Quora

Each would see the other seemingly slowed down while they are moving apart and speeded up while they are coming together. But the one who turns around will see the speed-up for exactly half of his or her travel time while the ones back home will only start seeing the speed up after seeing the turn around (which will be more than half way to the reunion as it will take some time for the signal from the turning traveller to get back to Earth).

Of course both are aware of the signal taking some time to travel between them, so neither would think that what they were seeing was actually happen exactly when they saw it. But after correcting for signal travel time both would infer that the other was ageing more slowly throughout both departure and return with the only difference being that the traveller would infer that the homie had speeded up (or suddenly jumped ahead) during the period of turn-around.

Source: (1002) Alan Cooper’s answer to What would happen if the twins in the Twin Paradox were theoretically able to video call each other during the duration of the trip? – Quora

Viktor Toth’s answer correctly describes how our current theory is constructed so as to have the kind of symmetry that leads to three quarks being required to make a proton, but says nothing about why the theory had to be constructed that way and even less about why physics should actually follow such a theory. The first question (of why our theory had to be built that way) is answered by looking at various patterns of relationships between the scattering cross sections for different interaction and decay processes of elementary particles (though the details are beyond my capacity to explain in a Quora answer). But the second question (of why physics actually is that way) is, so far as I am aware, something that no-one yet has an answer to. (It may turn out that the number three is for some reason the only one consistent with some more fundamental properties that we think physics should have, but I have not yet seen any such argument.)

Source: (1002) Alan Cooper’s answer to It takes three quarks to make a proton, not two and not four. Why? – Quora

The best colour for a visible “radiator” is whatever fits in best with your decor – since its reflectivity in the visible spectrum has no effect on its utility as a heating (or cooling) device.

Actually, most home heating (or car cooling) “radiators” transfer most of their heat by conduction (to the air) and convection, but even the efficiency of direct thermal radiation depends only on the “blackness” in the infrared part of the spectrum – which can be high even when the radiator is perfectly white in the visible part.

Confusingly, home heaters that rely primarily on radiation are generally not called “radiators” but “radiant heaters” and they typically consist of a heating element and a shiny reflector (which is definitely NOT black!). The heating element (which actually does radiate) is typically some kind of metal coil on which any paint would quickly burn off but whose efficiency may be somewhat enhanced by the fact that it usually has a dark oxidized surface layer (which probably reduces its reflectivity and so enhances its emitivity in the IR as well as the visible part of the spectrum).

Source: (1002) Alan Cooper’s answer to Why is black the best colour for a radiator? – Quora

The colour black does not, by itself, “make things get warmer”, and in fact it sometimes makes them get colder. But it does increase the rate at which they absorb energy from visible light and so increases the rate at which they will get warmed up by sunlight. The other side of the coin, however, is that if the blackness of an object extends into the infrared part of the spectrum then the object will get cold more quickly if exposed on a clear night. This is because the way physics works is that there is a universal connection between the rates at which an object absorbs and emits radiation at any given frequency, but the frequency distribution that it emits depends on its temperature. (The only reason we don’t normally see more light from a black body than a white one is that what we see from the white is not emission but reflection, and when the object is hot enough to emit visible radiation then in fact the “black” one will glow brighter.)

Source: (1002) Alan Cooper’s answer to Does the color black really make things get warmer? Why or why not? – Quora