Speed of light - why is it a constant?

[Parlyne]

So, according to you, mass and force are separate things, but energy and mass are the same thing. Right? Then you would have to define each of these 3 things for me. My understanding is simple: everything is energy. Forces are geometrical representations of energies (= energies "geometrized"). Mass is a particular geometrization of energy (or energies, if you will) that results in curvature of spacetime we call gravity.

Energy and mass are emphatically not the same thing, no matter how many bad popularizations claim otherwise. The content of E=mc^2 is to say that mass is a type of energy, not to say that mass and energy are totally equivalent. To take an extreme case, a (presumably massless) photon can carry energy.

Forces can't really be thought of as a representation of energy, particularly since it's not too hard to construct situations where the action of a non-zero force does not change the energy of any part of a system. (All you need here is a force which is always perpendicular to the motion of the object it acts on.) Operationally, you can define a force as anything which changes the momentum of an object. Mass represents an object's inertial resistance to its motion being changed. (This, of course, can be made into a more mathematically precise statement.) There's no need to go to any sort of geometrical construction. These definitions haven't changed conceptually since Newton. All that's changed is the math necessary to describe them in a manner consistent with the present understanding of space and time.

As for stress/energy tensor being the source of gravity, I confess that I have trouble with this "metaphysical" interpretation. I consider myself a pragmatist and realist. So in my layman view, saying that stress/energy tensor, which is a mathematical abstraction, is the source of gravity, which to me is a very real force that keeps me securely on Earth and satellites from falling, is not far removed from saying that Atlas is holding the sky on his shoulders, or like in medieval times they said that heavens were held up by the decree of God.

There got to be a more pragmatic interpretation of the source of gravity in GR. Like, according to Newton, it's just what goes on between two masses, which are "real" things (even though they act somewhat mysteriously at a distance, but still, this is a more "realistic" view). So, my head is satisfied that the tensor accurately describes the math involved. What is lacking is a pragmatic know-how acceptable for the benefit of my "gut feeling" that just keeps on rebelling.

I wasn't making some grand metaphysical statement. It seems like you're interpreting what I said as meaning that "the stress-energy tensor is why there is such a thing as gravity," when I actually meant that "the geometry of spacetime is determined by the stress-energy tensor of all the stuff in the spacetime in much the same way that the Newtonian gravitational field is determined by the mass of all the stuff in space."

In both cases, I visualize a sail inflated by wind. Which is only a 2D plane curved in 3D. There seems to me that to distinguish between inertial and invariant masses, from the geometrical standpoint, some additional dimensions are in order. What do you think?

You've lost me here. I don't really see a need to try to make mass a geometrical quantity; so, I don't really see your point.

This is an example of circular reasoning. The mathematics of SR are based on the assumption that speed of light, as "a law of nature", is invariant for all observers. You have to remove that initial assumption and prove that it works out the same in the end in order to claim that this as a logical outcome of the theory. (And the situation with GR in this regard is even worse, since it employs Minkowski's spacetime, which, in turn, stands on the axiom from which it follows a priori that nothing can ever possibly move faster than light in vacuum.)

It's only circular because you changed what I wrote. What I said was that the mathematics of SR requires that there be some speed which is invariant under boosts to any inertial reference frame. This has nothing to do with light or anything else, even though Einstein first came up with the mathematical structure by thinking of light. To put it more concretely, Einstein's original axioms are mathematically equivalent to:

1) The spacetime interval between to events (that is, points in spacetime), given by s=\sqrt{c^2\Delta t^2-|\Delta \vec{x}|^2}, is independent of the inertial frame in which the positions and times are measured.

and

2) Any path traveled by light in a vacuum will have spacetime interval of 0.

All of the usual SR discussion about time dilation, fast rockets, the twin paradox, and even the Lorentz transformation and Minkowski geometry follow from (1). (2) only comes into play when talking about light specifically. This is why I say that the massless nature of light is a separate issue from the structure of SR.

Oh, and to be clear, Minkowski geometry is a property of SR. The geometry is GR, while always having a Minkowski structure on a sufficiently local scale, is quite a bit more complicated, in general, as it is a dynamical quantity.

Once you start messing with the concept of a mass and make it loose like this, IMO this makes an entirely different theory than SR, let alone GR, which, essentially, is based on 3 concepts: light, matter and space, with mass being a property of matter but not light. The consequent equivalence of mass and energy does not invalidate the underlying geometry, from which it follows. It can't. For, otherwise it would be equivalent of pulling the carpet from under your own feet, or hacking off the brunch on which you sit. That's where, in my view, you're making a logical error in reasoning. Yes, everything is energy, but geometrically speaking, each expression of energy is distinct and has distinct "geometrical consequences".

I'm not making the concept of mass at all loose. I'm just pointing out that every observation which addresses the properties of light has finite precision and that, with added precision, we could always find something unexpected. An object with extraordinarily small mass and energy large enough to measure will be moving at speed very close to c. For sufficiently small mass, we would not yet have been able to measure the deviation, even if it is there.

The point that I'm trying to make is that relativity has nothing at all to do with light or with matter. SR is strictly about the geometry of spacetime, which has the effect of specifying what the kinematics of objects in the spacetime look like. GR adds the way that the geometry of the spacetime responds to the stress-energy tensor of the stuff in the spacetime; but, it does so with no reference to any specific properties of that stuff.

See, for me, the whole trouble with QM is in the fact that it replaced geometry of space with abstract properties of point-like particles of matter, which are also forces. This makes it very difficult, if not impossible, to visualize, and, consequently, to understand.

Quantum field theory (QFT) states that forces can be thought of (approximately) as resulting from the emission and absorption of certain kinds of particles. I don't know that this part is all that strange, since the emitted and absorbed particles are simple a way of moving energy and momentum from one particle to another. But, it's probably worthwhile to keep in mind that the geometry of SR is actually encoded into the structure of the QFTs we use to describe the world.

 

[kmarinas86]

What makes the speed of light a constant. I read the FAQ on special relativity but still don't understand why c (speed of light) exists as a constant.

It's like a rule like many others, why do they exist? Is there a part of space-time that limits this speed. Why are all the photons that ever existed limited by this speed?

Let's take an equation:

v^2 + u^2 = c^2

Given that all mass can be created from pure energy (light), we could say that there is energy inside of us that propagates and reflects at the speed of light c relative to some arbitrary frame (later on we can show how this can appear to be the case in other frames). Make sense yet?

Now look at this page titled The mirror problem a thought experiment on time dilation:

http://www.schoolphysics.co.uk/age16-19/Relativity/text/Time_dilation/index.html

[PLAIN]http://www.schoolphysics.co.uk/age16-19/Relativity/text/Time_dilation/images/1.gif

So imagine that we moved at v and light within us bounces within us at c. We would experience a time dilation equal to:

c/u = 1/sqrt(1-v^2/c^2)

This can be proven to be mathematically equivalent to the equation above:

u/c = sqrt(1-v^2/c^2)
u^2/c^2 = 1-v^2/c^2
u^2 = c^2-v^2
v^2 + u^2 = c^2

So while energy in an object does not move in a straight line, light that passes through the object can (if it is not disturbed) can. Two details to consider here:

1) Light that passes through an object transparent to it passes ahead of it at a relative velocity of c-v (if going in the same direction) or c+v (if going in the opposite direction).
2) The peak-to-peak time period between wave crests adjusts accordingly. If going in the same direction, this period increases by a factor * c / (c-v). If going in the opposite direction, this period decreases by a factor * c / (c+v).

As far as the object itself is concerned, it is time dilated by a factor of 1/sqrt(1-v^2/c^2), for whom (or 'which' if it is a thing and not a person) events of external origin occur in time intervals shorter by a factor of * sqrt(1-v^2/c^2). So for an object moving in the same direction as the light, the time period between peaks is observed to change by a factor of * [sqrt(1-v^2/c^2)] * [c / (c-v)], and so the frequency is seen to change by a factor of * [1/sqrt(1-v^2/c^2)] * [(c-v)/c]. These factors can be simplified to * \sqrt{\frac{\left(1+v/c\right)}{\left(1-v/c\right)}} and * \sqrt{\frac{\left(1-v/c\right)}{\left(1+v/c\right)}}, respectively.

The wavelength observed by an 'internal', rather than 'external', observer must in this case increase by a factor of * \sqrt{\frac{\left(1+v/c\right)}{\left(1-v/c\right)}}, as would be predicted by the relativistic doppler effect. This again breaks into two terms which need explaining:

1) * sqrt(1-v^2/c^2), this is caused by length contraction of the observer relative to the wavelength of the incoming wave.
2) * c / (c-v), this is caused by the parallel motion of both the light and the observer, having a slight "scrunching" effect on the waveform inside the object.

If it weren't for the length contraction of the observer, then the wavelength of the light would actually be seen to shortened. This would becomes clear if we decided to project a standing interference pattern inside the object (let's say it's a box) by shining light through two small slit openings; the faster the object moved in the same direction as the light, the more scrunched this standing interference pattern would, if it were not for the length contraction, appear. So by definition, the object must contract further lengthwise relative to external electromagnetic waves when accelerating to properly account for the wavelength change that is actually observed of light. The factor by which they are contracted and the factor by which they are time dilated together produce the result that the speed of light c that an 'external' observer sees is also the same speed of light c that an observer 'internal' to that object would also see. The origin of the length contraction hypothesis predates Einstein's Special Theory of Relativity: http://philsci-archive.pitt.edu/987/1/Michelson.pdf. The same is true for the idea of time dilation: http://en.wikipedia.org/wiki/Relativity_priority_dispute#Harvey_R._Brown_.282005.29.[/color]

The 'external' electromagnetic waves, which do not interfere with the object, are completely neutral to whether or not the object is accelerating, moving, or not at all. They are independent and do not change their fundamental nature, that is to say they do not without becoming 'internal' respond with any particular action at a distance, whatever the observers and objects involved in such action.

There is a frame in which the speed of internal "bouncing" of light u in an object is maximized such that u=c. This is called the rest frame of the object. If this rest frame were the same as that for all others, this would be called the Lorentzian Ether Frame. In Special Relativity, this frame would be unspecified, and even perhaps non-existent, though technically there can still be a frame in which the internal "bouncing" of light in mass u, or even that of any mass possessing degrees of freedom, is at an (unobservable) maximum u=c. In either case, the velocity of light changes apparent direction with respect to the directional movement of the observer, rather than speed, during frame changes of the observer, an effect which produces the aberration of light. The difference with the notion of a Lorentzian Ether Frame is that the length contraction has a component independent of any external observer's motion, and also, the time dilation has a physical component not relative to any external observer's motion. What do remain relative to the observer's relative motion are the frequencies and wavelengths of signals received from the object that notify the existence of the object to the observer, as well as the "observed" length contraction and time dilation of that object.

 

[PeterDonis]

The mathematics of SR are based on the assumption that speed of light, as "a law of nature", is invariant for all observers. You have to remove that initial assumption and prove that it works out the same in the end in order to claim that this as a logical outcome of the theory.

And the point of the paper that bcrowell linked to early in this thread is that it does exactly this: it removes the assumption that the speed of light is the same for all observers, and instead *derives* the theorem that there must be some invariant speed from the principle of relativity and the homogeneity and isotropy of space. The only way light comes into it is that we believe, based on our best current knowledge, that photons, particles of light, have zero rest mass, and any particle that has zero rest mass has to move at the invariant speed.

(And the situation with GR in this regard is even worse, since it employs Minkowski's spacetime, which, in turn, stands on the axiom from which it follows a priori that nothing can ever possibly move faster than light in vacuum.)

Minkowski spacetime is only one particular solution of the Einstein Field Equation, in which the stress-energy tensor is identically zero, there is zero cosmological constant, and the curvature is identically zero everywhere. There are lots of other spacetimes that are also solutions to the EFE but are very different from Minkowski spacetime.

GR does use the principle of *local* Lorentz invariance, i.e., a very small patch of any spacetime looks, locally, like a very small patch of flat Minkowski spacetime. But the logical basis for that works the same as I outlined above.

 

[Spacie]

Energy and mass are emphatically not the same thing...
a (presumably massless) photon...

I don't understand you. Sorry. To me you seem to contradict yourself, claiming that a photon may have mass, presumably because photon's energy may be interpreted as mass.. and then "emphatically" denying that. Are you simply messing with me, 'cause I'm a newb?

Forces can't really be thought of as a representation of energy...

All the time. Think of vectors.

Mass represents an object's inertial resistance to its motion being changed.

That's a good reminder for me, thanks. I am a strongly visual type, so I tend to "geometrize" everything. This view of mass says a lot about the properties of space.

There's no need to go to any sort of geometrical construction. These definitions haven't changed conceptually since Newton. All that's changed is the math necessary to describe them in a manner consistent with the present understanding of space and time.

I believe there is no understanding of space at all. There is no even theory of space, like, for example, what forces make up its dimensions, why 3, how space is formed and how it interacts with matter, etc, etc. And space and geometry go together.

I wasn't making some grand metaphysical statement. It seems like you're interpreting what I said as meaning that "the stress-energy tensor is why there is such a thing as gravity," when I actually meant that "the geometry of spacetime is determined by the stress-energy tensor of all the stuff in the spacetime in much the same way that the Newtonian gravitational field is determined by the mass of all the stuff in space."

My words were not directed at you, sorry if it seemed so. That's how it is said everywhere nowadays. Last time I consulted wiki, it said there too, that the stress-energy tensor is the source of gravity. A mathematical abstraction as a source of a very, very real force is... I am lost for words. So, no, my criticism was not directed at you but at this... incongruity.

The point that I'm trying to make is that relativity has nothing at all to do with light or with matter. SR is strictly about the geometry of spacetime, which has the effect of specifying what the kinematics of objects in the spacetime look like. GR adds the way that the geometry of the spacetime responds to the stress-energy tensor of the stuff in the spacetime; but, it does so with no reference to any specific properties of that stuff.

This makes no sense to me. The way I see it, these "advanced" interpretations of relativity only make people confused. The fundamental difference between light and matter is removed (everything is a point-like particle with properties in empty space), and this invites people to start comparing light with matter and treat them on par. This does not lead to clarity but has the opposite effect.

Quantum field theory (QFT) states that forces can be thought of (approximately) as resulting from the emission and absorption of certain kinds of particles. I don't know that this part is all that strange, since the emitted and absorbed particles are simple a way of moving energy and momentum from one particle to another. But, it's probably worthwhile to keep in mind that the geometry of SR is actually encoded into the structure of the QFTs we use to describe the world.

Really? I start thinking that you're simply messing with me.

 

[Spacie]

And the point of the paper that bcrowell linked to early in this thread is that it does exactly this: it removes the assumption that the speed of light is the same for all observers, and instead *derives* the theorem that there must be some invariant speed from the principle of relativity and the homogeneity and isotropy of space. The only way light comes into it is that we believe, based on our best current knowledge, that photons, particles of light, have zero rest mass, and any particle that has zero rest mass has to move at the invariant speed.

Yes, thank you very much, I am looking into this paper now. I have not done it before, because bcrowell's terminology seemed a bit over my head, when I first heard it (mainly because I have not used those words in years), so all I could do was duck, lol. That paper is exactly what I needed. Not because I doubt the constancy of the speed of light in empty space for all observers --quite to the contrary!-- but I have doubts about the conclusion that nothing can move faster than c. To me it seems that chargeless massive particles should be able to move >c and so I am trying to find the loophole in the theory that would allow that.

Minkowski spacetime is only one particular solution of the Einstein Field Equation, in which the stress-energy tensor is identically zero, there is zero cosmological constant, and the curvature is identically zero everywhere. There are lots of other spacetimes that are also solutions to the EFE but are very different from Minkowski spacetime.

GR does use the principle of *local* Lorentz invariance, i.e., a very small patch of any spacetime looks, locally, like a very small patch of flat Minkowski spacetime. But the logical basis for that works the same as I outlined above.

Thank you for all that. That's just what I needed. Minkowski spacetime is not good for my purposes, because, as I said, I found that it has the ceiling on the speed already "built in".

Thank you very much! :)

 

[PeterDonis]

To me it seems that chargeless massive particles should be able to move >c and so I am trying to find the loophole in the theory that would allow that.

Strictly speaking, the paper's argument does not prove that you can't have particles moving faster than c; it only proves that you can't take a particle that moves slower than c and boost it to faster than c (or vice versa). You could still have particles that always move faster than c and can never be slowed down to c or slower; in other words, tachyons:

http://en.wikipedia.org/wiki/Tachyon

 

[Parlyne]

I don't understand you. Sorry. To me you seem to contradict yourself, claiming that a photon may have mass, presumably because photon's energy may be interpreted as mass.. and then "emphatically" denying that. Are you simply messing with me, 'cause I'm a newb?

I swear, I'm not messing with you, whether or not you are, in fact, a newb.

One of the really bad concepts introduced early in the history of relativity was the idea of "relativistic mass." I have seen few other concepts that so universally lead people to the wrong ideas about relativity; so, I never use it (well, except to point out that it is in every way equivalent to energy). When I talk about an object having (or not having) mass, I mean rest mass. So, no, I wasn't talking about the idea of a photon's energy being interpreted as mass. I meant that there is nothing inconsistent about the idea that a photon could have mass in just the same manner as an electron. So far as we know, it isn't the case; but, that doesn't make the possibility inconsistent.

All the time. Think of vectors.

I do. Regularly. But, that doesn't make force equivalent to energy. Forces change the motion of an object. But, if the only change is to the direction of motion, the object's energy is unaffected. The correct way to make a connection between force and energy is through the work energy theorem, which involves the projection of force onto an object's trajectory.

I believe there is no understanding of space at all. There is no even theory of space, like, for example, what forces make up its dimensions, why 3, how space is formed and how it interacts with matter, etc, etc. And space and geometry go together.

We don't need to know why something is the way it is to know how to describe it correctly. Also, I don't know why you insist on trying to make everything about forces. It's perfectly consistent to imagine a universe with no forces at all that still has space and time.

My words were not directed at you, sorry if it seemed so. That's how it is said everywhere nowadays. Last time I consulted wiki, it said there too, that the stress-energy tensor is the source of gravity. A mathematical abstraction as a source of a very, very real force is... I am lost for words. So, no, my criticism was not directed at you but at this... incongruity.

The stress-energy tensor is no more a mathematical abstraction than the charge and current densities that show up in E&M. Just as with Maxwell's equations, specifying the specific mathematical structure of the source (charge and current densities in E&M, stress-energy tensor in GR) let's you (at least in principle, though the math can certainly get ugly) calculate the form of the field it generates (electric and magnetic fields in E&M, metric tensor in GR).

This makes no sense to me. The way I see it, these "advanced" interpretations of relativity only make people confused. The fundamental difference between light and matter is removed (everything is a point-like particle with properties in empty space), and this invites people to start comparing light with matter and treat them on par. This does not lead to clarity but has the opposite effect.

Exactly why shouldn't light and matter be treated on par? The differences in their behavior is an empirical fact, not an a priori one, which suggests that the treatment of motion in a relativistic spacetime ought to be used to understand what makes them different, not the other way around.

Really? I start thinking that you're simply messing with me.

I don't see why. It's not some big secret that treatment of fundamental particles needs to be consistent with relativity to even come close to describing reality correctly.

 

[skbrant]

You would be hard pressed to find a way to do this that wouldn't require a frequency dependent photon speed. The thing is, we use light over a range of frequencies that spans 20-some orders of magnitude. It would be hard to miss frequency dependence over that kind of range.

In particular, if you suggested that light simply had mass, you'd find that the speed of light looked like
v(\nu)=c\sqrt{1-\frac{m_\gamma^{\phantom{\gamma}2}c^4}{h^2\nu^2}}.

With this sort of behavior, there's no way it could look like all the light we use has anything close to the same speed, unless that speed was actually c.

I'll add that, from the standpoint of quantum field theory, interactions with vacuum fluctuations can only change the speed of a photon if the photon has mass in the first place.

The photon mass could be an effective mass which depends on the frequency in such a way that v is almost constant over the range of frequencies. Notice that the cosmic background radiation is always present, so that the effective photon mass is non-zero and certainly dependent on the frequency. So, when the photon propagates in the thermal medium it will acquire an effective thermal mass which may be computed from first principles. This mass is certainly dependent on the photon frequency.

 

[Spacie]

photon's mass? Another one?!

So, no, I wasn't talking about the idea of a photon's energy being interpreted as mass. I meant that there is nothing inconsistent about the idea that a photon could have mass in just the same manner as an electron. So far as we know, it isn't the case; but, that doesn't make the possibility inconsistent.

Nothing inconsistent? In relativity it makes no sense whatsoever. If light has mass, then how is it different from matter?

What you guys do with this sort of statements is this: you take a structure, say, made of lego-like blocks, break it apart and then proudly pronounce pointing to the pile on the floor: see, I told you! it's all made from the same stuff! (meaning that they are all energies). But what happened to the structure that there was? Structure is the most important thing. Without it there is no world but just a "pile" of energies. Structure is world is geometry. Light is what reveals the structure, by tracing it as it propagates through it.

But, that doesn't make force equivalent to energy. Forces change the motion of an object. But, if the only change is to the direction of motion, the object's energy is unaffected. The correct way to make a connection between force and energy is through the work energy theorem, which involves the projection of force onto an object's trajectory.

Force is a geometrical expression of energy. Above in bold what you call the object's energy I call it its structure. It's the same with space. Mass is a force that modifies the curvature of space, iow its structure. Absolutely everything in existence may be represented by a particular deviation(s) from Euclidean perfection in the structure of space. In fact, this view is much simpler: there is no matter, no particles, only deviations in the structure of space. No deviations = space is empty. See how simple? I'd say even elegant

I don't know why you insist on trying to make everything about forces. It's perfectly consistent to imagine a universe with no forces at all that still has space and time.

Yes, I can imagine space without time. It would be a perfect, never changing, the most beautiful and symmetrical structure ever. Time implies change and change is deltaE, making time just a byproduct of energy transformation. Energies are forces that shape the dynamic structure of space.

Exactly why shouldn't light and matter be treated on par? The differences in their behavior is an empirical fact, not an a priori one, which suggests that the treatment of motion in a relativistic spacetime ought to be used to understand what makes them different, not the other way around.

There is a huge difference between light and matter. One always propagates with constant rate, while the speed of the other varies and depends on many things. Light is the property of space, while matter, geometrically speaking, is its opposite. Yes, there is a way to make everything "the same", but it is not by assigning mass to everything (you just may end up assigning mass to space as well, lol). It is to represent everything as forces defining the dynamic geometry of space.

It's not some big secret that treatment of fundamental particles needs to be consistent with relativity to even come close to describing reality correctly.

-?! Surely you're pulling my leg. Everyone knows that at quantum scales space is no longer invariant throughout but has distinct structure and even orientation. All those numerous properties of subatomic particles clearly imply complex geometry. Besides, that's where those additional dimensions are lurking, right?

 

[PeterDonis]

Nothing inconsistent? In relativity it makes no sense whatsoever. If light has mass, then how is it different from matter?

You may be getting hung up on the term "light". I suggest a better terminology: what you are referring to as "light", try calling instead "massless particles". And what you are referring to as "matter", try calling instead "massive particles". The terms "massless" and "massive" refer to the particle's rest mass, which is the length of its 4-momentum vector.

The statement that "there is nothing inconsistent about the idea that a photon could have mass in just the same manner as an electron" is just saying that you could have a consistent theory in which the photon was a massive particle, not a massless particle. In the actual universe we observe, the photon appears to be a massless particle, but there's nothing inconsistent about a theory in which it is massive instead. Such a theory just doesn't match the data. Relativity does not require that any particular type of particle be massless; it just requires that *if* a particle is massless, it moves on a null worldline.

Everyone knows that at quantum scales space is no longer invariant throughout but has distinct structure and even orientation. All those numerous properties of subatomic particles clearly imply complex geometry. Besides, that's where those additional dimensions are lurking, right?

In string theory, yes, the properties of particles are due to geometry in additional dimensions; basically, each point of what we think of as 4-dimensional spacetime is really a "curled up" higher-dimensional space (a Calabi-Yau manifold, in the versions I'm familiar with, but that may not be the only such space that's used to build a string theory), and the geometry of that space determines the properties of particles. As I understand it, each "particle" is basically a different way of wrapping up a string inside the higher-dimensional space, though I admit I'm reaching the edge of my understanding here. (By the way, what you are calling "forces" are just the properties of particles as well; forces are just particles being exchanged by other particles.)

But none of this means that "space is no longer invariant". String theory still obeys Lorentz invariance, and the curled up higher dimensional space is the same at each point of spacetime.

 

[Spacie]

Thank you Peter, you explain things so well!

You may be getting hung up on the term "light". I suggest a better terminology: what you are referring to as "light", try calling instead "massless particles". And what you are referring to as "matter", try calling instead "massive particles". The terms "massless" and "massive" refer to the particle's rest mass, which is the length of its 4-momentum vector.

This billiard view is no substitute for geometry. Mass has very specific effect on the curvature of space. It cannot be arbitrarily assigned or taken away from a particle, a.k.a. point in space, like you could do with maybe spin or charge, which would change the way the particle interact with others, but would not have such a drastic effect on the surrounding space.

That's why my geometrical sensibilities are offended when mass it viewed simply like a property of a particle. It cannot be disengaged from being also a property of space.

The statement that "there is nothing inconsistent about the idea that a photon could have mass in just the same manner as an electron" is just saying that you could have a consistent theory in which the photon was a massive particle, not a massless particle. In the actual universe we observe, the photon appears to be a massless particle, but there's nothing inconsistent about a theory in which it is massive instead. Such a theory just doesn't match the data.

And the reason we entertain such far-fetched theories is because...?

Relativity does not require that any particular type of particle be massless; it just requires that *if* a particle is massless, it moves on a null worldline.

I thought the worldline represents the curvature of space, so this becomes relevant from the geometrical point of view. If a photon had mass, this would have a recursive effect on the curvature of space as it propagated through it. No? How could it be otherwise? The world with massive photons is vastly different from what we have. I thought this forums forbid entertaining crazy ideas like that. Why leniency in this regard?

In string theory, yes, the properties of particles are due to geometry in additional dimensions; basically, each point of what we think of as 4-dimensional spacetime is really a "curled up" higher-dimensional space (a Calabi-Yau manifold, in the versions I'm familiar with, but that may not be the only such space that's used to build a string theory), and the geometry of that space determines the properties of particles. As I understand it, each "particle" is basically a different way of wrapping up a string inside the higher-dimensional space, though I admit I'm reaching the edge of my understanding here. (By the way, what you are calling "forces" are just the properties of particles as well; forces are just particles being exchanged by other particles.)

The only way I can see "particles", if I see knots in the dynamic fabric of space. And the forces are threads that shape its structure. In this way I find the string theory very appealing. I can easily visualize space made up of these dynamic and vibrating strings.

But none of this means that "space is no longer invariant". String theory still obeys Lorentz invariance, and the curled up higher dimensional space is the same at each point of spacetime.

Does it have Lorentz invariance on all scales? That would make no sense to me. As for curled up dimensions at each point, that part I have difficulty with, too. To me space appears as a dynamic structure, and dimensions are created dynamically as well, when pressure on its structure is strong enough, which in our everyday world is right on the boundary between "matter" and "space". So, on those scales space should be very different "near" matter than where it is empty. There are no extra dimensions lurking in empty space. They may appear dynamically though, when pressures on the local structure become strong enough. (Or, alternatively, if curled up extra dimensions do exist at each point in space --by the way, how do they quantize space to get to those points?-- then those dimensions may grow or shrink in size dynamically in response to the local pressures.) But this is off topic here. Sorry, I got carried away.I read the Pal's paper (Nothing but Relativity), and it turned out such an easy and pleasant read that I failed to see its groundbreaking significance for my search for a loophole in relativity that would permit superluminal speeds for chargeless massive particles. How can I tackle it?

 

[DaveC426913]

I read a lot of responses but seem to have missed the one I was expecting.

The speed of light is not determined to be constant, the speed of light is postulated to be constant (in relativity). Every statement in Einstein's relativity is preceded with a supposition: "If the speed of light were constant then we would see..."
Turns out that, what we would see is exactly what we do see to many decimal places in uncountable tests.

Whether or not the postulate of relativity is "true" (whatever that means), it is spectacularly good at modeling what we really see. thus, we accept it - until it stops being so spectacularly good.

That is the short yet pretty much definitive answer.

 

[PeterDonis]

This billiard view is no substitute for geometry.

Now you may be getting hung up on the word "particle".

Bear in mind that we are talking about models of reality, not "reality itself". We are not saying that particles "really are" little billiard balls, point-like objects with no internal structure that somehow have properties like rest mass "attached" to them. We are only saying that, within a certain domain of applicability, we can model particles as point-like objects and make good predictions.

The view that "everything is geometry" is a model too. Possibly a more accurate one, but still a model. See further comments below.

Mass has very specific effect on the curvature of space. It cannot be arbitrarily assigned or taken away from a particle, a.k.a. point in space, like you could do with maybe spin or charge, which would change the way the particle interact with others, but would not have such a drastic effect on the surrounding space.

That's why my geometrical sensibilities are offended when mass it viewed simply like a property of a particle. It cannot be disengaged from being also a property of space.

Actually, spin and charge also affect the properties of space--more precisely, they affect spacetime curvature, hence geometry. Check out the Kerr-Newman metric for a spinning, charged black hole:

http://en.wikipedia.org/wiki/Kerr–Newman_metric

But there may also be a confusion lurking here. When we talk about an individual particle, such as an electron or photon, moving through spacetime, we are treating that particle as a "test particle". The Wikipedia page has a brief overview of the concept:

http://en.wikipedia.org/wiki/Test_particle

Any relativity textbook should also talk about this. The idea is that the particle's properties are used to determine its own motion, but the particle is so small that it does not affect the geometry of the background spacetime it is moving through. So we would assign a particle a rest mass (which might be zero, as with a photon, or nonzero, as with an electron), and an energy (more precisely, an energy-momentum 4-vector), but those properties would not affect the curvature of the spacetime; they would only be used to determine the particle's worldline in what, to the particle, looks like a fixed background spacetime. Again, this is just a model, and we are not claiming that real particles actually have zero effect on spacetime; just that, for the purposes of the model, that effect is so small that we can ignore it and still make good predictions.

And the reason we entertain such far-fetched theories is because...?

It could be a variety of reasons. In the case of a theory that gives the photon a non-zero rest mass, one reason to develop such a theory would be to come up with more and more accurate ways of testing whether the real photon's rest mass really is exactly zero. If your theory assumes from the outset that the photon's rest mass is exactly zero, it's hard to think about what the consequences would be if it were not, which is what you need to do to come up with good experiments to test the question.

I thought the worldline represents the curvature of space, so this becomes relevant from the geometrical point of view.

Again, it's good to be careful here to avoid possible confusion. There are several ideas that can easily become tangled:

(1) A worldline, for an individual particle, when we are modeling particles as point-like objects, is a one-dimensional curve in spacetime. That's all it is. By itself it doesn't give any information about the rest of the spacetime, only about the events on the worldline itself.

(2) The worldline, as a curve in spacetime, may be "straight" (a geodesic) or "curved" (a non-geodesic). A geodesic is the generalization of a "straight line" for manifolds that may themselves be curved, so the Euclidean definition of "straight line" can't be used as is. But it's perfectly possible to have a curved worldline in a flat spacetime (e.g., the worldline of an accelerating observer in Minkowski spacetime), or a "straight" (geodesic) worldline in a curved spacetime.

(3) As noted above, just a single worldline can't tell you about the curvature of the spacetime as a whole. But if you have information about multiple worldlines and how they relate to each other, that can tell you about the curvature of spacetime itself.

So to go back to the comment of mine that you were responding to, a massless particle always moves on a null worldline; that's true regardless of the spacetime it's moving through. But what a null worldline "looks like", in the spacetime as a whole, can certainly depend on the spacetime.

The only way I can see "particles", if I see knots in the dynamic fabric of space. And the forces are threads that shape its structure. In this way I find the string theory very appealing. I can easily visualize space made up of these dynamic and vibrating strings.

Yes, but as noted above, this is another model, which may cover a wider domain of applicability than the "point particle" model, but is still a model.

Does it have Lorentz invariance on all scales? That would make no sense to me.

As I said, I'm reaching the edge of my understanding here, but as I understand it, string theory does assume a (flat) background spacetime, which would be Lorentz invariant on all scales. However, it's quite possible that, at small enough scales (say around the Planck length), the background spacetime would be "unobservable". Someone better versed in string theory would have to weigh in on this.

 

[PeterDonis]

I read the Pal's paper (Nothing but Relativity), and it turned out such an easy and pleasant read that I failed to see its groundbreaking significance for my search for a loophole in relativity that would permit superluminal speeds for chargeless massive particles. How can I tackle it?

Well, as I noted before, the idea of tachyons is not, strictly speaking, inconsistent with relativity; where the problems come in is trying to construct a consistent model where tachyons can interact with things that aren't tachyons. That's really more of a quantum mechanics issue than a relativity issue; the Wiki page I linked to on tachyons mentions it briefly ("tachyonic instability").

 

[skbrant]

Thank you Peter, you explain things so well!This billiard view is no substitute for geometry. Mass has very specific effect on the curvature of space. It cannot be arbitrarily assigned or taken away from a particle, a.k.a. point in space, like you could do with maybe spin or charge, which would change the way the particle interact with others, but would not have such a drastic effect on the surrounding space.

By the way, photons also influence the geometry. Photons are mutually attracted by gravity. In an first order approximation there is a Feynman diagram involving the exchange of one graviton between a photon and something else (e.g. another photon or an electron, etc), in the same way as there is an exchange of one graviton between two massive particles. So, I do not understant why you are saying that only massive particles can affect the geometry.

 

[Spacie]

Oh Peter, thank you! Again you gave me so much info to chew on and you explain stuff so well, it's just... I'm lost for words. I'll study what you wrote and come back. Thank you.



skbrant, please don't take seriously what I say. I study physics on my own, so I have a non-standard view on things. Once I spent a whole day trying to find a Feynman diagram with gravitons in it, but alas, I found only one in some speculative paper. I still would like to see such a diagram, especially if it also involves photons (why, that would put us half way to a field drive, no?) Seriously, if you have a link to such a diagram, please post or PM me. Ansd if you have a few (with gravitons!), I'll be ecstatic :)

By the way, photons also influence the geometry. Photons are mutually attracted by gravity. In an first order approximation there is a Feynman diagram involving the exchange of one graviton between a photon and something else (e.g. another photon or an electron, etc), in the same way as there is an exchange of one graviton between two massive particles. So, I do not understant why you are saying that only massive particles can affect the geometry.

Well, as Peter explained above, charges also affect geometry, which, however, is a different effect from that of a mass. If we had a good understanding of these two effects on the geometry of space, one from massive particles and another from photons, then... a field drive would not be far away. Yay! Better yet, we'd have a very good understanding of what space really is.

And to keep it on topic, the constant speed of light, is a very important property of space, and viewed as such it seems natural. This constancy of the speed of light appears counter-intuitive when we view light as "particles" in empty space. Because then, what makes light different from any other particle, including particles of matter?

I'm trying to guess why you people want to imbue a photon with mass -- to work out some difficulty in a quantum theory?

 

[PeterDonis]

Oh Peter, thank you! Again you gave me so much info to chew on and you explain stuff so well, it's just... I'm lost for words. I'll study what you wrote and come back. Thank you.

You're very welcome!

And to keep it on topic, the constant speed of light, is a very important property of space, and viewed as such it seems natural. This constancy of the speed of light appears counter-intuitive when we view light as "particles" in empty space. Because then, what makes light different from any other particle, including particles of matter?

The fact that the photon has zero rest mass, according to our most accurate experiments to date. (I believe the current upper bound on a possible rest mass for the photon, based on experimental accuracy, is something like 10^-21 of the electron mass, and there is no data I'm aware of that suggests that the photon rest mass is anything but exactly zero.) Since our best current understanding is that neutrinos have a (very small) nonzero rest mass, the photon and the graviton are the *only* particles we know of that have zero rest mass, and our reasons for believing that gravitons exist are purely theoretical, since gravity is so weak that nobody expects to detect a graviton, even indirectly, any time soon. (We expect to directly detect gravitational *waves* fairly soon, and we already have good indirect evidence for them from binary pulsars, but gravitons would be *quantum* aspects of those waves, and those are *much* harder to detect than the waves themselves.)

I'm trying to guess why you people want to imbue a photon with mass -- to work out some difficulty in a quantum theory?

He wasn't saying that photons have mass, at least not in the sense of rest mass. He was saying that photons have energy, and anything that has energy is a source of gravity. In quantum terms, anything that has energy can couple to anything else that has energy via the exchange of gravitons. It's generally not a good idea to use the word "mass" unqualified if there is any possible ambiguity about whether you mean "rest mass" or just "energy".

Of course, viewing an object with energy this way means you are *not* viewing it as a "test particle" any longer; you are viewing it as part of the source of curvature of the spacetime you are working with. It's perfectly valid to view light (or photons, if you're talking in particle terms) this way, but don't confuse that model with the "test particle" model. Which one is more useful depends on what you are trying to do with the model.

 

[ravisastry]

i was going through the explanation of maxwells EM theory and i came to know that the speed of EM radiation is dependent only on permittivity or permeability of the medium in which it propogates.
Hence, come up with a material which can beat vacuum on permittivity & permeability values and you have have faster than c speeds in nature...
correct right ?

 

[ghwellsjr]

i was going through the explanation of maxwells EM theory and i came to know that the speed of EM radiation is dependent only on permittivity or permeability of the medium in which it propogates.
Hence, come up with a material which can beat vacuum on permittivity & permeability values and you have have faster than c speeds in nature...
correct right ?

All materials slow down the apparent speed of light. I say apparent because the speed of light is still c within a material, it just seems like the speed of light has slowed down because we are observing the net effect of all the charges interacting with the light. So we're not going to find a material that permits light to go even faster. Sorry.

 

[BruceW]

I think the speed at which information can propagate is limited to c. So the travel of information carried by the electromagnetic wave would be limited to c. This usually corresponds to group velocity. But the phase velocity can be far greater than c.

 

[ravisastry]

the way I am looking at this is...speed of light, is not its inherent characteristic, rather it is soley dependent on the permittivity and permeability of the medium.
If we start thinking in this way, then we probably can have a reasoning for the 2nd postulate of SR...
No matter what the speed of the source emitting light, photons will travel with a speed depending on permittivity and permeability of environment surrounding the source. Hence, in vaccum, its always C

 

[juanrga]

What makes the speed of light a constant. I read the FAQ on special relativity but still don't understand why c (speed of light) exists as a constant.

It's like a rule like many others, why do they exist? Is there a part of space-time that limits this speed. Why are all the photons that ever existed limited by this speed?

Why a cat is not dog, because it is not a dog. In our universe c is a constant, because this is how our universe is.

 

[ghwellsjr]

the way I am looking at this is...speed of light, is not its inherent characteristic, rather it is soley dependent on the permittivity and permeability of the medium.
If we start thinking in this way, then we probably can have a reasoning for the 2nd postulate of SR...
No matter what the speed of the source emitting light, photons will travel with a speed depending on permittivity and permeability of environment surrounding the source. Hence, in vaccum, its always C

No, photons travel at c. Why? Because we define them to travel at c. Einstein's second postulate defines all light to propagate through empty space at c. We cannot measure the speed of a photon or the propagation of light since these are one-way traverses and we have nothing with which to communicate back to the timing device at the source when the photon or light has reached its destination. We can only measure the round-trip speed of light because it now has arrived back at the source and we only need one timing device to make the measurement. Einstein postulates that the one-way speed equals the two-way speed for any inertial observer but it can never be measured, proven or demonstrated. So, there is no reasoning or explanation for the 2nd postulate, Einstein just uses this definition to devise his concept of a Frame of Reference.

Photons can only travel through empty space, even if it is only the short distance between a proton and an electron in an atom. As I said before, the apparent slowing down of light through a medium is due to the photons not taking a straight, unhindered path through the medium but rather interacting with the protons and electrons in the medium, being absorbed and re-emitted. But nobody can keep track of all those particles and so we don't model light in this way as it travels through a medium, rather we look at the net effect and part of that model includes permittivity and permeability which explains why an untold trillions of photons average out to travel at a speed less than c. But you're never going to use that explanation to tweak light to go faster than c by fiddling with the permittivity and/or the permeability, whatever that could possibly mean.

 

[PatrickPowers]

No, photons travel at c. Why? Because we define them to travel at c. Einstein's second postulate defines all light to propagate through empty space at c. We cannot measure the speed of a photon or the propagation of light since these are one-way traverses and we have nothing with which to communicate back to the timing device at the source when the photon or light has reached its destination. We can only measure the round-trip speed of light because it now has arrived back at the source and we only need one timing device to make the measurement. Einstein postulates that the one-way speed equals the two-way speed for any inertial observer but it can never be measured, proven or demonstrated. So, there is no reasoning or explanation for the 2nd postulate, Einstein just uses this definition to devise his concept of a Frame of Reference.

Photons can only travel through empty space, even if it is only the short distance between a proton and an electron in an atom. As I said before, the apparent slowing down of light through a medium is due to the photons not taking a straight, unhindered path through the medium but rather interacting with the protons and electrons in the medium, being absorbed and re-emitted. But nobody can keep track of all those particles and so we don't model light in this way as it travels through a medium, rather we look at the net effect and part of that model includes permittivity and permeability which explains why an untold trillions of photons average out to travel at a speed less than c. But you're never going to use that explanation to tweak light to go faster than c by fiddling with the permittivity and/or the permeability, whatever that could possibly mean.

You might be right. I thought that it could be done like this: send out a nice generous light pulse and throw some dust into the space. An observer can follow the light pulse by observing the reflections off of the dust. Presumably the photons that were not reflected were moving at the same speed.

By the way, there is a neat effect of this. Imagine light is very slow. You have a mirror one light/second away. You would see the reflections from the pulse take two seconds to travel to the mirror, then a big flash since all the reflections on the way back would arrive at the same time.