Is the speed of light actually constant or just always measured to be the same?

[DaveC426913]

Please focus on answering questions instead of criticizing the contributions and opinions of others, OK?

Seriously dude, are you going to just copycat me?


Can you explain what

"Time" isn't a "building block", it even has no substance!

has to do with the topic at-hand?

 

[harrylin]

Perhaps this also contributes nothing of significance, but what I am struggling with here is why anyone thinks that the constancy of the speed of light is open to question under relativity. It isn’t some side effect of relativity, it is one of the two postulates. Take it away and you are not discussing relativity. Or so it seems to me. Some one else on these forums pointed out that if you increase the value of c (hypothetically of course) you get closer and closer to Newtonian mechanics until, when c is infinity, hey presto! Newtonian mechanics! That is to say, the constancy of the speed of light is the difference between Newtonian mechanics and special relativity.

When c is infinity and c does not relate to the speed of light, then you obtain Newtonian mechanics. However, "Relativity" commonly means General relativity, in which the second postulate is only locally valid.

- http://www.bartleby.com/173/22.html

Cheers,
Harald

 

[Ken Natton]

Well okay, perhaps these are just the ramblings of someone who doesn’t understand very well, but it has always seemed to me to be a problem that we call the phenomenon ‘the speed of light’. It has a tendency to make people think that light is the issue. It isn’t. It isn’t about the speed of the propagation of electromagnetic waves. Light travels at that speed but it isn’t the driver of the phenomenon.

Here’s another point that I believed to be a significant insight, perhaps this is also wrong but maybe discussing it will help to clear up the misalignments of thought that are dogging the discussion. Something I read suggested that in point of fact the speed of everything is always constant through space time. The only variable is what proportion of your travel through space time is travel through space and what proportion is travel through time. When you are stationary in space, all of your travel through space time is taken up with travel through time. When you are traveling through space at c, time is stopped all together. The only variable is where you lie between these two extremes.

 

[harrylin]

Seriously dude, are you going to just copycat me?

Can you explain what

has to do with the topic at-hand?

Also seriously, that would be appropriate as your behavioral advice was really good. This was merely to illustrate that nit-picking on other contributors is not constructive - so I can but won't elaborate. Peace dude (yes that was a copycat).

 

[harrylin]

Well okay, perhaps these are just the ramblings of someone who doesn’t understand very well, but it has always seemed to me to be a problem that we call the phenomenon ‘the speed of light’. It has a tendency to make people think that light is the issue. It isn’t. It isn’t about the speed of the propagation of electromagnetic waves. Light travels at that speed but it isn’t the driver of the phenomenon. [..]

Yes that's an essential insight. The speed of light is a boundary condition from which the Lorentz transformations followed; light itself isn't an issue.

Harald

 

[netheril96]

It's more than semantics! Such questions relate to philosophy and physical models. Relativity was the natural outcome of the older physical models of mechanics and optics; however, the result was a theory that is based on principles (a "principle theory") which does not directly relate to physical models.

Philosophy is just semantics. Scientific method requires that we focus on the observable and testable, not something that "actually" happens according to your unsubstantiated belief system or philosophical system and that somehow cannot be measured in any way whatsoever or have any effect on the observable nature.

 

[Ken Natton]

The speed of light is a boundary condition from which the Lorentz transformations followed; light itself isn't an issue.

So then is it not important to be clear about what is being discussed? Are we discussing the speed of the propagation of electromagnetic waves, the possible variablility of which does not necessarily undermine the basic principles of relativity, or are we discussing the boundary condition, the speed that is the fastest it is possible to travel through space and at which time stops, whose invariabliity is central to the whole concept of relativity? Is that perhaps the source of the misunderstandings here?

 

[Passionflower]

Well, OK, you've linked to your own posts. Do you have any references that aren't you?

Let's get this out of the way by putting up the math, this is not the first time you are making innuendos I do know what I am talking about.

Let's take a pair of stationary test observers R2 and R3 in a Schwarzschild solution with a Schwarzschild radius of R.

Do you agree that the ruler distance between them is:

$$\rho = R \left( \sqrt {3}\sqrt {2}-\sqrt {2}+\ln \left( -\sqrt {3}+\sqrt {3} \sqrt {2}-\sqrt {2}+2 \right) \right)$$

If so do you agree that the radar distance T in coordinate time between them is:

$$T = R+R\ln \left( 2 \right)$$

And that the radar distance in proper time for R2 is:

$$\tau_{R2} = 1/2\, \left( R+R\ln \left( 2 \right) \right) \sqrt {2}$$

And for R3:

$$\tau_{R3} = 1/3\, \left( R+R\ln \left( 2 \right) \right) \sqrt {6}$$

With me so far or anything wrong with the math?

From this you can calculate the (average) speed of light, if you do this you will find that both the coordinate speed and the speed from r2 to r3 (r2 < r3) in proper time is always < c. Only the speed from r3 to r2 in proper time is > c.

Agreed? No? Where do I make a mistake?

For you reference if we value the R2 and R3 values we can chart it, here is a 2D plot.

Below is a plot of light speeds between pairs of static observers (o1, o2) separated a fixed ruler distance of 1 with the radar distance as measured by a clock at observer o1. In the plot you can see the ruler distance (which is 1 for each pair) divided by the radar distance, this ratio is larger for pairs closer to the EH.
[PLAIN]http://img169.imageshack.us/img169/4331/slowdownoflight.gif

And here is a 3D plot:
[PLAIN]http://img717.imageshack.us/img717/2414/001lightspeed3d.gif

Any mistakes?

If not, could you please stop making innuendos I am wrong?

 

[DaveC426913]

...this is not the first time you are making innuendos I do know what I am talking about...

If not, could you please stop making innuendos I am wrong?

I am not making innuendos, I am simply asking for a reference to something other than your own work for the claim you are making. I get to do that.

 

[Passionflower]

I am not making innuendos, I am simply asking for a reference to something other than your own work for the claim you are making. I get to do that.

The 'claim' that I am making is obvious if you follow the math. It is very simple: it is true or false, either my math is right or it is wrong.

So you think titles and reputations are more authoritative than the mathematics? If so I pity you.

 

[DrGreg]

When we measure the speed of light between two points in curved spacetime then the speed will generally not be c.

Yah, I'm not really sure what leads you to say this.

This is a well-known fact of non-inertial frames (and there are no such things as inertial frames in curved spacetime, only local approximations to them).

See for example Physics FAQ: Is The Speed of Light Constant? - General Relativity subsection

To clarify, in curved spacetime (or even in flat spacetime in a non-inertial frame) when you measure the speed of some light passing right next to you, you always get c (using proper distance and proper time) but if you measure light that is some distance away from you, you will almost always get a different answer.

 

[DaveC426913]

OK:

The 'claim' that I am making is obvious if you follow the math. It is very simple: it is true or false, either my math is right or it is wrong.

I do not have the math background to follow it. Why do you think I'm asking for a reference so I can read up on it?

So you think titles and reputations are more authoritative than the mathematics?

Where on Earth did that come from? Not from me.

No, I think that I like to verify something that goes against my understanding, by checking with multiple sources.

If so I pity you.

You don't have a middle zone do you? You're either normal or in Full Attack. Try being a little less defensive. And maybe a little less vicious.

I'm asking for references to your claim so I can understand it. I have not made the slightest suggestion that you are wrong. Go back and check.

 

[harrylin]

Philosophy is just semantics. Scientific method requires that we focus on the observable and testable, not something that "actually" happens according to your unsubstantiated belief system or philosophical system and that somehow cannot be measured in any way whatsoever or have any effect on the observable nature.

I agree with the focus of modern science - thanks for enhancing my point. However, I doubt that any philosopher will agree with your claim about their profession.

Harald

 

[harrylin]

So then is it not important to be clear about what is being discussed? Are we discussing the speed of the propagation of electromagnetic waves, the possible variablility of which does not necessarily undermine the basic principles of relativity, or are we discussing the boundary condition, the speed that is the fastest it is possible to travel through space and at which time stops, whose invariabliity is central to the whole concept of relativity? Is that perhaps the source of the misunderstandings here?

I do think that the OP is talking about the speed of light rays. However, I see no consequence for this thread of understanding this thread to be about either light rays or the limit speed, as they are supposed to be equal and the validity of relativity is not questioned here. What answer do you think would change with the interpretation of the question?

 

[harrylin]

[..]

See for example Physics FAQ: Is The Speed of Light Constant? - General Relativity subsection

To clarify, in curved spacetime (or even in flat spacetime in a non-inertial frame) when you measure the speed of some light passing right next to you, you always get c (using proper distance and proper time) but if you measure light that is some distance away from you, you will almost always get a different answer.

Yes it's very basic, it even was one of the first things that Einstein explained to the public about GR. Here's the reference once more: http://www.bartleby.com/173/22.html

Harald

PS: I now see that the writers of the FAQ are unfamiliar with the use of "velocity" in older English literature (and still some modern literature of other disciplines). It usually stands for "Geschwindigkeit" which commonly means speed; and here it is a translation of "Ausbreitungsgeschwindigkeit" which means propagation speed (that is, non-vectorial).
- http://www.ideayayinevi.com/metinler/relativitetstheorie/oggk03.htm
- http://de.wikipedia.org/wiki/Ausbreitungsgeschwindigkeit

And if you check his 1916 scientific paper on GR you will understand that his explanation only makes sense if it is understood to mean just that, from his use of the Huygens principle.

 

[Ken Natton]

I do think that the OP is talking about the speed of light rays. However, I see no consequence for this thread of understanding this thread to be about either light rays or the limit speed, as they are supposed to be equal and the validity of relativity is not questioned here. What answer do you think would change with the interpretation of the question?

Well okay, and perhaps my intervention has added nothing, I apologise if so. Clearly I was not successful in defusing the argument which is what I presumed to be doing. My perspective was just this – for someone who has a view of the reality in which they live that might be described as Newtonian mechanical – even though they themselves might not even know what that term means – it is a big struggle to understand how it can be possible for two different observers, one of whom is stationary and the other of whom is moving at some significant proportion of the speed of light, to both observe the same beam of light and measure its velocity to be the same. For such a person, grasping how it can be that all reference frames are relative and yet the speed of light is constant for all observers requires a fundamental shift in their understanding of the reality in which they live. Falling out over minute details about the speed of propagation of electromagnetic waves seems to me to be getting bogged down in a detail that is less than entirely essential.

 

[harrylin]

Well okay, and perhaps my intervention has added nothing, I apologise if so. Clearly I was not successful in defusing the argument which is what I presumed to be doing. My perspective was just this – for someone who has a view of the reality in which they live that might be described as Newtonian mechanical – even though they themselves might not even know what that term means – it is a big struggle to understand how it can be possible for two different observers, one of whom is stationary and the other of whom is moving at some significant proportion of the speed of light, to both observe the same beam of light and measure its velocity to be the same. For such a person, grasping how it can be that all reference frames are relative and yet the speed of light is constant for all observers requires a fundamental shift in their understanding of the reality in which they live. Falling out over minute details about the speed of propagation of electromagnetic waves seems to me to be getting bogged down in a detail that is less than entirely essential.

There is no need at all to change your views of reality - the early inception of relativity was fully based on a Newtonian view of reality! A classical understanding about the speed of propagation of electromagnetic waves is compatible ("only apparently irreconcilable", as Einstein put it) with relativity*. What needed to be abandoned was Newton's theory according to which measurements of time and length are "absolute". Examples of physicists who maintained the "old" view of reality are Lorentz, Langevin and perhaps Dirac (Einstein's opinion is a bit unclear, and it flip-flopped somewhat).

Cheers,
Harald

* http://www.fourmilab.ch/etexts/einstein/specrel/www/
PS: in the QM section the - for me surprising - view is advanced that a classical view of EM propagation is also quite compatible with QM.
- https://www.physicsforums.com/showthread.php?t=474537

 

[ApplePion]

<<Light always travels at c. Period. >>

Not in General Relativity.

 

[ApplePion]

<<FAQ: Is the speed of light equal to c even in an accelerating frame of reference?
The short answer is "yes.">>

Actually, the answer is "No". In such a frame, a ficticious gravitational field would exist, and the metric would be non-Lorentian.

 

[DrGreg]

<<FAQ: Is the speed of light equal to c even in an accelerating frame of reference?
The short answer is "yes.">>

Actually, the answer is "No". In such a frame, a ficticious gravitational field would exist, and the metric would be non-Lorentian.

Did you bother to read the long answer?

The long answer is that it depends on what you mean by measuring the speed of light...

...Silly conclusions like this one can be eliminated by specifying that c has a defined value not in all experiments but in local experiments. The Sagnac effect is nonlocal because the apparatus has a finite size. The observed effect is proportional to the area enclosed by the beam-path. "Local" is actually very difficult to define rigorously [Sotiriou 2007], but basically the idea is that if your apparatus is of size L, any discrepancy in its measurement of c will approach zero in the limit as L approaches zero.

So the speed of light is always c locally (i.e. measured over a short enough distance), but not necessarily "remotely".

 

[ApplePion]

<<So the speed of light is always c locally >>

That is not the case. One need not use Lorentzian coordinates locally.

 

[Passionflower]

<<So the speed of light is always c locally >>

That is not the case. One need not use Lorentzian coordinates locally.

You are incorrect ApplePion, locally the speed of light is always c. Of course strictly local there is no speed as a speed can only be measured between two distinct points. But in the limit it will be c even in curved spacetimes.

 

[WannabeNewton]

For pseudo - Riemannian manifolds you can say that on a local enough scale the space - time metric reduces to the minkowski metric.

 

[ApplePion]

<<You are incorrect ApplePion, locally the speed of light is always c>>

You can set up various different local coordinate systems. The ones where the metric is Lorentzian you have a speed of c. If it is not Lorentzian, the speed is not necessarily c.

For example, if you set up a local coordinate system where it is c, I can make a coordinate transformation x' = 2x, and in the primed coordinate system the speed of light is c/2.

I am actually not creating a pointless quibble. By appealing to these "local" coordinate systems where the speed is c, you are stripping the physics of physical meaning. This will be clear from the following analogy. You can always set up a coordinate system where something is not moving (e.g. making a Lorentz transformation to a frame where the object is at rest). So from your perspective that the speed of light is always c because a coordinate transformation can make it so, one could argue that all objects are at rest. It should be obvious that the statement "All objects are at rest" is bad.

 

[ApplePion]

<<For pseudo - Riemannian manifolds you can say that on a local enough scale the space - time metric reduces to the minkowski metric>>

And a coordinate transformation can always be made so that a particular person has a height of 6. But it is not good to from this conclude "Everyone's height is 6".

 

[ApplePion]

Since you think that the speed of light is always c, because one can make a local coordinate transformation to a locally Lorentzian metric, then... since you can always make a local coordinate transformation to make the affine connection vanish you must logically also think that the gravitational field is always zero.

So do you want to take the position that there is no such thing as a gravitational field?

 

[harrylin]

[..] I am actually not creating a pointless quibble. By appealing to these "local" coordinate systems where the speed is c, you are stripping the physics of physical meaning. This will be clear from the following analogy. You can always set up a coordinate system where something is not moving (e.g. making a Lorentz transformation to a frame where the object is at rest). So from your perspective that the speed of light is always c because a coordinate transformation can make it so, one could argue that all objects are at rest. It should be obvious that the statement "All objects are at rest" is bad.

Maybe not really bad, but poor yes (in the sense of empoverished). For example, Einstein's prediction of gravitational lensing was based on considering the speed of light as measured non-locally. That it's always c locally lacks physical information and can even be misleading.

 

[AstrophysicsX]

I woke up this morning thinking about special relativity. I read last night that light is always traveling at light speed, relative to anything. But there's a paradox. What about light, relative to light? Doesn't that mean that photons could travel at an undefined, infinitesimal speed? (Which seems impossible, but you never know when it comes to physics.) Any help?

 

[ApplePion]

I woke up this morning thinking about special relativity. I read last night that light is always traveling at light speed, relative to anything. But there's a paradox. What about light, relative to light? Doesn't that mean that photons could travel at an undefined, infinitesimal speed? (Which seems impossible, but you never know when it comes to physics.) Any help?

You are trying to introduce an inertial frame where one photon is at rest, and to describe the motion of a second photon in that frame.

The problem is that you cannot make a Lorentz transformation that would make that first photon at rest.

continued

 

[ApplePion]

continued

Here though is something you can do.

Consider an object moving at 99 percent of the speed of light. Ask what a photon looks like in that guy's frame.

To make that guy become at rest yiou need to make a Lorentz transformation to make him at rest. Just use the usual Lorentz transformation, with v/c in the formula being .99. That will do it.

So what is the photon doing in that frame? In the original frame the photon moves along the worldline x= ct. Now go use the Lorentz Transformation with .99 and transform x to x' and t to t'. After you do that divide x' by t'. You will get c. So in the new frame the photon moves at the speed c. Had you used .999 or .99999 instead of .99 the same thing would happen. Indeed, the Lorentz transformation was constructed specifically so that you would always get "c" regardless of what value you chose for v/c in the Lorentz Transformation.

 

[harrylin]

I woke up this morning thinking about special relativity. I read last night that light is always traveling at light speed, relative to anything. But there's a paradox. What about light, relative to light? Doesn't that mean that photons could travel at an undefined, infinitesimal speed? (Which seems impossible, but you never know when it comes to physics.) Any help?

That's a sloppy way of saying it - perhaps it led to a misunderstanding.
Light is always traveling at light speed as measured with (and relative to) any standard inertial reference system. I would not call that "anything". No reference system can co-move with a photon in vacuum.

As a matter of fact, the "closing" speed of two light rays relative to each other with respect to any such system can be up to 2c. [1, 2]

The details have already been explained by ApplePion.

[1] section 3 of http://www.fourmilab.ch/etexts/einstein/specrel/www/
[2] http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html#2

Cheers,
Harald