Why the speed of light is constant?

[Sturk200]

Here is a question that might be somewhat more philosophical than this community cares for. If so, I apologize in advance.

Are there any reputable theories as to why the speed of light is constant? I know that it is an empirical fact and therefore that it does not need to be proven. But on the other hand, the aim of physics has historically been to come up with satisfying theoretical explanations for empirical facts. Anyway, I'm just wondering if there are any reputable ideas out there that modern physicists are considering.

 

[PeterDonis]

Are there any reputable theories as to why the speed of light is constant?

The theory of relativity basically answers this question by saying that it's ill-formed; in the relativity view of spacetime, what we call "the speed of light" is really just a unit conversion factor between space units and time units, and since spacetime is unified in relativity, the unit conversion has to be the same everywhere.

Or, to look at it another way, in the theory of relativity, there are three fundamentally different kinds of worldlines in spacetime: timelike, spacelike, and null. The proper way of saying that something travels "at the speed of light" is to say that it travels on null worldlines. This is a geometric property of the worldline, and again, it has to be "the same" everywhere--the geometric definition of a null worldline doesn't change.

You could ask a different question, namely, why does light, the actual physical phenomenon, travel on null worldlines? Answering that requires going beyond the theory of relativity; it's a question about quantum field theory and why the quantum field describing light is massless (which is the QFT way of saying "travels on null worldlines"). In relativity, the fact that light travels on null worldlines is taken as a given, a property of light that doesn't have any further explanation within that theory.

 

[Sturk200]

"the speed of light" is really just a unit conversion factor between space units and time units

Can I ask to you explain what it means to say that the speed of light is a conversion factor between space and time units? I know the rudiments of special relativity, namely that c acts as a conversion factor when going from the space-time units of one reference frame to those of another, but I don't think I've learned how light speed acts as a conversion factor between the space and time units of a single reference frame.

You could ask a different question, namely, why does light, the actual physical phenomenon, travel on null worldlines? Answering that requires going beyond the theory of relativity; it's a question about quantum field theory and why the quantum field describing light is massless (which is the QFT way of saying "travels on null worldlines"). In relativity, the fact that light travels on null worldlines is taken as a given.

Yes, I think this is getting more to the heart of the kind of answer I would find satisfying. Only I would tack one more question in there between the lines (particularly, the question concerns your parenthetical). Not only would I ask why the quantum field describing light is massless, but also this: why does a massless field describe the phenomenon of "traveling on null worldlines"? In other words, what is the connection between having or not having mass and traveling at a speed that is independent of the speed of the source? Because even if we could answer the question of why light is massless, that would still leave open the question of why massless things travel at constant speed. Are there any stabs at an answer to that second question out there?

 

[gleem]

the aim of physics has historically been to come up with satisfying theoretical explanations for empirical facts.

Actually the aim of physics is to determine how things happen. i.e. to relate an initial state to a final state after an interaction. This may involve empirical facts or assumptions consistent with these facts.

 

[PeterDonis]

Can I ask to you explain what it means to say that the speed of light is a conversion factor between space and time units?

In relativity, it is useful to use the same units for space and time. Any such system of units will relate space and time using the speed of light: for example, years for time and light-years for space (which is common in cosmology).

I know the rudiments of special relativity, namely that c acts as a conversion factor when going from the space-time units of one reference frame to those of another

No, that's not what $c$ does. Units of space and time (like years or light-years) aren't associated with any particular reference frame. See above.

why does a massless field describe the phenomenon of "traveling on null worldlines"?

Because that's how the geometry of spacetime works. An object with mass (more precisely, one with nonzero rest mass, aka invariant mass) travels on a timelike worldline. An object that is massless (more precisely, one with zero rest mass aka invariant mass) travels on a null worldline. The property of invariant mass is what distinguishes these two types of worldlines.

what is the connection between having or not having mass and traveling at a speed that is independent of the speed of the source?

The fact that the speed of any massless object is independent of the speed of its source is a side effect of the way the geometry of spacetime works. The speed of any object moving on a null worldline is the same in all inertial frames; that's a fact of spacetime geometry. Since it's the same in all inertial frames, it must be independent of the speed of the source.

If you ask, why is the speed of any object moving on a null worldline the same in all inertial frames, that is because the way Lorentz transformations act on timelike vectors is fundamentally different from the way they act on null vectors. Lorentz transformations change the "direction in spacetime" of timelike vectors; that corresponds to changing the "speed" associated with the vector, in the new frame, as compared to the old. In other words, Lorentz transformations "rotate" timelike vectors in spacetime (they are the hyperbolic geometry counterpart of ordinary rotations in 3-space).

But Lorentz transformations don't rotate null vectors in spacetime; they only "dilate" them. What that means is that a Lorentz transformation doesn't change the speed of, say, a light beam; it only changes its frequency (or wavelength; they're equivalent). So a given light beam will have different frequencies (or wavelengths) in different frames, but not different speeds.

 

[Nugatory]

Are there any reputable theories as to why the speed of light is constant? I know that it is an empirical fact and therefore that it does not need to be proven. But on the other hand, the aim of physics has historically been to come up with satisfying theoretical explanations for empirical facts. Anyway, I'm just wondering if there are any reputable ideas out there that modern physicists are considering.

A different (and less modern) way of thinking about it is to consider that the speed of light can be calculated from the classical laws of electricity and magnetism. Maxwell did exactly that in 1861, and his suggestion that light was an example of the electromagnetic radiation that his equations predicted was quickly accepted. However, we also expect that the laws of physics don't change just because you're in uniform motion - because of the Earth's rotation, your speed changes by many kilometers a second between noon and midnight, but you don't expect the laws of physics in general or E&M in particular to change out from under you. You end up calculating the same speed of light at all hours of the day.

That doesn't answer your "why?" question, it just transforms it into the question of why the laws of E&M are what they are... But it was a pretty good hint from nature that we shouldn't be surprised to find that the speed of light is in fact constant. It took a half-century before Einstein picked up on this hint in 1905, and another decade or so after that to hammer out the modern mathematical formulation of special relativity, in which the constant speed of light appears as an experimentally supported fundamental assumption.

 

[Sturk200]

Thanks so much for your generous replies. I have much to learn.

Feel free to draw the line of demarcation here between legitimate question and crackpot question, but here goes one more. I hope that the following won't read as totally uninteresting and misguided babble, but I'd like to know what a physicist would make of this line of thought.

The velocity of a rigid-body projectile (e.g. a tennis ball) is altered by the velocity of its source for the reason that the source communicates its own velocity to the projectile by means of a contact force, which (correct me if I'm wrong) is an electromagnetic interaction between charged particles. Light, however, unlike a rigid body, is not composed of charged particles, but rather of neutral photons. Therefore there can be no contact force and no communication of the velocity of the source to a light beam (and thus c is constant). Has this argument been made in the past, and if so why is it rejected?

 

[rootone]

Light is not a rigid body but photons do have momentum, and that could be of some practical use.
https://en.wikipedia.org/wiki/Solar_sail

 

[PeterDonis]

The velocity of a rigid-body projectile (e.g. a tennis ball) is altered by the velocity of its source for the reason that the source communicates its own velocity to the projectile by means of a contact force, which (correct me if I'm wrong) is an electromagnetic interaction between charged particles.

This is sort of correct, but not completely. First, contact forces aren't purely electromagnetic repulsion between the electrons in neighboring atoms; part of it is also the Pauli exclusion principle, which makes atoms resist being compressed. (The uncertainty principle also plays a role here; the stability and behavior of solid objects is actually quite a bit more complicated than it appears on the surface.)

Second, what the source "communicates" to the projectile by this means is momentum, not velocity. And the source itself also has to change momentum as a result, because of conservation of momentum (this is what "recoil" is, for example when firing a gun). In other words, when viewed from a fixed inertial frame, both the projectile and the source change velocity. So it's not just a simple "communication of velocity" from source to projectile; the kinematics is more complicated than that.

Finally, this kind of analysis doesn't account for objects which cannot be viewed as "projectiles" fired from a "source". All objects with nonzero rest mass will have different velocities in different frames, regardless of how they got that way. So any analysis that is fully general must be based on something more fundamental than a specific mechanism for imparting velocity. That's why I cited the geometry of spacetime in my explanation.

Light, however, unlike a rigid body, is not composed of charged particles, but rather of neutral photons. Therefore there can be no contact force and no communication of the velocity of the source to a light beam (and thus c is constant).

The problem with this is that it assumes that light is a pre-existing thing that is made to move at $c$ somehow. In fact, light gets created at its source--a given light beam doesn't exist at all until its source emits it. When it is emitted, it is emitted already in the state of "moving at $c$", but a better way to say it is that it is emitted as a massless object, on a null worldline, and a null worldline is fundamentally different from a timelike one.

Also, as rootone points out, light has momentum and can push against things; and sources that emit light show recoil, just as sources that emit timelike projectiles. So it's not correct to think of light as somehow not being subject to "contact forces"; light exchanges momentum with other things just like any other object.

 

[bcrowell]

The answer to this question depends on what you take as fundamental assumptions. The 1905 approach is to take constancy of the speed of light as a fundamental assumption. A more modern approach is to take certain symmetry principles as your fundamental assumptions. If you do that, then it follows that there is an invariant speed, and that massless phenomena such as light travel at that speed. For an example of such a treatment, see Pal, "Nothing but relativity," http://arxiv.org/abs/physics/0302045 .

 

[Nugatory]

. Therefore there can be no contact force and no communication of the velocity of the source to a light beam (and thus c is constant). Has this argument been made in the past, and if so why is it rejected?

As I am floating in space, you come rushing past in a spaceship moving at .5c. Just as you pass me, you switch on a light on the nose of your spaceship to send a flash of light forward in the direction of you motion. Your "no communication of the velocity" idea would explain why the flash of light ends up moving at c relative to me - but it fails to explain how the flash of light can then also be moving at the speed of light relative to you.

(There are other problems with the idea as well: Photons aren't what you're thinking they are and light is not composed of them, at least not as the word "composed" is usually understood; light does exert a force on its source as it is emitted so there is a transfer of momentum from the source to the light; there are massive neutral particles and they don't travel at the speed of light and their speed is not independent of the source).

The Physics Forums rules prohibit posting speculation and personal theories of this sort. Please don't do it any more.

 

[Sturk200]

Thanks again for your replies. And sorry if my question was against regulations.

there are massive neutral particles and they don't travel at the speed of light and their speed is not independent of the source

Where can I read more about these particles?

 

[PeterDonis]

Where can I read more about these particles?

The most common one is the neutron, which is in almost every atomic nucleus (the only exception is hydrogen-1) and is produced by a number of nuclear reactions.

 

[Gaz]

I just think of it like say your going 80 mph and instead of the tennis ball you fire a rocket that's top speed is 100 mph that rocket isn't going to accelerate to 180 mph is it.

 

[vanhees71]

You could ask a different question, namely, why does light, the actual physical phenomenon, travel on null worldlines? Answering that requires going beyond the theory of relativity; it's a question about quantum field theory and why the quantum field describing light is massless (which is the QFT way of saying "travels on null worldlines"). In relativity, the fact that light travels on null worldlines is taken as a given, a property of light that doesn't have any further explanation within that theory.

That's again a tricky "why question". First of all I don't know, what you take as basis for an "explanation", because any "explanation" must start from something you consider as a fundamental law of nature, and we can only figure these out by observations and careful quantitative experiments.

In my opinion, the status of the question, why electromagnetic fields are described by massless vector fields is not clear at all, and one must indeed take it as a fundamental law fitting all known observations so far with astonishing precision. So one could stop here, but it's anyway interesting to follow the question a bit.

I try to answer it on the level of special relativity (i.e., leaving the general relativity and thus gravity out of this discussion, because then we really would leave safe ground ;-)). The most fundamental theory we have about the world is indeed the special-relativistic space-time model, describing space and time as a four-dimensional continuum, called the Minkowski space together with quantum-field theory based on it. Here the most comprehensive model we have is the Standard Model of elementary particles.

So the question can be split in two questions: First of all, "why" is it the Minkowski space which describes the observed properties of what we call space and time well. Here the answer also is that of all space-time models it describes very many phenomena best (it's known that it must be modified again when taking into account gravity, leading to general relativity). You may argue in a bit more depth by invoking symmetry principles. One can start with the assumption that the principle of inertia holds, i.e., that there is a class of reference frames, where a body upon which no forces act, always move with constant velocity with respect to the corresponding observer who is at rest in one of these reference frames, the socalled inertial frames. Further, assuming that any inertial observer finds when measuring lengths of objects that are at rest relative to him that the corresponding geometry is Euclidean, implying that his space is homogeneous and isotropic. Further also time is assumed to be homogeneous, i.e., the laws of nature do not depend on the space and time where and when an inertial observer observes them. An analysis of the then following possible space-time symmetries shows that only two space-time models are left, namely the Galilei-Newton and the Einstein-Minkowski spacetime. The main difference is that in Einstein-Minkowski space time there is a fundamental "limiting speed", i.e., any object can only move with a velocity with respect to any inertial observer with at most this limiting speed $c$, while in the case of Galilei-Newton space-time no such fundamental speed parameter exists. You can criticize this pretty complicated approach, however, because the assumptions going into it are pretty strong, but in my opinion it gives an idea, why there may exist space-time models with a fundamental limiting-speed parameter, independent of a concrete physical model like classical electrodynamics, which was the historical starting point for the theorists in the 19th century to think about these issues, with Einstein the one who has given the most convincing argument in terms of a space-time model (Einstein 1905).

Now around 1925 it was discovered that the classical description of matter is inadequate too, and one discovered quantum theory as a better description. First attempts to formulate quantum theory within relativistic physics was not very successful and that's why first the non-relativistic theory was developed (Heisenberg+Born+Jordan 1925, Schrödinger 1926, Dirac 1926). Then of course, after having learned to deal with non-relativistic quantum theory, also the relativistic theory was worked out. Soon it became clear that it is very hard to find a consistent theory which describes only a single interacting particle. This is understandable nowadays, because we deal with the creation and destruction of particles in accelerators of the highest energies on a quite familiar basis.

Now it was also known from non-relativistic quantum theory that for many-body systems or systems with a non-fixed number of particles, there is an equivalent description of quantum theory, known as quantum field theory, because it can heuristically derived by taking the Schrödinger equation, formulating it with Hamilton's principle (analogous to canonical mechanics of point particles) and "quantize" it, i.e., making the fields operator valued, and the field describing annihilation and destruction processes of particles. This was the perfect starting point for a relativistic quantum field theory, and one can again use the powerful tool of group theory and the space-time symmetries of the Einstein-Minkowski spacetime, with the Poincare group as symmetry group (Wigner 1940). Together with some additional assumptions (locality, microcausality, existence of a state of lowest energy) you are lead to the local relativistic quantum field theories which are very successful (although not yet free of all mathematical obstacles for interacting particles).

In this analysis it occurred that there are two rough classes of fields, belonging to two posibilities to realize Poincare symmetry in the sense of quantum theory: the massive and the massless fields. Quantizing the non-interacting massive fields leads to massive particles with any type of spin 0, 1/2, 1,3/2,... The corresponding field equations are the Klein-Gordon equation, the Dirac equation, etc. These have a well-defined non-relativistic limit leading to non-relativistic quantum theory of the corresponding particles with spin.

There's however also the class of field theories with massless fields. It's quantization is a bit more tricky, and they have no non-relativistic limit (this is also a deep property of the underlying space-time symmetries; while in Minkowski space massless fields (and even classical particles to some extent) make sense, massless particles make no sense in non-relativistic quantum theory, which is due to the different structure of the underlying space-time symmetry groups (Poincare group in the case of Einstein-Minkowski and the Galilei group in the case of the Galilei-Newton space-time).

The standard model is built on these general QFT structure, but it took more discoveries of more symmetries concerning the whole zoo of particles found since the 1950ies. One of the most important discoveries is that of the socalled local gauge theories. The above mentioned analysis of the Poincare group reveals that massless particles with spin $s \geq 1$ cannot be simply described by fields but by classes of fields. This is known already from classical electrodynamics: Using the four-potential several four-potentials which just differ in a four-gradient field, describe the same situation. Taking this symmetry into account and quantizing it (which is a puzzling business and an interesting story of its own) leads among other things to the fact that a massless vector particle has not three spin states as a massive vector particle, but only two (represented by, e.g., helicity eigenstates with the helicity being the projection of the total angular momentum two the momentum direction of the particle and taking only the two values $\pm 1$).

The other way around, starting from gauge symmetry, it is most naural to assume that the corresponding vector field is massless. Of course, you also want to introduce charged matter particles to make a model for electromagnetically interacting charged particles and the electromagnetic field. Gauge invariance implies that necessarily electromagnetic charge must be conserved and that it is most simple to couple the vector field to a conserved current. The gauge transformation of the matter fields is invariance of the equations of motion under multiplication of these fields with a space-time dependent phase factor, with the phase (modulo multiplicative constants which represent the coupling strength between the particles and the vector field) being the same as in the gauge transformation of the vector field. Since the multiplication with a phase factor corresponds to symmetry under the Ablian group U(1), this is called an Abelian gauge theory, and it was pretty soon clear that such a theory describes electromagnetism very well, leading to quantum electrodynamics.

However, as it turns out, you can as well formulate the theory with massive vector bosons, still keeping the theory gauge symmetric (Stueckelberg model). So gauge invariance is not a true "answer" to the question, why photons are massless quanta of a vector field. So it's still not answering the question, "why" photons are massless.

Now the Standard Model rests on an even more general type of gauge symmetry. Already in the 1940ies Heisenberg discovered that one an describe also observed symmetries among particles with help of group theory. In his case he took the proton and the neutron which have (almost) the same mass as one and the same particle but just carrying another quantum number (called isospin). Thus he took proton and neutron as a isospin 1/2 doublet, i.e., the two eigenstates of the isospin-z component (with isospin +1/2 for the proton and isospin -1/2 for the neutron). As long as you consider only the strong interaction in scattering processes the isospin is (approximately) conserved.

Then Yang and Mills had the brillant idea to ask what happens, if you "gauge" such non-Abelian symmetries (in this case under the isospin group SU(2)). "Gauging" means you assume that a global symmetry (you can rotate only with a constant SU(2) transformation in isospin space, but not locally, because the field theory contains derivatives which by themselves do not lead to simple transformation laws for the field derivatives when the SU(2) transformation is made space-time dependent) becomes global. It turns out that you can make a global symmetry of this kind a local symmetry by introducing appropriate vector fields, the gauge bosons of this symmetry. Although the original Yang-Mills model was not successful in describing the strong interactions, the gauge models turned out to be the key to build the Standard Model.

Here it turned out that, contrary to the Abelian case, it is very difficult to give the gauge bosons a mass without distroying local gauge invariance. Only the famous Higgs mechanism could provide such a thing. So still you can make the non-Abelian gauge bosons massive, i.e., there is no real veto for massive vector bosons based on non-Abelian gauge symmetry.

So the short conclusion of this long-wound try to "explain" the masslessness of the photon is: We don't have a better answer than the fact that all empirical observations are to a very high accuracy consistent with the assumption of a massless photon, being described in the standard model as a U(1) gauge theory with the gauge boson assumed to be massless.

 

[Sturk200]

The most common one is the neutron, which is in almost every atomic nucleus (the only exception is hydrogen-1) and is produced by a number of nuclear reactions.

So what kind of force exists between a neutron and some ordinary piece of matter? Would the interaction be purely magnetic owing to the neutron's characteristic absence of charge but possession of a magnetic moment? I guess there is also the nuclear force.

What about photons -- what kind of force exists between the photon and ordinary matter? If I remember correctly light is subject to gravity. Is there anything else? What, for instance, is responsible for the photon's ability to transfer momentum to a "solar sail".

 

[Nugatory]

So what kind of force exists between a neutron and some ordinary piece of matter? Would the interaction be purely magnetic owing to the neutron's characteristic absence of charge but possession of a magnetic moment? I guess there is also the nuclear force.

There is indeed a nuclear force, and it's most often responsible for fast-moving neutrons.

What about photons -- what kind of force exists between the photon and ordinary matter? If I remember correctly light is subject to gravity. Is there anything else? What, for instance, is responsible for the photon's ability to transfer momentum to a "solar sail".

I'll repeat what I said a few posts above: photons are not what you're thinking they are. You'll be properly introduced after you've worked through special relativity and then quantum mechanics, so have the background needed to take on quantum field theory which reconciles QM and SR. Until then, you will be better off working with the classical model of light as electromagnetic radiation; that's what SR is built on.

And with that said: There's no meaningful way of talking about the force between a photon and ordinary matter - that's just not how photons work. However, electromagnetic radiation can carry energy and momentum; this is transferred to ordinary matter when the time-varying electrical and magnetic fields (that's what electromagnetic radiation is) act on the charged particles in the matter. So the force in question is electromagnetic, and a detailed explanation of how it works is built on Maxwell's equations of classical electrodynamics, discovered a half-century before relativity.

 

[NickAtNight]

Are there any reputable theories as to why the speed of light is constant? I know that it is an empirical fact and therefore that it does not need to be proven.

You might want to refine your question because the speed of light is not constant ! The speed of light in a vacuum is constant.

The speed of light through denser materials such as water or glass is slower.

 

[vanhees71]

First of all everything that has energy and momentum (i.e., everything that exists at all) participates in the gravitational interaction, i.e., it is subject to gravitational force as well as a source of gravity (which is described as the curvature of space-time by Einstein's General Relativity Theory).

The rest of the known matter is described by relativistic quantum-field theory in terms of the Standard model of elementary particle physics. According to this model, all known matter consists of the following particles (all described by Spin-1/2 quantum fields with the corresponding quantum particles being fermions):

Leptons: (electron, e; Muon $\mu$, Tauon $\tau$) all carrying 1 negative electric charge unit and corresponding 3 sorts of neutrinos. These particles only participate in the electroweak interaction and gravity. In addition to the electric charge of the charged leptons both the charged leptons and their neutrino partners carry another charge, called "weak isospin".

Quarks: [(up,down); (charm, strange); (bottom/beauty, top)] These participate in all interactions, i.e., the electroweak, the strong and the gravitational interaction. Each pair of quarks carries +2/3 and -1/3 elementary charges respectively. In addition they cary weak-isospin charge and the color charge of the strong interaction.

Further there are the "force particles". A more scientific name is "the gauge bosons". They are described by fields, of which we best know the electromagnetic field, and only this electromagnetic field can be observed in a direct way also as a classical field (which from the point of view of quantum field theory are socalled coherent states of the electromagnetic quantum field). The gauge bosons all have spin 1 (that's why they must be bosons according to the spin-statistics theorem, which tells us that all particles with a half-integer spin number are fermions and those with an integer spin number are bosons). In a very rough sense (the full story is not so simple and involves some abstract mathematics, called group theory, for a complete understanding) we have the following gauge bosons in the standard model:

Photons: Quanta of the electromagnetic field, coupling to anything that carries a non-zero electric charge (which is also not completely accurate, because quantum effects let them also interact via quantum fluctuations with uncharged particles, including themselves, but in the case of photons that's a very weak effect). The photons themselves are uncharged.

3 weak gauge bosons: The W bosons (one carrying 1 positive and one carrying 1 negative elementary charge) and the Z bosons (having no electric charge); all couple to the weak-isospin charge and carry themselves also weak-isospin charge. The photons and weak gauge bosons are "carriers" of the electroweak interaction.

8 gluons: they are electrically and iso-spin charge neutral and mediate the strong interaction and thus directly couple to everything that carries color charge (quarks and gluons themselves, which also carry (a different kind) of color charge).

The strong force is special, because it shows confinement, i.e., we don't observe any objects carrying a non-vanishing color charge, but the quarks and gluons are always bound in color less composite objects. This is a very complicated state of affairs, which is not fully understood yet. We know from big computer simulations (called lattice-QCD calculations) that Quantumchromodynamics (on the fundamental level the theory describing the strong interactions among quarks and gluons as a gauge theory) seems to be the correct desription, particularly it is possible to calculate the masses of all known hadrons and predicts even the existence of some other hadrons not yet seen in experiments. Hadrons are the bound states of quarks and gluons. We know two types for sure today, namely the socalled mesons which consist of a valence quark and a valence antiquark and a lot of virtual quarks, antiquarks and gluons (as I said that's a hand-waving picture, not fully understood yet). The mesons carry all integer spin-quantum numbers and thus are bosons. They are all unstable. Then there are the baryons consisting of three valence quarks and a lot of virtual quarks, antiquarks, and gluons. The most prominent ones are the proton and the neutron, which themselves are the building blocks for all atomic nuclei of the every-day matter around us. The nuclei are hold together by the strong force. Although the hadrons are color neutral, there is still strong interaction left. You know this, e.g., from the analogous behavior of electrically neutral material, which still can interact electromagnetically, because the charged particles it is made up, are a bit distorted from the equilibrium positions due to some electric charges brought close to them. This "polarizes" the material leading to an electromagnetic interaction with the nearby charges. Even neutral molecules interact electromagnetically with each other, i.e., for composite neutral objects there's still some remnant electromagnetic interaction left.

Then you are also right that the charged elementary particles not only carry this charge but also have a magnetic moment (which is due to their spin and the specific way each field, describing these particles, couple to the electromagnetic field). So it is understandable that the neutron also has a magnetic moment, which is due to the magnetic moments of the quarks and their "motion" (correctly their orbital angular momentum) within the hadronic bound state. The same is true for the proton, which carries one positive electric elementary charge and also has a magnetic moment. For the same reason neutral molecules still interact electromagnetically, also the neutrons do due to the charged valence down quarks and up quark as well as the virtual cloud of charged quarks contained in them.

 

[NickAtNight]

Woah. That is a lot to try to explain without pictures and tables ! :)

...The rest of the known matter is described by relativistic quantum-field theory in terms of the Standard model of elementary particle physics.

Who has the best poster/picture of the Standard model these days?
http://www.pha.jhu.edu/~dfehling/particle.gif
From: http://www.pha.jhu.edu/~dfehling/particle.gif

 

[Sturk200]

Thank you, what a wonderful wealth of information -- I certainly have my reading cut out for me.

I'm still a bit curious about one thing. Is the question of the mechanism underlying special relativity an active area of research among physicists today? For instance, are there people trying to explain the constancy of c using the tools in the standard model? PeterDonis mentioned that the dominant theory today is that the constancy of c is a straightforward consequence of the "geometry of space-time." I feel like I'm not at a point where I can stomach that. Of course this might change as I learn more of the nuts and bolts. But I want there to be an explanation that invokes some kind of intelligible mechanism beyond merely saying that the geometry of space-time necessarily transforms as a result of relative motion. That just feels like so much mathematical form without physical content. Maybe I am wrong to be frustrated -- probably I am. But I guess what I am asking is whether there is any active theoretical research at present seeking to explain the mechanism underlying the constancy of c and the consequent need for a Lorentz transformation, and seeking to explain these phenomena in terms of, for instance, the physical properties of light and the way that light interacts with matter, rather than in terms of the geometry of space-time?

You'll be properly introduced after you've worked through special relativity and then quantum mechanics, so have the background needed to take on quantum field theory which reconciles QM and SR.

I do have a bad habit of trying to make the gas burn by spinning the wheels. Thanks for your patience.

 

[vanhees71]

This is one of the best, showing a lot on just one poster. It is incomplete, as was my posting before, because it leaves out the Higgs field and the Higgs boson, which now is discovered at the LHC with its properties getting more and more confirmed the more of the data of Run 1 are analyzed and I'm pretty sure also with the new data at the higher energies it will be more and more confirmed. The corresponding part that is observable as a particle in the physical spectrum, the Higgs boson, is a spin-0 boson which takes part of the gravitational and the weak interaction. Three components of the Higgs field are absorbed into the weak gauge bosons, making them massive (providing the third longitudinal spin component of the massive vector bosons, while massless have only 2 physical degrees of freedom (helicity states)).

This refers to the socalled "minimal Higgs model", i.e., with the minimal field content. It's only one weak-isospin doublet, and then the physical Higgs particle is electrically neutral. You can extend the Higgs sector of the standard model keeping all goodies of this theory, and I guess the search for possible other Higgs bosons (among them also possible charged ones) will go on at the LHC.

A very comprehensive review comes out every two years (even years) and can be ordered from CERN (Europe) or the Lawrence Berkeley National Lab (US) free of charge:

http://pdg.lbl.gov/2014/html/receive_our_products.html

On the homepage of the particle data group you find the content of this and much more in various online versions. Also the outreach section with the Particle Advanture is highly recommended:

http://www.particleadventure.org/

I realized only now that they have an Android up now. I must run and get my tablet, immediately ;-)...

 

[PeterDonis]

I want there to be an explanation that invokes some kind of intelligible mechanism beyond merely saying that the geometry of space-time necessarily transforms as a result of relative motion. That just feels like so much mathematical form without physical content. Maybe I am wrong to be frustrated -- probably I am.

Yes, you are. You can't expect explanations of things far outside your everyday experience to fit with intuitions that are derived from your everyday experience. It is true that physicists are looking for some deeper level beneath "the geometry of spacetime"--this is driven by the desire to have a quantum theory of gravity, which requires figuring out how what we see as "spacetime" at the classical level emerges from some underlying quantum theory. But whatever that underlying theory is, it's not going to be "some kind of intelligible mechanism" by your definition any more than "the geometry of spacetime" is.

Btw, "geometry" itself is by no means "mathematical form without physical content". The way geometry is taught in school obscures this by making it all about proving theorems from axioms, instead of about how the math matches up with actual physical measurements. But geometric statements like "the surface of the Earth is curved" are not mathematical statements without physical content; after all, we discovered that the surface of the Earth was curved by making measurements, not by proving theorems.

what I am asking is whether there is any active theoretical research at present seeking to explain the mechanism underlying the constancy of c and the consequent need for a Lorentz transformation, and seeking to explain these phenomena in terms of, for instance, the physical properties of light and the way that light interacts with matter, rather than in terms of the geometry of space-time?

No. This would be going backwards; the physical properties of light and the way that light interacts with matter are based on the geometry of spacetime (and the Standard Model of particle physics). The geometry of spacetime is more fundamental than those other things. What physicists are doing, as I said above, is looking for a theory that explains how the geometry of spacetime emerges from an underlying quantum theory of gravity.

 

[NickAtNight]

Ah yes, the Particle Adventure. I have not been there in a long while. It looks like they have a good bit of information up on the newly found Higgs Boson found at the LHC at CERN.

Also the outreach section with the Particle Adventure is highly recommended:
http://www.particleadventure.org/

 

[NickAtNight]

and an iPad too ! AWESOME.

I realized only now that they have an Android up now. I must run and get my tablet, immediately ;-)...

They seem a bit weak on the Gell-Mann's the 8fold way. Perhaps I just missed it.

Also the outreach section with the Particle Adventure is highly recommended:...

Where are the great graphics locations for the Eightfold way. Here is one site, but only so so graphics. It really helps tie together the incredible particle zoo that appeared from the particle accelerators. (Note where the proton and neutron are: On the Baryon chart, top graphic, back of the bottom row. The neutron is on the left with two down quarks and one up quark. The proton is on the right with two up quarks and one down quark)

Unraveling the Confusion: the Eightfold Way
The first steps in resolving the particle proliferation problem were taken by Murray Gell-Mann and Yuval Ne'eman in 1962. They realized that many of the known particle could be fit into a series of families based on an abstract mathematical construct (called the su(3) group). Gell-Mann called this the Eightfold Way, after the Buddha's eightfold path to truth.

Some of these families are illustrated below.​

From that site. Meson family

and Baryon family

 

[Ankel]

The theory of relativity basically answers this question by saying that it's ill-formed; in the relativity view of spacetime, what we call "the speed of light" is really just a unit conversion factor between space units and time units, and since spacetime is unified in relativity, the unit conversion has to be the same everywhere.

Or, to look at it another way, in the theory of relativity, there are three fundamentally different kinds of worldlines in spacetime: timelike, spacelike, and null. The proper way of saying that something travels "at the speed of light" is to say that it travels on null worldlines. This is a geometric property of the worldline, and again, it has to be "the same" everywhere--the geometric definition of a null worldline doesn't change.

You could ask a different question, namely, why does light, the actual physical phenomenon, travel on null worldlines? Answering that requires going beyond the theory of relativity; it's a question about quantum field theory and why the quantum field describing light is massless (which is the QFT way of saying "travels on null worldlines"). In relativity, the fact that light travels on null worldlines is taken as a given, a property of light that doesn't have any further explanation within that theory.

I understand and revere the fact that you're a veteran mentor around here, and I am sure you have acquired an admirable image during this time, but I must say that this answer is perhaps the worst explanation for the constancy of the speed of light ever given. It's just very sad, it shows how unimaginative physicists are getting in the modern era.

Einstein answers this very nicely, purely through physical intuition, in one of his revolutionary papers on Special Relativity.

EDIT: If I remember correctly, Feynman also addressed this question in a lecture given at Cornell in the 60s. (1964?) and he too, approaches the question with an imaginative and a intuitive approach. The lectures are archived on YouTube for the questioner's pleasure.

 

[NickAtNight]

Chase what excites you ! Some of the greatest discoveries have come from new thinking on old issues.

I do have a bad habit of trying to make the gas burn by spinning the wheels. Thanks for your patience.

I'm still a bit curious about one thing. Is the question of the mechanism underlying special relativity an active area of research among physicists today?

If you can think it or imagine it, someone is probably researching it. The world is drowning in new data for you to theorize on !

...They are looking for gravity waves at LIGO.

... The James Webb space telescope is going to be launched soon.

... The large hadron collider (LHC) has just been restarted to work on collisions at "unprecedented energy of 13 TeV". The ALICE detector from CERN issued a new report on precisely comparing the light nuclei and antinucleii

... The new results from the Cosmic Background Radiation from COBE and WMAP are still being analyzed.

Choose your poison and go have some fun.

 

[PeterDonis]

Einstein answers this very nicely, purely through physical intuition, in one of his revolutionary papers on Special Relativity.

Reference, please? Not the paper itself, but what particular statement of Einstein's you are referring to. The reason I am asking is that, in his SR papers, Einstein took the constancy of the speed of light as an axiom. You can't take something as an axiom and then claim to have "explained" it using an argument starting from that axiom.

If I remember correctly, Feynman also addressed this question in a lecture given at Cornell in the 60s. (1964?) and he too, approaches the question with an imaginative and a intuitive approach.

Can you give a simple summary of Feynman's answer?

 

[NickAtNight]

Perhaps he was referring to Einstein's 1912 Manuscript on the special theory of relativity? Einstein develops the speed of light from Maxwell's equations and Lorentz's theory.

(typos mine. first stab at Latex)

Section 2: Elementary Exposition of the Foundations and Most Important Consequences of the Relativity Theory.

5. Principle of the Constancy of the Velocity of Light.

As we have seen Lorentz's theory, which was explained in Section 1 and which is the only viable refinement of Maxwell's theory so far, is based first of all on the assumption of the general validity of equations (I). But according to these equations, the propagation of light in empty space always occurs in accordance with equations of the form

$\Delta \, \varphi - \frac {1}{c^2}\frac{\partial^2\varphi}{\partial \,t^2} = 0 \dots$ equation (13)
​

For if one differentiates the first of equations (I) with respect to time and then eliminates h(dot) with the help of the third of equations (I), one obtains for the case where p vanishes according to the mathematical rule (),

$\frac {1} {c} \, \ddot{\textbf{e}} = curl \, \dot{\textbf{h}} = c \, curl \, (curl \, \textbf{e}) = -c \,(-\Delta \, \textbf{e} + grad \,(div \, \textbf{e})] = c \, \Delta \textbf{e}$
​

Thus, (13) holds for c and its components and also, as can easily be shown, for h and its components. But, as we know, equation (13)is solved by f(x+- ct) which form allows one to see that it represents an excitation that propagates in the form of a plane waver with velocity c. In virtue of equations (I), only electromagnetic waves propagating in vacuum with velocity c are actually possible in the case where p = 0.

Hence, in accordance with Lorentz's theory we can proclaim the following principle, which we call "the principle of the constancy of the velocity of light"

"There exists a coordinate system with respect to which every light ray propagates in vacuum with the velocity c."

This principle contains a far-reaching assertion. It asserts that the propagation velocity of light depends neither on the state of motion of the light source nor on the states of motion of the bodies surrounding the propagation space. The question as to what extent this principle can be considered certain is of fundamental significance for the theory of relativity. For the time being we will content ourselves with the realization that this principle is demanded by Lorentz' theory.​

 

[Nugatory]

Perhaps he was referring to Einstein's 1912 Manuscript on the special theory of relativity? Einstein develops the speed of light from Maxwell's equations and Lorentz's theory.

Actually Maxwell did that in 1861, a half-century before Einstein. Einstein was using Maxwell's brilliant and widely appreciated discovery to motivate the "far-reaching assertion" about the invariance of the speed of light in a vacuum.

However, all Einstein's argument here does is make it very plausible that the speed of light should be constant - indeed, once you've worked through the argument, you will be convinced that it would be really weird and logically inconsistent if it were not constant. But however well-motivated and convincing that assumption, it's still an assumption. Einstein's argument doesn't answer Sturk200's "What is the mechanism that makes it have to be that way?" question.

Other than not satisfying Sturk200, is this a problem? I don't think so. We have the same issue with Newton's first law - no one has ever been able to provide a mechanism that explains why Newton's first law has to be true as opposed to being a very well-supported assumption with no plausible alternative - and we've been able to make our peace with this foundational concern.

 

[Hornbein]

Here is a question that might be somewhat more philosophical than this community cares for. If so, I apologize in advance.

Are there any reputable theories as to why the speed of light is constant? I know that it is an empirical fact and therefore that it does not need to be proven. But on the other hand, the aim of physics has historically been to come up with satisfying theoretical explanations for empirical facts. Anyway, I'm just wondering if there are any reputable ideas out there that modern physicists are considering.

Suppose the speed of light depended on the speed of the object that emitted it. Different parts of distant astronomical objects are moving at different speeds relative to us. Light from different parts of those objects would arrive at different times. Distant astronomical images would be all blurred. So looking at those Hubble images tells you that the speed of light is constant. Well... at least it tells you that it doesn't depend on the motion of the emitter.

 

[PeterDonis]

Light from different parts of those objects would arrive at different times.

That happens anyway, since different parts of those objects are at different distances from us. A typical galaxy might be 100,000 light years across; that means there could be a difference of up to 100,000 years in the light travel time to us between the closest and furthest part of that galaxy.

Distant astronomical images would be all blurred.

By this argument, they should be blurred anyway because of the difference in light travel times from different parts, as above. So your argument can't be right.

 

[vanhees71]

and an iPad too ! AWESOME.


They seem a bit weak on the Gell-Mann's the 8fold way. Perhaps I just missed it.


Where are the great graphics locations for the Eightfold way. Here is one site, but only so so graphics. It really helps tie together the incredible particle zoo that appeared from the particle accelerators. (Note where the proton and neutron are: On the Baryon chart, top graphic, back of the bottom row. The neutron is on the left with two down quarks and one up quark. The proton is on the right with two up quarks and one down quark)

Unraveling the Confusion: the Eightfold Way
The first steps in resolving the particle proliferation problem were taken by Murray Gell-Mann and Yuval Ne'eman in 1962. They realized that many of the known particle could be fit into a series of families based on an abstract mathematical construct (called the su(3) group). Gell-Mann called this the Eightfold Way, after the Buddha's eightfold path to truth.

Some of these families are illustrated below.​

From that site. Meson family

and Baryon family

These diagrams are from the Review of Particle physics. There are great review articles:

http://pdg.lbl.gov/2014/reviews/contents_sports.html

For the Quark Model, see

http://pdg.lbl.gov/2014/reviews/rpp2014-rev-quark-model.pdf

 

[vanhees71]

However, all Einstein's argument here does is make it very plausible that the speed of light should be constant - indeed, once you've worked through the argument, you will be convinced that it would be really weird and logically inconsistent if it were not constant. But however well-motivated and convincing that assumption, it's still an assumption. Einstein's argument doesn't answer Sturk200's "What is the mechanism that makes it have to be that way?" question.

Other than not satisfying Sturk200, is this a problem? I don't think so. We have the same issue with Newton's first law - no one has ever been able to provide a mechanism that explains why Newton's first law has to be true as opposed to being a very well-supported assumption with no plausible alternative - and we've been able to make our peace with this foundational concern.

The history is very clear, and Einsteins paper of 1905 resolves a several decades long big puzzle of 19th century physics. All the math was there before, but the physics understanding was due to Einstein in this paper, and the first sentence of this paper is very remarkable [translation from German mine; it's very hard to get Einstein's masterful prose]

It is known that Maxwell's electrodynamics -as it is interpreted today- leads to asymmetries when applied to moving bodies that seem not to be inherent to the [observed] phenomena.

The point was that the Galilei transformations, which is the symmetry group of Galilei-Newton space time, is not a symmetry group for the Maxwell equations. Initially, Maxwell got his equations by making pretty abstract mechanical models by the assumption that electromagnetic fields are states of a substance dubbed the ether (or aether). From this point of view, it's not so surprising that Galilei symmetry may be broken, because there is simply a preferred reference frame, defined as the restframe of the ether. Maxwell's greatest achievement was the discovery that electromagnetic fields propagate as waves (thanks to his introduction of the "displacement current", i.e., the term $\partial_t \vec{E}/c$ on the right-hand side of Ampere's Law, extending it to one of the fundamental Maxwell equations, the Ampere-Maxwell Law), and that these transverse waves propagate with the speed of light and that also the known properties of light fit with the conclusion that light is nothing else than electromagnetic waves in a certain part of the spectrum (wavelength roughly from 400 to 800 nm). Now, if there is a preferred rest frame due to the presence of the ether, it should be possible to observe the motion of another reference frame against the ether. This however, was not the case. Einstein mentions the example of a wire loop moving against a magnet at rest and the other situation with the loop at rest and the magnet moving. There was also the famous Michelson-Morley experiment, trying to measure the motion of the Earth through the ether by measuring the difference in the velocity of light using the famous MM interferometer, which was ending with a negative result (to Michelson's great dismay, because he never liked relativity later).

Before, many brilliant physicists had found the symmetry of the Maxwell equation under transformations we now call Lorentz boosts (the earliest one I know of was by Woldemar Voigt in the 1880ies), and Poincare immediately figured out that these together with spatial rotations build a group. Of course also Lorentz wrote down these transformations in connection with his masterpiece, the theory of electrons, and there were many more physicists.

But Einstein was the one who found the much simpler but at his time most radical solution! It's not the Maxwell equations which are asymmetric under transformations from one inertial frame to another, moving relative to it with a constant velocity, but Newtonian mechanics was flawed, and this in its very foundations, namely the space-time model itself. So Einstein came to the conclusion that the space-time model must be adapted to get rid of the apparent "asymmetries" of Maxwell's equations, and the ingenious point of his paper is that he starts out from this right away by picking the one (for us today pretty simple) feature of the Maxwell equations which is related to the space-time structure, namely the appearance of the speed of light in the fundamental Maxwell equations (which at this time fortunately where written in terms of natural units, namely Gaussian units, where this is manifest, i.e., that there is only one fundamental constant in electromagnetism, which is the speed of light in vacuo). If now the entire set of Maxwell's equations should be invariant under boosts from one inertial frame to another this implies that the speed of light must be independent of the speed of its source, and thus he did not put the Maxwell equations as the postulates but just the Newtonian principle of inertia plus the invariance of the speed of light and then analyzed how one has to describe space and time to agree with these postulates, and the result is the Lorentz boost instead of the Galilei boost as the transformation equation from one inertial frame to another moving with constant velocity against the former. This derivation is easily understandable by high-school students, and this makes out the great value of this paper. The further parts are pretty difficult, but there Einstein shows that now indeed the Maxwell equations are invariant under Lorentz boosts and gives also the derivation of the relativistic mechanics of an electron. This was all correct but not in final form, which came with Minkowski's mathematical reanalysis of the space-time structure in terms of a four-dimensional affine manifold with an indefinite fundamental form of signature (1,-1,-1,-1).

 

[NickAtNight]

Very true.

Actually Maxwell did that in 1861, a half-century before Einstein. Einstein was using Maxwell's brilliant and widely appreciated discovery to motivate the "far-reaching assertion" about the invariance of the speed of light in a vacuum.

The Maxwell paper is available, both in book form and online pdf. Perhaps Sturk200 would care to read it?

A Dynamical Theory of the Electromagnetic Field Paperback – November 6, 2013
by James Clerk Maxwell

2013 Reprint of 1865 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. One of the unquestioned triumphs of nineteenth century physics was Maxwell's discovery of the equations for the electromagnetic field. "A Dynamical Theory of the Electromagnetic Field" is the third of James Clerk Maxwell's papers regarding electromagnetism, published in 1865. It is the paper in which the original set of four Maxwell's equations first appeared. The concept of displacement current, which he had introduced in his 1861 paper "On Physical Lines of Force", was utilized for the first time, to derive the electromagnetic wave equation.​