Please explain SR photon energy question
s...@saverworld.com
A ligtht source is at x=0, and an ideal mirror (reflects all light) is
tat x=L. The source and mirror have zero relative velocity. A pulse
of light travels to the mirror and back to the source. Ideally, the
same amount of energy that left the source returns to the source.
Let an observer move with velocity -V along the x-axis relative to the
rest frame. He measures the light to be of some frequency f0. When
light reflects off the moving mirror, according to SR it must change
frequency, say to f1. According to Einstein's photo-electric effect
hypothesis, photons of different frequencies have different energies.
How does a moving observer measure the same energy hitting the mirror
as reflecting off the mirror? It seems to me that observers in all
frames must count the same number of photons. In the rest frame, all
the photons are the same frequency. In the moving frame, the incident
photons are frequency f0 and the reflected photons are frequency f1.
Can you explain what is happening here?
Thanks,
David Seppala
EjP
> Can someone please explain this simple experiment.
> A ligtht source is at x=0, and an ideal mirror (reflects all light) is
> tat x=L. The source and mirror have zero relative velocity. A pulse
> of light travels to the mirror and back to the source. Ideally, the
> same amount of energy that left the source returns to the source.
>
OK.
> Let an observer move with velocity -V along the x-axis relative to the
> rest frame. He measures the light to be of some frequency f0. When
> light reflects off the moving mirror, according to SR it must change
> frequency, say to f1. According to Einstein's photo-electric effect
> hypothesis, photons of different frequencies have different energies.
> How does a moving observer measure the same energy hitting the mirror
> as reflecting off the mirror?
Energy is not an invariant, and this is not specific to relativity.
Do the same problem with completely Newtonian mechanics using, say,
ping pong balls hitting a wall of a train car and you'll find yourself
in precisely the same situation.
> It seems to me that observers in all
> frames must count the same number of photons.
They do, just like the observer in the above problem would see
the same number of ping pong balls as the man on the train.
> In the rest frame, all
> the photons are the same frequency. In the moving frame, the incident
> photons are frequency f0 and the reflected photons are frequency f1.
As I said, this is not a problem. In both cases, energy is actually
conserved by imparting a small amount of momentum to the mirror/wall.
If you go through all the details of both problems, you'll find that
everything works out.
> Can you explain what is happening here?
I hope I have.
-E
> Thanks,
> David Seppala
Bilge
Cesar Sirvent
<s...@saverworld.com> escribió en el mensaje
news:404894f7....@news-server.austin.rr.com...
David, the frequency of the photon is different for another observer, but
the interaction is also seen differently.
At the end, when making all calculations, you will find that the phenomenon
are identical, i.e., you won't find a situation where the photoelectric
effect occurs and other when it doesn't. Notice that the effect has to do
with an interaction among photon and matter, so why do you consider just one
part of the problem (the photon)?
Cesar
luke
I'll take a crack at it..
A couple problems here, one is that a mirror reflecting a photon
recoils and the reflected photon has less energy. The other is just
that energy is not conserved when moving between different inertial
frames, as E=h*nu shows after putting in the doppler shifted nu. I
don't see how the number of photons is a problem.. you're not talking
about the Unruh effect are you?
Dirk Van de moortel
"luke" <fun...@yahoo.com> wrote in message news:e1b04639.04030...@posting.google.com...
That is not the way this troll works.
You are supposed to work on his problem during at least half an
hour. Then he will say "Thanks for your answer. But..." without
having looked at it, and he will come with an entirely different
problem.
He has been doing this since 1996.
Dirk Vdm
Cesar Sirvent
"Dirk Van de moortel" <dirkvand...@ThankS-NO-SperM.hotmail.com>
escribió en el mensaje news:tB62c.24339$S35.1...@phobos.telenet-ops.be...
Androcles made the same with me, and even worst, because he is now insulting
me constantly.
Cesar
> Dirk Vdm
>
>
Dirk Van de moortel
"Cesar Sirvent" <8UMU...@SPAxMterrMAPSa.esSPAxM> wrote in message news:SZ62c.3799989$uj6.11...@telenews.teleline.es...
>
> "Dirk Van de moortel" <dirkvand...@ThankS-NO-SperM.hotmail.com>
> escribió en el mensaje news:tB62c.24339$S35.1...@phobos.telenet-ops.be...
[snip]
> >
> > That is not the way this troll works.
> > You are supposed to work on his problem during at least half an
> > hour. Then he will say "Thanks for your answer. But..." without
> > having looked at it, and he will come with an entirely different
> > problem.
> > He has been doing this since 1996.
>
> Androcles made the same with me, and even worst, because he is now
> insulting me constantly.
My advice: *never* talk about physics with these people.
Don't even *think* about it.
See nr 18 of
http://www.manbottle.com/humor/Dilbert_Quotations.htm .
Dealing with morons and/or trolls - specially with combinations
like Androcles - is a Fine Art.
Dirk Vdm
Bilge
>"Cesar Sirvent" <8UMU...@SPAxMterrMAPSa.esSPAxM> wrote:
>> Androcles made the same with me, and even worst, because he is now
>> insulting me constantly.
>
>My advice: *never* talk about physics with these people.
>Don't even *think* about it.
Discussing physics with them would also be bad netiquette, since
in order to do so, one would have to change the subject of their
posts to something related to physics.
>See nr 18 of
> http://www.manbottle.com/humor/Dilbert_Quotations.htm .
>Dealing with morons and/or trolls - specially with combinations
>like Androcles - is a Fine Art.
You have an extra "ine" there.
s...@saverworld.com
wrote:
>s...@saverworld.com wrote:
>> Can someone please explain this simple experiment.
>> A ligtht source is at x=0, and an ideal mirror (reflects all light) is
>> tat x=L. The source and mirror have zero relative velocity. A pulse
>> of light travels to the mirror and back to the source. Ideally, the
>> same amount of energy that left the source returns to the source.
>>
>
>OK.
>
>> Let an observer move with velocity -V along the x-axis relative to the
>> rest frame. He measures the light to be of some frequency f0. When
>> light reflects off the moving mirror, according to SR it must change
>> frequency, say to f1. According to Einstein's photo-electric effect
>> hypothesis, photons of different frequencies have different energies.
>> How does a moving observer measure the same energy hitting the mirror
>> as reflecting off the mirror?
>
>Energy is not an invariant, and this is not specific to relativity.
>
>Do the same problem with completely Newtonian mechanics using, say,
>ping pong balls hitting a wall of a train car and you'll find yourself
>in precisely the same situation.
Look at Einstein's theory of the photon and SR. Let's say 10000
photons hit an ideal mirror, and 10000 photons are reflected. The
moving frame observers say that more energy hit the mirror than is
reflected off the mirror, whereas in the rest frame the incident
energy is equal to the reflected energy, so we conclude from
Einstein's theory that ideal mirrors don't exist. So now we look at
10000 photons hitting the mirror, and 9000 photons being reflected,
and 1000 photons being absorbed. The rest frame observers say that 90
percent of the energy is reflected. The moving frame observers
disagree. They say for example, that only 60 percent of the incident
energy is reflected. I don't see how this is physically possible.
Don't they both have to agree on what percentage of energy is absorbed
and reflected?
Thanks,
David
s...@saverworld.com
Please comment on my response I posted to EjP.
Thanks,
David
Cesar Sirvent
The energy of the light beam is a function of both the number of photons and
their frequency.
I don't see then where you extract from the result of different number of
photons being reflected.
I would suggest that you modeled your examples in the simpler way, it is
something than make things much easier to deal with. So restrict yourself to
one photon, and even, I would suppress the mirror and would use particle
interactions, for example, interaction with a free electron. In such case,
you cannot have complete absorption or reflection of the photon. Look at
Compton effect in Google, and if you have more questions, feel free to ask.
A nice schematic introduction here:
http://scienceworld.wolfram.com/physics/ComptonEffect.html
In practice, the electrons are not completely free, but "loosely bound", but
you can model them as free. When you understand this, we can next up one
step to the mirror example.
Thanks.
Cesar
Cesar Sirvent
Done in the appropriate level of the thread.
> Thanks,
You're welcome.
> David
>
Dirk Van de moortel
"Bilge" <dub...@radioactivex.lebesque-al.net> wrote in message news:slrnc4id19...@radioactivex.lebesque-al.net...
:-))
Dirk Vdm
s...@saverworld.com
>
>The energy of the light beam is a function of both the number of photons and
>their frequency.
>something than make things much easier to deal with.
Let each laser put out an identical pulse of light. Let's say each
laser puts out N photons. Each laser uses the same amount of energy
to produce the pulse. In the rest frame of the lasers, both pulses
have the same amount of energy. In frames moving along the X-axis
with velocity V relative to the rest frames, according to Einstein's
photon hypothesis and SR, the two pulses do not have the same energy.
How do the observers in the moving frame account for the energy
difference? Doesn't the energy going in have to equal the energy
coming out? If the same amount of energy goes into each laser, but a
different amount of energy comes out, doesn't something else have to
change to make up the difference? Where does the energy go?
Thanks, Cesar.
>photons being reflected.
mirror as hit the mirror (an ideal lossless mirror), the moving
observer would observe that energy disappeared (or was created) while
the rest frame observer would not. I did not see how that was
possible, so I suggested ideal mirrors cannot exist with Einstein's
photon hypothesis and SR, so I thougth his theory must require that
some of the photons to be absorbed by the mirror.
David
Ken S. Tucker
>On Fri, 05 Mar 2004 10:23:57 -0600, EjP <nos...@hackers.are.bad>
>wrote:
Good question David....
>>s...@saverworld.com wrote:
>>> Can someone please explain this simple experiment.
>>> A ligtht source is at x=0, and an ideal mirror (reflects all light) is
>>> tat x=L. The source and mirror have zero relative velocity. A pulse
>>> of light travels to the mirror and back to the source. Ideally, the
>>> same amount of energy that left the source returns to the source.
>>> Let an observer move with velocity -V along the x-axis relative to the
>>> rest frame. He measures the light to be of some frequency f0. When
>>> light reflects off the moving mirror, according to SR it must change
>>> frequency, say to f1. According to Einstein's photo-electric effect
>>> hypothesis, photons of different frequencies have different energies.
>>> How does a moving observer measure the same energy hitting the mirror
>>> as reflecting off the mirror?
>>Do the same problem with completely Newtonian mechanics using, say,
>>ping pong balls hitting a wall of a train car and you'll find yourself
>>in precisely the same situation.
>> -E
That's somewhat how I see it too.
Think of a series of balls each with the same energy N.
Each of these beams have the same energy,
incident beam f0 ooooooo
reflected beam f1 o o o o o o o o
The total energy of each beam is 7*N.
But, f0 = 2*f1 where frequency is sometimes called
N cycles/second, and each cycle has an equal amount
of energy independant of frequency. So frequency is
how many balls/second hit the mirror.
Wavelength w0 = w1 /2 are the lengths of the cycle,
which is the distance between the balls.
The speed of light c = f*w =f0*w0 = f1*w1
remains the same for any beam.
Regards
Ken S. Tucker
s...@saverworld.com
<dirkvand...@ThankS-NO-SperM.hotmail.com> wrote:
>
>"Bilge" <dub...@radioactivex.lebesque-al.net> wrote in message news:slrnc4id19...@radioactivex.lebesque-al.net...
>> Dirk Van de moortel:
>> >"Cesar Sirvent" <8UMU...@SPAxMterrMAPSa.esSPAxM> wrote:
>>
>> >> Androcles made the same with me, and even worst, because he is now
>> >> insulting me constantly.
>> >
>> >My advice: *never* talk about physics with these people.
>> >Don't even *think* about it.
>>
>> Discussing physics with them would also be bad netiquette, since
>> in order to do so, one would have to change the subject of their
>> posts to something related to physics.
>
>Dirk Vdm
>
Discussing arrogance with me is another subject you and others have a
lot more expertise in.
David
Dirk Van de moortel
<s...@saverworld.com> wrote in message news:4049dcae...@news-server.austin.rr.com...
We do have an excellent practice ground here to see real
arrogance in action. But I don't recall having discussed it
with you - besides, you aren't arrogant - you are merely
devious.
Dirk Vdm
s...@saverworld.com
wrote:
Yes, if I look at it that way there's no problem with understanding
what happens. However, Einstein's photon hypothesis does not work
that way (as I read it). The same number of photons are emitted by
each laser. The energy of each photon is proportional to the light
frequency of the emitted photon. So your explanation conflicts with
Einstein's photon hypothesis. But Einstein's hypothesis doesn't seem
to make sense to me. If the rest frame observer and the moving frame
observer count the same number of photons being emitted in the pulse
of light from each laser, then energy must disappear or be created.
On the other hand, the energy problem disappears if observers in
different frames count a different number of photons, but that would
imply that observers in some frames can detect photons that other
frames cannot with is also contradictory to the theory.
There are other problems with Einstein's photo-electric theory
too. Namely, in practical experiments, the amount of energy seems to
be related to the light intensity, not the frequency of light.
Physicists seem to throw in what we used to call a "fudge factor" to
make the lab results match the theory. In this case its call "photon
efficiency".
If Germer and Davisson did their experiment showing the wave
properties of matter prior to the widespread acceptance of Einstein's
photon theory, matter and light would both be considered to be
comprised of waves and not particles. It really seems to me that
physicists have things backward in this area.
David
s...@saverworld.com
Per Cesar's suggestion I simplified the question. Instead of light
reflecting off a mirror, consider two laser sources on the x-axis,
which I'll call laser A and laser B. Let them point in opposite
directions along the x-axis. They each emit an identical pulse of
light along the x-axis, but in the pulses travel in opposite
directions. In doing so, they each use the same amount of energy to
generate the pulse. Observers in the rest frame observe that the two
emitted pulses have the same frequency and energy.
In a frame which is moving at constant velocity V along the
x-axis, the two emitted pulses are not identical. They differ in
frequency and they differ in pulse width. Observers in the moving
frame measure that the same amount of energy was used by laser A and
laser B to generate their respective pulses. Therefore, if energy is
conserved in the respective inertial frames, the moving frame
observers must measure the same energy in pulse A as they measure in
pulse B. But this conflicts with Einstein's photon theory in which
the energy of each photon is proportional to the light frequency. One
might suggest that the moving frame observers measure a different
number of photons being emitted from laser A than are emitted from
laser B, but that implies that the rest frame observers can detect
photons that the moving frame observers do not detect. I don't see
how to resolve this issue other than saying Einstein's photon theory
conflicts with SR.
David
Ken S. Tucker
That's quite right David, I think your objection is
sound. That's why I assign *length* to a photon,
to the chagrine of Quantum theorists, as the
diagram above indicates. I assigned each
*cycle* an invariant energy N.
>So your explanation conflicts with
>Einstein's photon hypothesis.
My intro was classical, just move the units,
E= hf = h(1/t) = h(c/t) = h(s/t^2) = ha
where a = acceleration.
If the photon (ha) is insufficient to move the
electron, reflection occurs, otherwise the "ha"
accelerates the electron to a new orbital and
the photon is absorbed.
Ok, the timing between my invariants, oooo above
determines the acceleration and force increments
applied to the a receptive particle.
How does that look?
> Einstein's hypothesis doesn't seem
>to make sense to me.
I agree, I find it difficult to understand too.
>If the rest frame observer and the moving frame
>observer count the same number of photons being emitted in the pulse
>of light from each laser, then energy must disappear or be created.
>On the other hand, the energy problem disappears if observers in
>different frames count a different number of photons, but that would
>imply that observers in some frames can detect photons that other
>frames cannot with is also contradictory to the theory.
> There are other problems with Einstein's photo-electric theory
>too. Namely, in practical experiments, the amount of energy seems to
>be related to the light intensity, not the frequency of light.
One good achievement of the photo-electric theory
was to find electrons liberated by photons impacting
metal had nothing to with intensity but instead had to
do with the frequency of light. Einstein got the Nobel
prize for taking Plancks Quantum hypothesis of light
and applying that to the Photo-electric Effect.
I welcome corrections if I errorred.
>Physicists seem to throw in what we used to call a "fudge factor" to
>make the lab results match the theory. In this case its call "photon
>efficiency".
> If Germer and Davisson did their experiment showing the wave
>properties of matter prior to the widespread acceptance of Einstein's
>photon theory, matter and light would both be considered to be
>comprised of waves and not particles. It really seems to me that
>physicists have things backward in this area.
>David
Most physicist's don't go near relativity, they get
Phd's on relative navel lint. You would need to be
a mathematical Machoist to do a Ph.d in GR+.
.........follow the money............
Anyway David, I'll be looking forward to your
response. I hope you will not be discouraged
by Dirk Vd et ilk,...just ignore those pricks as
long as you take yourself seriously, which I do.
Regards
Ken S. Tucker
EjP
I think your confusion comes from the fact that it is the frequency,
not the number, of photons that changes in the moving frame. An
ideal mirror would reflect 100% of the photons in either frame
but the photons would be red shifted if the mirror were
moving away from the source.
-E
shuba
> just ignore those pricks as
> long as you take yourself seriously, which I do.
I've had that problem, too. Mostly in the past.
---Tim Shuba---
luke
OK, sounds valid so far. This approach is much better, we are coming
to your point quicker I think.
> In a frame which is moving at constant velocity V along the
> x-axis, the two emitted pulses are not identical. They differ in
> frequency and they differ in pulse width. Observers in the moving
> frame measure that the same amount of energy was used by laser A and
> laser B to generate their respective pulses.
This is perhaps a weak point in your construction. What is the energy
source? How can we guarantee that lasers A and B use the same amount
of energy (in the moving frame)? For example, consider as the energy
source two identical baseballs thrown at identical speeds (in the rest
frame) from the midpoint of the two lasers. The kinetic energy is
converted to electricity and to the laser identically by simple
machines at each laser. In this construction, the moving frame does
not agree that they each receive the same energy..
> Therefore, if energy is
> conserved in the respective inertial frames, the moving frame
> observers must measure the same energy in pulse A as they measure in
> pulse B. But this conflicts with Einstein's photon theory in which
> the energy of each photon is proportional to the light frequency. One
> might suggest that the moving frame observers measure a different
> number of photons being emitted from laser A than are emitted from
> laser B, but that implies that the rest frame observers can detect
> photons that the moving frame observers do not detect.
This is a possiblity, but I won't consider until you answer my first
point above. Sorry :)
> I don't see
> how to resolve this issue other than saying Einstein's photon theory
> conflicts with SR.
> David
-luke
s...@saverworld.com
In the baseball example, the moving frame must see energy being
conserved. The velocity of each baseball is different as measured in
the moving frame, but so is the mass of each baseball. If any
situation results in energy disappearing or being created then there
is a problem with the theory.
David
s...@saverworld.com
wrote:
The problem I have is Einstein's photon hypothesis states the energy
of each photon is proportional to the light frequency. If there are
the same number of photons in each pulse, and the frequency of the
light is different in each pulse, then we must conclude that the
amount of energy is different in each pulse. But this cannot be. If
that were the case energy either disappeared or was created. If it
disappeared, where did it go. If it was created, where did it come
from? It makes much more sense to me to hypothesize that the energy
of a pulse of light is proportional to intensity and pulse width
instead of frequency.
David
Ken S. Tucker
Ha, well if the question is a good one, reasonably
well expressed, then I don't give a damn about the
motivation of the poster. But if answers to the
question are discouraged, or the OP needs to
take a defensive attitude, because of some past
mispoken words, then nobody would be able to
post.
Ken S. Tucker
EjP
> (...snip...)
>
> The problem I have is Einstein's photon hypothesis states the energy
> of each photon is proportional to the light frequency. If there are
> the same number of photons in each pulse, and the frequency of the
> light is different in each pulse, then we must conclude that the
> amount of energy is different in each pulse. But this cannot be. If
> that were the case energy either disappeared or was created. If it
> disappeared, where did it go. If it was created, where did it come
> from?
It's a shame that you keep willfully ignoring the ping-pong ball
example that I and a couple of others keep pointing you to, since
it answers your question quite nicely.
From the quantum mechanical standpoint, a "perfect reflection"
is just a fully elastic collision with the mirror, just
like the fully elastic collision of the ping-pong balls with
the "stationary" wall of a train.
In either case, a *very small* amount of momentum is transfered
to the "fixed" reflecting surface. Now the sublety is that the amount
of kinetic energy represented by a particular momentum transfer
is not an invariant if you go from one frame to another, and if
you carefully work this out, you'll find that the "missing" kinetic
energy in each case is fully accounted for if you correctly consider
the momentum which must be transferred to the mirror or train car.
> It makes much more sense to me to hypothesize that the energy
> of a pulse of light is proportional to intensity and pulse width
> instead of frequency.
Well, no offense, but in science, agreeing with experimental
data is usually given a higher weight than making sense to
someone on an internet newsgroup.
Did you take physics in college? If so, you must have
done a Compton scattering, which demonstrates very nicely
the kinematics of elastic photon collisions.
Also, if you have a hard time accepting that reflected
EM waves are red/blue shifted from a moving surface,
you'll have a very hard time explaining how a radar
detector works.
-E
s...@saverworld.com
wrote:
>s...@saverworld.com wrote:
>
> > (...snip...)
>>
>> The problem I have is Einstein's photon hypothesis states the energy
>> of each photon is proportional to the light frequency. If there are
>> the same number of photons in each pulse, and the frequency of the
>> light is different in each pulse, then we must conclude that the
>> amount of energy is different in each pulse. But this cannot be. If
>> that were the case energy either disappeared or was created. If it
>> disappeared, where did it go. If it was created, where did it come
>> from?
>
>It's a shame that you keep willfully ignoring the ping-pong ball
>example that I and a couple of others keep pointing you to, since
>it answers your question quite nicely.
>
> From the quantum mechanical standpoint, a "perfect reflection"
>is just a fully elastic collision with the mirror, just
>like the fully elastic collision of the ping-pong balls with
>the "stationary" wall of a train.
>
>In either case, a *very small* amount of momentum is transfered
>to the "fixed" reflecting surface. Now the sublety is that the amount
>of kinetic energy represented by a particular momentum transfer
>is not an invariant if you go from one frame to another, and if
>you carefully work this out, you'll find that the "missing" kinetic
>energy in each case is fully accounted for if you correctly consider
>the momentum which must be transferred to the mirror or train car.
You say "going from one frame to another". I am not talking about
going from one frame to another. I talking about what happens in the
moving frame. Or what happens in the rest frame. Not what happens in
going from one frame to the other. Let's do some experiments. Let's
say we have a laser which generates a series of pulses of light. We
measure how many pulses we can generate from a standard battery. We
repeat this same experiment with the laser pointing in different
directions. We find that the laser number of pulses we can generate
from a standard battery is independent of the direction the laser is
pointing. Observers in all inertial frames agree that the battery
goes dead after the laser generates the same number of pulses,
independent of direction. The next experiment we do is to measure
the energy in the light pulses output by the laser. In the rest frame
of the laser, we find that the energy in the series of pulses is
independent of the direction the laser is pointing. In the moving
frame, we find that the energy in the series of pulses depends on the
direction the laser is pointing. Now we ask, in the moving frame what
accounts for the dependence of output energy on the direction the
laser is pointing. If we believe in the conservation of energy, we
must conclude that the difference between the input energy to the
laser and the output energy from the laser must remain within the
laser. This can happen in two ways. One the temperature of the laser
can change, or two the laser can change velocity (accelerate). Now we
do a test with two lasers pointing in opposite directions and
physically tied to the same platform. In the laser/platform system,
the velocity does not change. In the rest frame of the laser/platform
system, the temperature of one laser equals the temperature of the
other laser. With no change in velocity of the lasers, and no
temperature change in the lasers, what do observers in the moving
frame say happened to the input energy?
>
>> It makes much more sense to me to hypothesize that the energy
>> of a pulse of light is proportional to intensity and pulse width
>> instead of frequency.
>
>Well, no offense, but in science, agreeing with experimental
>data is usually given a higher weight than making sense to
>someone on an internet newsgroup.
With no offense, when anyone does the simplest of experiments
generating electro-magnetic waves they find that the amount of energy
needed to used in a red LED and a green LED depends on the intensity,
not the emitted frequency, or to generate a 90 MHz radio signal versus
a 110 MHz radio signal depends on the signal level, not the frequency.
One has to introduce the concept of "photon efficiency" to explain
this simple experiment. Photon efficiency is not part of Einstein's
hypothesis, and it has the property of making energy proportional to
intensity not to frequency. The hypothesis of photon efficiency can
be tested, but I've found no experimental results to verify the
hypothesis.
>
>Did you take physics in college? If so, you must have
>done a Compton scattering, which demonstrates very nicely
>the kinematics of elastic photon collisions.
>
>Also, if you have a hard time accepting that reflected
>EM waves are red/blue shifted from a moving surface,
>you'll have a very hard time explaining how a radar
>detector works.
Where do you get I have a hard time accepting that reflected waves
from a moving surface change frequency? That is well documented, I
just can't see how the moving frame observers account for the energy
in the above experiments.
David