In Feynman's book "QED" he states that the speed of light is a random
variable with a normal distribution. The published values of c are
averages. This brings to mind some questions.

What is the standard deviation? This should not be all that hard to
measure. Does the standard deviation increase with time/distance
traveled or is it a constant?

Patrick Powers wrote:

In Feynman's book "QED" he states that the speed of light is a random
variable with a normal distribution. The published values of c are
averages. This brings to mind some questions.

What is the standard deviation? This should not be all that hard to
measure. Does the standard deviation increase with time/distance
traveled or is it a constant?

Please cite page where Feynman makes a statement about standard
deviation with respect to light speed.


QED Pgs 89-90

"it may surprise you that there ia an amplitude for a photon
to go at speeds faster or slower than the convetional speed, c.
The amplitudes for these possibilities are very small compared
to the contribution from speed c; in fact, they cancel out when
light light travels over long distances. However, when the
distances are very short--as in many of the diagrams I will be
drawing--these other possibilities become vitally important and
must be considered".

Feynman is referring to interaction on the atomic level.

Patrick Powers wrote:

In Feynman's book "QED" he states that the speed of light is a random
variable with a normal distribution. The published values of c are
averages. This brings to mind some questions.

What is the standard deviation? This should not be all that hard to
measure. Does the standard deviation increase with time/distance
traveled or is it a constant?

New loud idiot on board.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
"Quis custodiet ipsos custodes?" The Net!

"Sam Wormley" wrote in message
...
Patrick Powers wrote:

In Feynman's book "QED" he states that the speed of light is a random
variable with a normal distribution. The published values of c are
averages. This brings to mind some questions.

What is the standard deviation? This should not be all that hard to
measure. Does the standard deviation increase with time/distance
traveled or is it a constant?

Please cite page where Feynman makes a statement about standard
deviation with respect to light speed.


QED Pgs 89-90

"it may surprise you that there ia an amplitude for a photon
to go at speeds faster or slower than the convetional speed, c.
The amplitudes for these possibilities are very small compared
to the contribution from speed c; in fact, they cancel out when
light light travels over long distances. However, when the
distances are very short--as in many of the diagrams I will be
drawing--these other possibilities become vitally important and
must be considered".

Feynman is referring to interaction on the atomic level.

Yes and on the atomic level
when an atom absorbs a photon
how is it know which other atom this photon came from?
Please tell how Feyman measure the velocity of his photons.

keith stein

"Patrick Powers" wrote in message
om...
In Feynman's book "QED" he states that the speed of light is a
random
variable with a normal distribution. The published values of c are
averages. This brings to mind some questions.

What is the standard deviation? This should not be all that hard to
measure. Does the standard deviation increase with time/distance
traveled or is it a constant?

The quantity c is now a *defined* constant. It can no longer be be
measured.

Franz

"Patrick Powers" wrote in message
om...
In Feynman's book "QED" he states that the speed of light is a random
variable with a normal distribution. The published values of c are
averages. This brings to mind some questions.

What is the standard deviation? This should not be all that hard to
measure. Does the standard deviation increase with time/distance
traveled or is it a constant?

The speed of light isn't derived, not even approximately.
Until recently, it was measured. Now, it's defined, and
time and distance are measured with respect to it, but
that's a matter of conventions and standards, not physics.

[Old Man]

Sam Wormley wrote in message ...
Patrick Powers wrote:

In Feynman's book "QED" he states that the speed of light is a random
variable with a normal distribution. The published values of c are
averages. This brings to mind some questions.

What is the standard deviation? This should not be all that hard to
measure. Does the standard deviation increase with time/distance
traveled or is it a constant?

Please cite page where Feynman makes a statement about standard
deviation with respect to light speed.


QED Pgs 89-90

"it may surprise you that there ia an amplitude for a photon
to go at speeds faster or slower than the convetional speed, c.
The amplitudes for these possibilities are very small compared
to the contribution from speed c; in fact, they cancel out when
light light travels over long distances. However, when the
distances are very short--as in many of the diagrams I will be
drawing--these other possibilities become vitally important and
must be considered".

Feynman is referring to interaction on the atomic level.

Aha, this answers my question. What I was interested in is
uncertainty.
The position of a photon is uncertain with a probability distribution.
So is this uncertainty part of the collapse of the wave function or is
the photon actually moving in an uncertain manner? So the former is
true. The mean of the distribution moves steadily at a constant
speed, and there is some true certainty in the situation.

Bjoern Feuerbacher wrote in message ...
Patrick Powers wrote:
Sam Wormley wrote in message ...

Patrick Powers wrote:

In Feynman's book "QED" he states that the speed of light is a random
variable with a normal distribution. The published values of c are
averages. This brings to mind some questions.

What is the standard deviation? This should not be all that hard to
measure. Does the standard deviation increase with time/distance
traveled or is it a constant?

Please cite page where Feynman makes a statement about standard
deviation with respect to light speed.


QED Pgs 89-90

"it may surprise you that there ia an amplitude for a photon
to go at speeds faster or slower than the convetional speed, c.
The amplitudes for these possibilities are very small compared
to the contribution from speed c; in fact, they cancel out when
light light travels over long distances. However, when the
distances are very short--as in many of the diagrams I will be
drawing--these other possibilities become vitally important and
must be considered".

Feynman is referring to interaction on the atomic level.


Aha, this answers my question. What I was interested in is
uncertainty.

The probability amplitude for a photon to propagate with the
four-momentum p is 1/p^2. Does this help in any way?


The position of a photon is uncertain with a probability distribution.
So is this uncertainty part of the collapse of the wave function or is
the photon actually moving in an uncertain manner?

The question is rather vague. "collapes of the wave function" usually
refers to the fact that after an observation, the wave function is
suddenly an eigenfunction of the relevant observable. This has little to
do with the position of the photon being uncertain.

Aha, I was thinking the position becomes certain when measured, but
this is not correct. How about this: before the
measurement/observation is made, we have only a vague idea of where a
photon might be. We can show probability distributions but no more.
After an observation/measurement the uncertainty has been reduced to
(at best) the Heisenberg minimum. It is also true that the means used
to measure/observe are uncertain in several ways. The same sort of
siTuation obtains concerning the number of photons.


So the former is
true. The mean of the distribution moves steadily at a constant
speed, and there is some true certainty in the situation.

I don't understand totally what you want to say here, but it sounds
right. ;-)

I meant that with certain kinds of uncertainty images would always
become blurred with travel through space. They would be blurred with
respect to time: we would see photons from the same point source with
varying ages. I've never heard of such a thing, so there is some true
certainty with photons.


Bye,
Bjoern

Patrick Powers wrote:
Bjoern Feuerbacher wrote in message ...

Patrick Powers wrote:


[snip]


The position of a photon is uncertain with a probability distribution.
So is this uncertainty part of the collapse of the wave function or is
the photon actually moving in an uncertain manner?

The question is rather vague. "collapes of the wave function" usually
refers to the fact that after an observation, the wave function is
suddenly an eigenfunction of the relevant observable. This has little to
do with the position of the photon being uncertain.


Aha, I was thinking the position becomes certain when measured, but
this is not correct.

The position is only certain within the limits of the measurement.

I.e. the wave function collapes to something like a narrow Gaussian
distribution centered on the position where one thinks to have observed
the photon, with a width corresponding to the resolution of the measurement.



How about this: before the
measurement/observation is made, we have only a vague idea of where a
photon might be. We can show probability distributions but no more.

After the measurement, this is still valid. The only difference is
that the distribution has become narrower.


After an observation/measurement the uncertainty has been reduced to
(at best) the Heisenberg minimum.

Huh? Heisenberg's principle applies to measurements of *both* position
*and* momentum.


It is also true that the means used
to measure/observe are uncertain in several ways.

Yes, obviously.


The same sort of siTuation obtains concerning the number of photons.

Well, let's say, a similar sort.


So the former is
true. The mean of the distribution moves steadily at a constant
speed, and there is some true certainty in the situation.

I don't understand totally what you want to say here, but it sounds
right. ;-)


I meant that with certain kinds of uncertainty images would always
become blurred with travel through space.

Well, they do. A wavepacket becomes broader with passing time.


They would be blurred with
respect to time: we would see photons from the same point source with
varying ages. I've never heard of such a thing, so there is some true
certainty with photons.

I don't see how one should be able to measure the "age" of a photon...


Bye,
Bjoern

Bjoern Feuerbacher wrote in message ...
Patrick Powers wrote:
Bjoern Feuerbacher wrote in message ...

Patrick Powers wrote:


[snip]


The position of a photon is uncertain with a probability distribution.
So is this uncertainty part of the collapse of the wave function or is
the photon actually moving in an uncertain manner?

The question is rather vague. "collapes of the wave function" usually
refers to the fact that after an observation, the wave function is
suddenly an eigenfunction of the relevant observable. This has little to
do with the position of the photon being uncertain.


Aha, I was thinking the position becomes certain when measured, but
this is not correct.

The position is only certain within the limits of the measurement.

I.e. the wave function collapes to something like a narrow Gaussian
distribution centered on the position where one thinks to have observed
the photon, with a width corresponding to the resolution of the measurement.



How about this: before the
measurement/observation is made, we have only a vague idea of where a
photon might be. We can show probability distributions but no more.

After the measurement, this is still valid. The only difference is
that the distribution has become narrower.


After an observation/measurement the uncertainty has been reduced to
(at best) the Heisenberg minimum.

Huh? Heisenberg's principle applies to measurements of *both* position
*and* momentum.


It is also true that the means used
to measure/observe are uncertain in several ways.

Yes, obviously.


The same sort of siTuation obtains concerning the number of photons.

Well, let's say, a similar sort.


So the former is
true. The mean of the distribution moves steadily at a constant
speed, and there is some true certainty in the situation.

I don't understand totally what you want to say here, but it sounds
right. ;-)


I meant that with certain kinds of uncertainty images would always
become blurred with travel through space.

Well, they do. A wavepacket becomes broader with passing time.

Really!

They would be blurred with
respect to time: we would see photons from the same point source with
varying ages. I've never heard of such a thing, so there is some true
certainty with photons.

I don't see how one should be able to measure the "age" of a photon...

Not directly, but there are a number of ways to tell whether the
photons from a point source are all taking the same amount of time to
arrive. Such as a wavepacket becoming broader with passing time. If
all the photons moved at the same speed, I would think the packet
would stay the same size, unless it is scattering or something like
that. More fun though is to think of observing someone in his daily
life on a far-distant planet. The image would be spread out in time
so you could see a stretched-out image of what he had been doing for a
period of time. A truely four-dimensional image.






Bye,
Bjoern