Is the speed of light constant?

[JohnvR]

I suppose the speed of light is determined by the refractive index of the medium it is traveling through. I wonder whether the energy density and the refractive index of 'space' are constant in an expanding universe. Suppose the refractive index of space / vacuum used to be bigger or smaller than it is now, would this mean the speed of light would be different too? I wonder whether the speed of light is measured regularly and what time interval should be taken to be able to notice a deviation beyond the uncertainty.

 

[DaveC426913]

The speed of light is constant. Though its passage thorugh a medium may cause it ro propogate slower.

If subway trains all moved at exactly 35mph, but you chose to jump off at every stop and take the next one, your propogation along the subway line would be much slower than your constant velocity of 35mph while aboard the trains.

 

[HallsofIvy]

That wasn't quite the question. The question was whether there is evidence that the speed of light has been the same constant throughout the history of the universe. I think we can only say that as long as we have been measuring the speed of light, it has remained constant, at least within measurment error.

 

[Loren Booda]

Most standards of physics rely directly or indirectly on a constant speed of light. Until physics is observed to deviate substantially in some way from its current bases, constant light speed will maintain its central and pervasive role. If photons were shown to possesses mass (likely <10^-66 gm, a limit from the de Broglie wavelength of a photon traversing the observable universe), it also would vary in velocity and thus (perhaps circularly) wavelength.

 

[neutrino]

That wasn't quite the question. The question was whether there is evidence that the speed of light has been the same constant throughout the history of the universe. I think we can only say that as long as we have been measuring the speed of light, it has remained constant, at least within measurment error.

How will one actually come to the conclusion that speed of light has been different some time in the past? If I'm not mistaken, the speed of light has been defined to be 299,792,458 m/s for the past couple of decades or so, and any change observed would lead to the refinement of the metre, right?

 

[f95toli]

How will one actually come to the conclusion that speed of light has been different some time in the past? If I'm not mistaken, the speed of light has been defined to be 299,792,458 m/s for the past couple of decades or so, and any change observed would lead to the refinement of the metre, right?

Right, but there are astronomical measurements of the fine structure constant that seem to suggest that it has changed over the past few billion years. So it is possible.
Also, compared to some of the other problems with the SI system this is just a minor problem; the changes we are talking about are so small that they would not have any practical effects.

 

[Claude Bile]

Suppose the refractive index of space / vacuum used to be bigger or smaller than it is now, would this mean the speed of light would be different too?

The refractive index of a vacuum is 1 by definition! The quantity I think you are looking for is the permittivity and permeability of free space, and yes, if those quantities were to change then the speed of light in a vacuum would also change.

There is no evidence to suggest that the speed of light has been any different to the currently known value in the history of the universe. There is some speculation that the speed of light has been different in the past, but to my knowledge this is just a hypothesis and no testable theories have emerged from this.

Claude.

 

[Paul H]

299,792,458 m/s hummm?
so how long is a second? doesn't this vary with gravity?
Is it possible that a photon would continue to move at its constant but the length of the second could slow with a stronger gravitational field thus it would then appear (depending on where the observer was) that the photon changed speed.

I have wondered about this for a long time (pun intended)

 

[neutrino]

1 second = 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.

 

[Paul H]

1 second = 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.

I was really asking about the effects on time caused by gravity.
can you help me out with this?
Let me as a different question,
if time slows in a higher gravity, how strong does the gravity have to be to stop time?

 

[tabchouri]

Let me as a different question,
if time slows in a higher gravity, how strong does the gravity have to be to stop time?

It is not possible to stop the flow of time, in any configuration, the flow of time is constant when the observation and the measuring positions are the same.
If you mean the flow of time as seen by a far away oberver not experiencing the gravitational field, the gravity must be infinite, else that RELATIVE flow of time won't be null.
Even then, the observer must be infinitely far from the measuring point in order not to feel the gravity.

 

[neutrino]

I was really asking about the effects on time caused by gravity.
can you help me out with this?
Let me as a different question,
if time slows in a higher gravity, how strong does the gravity have to be to stop time?

I think this question maybe slightly off-topic in this thread. I'm no expert in General Relativity, but you could find an answer if you look through the threads (or post one, if you don't find an answer) at the Special & General Relativity forum.

 

[Paul H]

It is not possible to stop the flow of time, in any configuration, the flow of time is constant when the observation and the measuring positions are the same.
If you mean the flow of time as seen by a far away oberver not experiencing the gravitational field, the gravity must be infinite, else that RELATIVE flow of time won't be null.
Even then, the observer must be infinitely far from the measuring point in order not to feel the gravity.

Actually I did mean both and you answered both. Thank you.
This leads me to wonder if an event horizon only has a fixed diameter to a given observers location.

 

[turbo]

Einstein claimed that the constancy of the speed of light in a vacuum was confined to a special case (the Special Theory of Relativity) and was invalidated when the gravitational effects of embedded masses needed to be considered. He regarded gravitational lensing as an example of classical refraction, and spent much of the rest of his life trying to determine what properties of space could be modified by embedded matter, and how the variations in these properties affected the propagation of EM through the vacuum.

In the second place our result shows that, according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position. Now we might think that as a consequence of this, the special theory of relativity and with it the whole theory of relativity would be laid in the dust. But in reality this is not the case. We can only conclude that the special theory of relativity cannot claim an unlimited domain of validity; its result hold only so long as we are able to disregard the influences of gravitational fields on the phenomena (e.g. of light).

What if he was right?

 

[yogi]

I think we limit our ability to forge new concepts when we constrain our parameters to present day measurments - There is nothing in GR or SR that cannot be accommodated by a discovery that revealed the universe to be different in other epochs. In my opinion, it is unlikely that the properties of space would be the same when the universe were the size of a basketball as it is when it has a scale factor approximately 10^26 meters

 

[f95toli]

There is no evidence to suggest that the speed of light has been any different to the currently known value in the history of the universe. There is some speculation that the speed of light has been different in the past, but to my knowledge this is just a hypothesis and no testable theories have emerged from this.

As I pointed out above, there ARE astronomical measurements that seem to suggest that the speed of light HAS changed, not by much but by a measurable amount. You can find quite few papers on this using Google Schoolar. There was a nice PRL on this about a year ago where did measure a change (unfortunately, I don't remember the name of the authors), that got quite a lot of attention when it was published.
However, there have also been other measurements that have tried to detect if alpha is changing today and they have all -as far as I know- come up negative, Hence, it could be that the speed of light was changing relatively rapidly just after big bang but that it later stabilized and is now changing so slowly that it can't be detected.

The nice thing about measurements of the fine structure constant (and therefore c) is that it can be done with extremely high precision meaning even very small changes can be detected.

 

[rbj]

Right, but there are astronomical measurements of the fine structure constant that seem to suggest that it has changed over the past few billion years. So it is possible.

if $\alpha$ changes sufficiently to be measure, that means something. something tangible in physical reality actually changed. no so for any dimensionful constant such as c or G or similar.

$$\alpha = \frac{e^2}{4 \pi \epsilon_0 \hbar c}$$

how would we know that a change in $\alpha$ is due to c? why not $\hbar$? or e? or even $\epsilon_0$ (never mind that it is a defined constant, so is c and that doesn't seem to bother anyone)? no one is yet suggesting that the value of 4 or $\pi$ has changed.

my question is that if somehow you were omniscient and knew that the change of $\alpha$ was due to c, how would the physical world be different, from the POV of its own measurement devices or experience of reality, if it was due to a change in $\hbar$?

if the fine-structure constant changes, that's salient but that is all that there is, $\alpha$ changed. it doesn't matter which of the constituent dimensionful components to $\alpha$ had changed since that is a reflection of which system of (natural) units you decided to use to measure and express physical quantity. Mother Nature doesn't give a rat's ass which system of units we or the aliens on the planet Zog choose to use to measure things.

like measuring a length with a ruler or tape measure and counting the tick marks on the measurement standard, that is how we measure, or even perceive, all of physical reality. we really only measure or perceive dimensionless values when we measure anything. if we think (by our anthropometric measurement) that the speed of light changed, what really changed is the number of Planck lengths per meter or the number of Planck times per second or maybe both. but both of those values are dimensionless and are the salient values.

Also, compared to some of the other problems with the SI system this is just a minor problem; the changes we are talking about are so small that they would not have any practical effects.

the change of a dimensionful constant is just not meaningful. if some dimensionless constant changes that's a big deal and that is what changed, the dimensionless value. we do not know what to attribute that change to and, what dimensionless value we choose to attribute a change of $\alpha$ to is essentially a consequence of the system of units we choose to use to express physical quantity.

 

[888eddy]

measurements of light speed have been found to be decreasing. be it this is from very early measurments but despite innacurcys a trend has been observed that measurements are getting slower. it could be an increddible coincidence that all the results where innacurate in a way that produced an exponential curve of c slowing. infact i read a thing recently that suggested that 2000 years ago light could have been 20-30% faseter. our knowledge of the age of the universe is based on a constant value of c and if it was varying by this much the universe could be as young as 15000 years. i was astonished that i couldn't find anything written disproving this. i mean we have evidence that Earth has been around longer than that right. wrong, the our knowledge of the age of the Earth is based on radioactive decay dating and the rate of radioactive decay is proportional the the speed of light. i'll admit I am sceptical about the universe being 15000 years old but still astounded that the idea holds water.

 

[DaveC426913]

measurements of light speed have been found to be decreasing. ... i was astonished that i couldn't find anything written disproving this.

Let's start with the evidence in favour.

Do you have any references for this claim?

 

[DaveC426913]

[EDITED so as not to look like a loonie]

Lacking any credible references, it's safely outside the realm of "holding water". Is there any reason this is more astounding to you than whether or not Britney really lost her virginity at 14?

 

[888eddy]

also found out that the speed of light has been measured 168 times by 16 different methods over the last 300 years. the max error in these measurements can be quite accurately predicted. a graph plotted with the values for the speed of light against time and the 'best fit' exponential curve of the speed slowing shows how all the results are within the max error from the line. i would like to know if, when you plotted a graph of the lower extreme that the measurements could have been would this line be decreasing and prove that its not just a coincidence that the values form an exponetial curve or would it prove that is is possible that it could just be coincidence. i mean 168 measurements is enough to make it incredibly unlikely but someone in scotland won the lotto jackpot twice which there is billions to one chance would happen to anyone ever. my point is, unlikely does happen.

 

[Doc Al]

Well, one of the links is obviously Creationist, the other two are personal websites (one of which is disproving it).

Indeed.

888eddy, I deleted that last post: Please do not reference or link to obviously religious sites as "evidence" for your claims.

[ EDIT: Wha? You deleted your post? Now mine makes me look like a loonie! ]

Sorry Dave, I was the one who deleted that post.

 

[Gokul43201]

also found out that the speed of light has been measured 168 times by 16 different methods over the last 300 years. the max error in these measurements can be quite accurately predicted. a graph plotted with the values for the speed of light against time and the 'best fit' exponential curve of the speed slowing shows how all the results are within the max error from the line. i would like to know if, when you plotted a graph of the lower extreme that the measurements could have been would this line be decreasing and prove that its not just a coincidence that the values form an exponetial curve or would it prove that is is possible that it could just be coincidence. i mean 168 measurements is enough to make it incredibly unlikely but someone in scotland won the lotto jackpot twice which there is billions to one chance would happen to anyone ever. my point is, unlikely does happen.

You know what? The speed of light has been increasing. Newton and Romer measured it in the late 17th Century, and got about 210,000 to 220,000 km/s; about 30 years later, Bradley measured it at 298,000 km/s; and 2 centuries later, Michelson measured it at 299,796 km/s!

PS: Still no supporting evidence presented; you risk having yourself labeled a crackpot.

 

[888eddy]

Well, one of the links is obviously Creationist, the other two are personal websites (one of which is disproving it).

So far, it's safely outside the realm of "holding water". Is there any reason this is more astounding to you than whether or not Britney really lost her virginity at 14?

have you read the one trying to disprove it? its not very convincing. i know its questionable how solid the 'facts' are but i would like to think the idea will be (or is already being) looked into in a completely unbiased manner that can give very reliable results. however if the results i have seen are accurate i would say the idea of light slowing has a fairly strong grounding. i mean it would be very hard to think of a reason why the results have been getting lower in the way they have and i can't find anything attempting even a rough theory to explain it. infact there is no solid point saying it couldn't be possible. and by saying the idea 'holds water' i meant that no one can say why it wouldn't work yet.

 

[888eddy]

by 'substantial piece of evidence against' i meant something as strong as; the speed of light couldn't be constant beacuase that would mean the universe was accelerating which is not possible (with current understanding). the point being that looked at from the other side it would be much harder to prove that light speed is constant. if the evidence was on the side of constant as strong as its on the side of variable right now the idea of variable would be completely dismissed.

 

[888eddy]

You know what? The speed of light has been increasing. Newton and Romer measured it in the late 17th Century, and got about 210,000 to 220,000 km/s; about 30 years later, Bradley measured it at 298,000 km/s; and 2 centuries later, Michelson measured it at 299,796 km/s!

PS: Still no supporting evidence presented; you risk having yourself labeled a crackpot.

thats a terrible example. three of the most inacurate results say its going up against the majority saying its going down following a pattern with strong correlation. i think you just don't understand why that's a good piece of evidence. tell you what, give me a while and i will see if i can get the history of measurments taken and the predicted levels of inacuracy. then i will plot a graph so people can see the correlation. to be honest i would be interested to see just how good the correlation is, either i appologise in advance because there is little correlation and the whole idea can be forgotten, or the scientists who are researching this are telling the truth and it does have good correlation and very little chance of being a coincidence making it a huge piece of evidence.

 

[rbj]

Right, but there are astronomical measurements of the fine structure constant that seem to suggest that it has changed over the past few billion years. So it is possible.

there is serious dispute (among real physicists, not mere armchair physicists like me) that it is possible or even meaningful. the issue is a little broader: Is there any meaning to the variation of dimensionful "constants", be it c or G or $\hbar$? What meaningful difference would it make? How would we know the difference?

a variation in $\alpha$ (a dimensionless number) does, itself, have meaning. but $\alpha$ is not c:

$$\alpha = \frac{e^2}{4 \pi \epsilon_0 \hbar c}$$

perhaps (if you use Planck Units), it's a changing e that caused $\alpha$ to change. or, if you're using Stoney Units, a change in $\alpha$ is caused by a changing $\hbar$. or perhaps you're using Atomic Units, then a change in $\alpha$ is caused by a change in c.

but nature doesn't give a rat's ass which units of measurement we (or some aliens on the planet Zog) choose to use to measure things. and neither we, nor the Zoglings, measure any dimensionful physical quantity directly; we measure it against a standard (a "unit" if you want to call it such) of the same dimension of quantity. (this is literally what we do when we measure a length with a ruler, we count tick marks and end up with a dimensionless quantity.) a ratio of like-dimensioned quantities is a dimensionless number and that is the salient parameter. quoting John Barrow:

[An] important lesson we learn from the way that pure numbers like $\alpha$ define the world is what it really means for worlds to be different. The pure number we call the fine structure constant and denote by $\alpha$ is a combination of the electron charge, e, the speed of light, c, and Planck's constant, h. At first we might be tempted to think that a world in which the speed of light was slower would be a different world. But this would be a mistake. If c, h, and e were all changed so that the values they have in metric (or any other) units were different when we looked them up in our tables of physical constants, but the value of $\alpha$ remained the same, this new world would be observationally indistinguishable from our world. The only thing that counts in the definition of worlds are the values of the dimensionless constants of Nature. If all masses were doubled in value [including the Planck mass m_P] you cannot tell because all the pure numbers defined by the ratios of any pair of masses are unchanged.

 

[rbj]

i didn't realize that this is the same as that older thread.

so, i would suggest that 888 ask himself or herself: how, precisely, is (more likely was) the speed of light measured? what were the standards? what were the raw quantities measured?

 

[888eddy]

actually i don't think i need to create a graph. i found a very good article explaining how there is so much indisputable evidence that the speed of light is slowing down and that everything fits into that model so well. yet it hasnt been accepted by the physics community because it suggests the universe is so young that evolution would not have had enough time to get to where it is today. this is the kind of huge piece of evidence against the slowing light speed theory i was talking about in an earlier post saying how the idea 'holds water' until someone states a reason why it wouldn't work. alotho i would be interested to know how they predicted how long evolution has taken. if light speed was higher years ago there would be more radiation therefore more chance of a mutation to occur in an organism. i wonder if they used the current probability of a mutation happening as being a constant value. I am probably wrong, i don't know much at all about evolution. < link to religious site deleted >

 

[rbj]

actually i don't think i need to create a graph.

dunno if a graph is relevant. maybe some understanding of what, fundamentally, is measured when we measure anything.

i found a very good article explaining how there is so much indisputable evidence that the speed of light is slowing down and that everything fits into that model so well.

indisputable?

http://www.arxiv.org/abs/hep-th/0208093

http://xxx.lanl.gov/abs/physics/0110060 (check out the section: "The operationally indistinguishable world of Mr. Tompkins" .)

 

[Doc Al]

i found a very good article explaining how there is so much indisputable evidence that the speed of light is slowing down and that everything fits into that model so well.

...

...im probably wrong, i don't know much at all about evolution.

For the last time, do not post links to religious sites. You are welcome to reference articles published in mainstream, peer-reviewed science journals.

FYI: This "evidence" for the slowing down of the speed of light is a standard creationist claim. (See claim CE411 on talkorigins.org.)

 

[Kristy234]

I'm confused. If the speed of light is changing, does that mean that a vacuum's refractive index is also changing? What effect would the speeding up / slowing down of lights speed have on various models etc...

Also, I read somewhere about light being refracted by gravity...but how does this work since it has no mass. My original thoughts were about general relativity and how gravity affects time, so if light is near a massive object, time is slower and therefor it will go slower...? Can anyone tell me how this works?

 

[Chris Hillman]

A Quick Overview of Some Elementary Aspects of the General Theory of Relativity (GTR)

Hi, Kristy234, and welcome to PF!

I'm confused. If the speed of light is changing

I think you misunderstood Gokul4320's jest (read his post again).

Also, I read somewhere about light being refracted by gravity...but how does this work since it has no mass. My original thoughts were about general relativity and how gravity affects time, so if light is near a massive object, time is slower and therefor it will go slower...?

First, there is a distinction between infinitesimal velocity (for electromagnetic or gravitational radiation, according to the general theory of relativity (gtr), the infinitesimal speed of light in a vacuum is always unity), velocity in the large (multiple distinct operationally significant notions), and coordinate speed. In gtr, the coordinate speed of light would be something like $dx/dt$ where x(t) is a null geodesic and where the time coordinate t need not correspond to proper time. Such a coordinate speed need not be unity.

However, coordinates are in general not physically significant so this does not contradict the fact that in gtr the speed of light in vacuum is always unity. To take a more familiar example, in a polar coordinate chart on the euclidean plane, with line element
$$ds^2 = dr^2 + r^2 \, d\phi^2, \; 0 < r < \infty, \; -\infty < \phi < \infty$$
the equation of a straight line has the form $r = r_0 \, \sec(\phi-\phi_0)$, and $d^2r/d\phi^2 \neq 0$, but this does not mean that the line is really "bending"! A coordinate-free notion of bending is provided by the covariant derivative of the tangent to a curve.

(In gtr, the covariant derivative taken along a timelike curve of the unit tangent vector to said curve is the acceleration vector whose magnitude, the path curvature, tells us whether or not the particle whose world line is represented by this curve is bending, i.e. whether or not our particle feels any acceleration. If not, the pathc curvature vanishes and our timelike curve is a timelike geodesic.)

Second, all gravitational phenomena are represented in gtr by the curvature of spacetime itself (to be be precise, by the Riemann curvature tensor), and mathematics tells us that one way in which curvature becomes manifest is that initially parallel geodesics (the analog, in a curved manifold, of a "straight line") will diverge or converge. This effect is called geodesic deviation. You can see how it works on the surface of a globe of the world: the longitude lines are geodesic paths, and neighboring longitudes are parallel at the equator but converge as you move North or South. This convergence is one hallmark of positive Gaussian curvature; on a "saddle surface", which has negative Gaussian curvature, initially parallel geodesics will diverge (you can see this in Escher's Circle Limit woodcuts).

In gtr we use curved Lorentzian manifolds to model the geometry of spacetime. The spacetime model plays a dual role: not only does it provide the geometric setting for nongravitational physics, but its curvature competely describes all gravitational phenomena. In gtr, the world of a laser pulse (or "photon" if you prefer) traversing a vacuum region is represented by a special kind of geodesic called a null geodesic. (Because a photon is a massless particle; the world line of a particle with positive mass is a timelike geodesic if this particle is in a state of inertial motion.) The appropriate component of the curvature tensor near a massive object is negative, which means that in this scenario, initially parallel null geodesics will diverge. This leads to the so-called gravitational red shift effect, one of the four classical solar system tests of gtr (or better say, test comparing metric theories of gravitation including gtr and various competing theories).

Coming back to "speed of light", there are speculative variable speed of light theories, but these have not been accepted and so far seem to have no widely accepted experimental support. These theories are talking about something different from the effects we have discussed so far, in the context of our gold standard theory of gravitation, gtr.

As for "refraction", I can only assume that you were misled by this comment:

Einstein claimed that the constancy of the speed of light in a vacuum was confined to a special case (the Special Theory of Relativity) and was invalidated when the gravitational effects of embedded masses needed to be considered. He regarded gravitational lensing as an example of classical refraction, and spent much of the rest of his life trying to determine what properties of space could be modified by embedded matter, and how the variations in these properties affected the propagation of EM through the vacuum.

This is a good example of why ascribing what would now be considered a fringe viewpoint to Einstein entirely out of what is invariably a complex and subtle historical context tends to be (IMO) perversely unhelpful. Although I am sure turbo meant well, he terribly misled you here, Kristy. My reasons for this judgement are too numerous to list, but let me just say this: even if turbo had accurately described AE's views V(T,C) at time T in their full historical context C--- which he most certainly did not--- and even if V(T,C) would now be considered flat out wrong--- which is not true in this case, if one restores the missing context!--- Einstein died in 1955, before the Golden Age of Relativity (c. 1960-1975), which completely transformed our knowledge and appreciate about gtr and its applications to astronomical observations, so it makes sense to direct newbies to modern textbooks, rather than writings by Einstein which would require vast additional reading in the contemporary physics literature (plus published private correspondence) in order to properly appreciate the context in which his public and private statements must be understood. In addition, it is essential that you understand that Einstein's views (as expressed in his papers and in his private letters) changed frequently and drastically, particularly those pertaining to physical issues. In his thoughtful scientific biography, Abraham Pais writes that this changeable character is in fact one hallmark of Einstein's genius.

Turbo, I hope that in future you will be more careful to avoid the appearance of pushing a fringe viewpoint by presenting a misleading description of some mythical "Einstein's view" (To mention just one objection, while by an arguably perverse shift in viewpoint one can model weak-field lensing in terms of a kind of "refraction", you seem to have forgotten about strong field lensing, which is much more complicated, yet described in fully nonlinear gtr exactly the same way--- see Chandrasekhar, Mathematical Theory of Black Holes.)

Can anyone tell me how this works?

If you want to truly understand all this, you need to study the math. In order to understand gtr you need to have a solid grasp on many subtleties involving curved spacetime geometry, and to grasp these you need to have a solid grasp on various subtleties involving flat spacetime geometry, the kind used in str. A good place to begin is Taylor & Wheeler, Spacetime Physics. After that you can try the undergraduate level gtr textbook by D'Inverno, Understanding Einstein's Relativity.

 

[Kristy234]

First, there is a distinction between "infinitesimal velocity" (for electromagnetic or gravitational radiation, according to gtr, the infinitesimal speed of light in a vacuum is always unity), "velocity in the large" (multiple distinct notions), and "coordinate speed". In gtr, the coordinate speed of light would be something like $\partial x/ \partial t$ where x(t) is a null geodesic, and this need not be unity, but coordinates are in generally not physically significant so this does not contradict the fact that in gtr the speed of light in vacuum is always unity.

sorry, this might sound like a stupid question but what does 'gtr' stand for? general something relativity? But apart from that, thanks, makes a bit more sense (kinda) now.

Second, all gravitational phenomena are represented in gtr by the curvature of spacetime itself, and mathematics tells us that one way in which curvature becomes manifest is that initially parallel geodesics (the analog, in a curved manifold, of a "straight line") will diverge or converge. You can see this on the surface of a globe of the world: the longitude lines are geodesic paths, and neighboring longitudes are parallel at the equator but converge (positive curvature!) as you move North or South.
In gtr we use curved Lorentzian manifolds to model the geometry of spacetime; the curvature of such a spacetime model represents gravitational phenomena; the spacetime model also provides the geometric setting for nongravitational physics. In gtr, the path of a laser pulse (or "photon" if you prefer) is represented by a special kind of geodesic called a null geodesic. (Because a photon is a massless particle, if you like.) Because a certain "component" of the curvature tensor near a massive object is negative, initially parallel null geodesics will diverge. This leads to the so-called "gravitational red shift" effect, one of the four classical solar system tests of gtr (or better say, test comparing metric theories of gravitation including gtr and various competing theories).

Ahh, i see, good analogy... but with the earth, it is curved in the third dimension...how is spacetime curved?

If you want to truly understand all this, you need to study the math. In order to understand gtr you need to have a solid grasp on many subtleties involving curved spacetime geometry, and to grasp these you need to have a solid grasp on various subtleties involving flat spacetime geometry, the kind used in str. A good place to begin is Taylor & Wheeler, Spacetime Physics. After that you can try the undergraduate level gtr textbook by D'Inverno, Understanding Einstein's Relativity.

Cool, thanks

 

[Chris Hillman]

Try reloading to see the change I just made to my Post #33 to answer your question. (I have written essentially the same post, addressing dozens of newbies, dozens of times, so as you can probably appreciate, it is hard not to get a bit sloppy!)

the Earth ... is curved in the third dimension...how is spacetime curved?

You are thinking of the surface of the Earth as what mathematicians call an embedded submanifold of three-dimensional euclidean space. Surfaces have both extrinsic curvature, which tells (in a description-invariant way) how they bend in the embedding space, and intrinsic curvature, which determines all curvature effects which can be detected within the surface itself, e.g. by measuring geodesic deviation. In gtr, only the intrinsic curvature of spacetime (measured by the Riemann curvature tensor) is physically significant.

A very good nontechnical discussion of extrinsic versus intrinsic phenomena can be found in Lawrence Sklar, Time, Space, and Spacetime.