Speed of light
Jon Lester
parts, is covered in the physics FAQ. Anyhow, my point is to see if this
conceptual matter is covered somewhere in the literature.
The question is connected to the fact, that seems unavoidable, if one wants
to measure the speed of light, to use a closed path for the light. Do things
stay really this way? Is it a conceptual fact the need for a closed path or
one can devise a way to measure speed of light some other means with a
one-way path? Does any literature exist about also with experiments?
Jon
Stephen Speicher
> The question is connected to the fact, that seems unavoidable,
> if one wants to measure the speed of light, to use a closed
> path for the light. Do things stay really this way? Is it a
> conceptual fact the need for a closed path or one can devise a
> way to measure speed of light some other means with a one-way
> path? Does any literature exist about also with experiments?
Given the absence of any universal time or absolute reference
frame in special relativity, it is not possible in general to
measure one-way light speed (OWLS). Special relativity
constructs the inertial frame from the more fundamental
definition of local time, i.e., what a clock reads at a specific
location within the frame. There does not exist any physical
meaning amongst the various clocks at differing locations, until
the clocks are synchronized with each other. The method of
performing such a synchronization is what is meant by a
definition of simultaneity.
In order to synchronize any pair of inertial clocks, a signal
must be sent between them. There is no necessity that it be an
electromagnetic signal, but because of various properties of
electromagnetic signals, they are chosen as the closest to ideal.
Assume two standard clocks in this inertial frame, one located at
event A, the other at event B. We synchronize these two clocks
through the exchange of light signals. Assuming the spatial
distance separation between the events to be r, we denote a
one-way velocity between A to B as c_ab, and the one-way velocity
between B to A as c_ba. Let's say that a signal is sent from A
at time t_a on the clock at event A, and the signal arrives at B
at time t_b on the clock at event B. We would then say that the
clocks are synchronized if t_b = t_a + r/c_ab.
Likewise, if we then send a signal from B to A, we would say that
the clocks are synchronized if t'_a = t_b + r/c_ba.
Then we can write the one-way velocities as,
c_ab = r/(t_b - t_a)
c_ba = r/(t'_a - t_b)
These difference quantities, (t_b - t_a) and (t'_a - t_b), are
the coordinate time intervals, and these are dependent on the
definition of simultaneity. By contrast, if we define the two-way
velocity of the signal sent from A to B, and back again to A, as
the sum of the two one-way velocities, denoted by c, then we
arrive at
c = 2r/(t'_a - t_a)
Here the difference (t'_a - t_a) is _not_ dependent on the
definition of simultaneity, and it is a proper time interval.
This demonstrates that the two-way light speed (TWLS) is a
measurable quantity because it is dependent on a proper time
interval, but OWLS is completely dependent on the definition of
simultaneity.
Einstein synchronization _guarantees_ that OWLS will be c for
each direction. Note that the Einstein definition of simultaneity
leads to the usual Lorentz transformations, but there are other
definitions of simultaneity, such as the Edwards' definition
which does not require the one-way speed to be isotropic.
Edwards' definition of simultaneity leads to a generalization of
the Lorentz transformation which maintains the two-way speed of
light -- and is therefore consistent with experiment -- but
allows the one-way velocity of light to vary in terms of a
directional parameter. Here are some of the results which apply
to this Edwards generalization.
In the general direction r, the two-way speed of light along a
back and forth path is given by
2(c_r+)(c_r-)
c_r = ---------------
(c_r+) + (c_r-)
c_r+ is the one-way velocity of light along the forward path, and
c_r- is the one-way velocity of light along the return path, and
they are given by
c_r c_r
c_r+ = ------- , c_r- = -------
1 - q_r 1 - q_r
where q_r is the directional parameter in the direction r, given
by
-1 <= q_r <= 1.
So, for instance, in x-y-z coordinates, we would have
c_i c_i
c_i+ = -------, c_i- = -------
1 - q_i 1 + q_i
-1 <= q_i <= 1, i = x,y,z.
In these x-y-z coordinates, for simplicity sake, we will assume
the directional parameter is of the form (q, 0, 0), so that in
frame F we have
c c
c_x+ = ------, c_x- = ------, c_y+ = c_y- = c_z+ = c_z- = c,
1 - q 1 + q
where c is now a constant two-way speed of light. Likewise, for
another frame F', we have
c c
c'_x+ = ------, c'_x- = ------, c'_y+ = c'_y- = c'_z+ = c'_z- = c,
1 - q' 1 + q'
With this as a basis one can then derive, after a lot of algebra,
the Edwards' form of the generalized Lorentz transformation,
which result is
x' = G(x - vt),
y' = y,
z' = z,
t' = G{[1 + (q + q')v/c]t - [(1 - q^2)v/c + (q' -q)]x/c},
1
where G = -----------------------------
sqrt[(1 + qv/c)^2 - (v/c)^2
and v, as usual, is the relative velocity between frames F and
F'.
Note that if the directional parameter is identically zero,
meaning that there is no directional variability to the speed of
light, then this generalized Lorentz transform reduces to the
standard form.
Also, note that another level of complexity is introduced by
assuming that the two-way velocity of light is equal to the
one-way velocity, but allow that velocity to be generally
anistropic, though it remains independent of the motion of the
source. This is known as a Robertson inertial frame, for H.P.
Robertson who first formulated this in 1949. And, just as using
the Edwards notion of simultaneity led to a generalization of the
Lorentz transformation with a one-way directional variability of
the speed of light, so the Robertson notion of simultaneity leads
to a further generalization of the Lorentz transformation. The
next level of complexity was introduced by R. Mansouri and R.U.
Sexl in 1977, where they introduced a directional parameter to
the Robertson formulation which leads to a further generalization
of the Lorentz transformation equations. The form of this
generalization is similar to the one I outlined above, but
obviously with somewhat more complicated expressions.
So one can arrive at various forms of an anisotropic
4-dimensional spacetime by relaxing the physical assumptions
imposed in the standard formulation. Below are references of
Edwards', Robertson's, and Mansouri & Sexl's initial work, as
well as a reference to an excellent book which contains these
formulations which I have presented, and does so in the context
of experimental relativity.
W.F. Edwards, A. J. Phys. 31 (1963) pp. 482-489.
H.P. Robertson, Rev. Mod. Phys. 21 (1949) p. 378.
R. Mansouri and R.U. Sexl, Gen. Relativ. Grav. 8 (1977) p. 407.
Y. Z. Zhang, "Special Relativity and its Experimental
Foundations," _World Scientific, 1997.
--
Stephen
s...@speicher.com
Ignorance is just a placeholder for knowledge.
Printed using 100% recycled electrons.
-----------------------------------------------------------
[Moderator's note: followsup have been set to sci.physics.relativity. - jb]
Steven Gray
news:CmeJa.224030$g92.4...@news2.tin.it:
In principle, you don't need a closed path to measure the speed of light.
Take two accurate clocks and place them some known distance apart and at
rest in the same inertial frame of reference. Put a strobe light midway
between them. Fire the strobe, and set each clock to an agreed upon time
when the light pulse is seen. Now the clocks are synchronized. (Note that
you don't need to know the speed of light to do this.)
Now place a strobe at clock 1 and fire it at an agreed upon time. Note the
time that the flash is seen at clock 2, and use the known distance between
them to calculate the speed of light.
--
Steve Gray
sgr...@cfl.rr.com
robert bristow-johnson
ast...@hotmail.com wrote on 06/23/2003 19:41:
> This may seems a rather simple question about relativity and, for some
> parts, is covered in the physics FAQ. Anyhow, my point is to see if this
> conceptual matter is covered somewhere in the literature.
>
> The question is connected to the fact, that seems unavoidable, if one wants
> to measure the speed of light, to use a closed path for the light. Do things
> stay really this way? Is it a conceptual fact the need for a closed path or
> one can devise a way to measure speed of light some other means with a
> one-way path?
dunno what the lit says, but it seems like a problem similar to the (human)
timers for the 100-yard dash in a competitive track meet. it's good that
the speed of light far exceeds the speed of humans runners so that the
timers (who are at the finish line) can see the pistol smoke (or sometimes
the put a balloon over the muzzle) at, relatively, the correct time.
imagine if the timers couldn't see the pistol and when the starter started
the race, a messenger had to run from the starter to the timers to tell them
to click their stopwatches. in a closed loop (400-meter and longer), there
is no need and, in fact the timers just listen for the bang.
i can't think of how to measure the speed of light without a closed loop,
but what do i know?
r b-j
Uncle Al
The original large scale lightspeed experiment - timing of Jupiter's
Galilean moons - was strictly one-way. Ditto epheremides corrected
for light time.
Burp a timed ~nanosecond of mode-locked laser light. Blow it through
a dilute fluorescent gas. Observe with a fast strobe shutter (Pockels
or Stark cell, whatever). Measure the length of the pulse against a
calibrated background. No return path, no elasped time remote clock,
refractive index arbitrarily close to 1.0.
Lightspeed is not debatable or none of your electronics would work,
ditto beam corrections send across the diameter of the ring while the
beam travels the circumference for particle accelerator rings.
It's not like the Michelson-Morley experiment was the end,
Phys. Rev. Lett. 88(1) 010401 (2002)
Phys. Rev. Lett. 90 060403 (2003)
Phys. Rev. Lett. 42(9) 549 (1979)
Phys. Bull. 21 255 (1970)
--
Uncle Al
http://www.mazepath.com/uncleal/eotvos.htm
(Do something naughty to physics)
Bill Rowe
"Jon Lester" <ast...@hotmail.com> wrote:
> The question is connected to the fact, that seems unavoidable, if one wants
> to measure the speed of light, to use a closed path for the light. Do things
> stay really this way? Is it a conceptual fact the need for a closed path or
> one can devise a way to measure speed of light some other means with a
> one-way path?
The only way I can see to do a physically realizable experiment to
measure the speed of light over a one-way path would be to have two
clocks. Now the problem becomes one of how to synchronize the clocks.
If you use light signals to synchronize the clocks, you effectively
assume what you are trying to measure.
If you synchronize the clocks by having then together then separate them
via slow transport, how do you verify the synchronization is unchanged
by the transport operation?
The only way to get around the clock synchronization issue is to have
one clock. But then you need a closed light path which is what you are
trying to avoid.
Paul White
... Is it a conceptual fact the need for a closed path or
> one can devise a way to measure speed of light some other means with a
> one-way path? Does any literature exist about also with experiments?
>
> Jon
>
Ole Roemer. He determined the speed by noting the variations in the expected
positions of the satellites of Jupiter when at opposition as opposed to
conjunction. The difference turned out to be about 1000 seconds and,
knowing the diameter of the earth's orbit the approximate speed of light
was determined to be 186,000 miles per second. I don't believe he got
that exact number but he was close. No actual astronauts were sent to
Jupiter.
Paul
Russell Blackadar
[snip]
> The original large scale lightspeed experiment - timing of Jupiter's
> Galilean moons - was strictly one-way.
One that relied on slow clock transport for its
synchronization. Also I don't think you could call it
*strictly* one way since that would imply that you've
measured light traveling exactly the same path in space,
in two measurements taken some months apart.
Ditto epheremides corrected
> for light time.
>
> Burp a timed ~nanosecond of mode-locked laser light. Blow it through
> a dilute fluorescent gas. Observe with a fast strobe shutter (Pockels
> or Stark cell, whatever). Measure the length of the pulse against a
> calibrated background. No return path, no elasped time remote clock,
> refractive index arbitrarily close to 1.0.
But the fluorescence from front and back of the beam must
travel to your shutter to be imaged. Those two paths,
along with the beam itself, form a closed triangle.
[snip]
Steve Carlip
> Is it a conceptual fact the need for a closed path or
> one can devise a way to measure speed of light some other means with a
> one-way path? Does any literature exist about also with experiments?
This isn't a direct answer, but is relevant:
In order to measure a one-way speed of light, you need to have clocks
at two different locations -- the start and end of the path -- that are
somehow synchronized. So the question becomes one of what it means
to synchronize clocks at different locations, that is, how to determine
simultaneity. There's a huge literature about this issue, and in
particular about whether there is in any sense a unique way to
synchronize clocks. You might start with
http://plato.stanford.edu/entries/spacetime-convensimul/
and the follow the references.
Steve Carlip
Stephen Speicher
On Wed, 25 Jun 2003, Steven Gray wrote:
> In principle, you don't need a closed path to measure the speed of
> light. Take two accurate clocks and place them some known distance
> apart and at rest in the same inertial frame of reference. Put a
> strobe light midway between them. Fire the strobe, and set each
> clock to an agreed upon time when the light pulse is seen. Now the
> clocks are synchronized. (Note that you don't need to know the speed
> of light to do this.)
>
> Now place a strobe at clock 1 and fire it at an agreed upon time.
> Note the time that the flash is seen at clock 2, and use the known
> distance between them to calculate the speed of light.
This suggested procedure just demonstrates again the inevitable
consequence that the measured value for the speed of light
depends on one's definition of simultaneity. The implicit
assumption used was isotropy of the one-way speed of light in
order to perform the specified synchronization.
--
Stephen
s...@speicher.com
Ignorance is just a placeholder for knowledge.
Printed using 100% recycled electrons.
-----------------------------------------------------------
[Moderator's note: followups have been set to sci.physics.relativity,
which is the right place for discussions of this sort. - jb]
Charles Francis
<ast...@hotmail.com> writes
>Is it a conceptual fact the need for a closed path or one can devise
>a way to measure speed of light some other means with a one-way path?
To measure a speed you have to determine the time at start and finish of
a measured distance, which means you have to have a way to synchronise
clocks at two places. By definition this is done by two way messaging.
Using a closed path for light offers an alternative, and more precise,
methodology.
Regards
--
Charles Francis
[Moderator's note: followups have been set to
sci.physics.relativity. - jb]
Jon Bell
Bill Rowe <bjr...@earthlink.net> wrote:
>
>The only way I can see to do a physically realizable experiment to
>measure the speed of light over a one-way path would be to have two
>clocks. Now the problem becomes one of how to synchronize the clocks.
>
>If you use light signals to synchronize the clocks, you effectively
>assume what you are trying to measure.
Place a flash bulb halfway between the two bulbs. Set it off and set each
clock to zero when the flash reaches it. Or if you prefer not to use
light (perhaps you're worried about possible ether-wind effects), you can
use, say, a pair of snails trained to move at constant (and equal) speeds.
--
Jon Bell <jtbe...@presby.edu> Presbyterian College
Dept. of Physics and Computer Science Clinton, South Carolina USA
Pentcho Valev
> On Mon, 23 Jun 2003, Jon Lester wrote:
>
> > The question is connected to the fact, that seems unavoidable,
> > if one wants to measure the speed of light, to use a closed
> > path for the light. Do things stay really this way? Is it a
> > conceptual fact the need for a closed path or one can devise a
> > way to measure speed of light some other means with a one-way
> > path? Does any literature exist about also with experiments?
>
> Given the absence of any universal time or absolute reference
> frame in special relativity, it is not possible in general to
> measure one-way light speed (OWLS).
This is part of the mythology in relativity. In the track - train
setup the experiment will look like that. There are two synchronized
(in the train frame) clocks at the front and back ends of the train. A
light beam emitted by a source in the track frame first reaches the
back end of the train and stops the clock there. A portion of the
light passes through a hole, goes the the front clock and stops it.
The time difference between the two clocks would allow the passenger
to determine the speed of light and see if it is independent of the
speed of the train.
Pentcho Valev
Stephen Speicher
>
> The original large scale lightspeed experiment - timing of Jupiter's
> Galilean moons - was strictly one-way.
Not really. In Roemer's experiment the Jupiter system itself
becomes the equivalent of a slowly transporting clock. See the
Zhang reference I gave, particularly pp. 91-94 and pp. 120-122
for a detailed mathematical analysis of Roemer's experiment in
the context of definitions of simultaneity.
Y. Z. Zhang, "Special Relativity and its Experimental
Foundations," _World Scientific, 1997.
As I discussed in my previous post, the one-way speed of light is
simply not a measurable quantity, unless there exists an absolute
frame and a universal time.
Mark Palenik
"Bill Rowe" <bjr...@earthlink.net> wrote in message
news:bjrowe-1D8AFA....@nnrp04.earthlink.net...
How about two clocks and a light, all at rest with respect to each other
in the shape of an equilateral triangle (or isocoles with the two legs
from the clocks to the light being equal). The light sends out a pulse
toward each clock, which resets them both to 0, and we time a beam of
light with the two clocks as it travels from one to the other.
Obviously this still begs the old simultanaity question, since we can
create a reference frame where one path of the synchronization signal is
shorter than the other, but since we're conducting the experiment as if
all three objects are at rest, it doesn't seem to me that this should
matter.
Stephen Speicher
>
> As I recall, the very first determination made of the speed of light was by
> Ole Roemer. He determined the speed by noting the variations in the expected
> positions of the satellites of Jupiter when at opposition as opposed to
> conjunction. The difference turned out to be about 1000 seconds and,
> knowing the diameter of the earth's orbit the approximate speed of light
> was determined to be 186,000 miles per second. I don't believe he got
> that exact number but he was close. No actual astronauts were sent to
> Jupiter.
>
In 1666, when the "Academie Royale des Sciences" was first
founded, one of its first tasks was to develop more accurate maps
than those currently available. The Academie sought some
astronomical means to help determine the unknown longitude of one
location, granted the known longitude of another location, using
simultaneous observations. Tables were made of the motions of the
four satellites of Jupiter, which satellites Galileo had
discovered half a century earlier in 1610. It was hoped that the
eclipses of Jupiter's satellites would provide the astronomical
event needed for simultaneous observation.
It was here that Roemer made his mark. Roemer predicted in
September of 1676 that the eclipse of the first satellite, which
was expected November 9 at 5 hours, 25 minutes, 45 seconds, would
actually occur 10 minutes later than expected. Observations on
that date confirmed Roemer's prediction exactly, a difference
from others' expectations of 600 seconds. Roemer's famous 1676
paper did not specify a speed for light; that speed was mostly
deduced from Roemer's observations of Jupiter's first satellite
that light takes approximately 22 minutes to complete the orbit
of the Earth.
Until relatively recently the scientific literature -- literally
hundreds of papers, books on physics and the history of science
-- ascribed to Roemer a rather amazing variation as to his
deduction of the speed of light, varying from as little as
120,000 to 200,000 miles/sec. One needs to use the data
available to Roemer at that time, as to the values for the
Earth-Sun distance and the like. The best estimates show that
Roemer's figure for the speed of light would be between 130,000
and 138,000 miles/sec. The history books written in the 18th and
19th centuries were mostly wrong about Roemer's estimate, and
also so through the early part of the 1900s. (If anyone is
interested I have a paper around I can dig up which documents
something like a couple of hundred references to mistaken
values.)
Starblade Darksquall
Actually that's not necessarily true. What about using a worm hole?
Say I have a transmitter which flashes a beam of light to one end of a
far away worm hole. Then I have the other end of the worm hole right
next to me, where I have a receiver of the light. The clock is then
attached to both the transmitter and receiver and times the difference
between the two events.
Now, the only problem is figuring out how much time is spent in the
worm hole, and the distance through the worm hole. But suppose that
you've found a way to make the time spent and space traversed constant
and precice. Then all you have to do is factor that into your
equation.
Then again, you also do have the problem of actually measuring the
metric of timespace so that you can get a more accurate description of
the curvature of timespace so that you know how light is effected. But
unless you're measuring VERY precise, you should not have to worry
about this. And, anyways, by the time we have wormholes, I'm guessing
we'll also have a device that accurately measures the gravitational
field in a region.
Of course, with the worm hole and gravity field type stuff, you'd
basically be using the speed of light to measure it, which again,
presupposes knowledge about the propogation of electromagnetic
radiation through timespace. ;p
A better way to measure the speed of light is to simply take the
square root of the reciprocal of the product of the permeability of
free space and the permittivity of free space, as was done by Maxwell
in his electromagnetic theory. It's a LOT simpler.
Then again, since the speed of light is now a fundamental constant,
all you have to do now is plug in the value defined by SI. Now the
only problem is measuring the length of the meter relative to the
duration of the second. ;>
(...Starblade Riven Darksquall...)
Tom Kerruish
frequency of a laser's light and multiplying. This would seem to obviate
the need for a closed path.
Per Erik Lindgren
"Jon Lester" <ast...@hotmail.com> wrote in message
news:CmeJa.224030$g92.4...@news2.tin.it...
You could use the GPS time system to synchonize two clocks. The satellites
are synchronized when they travel around the earth and they all show the
same time simultaneously. So use two GPS recievers, one at point A and one
at point B, fire a laser from A at 12:00 PM using GMT and measure the time
at point B when the light arrives there, also using GMT. Because of the
Sagnac effect, light travelling west will, according to the measured time,
travel faster then light travelling east with the same magnitude as the spin
of the earth where the experiment is conducted.
Per Erik Lindgren
Uncle Al
The need for *any* clocks to actively measure lightspeed is not
strictly true. One passive clock will do it. If you can generate a
slug of light with an accurately gated clock, all you need do is
visualize how physically long the slug is to get a good approximation
of lightspeed. A mode-locked laser will give accurate interval timed
sharp-edged slugs of light, so will a fast-pulsed diode laser. Or
chop the ends with a Pockels or Stark effect cell. Run the light
slugs through a beam splitter so two half intensity slugs 180 degrees
pass through each other in a dilute two-photon fluorescent gas or a
bit of like nanodust suspended in a volume of air (or
electrostatically in vacuum). Have a camera with an open shutter in
otherwise darkness take a pic of the glowing bar against a calibrated
background.
You will see a dim smear with a bright bar, intensity of the glow
varies as (intensity)^2 of the light. The light is its own clock.
The length of the bar and the chop window gives you lightspeed. Since
lightspeed is identical in all inertial reference frames... all you
need is not to be relativistic vs. your light souce slug timer.
Pentcho Valev
> This may seems a rather simple question about relativity and, for some
A suggestion. In the track-train
setup the experiment may look like that. There are two synchronized
(in the train frame) clocks at the front and back ends of the train. A
light beam emitted by a source in the track frame first reaches the
back end of the train and stops the clock there. A portion of the
light passes through a hole, goes the the front clock and stops it.
The difference between the two clocks' readings would allow the
Stephen Speicher
> Stephen Speicher <s...@speicher.com> wrote in message news:<Pine.LNX.4.33.03062...@localhost.localdomain>...
> >
> > Given the absence of any universal time or absolute reference
> > frame in special relativity, it is not possible in general to
> > measure one-way light speed (OWLS).
>
> This is part of the mythology in relativity.
>
It has been my experience that the only "mythology" surrounding
the physics of relativity is that which is created by those who
do not understand the facts.
[Moderator's note: Let's stick to the physics and refrain from
speculation about who does and doesn't "understand the facts." -TB]
> In the track - train setup the experiment will look like that.
> There are two synchronized (in the train frame) clocks ...
>
As I demonstrated in my detailed posting, clock synchronization
is dependent upon one's definition of simultaneity, which in turn
leads to coordinate-dependent one-way measurements.
Tom Kerruish
Measure the average energy and momentum of photons from a good
monochromatic source and take the ratio.
Measure epsilon_0 and mu_0 and take the reciprocal of the square root of
their product. IIRC, this was done at NIST by charging a parallel plate
capacitor via parallel wires while measuring the forces between the
plates and between the wires. Note that this method needn't use light at
all!
greywolf42
news:Pine.LNX.4.33.03062...@localhost.localdomain...
> >
> > The original large scale lightspeed experiment - timing of Jupiter's
> > Galilean moons - was strictly one-way.
>
> Not really. In Roemer's experiment the Jupiter system itself
> becomes the equivalent of a slowly transporting clock. See the
> Zhang reference I gave, particularly pp. 91-94 and pp. 120-122
> for a detailed mathematical analysis of Roemer's experiment in
> the context of definitions of simultaneity.
>
> Y. Z. Zhang, "Special Relativity and its Experimental
> Foundations," _World Scientific, 1997.
>
> As I discussed in my previous post, the one-way speed of light is
> simply not a measurable quantity, unless there exists an absolute
> frame and a universal time.
I believe you mean "local frame of rest". This is not necessarily an
absolute frame. (An absolute frame of rest would define a local frame of
rest. But if the "rest" is due to an aether, then there may not be any
"absolute" relationship between any two local frames of rest.)
And a universal time is used everywhere except in relativity. All we need
to do is to avoid e-synching, and we can test for one-way light speeds.
greywolf42
ubi dubium ibi libertas
greywolf42
Tom Kerruish <tomys_...@webtv.net> wrote in message
news:3536-3F0...@storefull-2177.public.lawson.webtv.net...
I'm curious how one "measures" mu_0. Since it is an arbitrarily defined
quantity (that defines a coulomb), and since "c" is defined (not measured)
these days. Wouldn't you be "measuring" a change in charge?
Tom Kerruish
Two more ways:
Take a stable, collimated light beam and measure the ratio of its
intensity to exerted pressure. (Yes, this is just a variant of the
wavelength * frequency and energy / momentum methods, but would seem to
be the easiest to actually perform.)
Use SI units and declare that, by definition, c = 299,792,458 m/s :)
Tom Kerruish
arbitrary units, we may write electrostatic and magnetostatic force laws
analogous to Newton's gravitational law, with K_e and K_m taking the
place of G, respectively. The ratio K_e/K_m is the square of the speed
of light, IIRC.
robert bristow-johnson
In article 8992-3F0...@storefull-2173.public.lawson.webtv.net, Tom
Kerruish at tomys_...@webtv.net wrote on 07/11/2003 17:53:
> My references to epsilon_0 and mu_0 reveal my MKS-centrism. However, in
> arbitrary units, we may write electrostatic and magnetostatic force laws
> analogous to Newton's gravitational law, with K_e and K_m taking the
> place of G, respectively.
how exactly are K_e and K_m related to G?
> The ratio K_e/K_m is the square of the speed of light, IIRC.
i was suspicious that K_e and K_m were graviational counterparts to eps_0
and mu_0 until now. if you said 1/sqrt(K_e*K_m) then i would expect that.
r b-j
greywolf42
You asserted:
"Measure epsilon_0 and mu_0 and take the reciprocal of the square root of
their product. IIRC, this was done at NIST by charging a parallel plate
capacitor via parallel wires while measuring the forces between the plates
and between the wires. Note that this method needn't use light at all!"
And my question was:
"I'm curious how one "measures" mu_0. Since it is an arbitrarily defined
quantity (that defines a coulomb), and since "c" is defined (not measured)
these days. Wouldn't you be "measuring" a change in charge?"
Could you please answer the question? Thanks.
Tom Kerruish
units, K_e 1 / (4 pi eps_0) and K_m mu_0 / (4 pi).
Tom Kerruish
Heavens to Betsy! Is this what a fireball feels like? Post in haste,
repent at leisure.
I'll answer your question by withdrawing my (now obviously) incorrect
description of the relevant experiment. You are correct that mu_0 is
arbitrarily set to 4 pi x 10^-7 (although I think it's used to define
the ampere, not the coulomb). I'd like to point out my use of the
weaselly acronym "IIRC", which is clearly false in this case.
I will now formulate what is (I hope) a better position: that the
velocity of EM waves may be deduced from purely electrical and magnetic
observations. I certainly recall an account of Maxwell doing this and
noting that his result was remarkably close to the observed speed of
light, causing him to conjecture that light is EM radiation. Further, I
do remember reading of an experimental setup essentially as the one I
described, although the actual methodology of calculating c from the
measured forces has been lost in the haze of time (and something called
"Drop Day at Dabney House" :)
pst...@ix.netcom.com
In article <12789-3F1...@storefull-2172.public.lawson.webtv.net>,
tomys_...@webtv.net (Tom Kerruish) wrote:
To help with your mention of Maxwell's derivation, here is the section from
Maxwell's paper,
“...Now let n_1, and n_2, be the same quantities of
electricity measured statically, then we know by
definition of electrical quantity
n_1 n_2
F = ------- . . . . . . . . (128)
r^2
and this will be satisfied provided
n_1 =Ee_1, and n_2 = Ee_2 . . . . (129)
so that the quantity E previously determined in
Prop. XIII. is the number by which the
electrodynamic measure of any quantity of
electricity must be multiplied to obtain its
electrostatic measure.
That electric current which, circulating round
a ring whose area is unity, produces the same
effect on a distant magnet as a magnet would
produce whose strength is unity and length unity
placed perpendicularly to the plane of the ring,
is a unit current; and E units of electricity,
measured statically, traverse the section of
this current in one second, -- these units being
such that any two of them, placed at unit of
distance, repel each other with unit of force.
We may suppose either that E units of positive
electricity move in the positive direction through
the wire, or that E units of negative electricity
move in the negative direction, or, thirdly, that
[1/2]E units of positive electricity move in the
positive direction at while [1/2]E units of
negative electricity move in the negative
direction at the same time.
The last is the supposition on which MM. Weber
and Kohlrauscb* proceed, who have found
[1/2]E = 155,370,000,000 . . . . (130)
the unit of length being the millimetre, and that
of time being, one second, whence
E = 310,740,000,000 . . . . . (131)
Prop. XVI.-To find the rate of propagation of
transverse vibrations through the elastic medium
of which the cells are composed, on the supposition
that its elasticity is due entirely to forces
acting between pairs of particles. By the ordinary
method of investigation we know that
V = Sqrt(m/z) . . . . . (132)
where m is the coefficient of transverse elasticity,
and z is the density. By referring to the equations
of Part I., it will be seen that if z is the density
of the matter of the vortices, and u is the
"coefficient of magnetic induction,"
u = pi(z) . . . . . (133)
whence
pi(m) = uV^2 . . . . (134)
and by (108)
E = V Sqrt(u) . . . (135)
In air or vacuum u = 1, and therefore
V = E
= 314,858,000,000 mm/sec
= 195,647 miles per second (137)
The velocity of transverse undulations in our
hypothetical medium, calculated from the electro-
magnetic experiments of MM. Kohlrausch and Weber,
agrees so exactly with the velocity of light
calculated from the optical experiments of M.
Fizeau, that we can scarcely avoid the inference
that light consists in the transverse undulations
of the same medium which is the cause of electric
and magnetic phenomena. ...”
---------------------------------------------------------
Ref: "On the Physical Lines of Force", Part III, pgs 21-22
of "Philosophical Magazine and Journal Of Science"
Fourth Series January 1862
----------------------------------------------------------
Paul Stowe
greywolf42
>
> Heavens to Betsy! Is this what a fireball feels like? Post in haste,
> repent at leisure.
>
> I'll answer your question by withdrawing my (now obviously) incorrect
> description of the relevant experiment. You are correct that mu_0 is
> arbitrarily set to 4 pi x 10^-7 (although I think it's used to define
> the ampere, not the coulomb). I'd like to point out my use of the
> weaselly acronym "IIRC", which is clearly false in this case.
>
> I will now formulate what is (I hope) a better position: that the
> velocity of EM waves may be deduced from purely electrical and magnetic
> observations. I certainly recall an account of Maxwell doing this and
> noting that his result was remarkably close to the observed speed of
> light, causing him to conjecture that light is EM radiation.
Indeed, that exists in Maxwell's "On Physical Lines of Force", 1861. Which
was Maxwell's original derivation of "Maxwell's equations" (plus much else).
However, Maxwell was not using the modern terms mu_0 and epsilon_0. Nor the
modern rendition of charge. Maxwell could use actual measurements because
theory had not yet taken such a strong grip on the minds of academia.
> Further, I
> do remember reading of an experimental setup essentially as the one I
> described, although the actual methodology of calculating c from the
> measured forces has been lost in the haze of time (and something called
> "Drop Day at Dabney House" :)
Well, the methodology has not been lost in the haze of time, it has been
deliberately removed in two separate phases. The first phase was in the
1920's -- when mu_0 and epsilon_0 and the Coulomb unit were created..The
second phase was the 1990's -- when the standard for distance was converted
to the "official" speed of light.
Starblade Darksquall
pva...@bas.bg (Pentcho Valev) wrote in message news:<a5f8a53d.03062...@posting.google.com>...
The speed of light will remain constant. The reason why in our point
of view - assuming we're at the station - the light from the front of
the train hits the back of the train in a shorter time than the light
from the back of the train hits the front of the train is because
simultaneity is relative. From the train's point of view time it takes
to go either direction is the same, and is equal to the distance
divided by the speed of light. From the station's point of view
however, it takes t = d/(c+v) to go from the front to the back and t =
d/(c-v) to go from the back to the front. This does NOT mean that the
speed of light is in any way altered. This has to do with timespace
being tilted, as I mentioned earlier.
I hope this helps you!
(...Starblade Riven Darksquall...)