Quora Answers – Physics Notes

Do quantum fields have mass?

As so often happens, the answer to this question depends on what you mean by the words used.

Quantum fields are not things in the universe, but rather postulated quantities that are used in an attempt to provide descriptions of possible states of that universe. A state of the universe described in terms of such fields may or may not have mass, depending on the situation and on what you mean by “mass”.

And “mass” is also problematic. The parameter called “mass” in the equations defining a quantum field theory is related to the mass of a minimal (“single particle”) excitation of that field – and indeed this can sometimes be zero (as in the case of the Electromagnetic field for example). But a single photon does have energy and Viktor Toth tells us that Einstein said “E=mc^2” and so it must have mass. So what gives?

Well, when Einstein said “E=mc^2” (or perhaps a bit after the first time he said it) he understood that this was just in the particular situation of a system in its rest frame and a single photon does not have a rest frame!

For states involving many photons it may be possible to define a specific frame of reference by requiring some condition of balance between the observed frequencies (eg for two photons, the point from which they both appear to be departing in opposite directions with equal frequencies might perhaps be taken as the centre of mass). And in that case the force required to accelerate the entire system away from rest might be used to define a rest mass of the system that includes the kinetic energies of its components (in this case just the energies of the photons) as well as the masses of those components (which in the case of photons would be zero).

Source: (1001) Alan Cooper’s answer to Do quantum fields have mass? – Quora

Mass “Loss” in Chemical Reactions

In exothermic chemical reactions the combined masses of the resulting molecules is indeed slightly less than that of the inputs. But this does not make “the system’s mass appear to decrease” for two reasons. The superficial reason is that in chemical reactions the mass decrease due to energy loss from the system is far too small for us to detect, and so we did originally learn the very slightly wrong conclusion “that mass is conserved”. But the deeper reason is that, so long as the system is isolated (eg by including walls that reflect or absorb photons so that none can escape), then the system’s mass does not in fact decrease at all. This is because the system’s mass includes not just the masses of the individual molecules but also all of the energy in the system (including both photons and the thermal kinetic energy of relative motion of molecules). And if we do allow energy to escape, then the system’s mass is not conserved, as what we have learned more recently (though well over a hundred years ago now) is that what is conserved is not just the total mass of constituent particles but rather the total energy (where that includes a contribution from the masses of any particles within the system).

Source: (1001) Alan Cooper’s answer to In chemical reactions like CH₄ + 2O₂ → CO₂ + 2H₂O, we learn that mass is conserved.But since heat energy is released, E=mc² implies a tiny mass decrease. Heat is emitted as massless photons, so why does the system’s mass appear to decrease? – Quora

Mass to Energy easier than Energy to Mass?

The reason we say mass and energy are the same thing is because how we distinguish them is just a matter of bookkeeping – which depends on our point of view. But if you think of heat as a form of energy rather than of mass, then it is indeed easier to convert mass to energy than vice versa.

When a chemical reaction reorganizes matter into a state of lower potential energy, such as for example whenever we burn a fuel, the energy released typically gets converted to kinetic energy and quickly distributed among many particles of a larger system in the form of what we call heat (which is impossible to fully recover in the form of usable work). An observer looking in detail at the system will see each molecule as having a tiny bit less mass than its component atoms (by an amount corresponding to the binding energy) with the total of all these differences also corresponding to the increased kinetic (heat) energy of the molecules.

On the other hand, when we break apart a chemical bond then we must provide some amount of energy and the resulting masses of the components will add up to that much more than the mass of the molecule. But if we want to do so in a consistent way (such as in electrolysis of H2O or carbon capture from CO2) then we need to provide the energy in a very specific way that is not so trivially easy to set up as just exposing fuel to oxygen.

However, if we measure the mass of the system as a whole (either gravitationally, or as inertia at starting from rest), then the result we get includes not just the masses of all its molecules but also their kinetic energies relative to its centre of mass. And that total (which includes all of the heat energy in the system) remains absolutely constant and never either increases or decreases.

Source: (858) Alan Cooper’s answer to Why is converting mass to energy easier than converting energy to mass if they are the same thing? – Quora

Gravitational Force and “Relativistic” Mass

A Quoran asks: “I see questions about how mass increases with speed relative to an observer. Does the gravitational force between objects depend on the relative speed between them?”

I think the answer to this question is basically yes (although the way General Relativity predicts trajectories is not usually expressed in terms of forces between objects).

Actually, the quantity normally identified as the “mass” of an object is a property of the object itself (that used to be called “rest mass”) which does not depend on the observer, though it is true that the apparent resistance to acceleration (which used to be called “inertial mass” or “relativistic mass”) does depend on the object’s speed of motion relative to the observer (and to the direction of the applied force relative to that motion). So if gravity were due to (rest) mass alone we might expect the answer to be no.

But in General Relativity the trajectory of a freely falling object is governed by an equation in which all kinds of energy (and momentum) contribute. So it it reasonable to expect that a relatively moving object has a stronger effect than one which is stationary relative to the observer. However this is not completely obvious as we need to rule out the possibility that the momentum contributions cancel out those of kinetic energy (like they do in the equation E^2-p^2=m^2 for example).

In order to really answer the question we need to restrict our attention to a situation in which the idea of an inter-particle force does arise as a good approximation. One such is the case of a relatively tiny mass in free fall around a larger one, in which case the Schwarzschild metric provides a good approximation. And in that situation there is an extra non-Newtonian term in the effective potential so that the centripetal acceleration is slightly stronger when the distance is smaller (which gives an extra “kick” at perigee and contributes to the precession of orbits). This stronger attraction could perhaps be interpreted as Newtonian attraction with an increased gravitational mass, and since the orbiting body is moving faster when closer to the central mass it may well look as if the central mass increases with the speed of the orbiting observer.

Perhaps it would also be possible to calculate the second derivative of the distance to the central mass in the coordinates of the observer and I would not be surprised to find that this is proportional to the combined total of mass and kinetic energy of that mass in those observer coordinates.

On the other hand, we should NOT expect the gravitational force between two objects to appear stronger from the point of view of a third observer passing by at high speed (since that would shorten the orbital period while time dilation should make it seem longer).

Source: (899) Alan Cooper’s answer to I see questions about how mass increases with speed relative to an observer. Does the gravitational force between objects depend on the relative speed between them? – Quora

How do CO2 molecules heat their neighbours?

By hitting them!

A CO2 molecule in the atmosphere, after having absorbed an infrared photon, is vibrating or rotating more vigorously than it was before. When such a molecule collides with a neighbouring molecule (most likely an N2 or an O2) some of that vibrational energy contributes to the speed or vibration or rotation of the one it hits.

The atmosphere doesn’t continue heating up though, because in the equilibrium situation the molecules in the atmosphere collectively emit radiation at the same rate as they absorb it. But they do this equally in all directions, so what they are absorbing from below gets re-directed and only half of it ends up going outwards (with the other half going back down to warm the Earth’s surface).

Source: (901) Alan Cooper’s answer to How does a CO2 molecule in the atmosphere, after having absorbed an infrared photon, transmit that energy to neighbour air molecules to heat up the atmosphere? What’s the mechanism? – Quora

Why F=ma?

Because of Quora’s habit of applying answers to unrelated questions I need to clarify that the question I am responding to here is “Why is Newton’s second law written in the form F = ma, since a more accurate form based on the formula F = dp/dt should be F = m dv/dt + v dm/dt = ma + v dm/dt, since according to the theory of relativity, mass also changes, as does velocity?”

Well first, Newton’s second law is written in the form F = ma because that is essentially the way he wrote it and if it wasn’t written that way it wouldn’t be Newton’s law. The form F=dp/dt (which is more general but not more “accurate”) was known to him but he didn’t need to use it because he was referring to the special basic case of an object of a fixed mass (as opposed to something like a rocket expelling massive exhaust) and he chose to take just the simpler special case as his starting point and deduce the more general as a consequence.

He did not write his laws in Lorentz covariant form because he was unaware of almost everything about electromagnetism and radiation, and so had no reason to expect that the correct laws of physics were not actually perfectly Galilean covariant. (But in any case, as described in more detail in other answers, both the Lorentz covariant laws of special relativity and those of General Relativity can be expressed in a form which includes an equation of the form F=ma for appropriate definitions of F,m, and a).

But your claim that “according to the theory of relativity, mass also changes, as does velocity” is based on a concept of “relativistic mass” which is not a well defined property of an object and has long been abandoned as misleading and not useful.

ce: (960) Alan Cooper’s answer to Why is Newton’s second law written in the form F = ma, since a more accurate form based on the formula F = dp/dt should be F = m dv/dt + v dm/dt = ma + v dm/dt, since according to the theory of relativity, mass also changes, as does velocity? – Quora

Magnets Doing Work

Why do physicists say that a magnet can’t do work? They don’t!!!

What they do say is that a magnetic field does no work on a classical spinless point particle (and that a homogeneous magnetic field does no work on a particle with spin either). But this in no way precludes the field of a magnetic dipole doing work on another object with a magnetic moment – as we observe every day in electric motors, and when we see the attraction of oppositely oriented bar magnets (and the lifting of anything from iron filings to scrap ferromagnetic metal by virtue of the magnetization induced in them by a strong magnetic field).

The question of where the energy to do this work comes from is probably most simply answered by saying that it was put into the magnet by the work necessary to get its atomic spins into alignment, and then resides in the external magnetic field (which, when the magnet has done work, gets reduced or cancelled out by the opposite fields from the objects which have been attracted – but can be restored by pulling them apart again). What is completely wrong is the claim made in some answers (including the one with the highest number of upvotes!) that the source of energy has anything to do with the process of moving the magnet and holding it above the items it is lifting.

Of course, since magnetic fields (like all the other force fields we are familiar with) are conservative, there is no net work done in a cyclical process unless we have an external source of energy (like an electric current supply). But this is true of all physical systems and not any special property of magnets.

Source: (1002) Alan Cooper’s answer to Why do physicists say that a magnet can’t do work? Hold a magnet above a pile of iron powder, it lifts them. Work is done against the G field! How to explain this discrepancy? – Quora

Does Flat Imply Infinite?

There have been a couple of decent answers over the years but perhaps they could be expressed more briefly.

The existence of an initial singularity in a solution of General Relativity does not require that the early universe was infinitesimally small. It could indeed have infinite spatial extent at every time on every possible worldline (with “expansion” corresponding to reduction of density rather than increase of “size”).
Intrinsic flatness of space-time does not necessarily conflict with finiteness of space – related to the way a sheet of paper is intrinsically flat (in the sense of its own internal metric), even when rolled up into a cylindrical tube (which has finite “size” in the direction perpendicular to its axis).
Some claims of flatness for finite universes are only about the limiting behaviour for large time.

Source: (1001) Alan Cooper’s answer to I understand that the Big Bang was not an explosion which many people erroneously believe, but it was the start of space and time and our universe. However, if it started as infinitesimally small how can physicist say space may be infinitely flat? – Quora

Are people in superposition states?

For any quantum system, every pure state is a superposition. The moment we have complete specification of one observable we lose complete specification of another. (In more technical language, whatever eigenstate we are looking at is a superposition of eigenstates of the complementary observable.)

But noone has ever seen a macroscopic object of any kind in a pure state, so the state of our knowledge is even weaker. Every system that is not completely isolated is in a statistically mixed state. Just the slightest thermal interaction with an external environment introduces classical uncertainty that precludes the identification of a pure state; and even for a completely isolated system that is anything close to the size of a human, the amount of information required to specify a pure state makes it out of the question.

So the answer to your first question is that quantum mechanics does suggest that anything you ever look at is in an unknown superposition.

But the second question is just totally meaningless.

Source: (1001) Alan Cooper’s answer to Does quantum mechanics actually suggest people in other rooms to you are in a superposition? Does it deny the physical processes happening within spatially separated observers? – Quora

Planck Length – Concept vs Implications

The concept of the Planck length can be fully understood on the basis of only a bit of dimensional analysis applied to the apparent fundamental constants of c, h, and G (whose existences had all been identified long before black holes and even photons were considered to be “real”). It’s implications are by no means yet fully understood, but it is obvious that they will have something to do with the relationship between quantum and gravitational phenomena – perhaps (but not necessarily) as a limit on the possible “sizes” of black holes and/or the wavelengths of “photons”.

Source: (1001) Alan Cooper’s answer to The concept of the Planck length cannot be fully understood without a deep understanding of black holes and photons. So, how did this misconception, that Planck length presented by Planck with vague evidence in his papers written years before that? – Quora