On Sunday, October 17, 2021 at 12:41:50 PM UTC-7, tjrob137 wrote:
> On 10/17/21 10:52 AM, Richard Hertz wrote:
> > You just can't talk about velocity of light. This expression is not specific. You may talk about:
> > 1. The phase velocity is the velocity with which wavefronts propagate.
> > 2. The group velocity determines the speed with which intensity maxima propagate (e.g. the peaks of pulses).
> You forgot the important one for relativity:
> 3. The front velocity is the speed with which the front of a wave
> propagates when it is turning on; it is also the speed with
> which modulation propagates.

An unrelated aside: the front of a wave when it is turning on satisfies the
eikonal equation. This curious fact was proved in ca. 1940 by R. Luneburg
who specialized in optics. He showed that subject to some technical conditions
any discontinuity of a solution to Maxwell's equations propagates so that
it satisfies the eikonal equation. This means that one can define geometrical
optics in this way rather than by the commonly used short-wave limit method
of Sommerfeld and Runge (which is not as general). Curves perpendicular
to those surfaces can then be shown to obey Fermat's principle, hence can
be identified with the usual light rays, with the entire machinery
of geometrical optics thus reproduced directly from Maxwell's equations
(which had not been done before).

BTW, Luneburg's name was really Lüneburg (he was German) but in the
States he changed it to "Lueneburg" (which is sensible) but I guess the
"ue" business was confusing to Americans (as it's on this NG :-) ) so
he changed it again to "Luneburg".

--
Jan

On Sunday, October 17, 2021 at 4:41:50 PM UTC-3, tjrob137 wrote:

<snip>

> In relativity, we only discuss the front velocity, and often omit the adjective.
>
> > [... further nonsense omitted.]
>
> Tom Roberts

But you didn't hesitate to adjective my post as nonsense, infallible Tom!

Deal with this guy's nonsense, then (he's a PhD, you know, and a relativist as well):

https://www.rp-photonics.com/velocity_of_light.html

Velocity of Light

More specific terms: phase velocity, group velocity, velocity of information transport
German: Lichtgeschwindigkeit

Author: Dr. Rüdiger Paschotta

*****************************************************************************

Whereas the velocity of some particle is a quantity which is based on a fairly simple and unambiguous concept, the velocity of light (as of other wave phenomena) is a much more sophisticated matter. There are different kinds of velocities, which are different conceptually and can (particularly for light propagation in media) have substantially different values:

The phase velocity is the velocity with which wavefronts propagate.
The group velocity determines the speed with which intensity maxima propagate (e.g. the peaks of pulses).
The velocity of information transport can differ from both phase and group velocity, see the article on causality.

Figure 1 illustrates the different velocities. In that example, the phase velocities of different frequency components vary linearly with frequency: the wavefronts of the higher-frequency components (drawn at higher positions) travel more slowly. The pulse maximum forms where the wavefronts coincide, and propagates with the (lower) group velocity. More details are given in the article on group velocity.
illustration of group velocity

Figure 1: Propagation of a light pulse in a dispersive medium. Note that the phase fronts of different frequency components (shown as straight lines) propagate with different velocities, and the pulse propagates with the group velocity, which is lower than all the phase velocities.

Further complications can arise from light propagation in inhomogeneous media, particularly in waveguides.

In vacuum, phase and group velocity (defined for plane waves) are identical at c = 299 792 458 m/s. Within the International System of Units (SI), the vacuum velocity of light has been defined to match this value exactly. Together with the definition of the second (via a hyperfine transition of cesium atoms), this determines the length of a meter.

In some situations, often associated with absorption or gain resonances, the phase velocity or even the group velocity of light can exceed the vacuum velocity of light (→ superluminal transmission, “fast light”), although this is not associated with a violation of causality. There are other situations where the group velocity of light at least within a narrow spectral region is reduced (slow light). Enormous velocity reductions can be observed for narrowband resonances, as occur e.g. in ultracold gases.

The perhaps most peculiar effect is the occurrence of negative group velocities in situations with strongly negative dn / dω.
Velocity of Light and Theory of Relativity

The vacuum velocity of light plays a very important role in fundamental physics. One of the cornerstones of Einstein's theory of relativity is that the vacuum velocity of light is constant, i.e., it is the same in all inertial systems and does never depend on the propagation direction. In other words, there is not such a thing as a light aether, defining a single system where light has its “default” velocity. This seemingly innocent assumption lead Einstein to very far-reaching conclusions concerning the nature of space and time. Examples are the experimentally well confirmed phenomena of time dilatation, length contraction of moving objects, and the impossibility for any massive objects to reach or exceed the vacuum velocity of light.

The central role of light in this theory indicates that electromagnetism is intimately related to the nature of spacetime, although that relation is still not entirely understood.

Questions and Comments from Users

Here you can submit questions and comments. As far as they get accepted by the author, they will appear above this paragraph together with the author’s answer. The author will decide on acceptance based on certain criteria. Essentially, the issue must be of sufficiently broad interest.

*****************************************************************************

On Sunday, October 17, 2021 at 11:23:55 AM UTC-5, tjrob137 wrote:
> On 10/16/21 8:43 PM, Prokaryotic Capase Homolog wrote:
> > On Saturday, October 16, 2021 at 7:53:32 PM UTC-5, Thomas
> > 'PointedEars' Lahn wrote:
> >> Paul B. Andersen wrote:
> >>> But we now know that the speed of light isn't affected by
> >>> gravity, but the velocity of light is.
> >>>
> >>> If the speed of light had been affected by gravity, the GPS
> >>> wouldn't work.
> >> That is utter nonsense; you should know better.
> >>
> >> Neither is affected by gravity as gravity does not exist in that
> >> theory, or IOW it is reduced to an observable effect due to the
> >> curvature of spacetime.
> >
> > You are being overly pedantic.
> This is not overly pedantic, the original statements quoted above are
> too imprecise, and are basically false.

As you noted in a following post, "speed of light" may refer to phase,
group, or front velocity, remarking that "In relativity, we only discuss the
front velocity, and often omit the adjective."

That last remark of yours is false. "Speed of light" does not refer ONLY
to the front velocity of an electromagnetic signal, but has various other
meanings in physics. For example, it is used to refer to the constant "c"
which interrelates space and time, a usage of the term that is independent
of its usage referring to a physical property of electromagnetic radiation.

Would it not be pedantry of me to use insulting language to insist that
one qualify *every* usage of the term "speed of light" so that the meaning
of the term is clear even when a sentence using the term "speed of light" is
read completely isolated from all context?

My issue with Tom was his use of insult to make his point, not his point
per se.

On Sunday, 17 October 2021 at 21:41:50 UTC+2, tjrob137 wrote:
> On 10/17/21 10:52 AM, Richard Hertz wrote:
> > You just can't talk about velocity of light. This expression is not specific. You may talk about:
> > 1. The phase velocity is the velocity with which wavefronts propagate.
> > 2. The group velocity determines the speed with which intensity maxima propagate (e.g. the peaks of pulses).
> You forgot the important one for relativity:
> 3. The front velocity is the speed with which the front of a wave
> propagates when it is turning on; it is also the speed with
> which modulation propagates.
>
> [All three use the word "velocity", but in the German
> sense that does not distinguish velocity from speed.]
>
> Both phase and group velocity can be either larger or smaller than c
> [@], depending on the properties of the medium in which the wave is
> propagating; neither of them can transfer information, as they are
> properties of an established, unmodulated wave. The front velocity [#]
> is the one that applies to the transfer information, and it is strictly
> <= c, with equality only in vacuum.

In the meantime in the real world, however, GPS clocks
keep measuring t'=t, just like all serious clocks always
did.

Prokaryotic Capase Homolog wrote:

>> This is not overly pedantic, the original statements quoted above are
>> too imprecise, and are basically false.
>
> As you noted in a following post, "speed of light" may refer to phase,
> group, or front velocity, remarking that "In relativity, we only discuss
> the front velocity, and often omit the adjective."

Fully Vaccinated Former SecState Colin Powell Dies From COVID
Complications

Paul B. Andersen wrote:

> |>> On Tuesday, October 5, 2021 at 4:09:28 PM UTC-3, Paul B. Andersen
> |>> wrote:
> |>>>
> |>>> Whether or not the speed of light is invariant can only be tested
> |>>> by real experiments in the real world.
>
> The issue is the invariance of the speed of light.

But it is not invariant in general relativity.
> |> Richard Hertz responded:
> |>>
> |>> <snip>
> |>>
> |>>
> |>> 3) I don't know if the speed of light is affected by gravity.
>
> Meaning that he doesn't know if light is falling
> and accelerating in a gravitational field.
> (With reference to Einstein's 1911 paper.)
>
> Note that 'gravity' is used as a synonym for 'gravitation'.

That does not make your statement any less wrong. As you should know, in GR
both gravity/gravitation and the variable coordinate speed of light are a
consequences of the curvature of spacetime.

So it is simply NOT so that in GR gravity would affect light. That is
oversimplifying the issue, at best.

And your making a difference between the speed and the velocity of light
there is nonsense, too.
>> Paul B. Andersen responded:
>>> But we now know that the speed of light isn't affected by gravity,
>>> but the velocity of light is.
>>>
>>> If the speed of light had been affected by gravity,
>>> the GPS wouldn't work.
>>
>> That is utter nonsense; you should know better.
>
> No, it's correct

No, it is not, as Tom Roberts has pointed out, too.

> even if it appears imprecise and ambiguous

In general relativity, gravity is not a cause, but an effect.

End of story.

> The speed of light isn't affected by gravitation,
> but the velocity of light is.

Nonsense.

>> Neither is affected by gravity as gravity does not exist in that theory,
>> or IOW it is reduced to an observable effect due to the curvature of
>> spacetime.
>
> Gravitation does indeed exist in "the theory of gravitation" GR.

It exists as a consequence of the curvature of spacetime. Not as a cause.

> Gravitation isn't "reduced to an observable effect due to
> the curvature of spacetime",

But it is. Gravity/gravitation as a force does not exist in GR.

> it IS the curvature of spacetime.

That is a common misconception; it is unfortunate for me to see you having
it, too.

I had not expected that. Apparently you need to watch some basic
educational videos about it. In no particular order (you should watch them
all):

“PBS SpaceTime: Does Time Cause Gravity?”
<https://www.youtube.com/watch?v=UKxQTvqcpSg>
(presented by: Matt O’Dowd, PhD; Australian astrophysicist, Associate
Professor in the Physics and Astronomy Department at the Lehman College of
the City University of New York)

“Veritasium: Why Gravity is NOT a Force”
<https://www.youtube.com/watch?v=XRr1kaXKBsU>
(presented by: Derek Muller, PhD in Physics Education)

“The Science Asylum: The REAL source of Gravity might SURPRISE you...”
<https://www.youtube.com/watch?v=F5PfjsPdBzg>
(presented by: Nick Lucid, MSc in Physics from Eastern Michigan University)
I am recommending those three out of many others because I think that they
are the least confused and the least confusing (for example, they do NOT say
that gravity *is* the curvature, which it isn’t).

> So my statement is equivalent to:
> "The speed of light isn't affected by the curvature of spacetime,
> but the velocity of light is.

And that is nonsense.

>> The coordinate speed of light in vacuum is affected by the curvature of
>> spacetime as well (it is less than c₀); the local speed of light in
>> vacuum
>> is not. This manifests itself e.g. in Shapiro delay.
>
> Good grief! :-D
>
> If I say: "the speed of light is invariant",
> would you then say:
> "No, the coordinate speed of light isn't invariant"

Yes.

> Or:
> "No, the speed of light in a medium like glass isn't invariant."

Yes.

> Or:
> "No, the speed of light measured in an accelerated frame isn't invariant."

Yes.
> No, you wouldn't say that,

I would. Also, I would question under which transformation it would be
considered invariant.

PointedEars
--
A neutron walks into a bar and inquires how much a drink costs.
The bartender replies, "For you? No charge."

(from: WolframAlpha)