Here is a physics thought experiment examining conservation of energy
and EM propagation.  In answering, please address how the experiment
is resolved from a purely classical interpretation (i.e., how might
Maxwell have answered this question?); and, how a QM interpretation
might result in a different explanation?  Here is the experiment.  Let
us arrange a coherent monochromatic light beam, e.g. a laser beam, to
be split and directed along two paths.  With repect to the light's
wavelength, the paths are suitably arranged such that a half-cycle net
time delay exists between them.  These beams are then recombined
downstream, so as to destructively interfere there.  Question: where
does the light energy "go"?  Or, worded another way, what physical
part of this experiment "gets hot"?

If nothing else, 
                  deeptimer,
		  
I will at least add another specimen to your collection.
As an engineer, I hope you will appreciate  this explanation.

It is not quite original - this topic was discussed on sci.physics
few years back and this solution was offered , 
and similar  way of presenting it  was used..

 Solution is explained by parable: Imagine a robot walking in positive direction
 (x increasing) and pushing a load. Work is being done.
 Imagine identical robot, walking in opposite direction.
 
 When they meet, they still push, but no work is being done.
 Where does the energy goes?
 
I know you will say: Into the  robots, their motors will get hot.
                     In my case, there is no iron and copper to heat up...

 I will agree but say - assume (almost) perfect robots. Supra-conductive
 winding etc. Will that change things? Yes, it will.
 
 To see how, imagine a long horn, closed on one end, covered with membrane
 on the other end -- like a long drum.  My device has such a length that
 if I beat the covered end every second, I am in resonance - energy goes
 into compression and motion of the air. More and more they vibrate, and more
 and more gets dissipated. That medium, air, is your emg wave. Now I
will shorten the length so that I am half phase off the resonance.
When I hit, the membrane 'hits back'.
 That is the case of destructive interference. Engineer would say,
impedance of the device increased. Energy will find other pathways -
high impedance is like closed doors.
 
 To summariese this  for the folks: when you rig the beams as you said,
 other things being perfect, light (or any emg) will not enter the
device. It will reflect back into you source, into your laser.
Inversion will be maintained, and laser will consume less power, etc.
  
  so, there 
  
Quantum case will not change this. You would have to use second quantization
to represent the field, and even an enthusiast would demand more than $10 
(becouse it gets so messy) - but solution is the same.

  Hedgie

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Request for Answer Clarification by deeptimer-ga on 09 Mar 2005 07:59 PST

I left detailed thoughts toward your answer as another comment...

In (briefly) clarfying your answer, would you restate it in terms of
the proposed experimental setup (or one that would be essentially the
same in its rigorous analysis, e.g., microwaves & waveguides, etc.). 
It would suffice to state "where the energy is going" and why (what
the underlying physical mechanism is).

Many thanks!

---

Clarification of Answer by hedgie-ga on 09 Mar 2005 12:46 PST

Dear deep timer

             Could you kindly explain your reasoning about hansom return?
	     Kindly take into account the pricing guidelines
http://answers.google.com/answers/pricing.html
              and explain what you consider a to be a fair wages for a researcher.
	      Please use double accounting method so I can check your calculation. 
 I suppose you not check my other answers, 
http://answers.google.com/answers/search?q=hedgie-ga&qtype=all&btnG=Google+Search 
 so that you do not know that, based on statistical evaluation of
empirical data, e.g.
 
http://answers.google.com/answers/threadview?id=458232	

I have an allergy to people who keep adding to the question and promise a big tip.
It never works.

   The impedance of a stack is easy to calculate and math is independent of the
   exact nature of the stack. If you are an EE you know how to calculate impedance
   of the series of four-pole elements. Matrix transfer function of a stack is the
   matrix product of matrices for the elements. Method  is briefly
described here:
	 
   http://answers.google.com/answers/threadview?id=308586
   
   Kindly note that Dr, Baker put price $40 on his question and do the actual 
   calculation himself. As we say around here: 'Problem is solved, the
rest are engineering details'.
   I will be happy to withdraw my answer if you feel you did not get
your moneys worth.
   
   Hedgie

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Clarification of Answer by hedgie-ga on 09 Mar 2005 12:52 PST

I am looking at your

  "where the energy is going"

wonder if you really do not understand what I said in the answer:

namely
It will reflect back into you source

After steady state is reached, if you eliminated all losses,
your beam splitter will become a perfect mirror.
No new energy will enter the system.

 The same thing, with visible light happens with multilayer optical coating,
which makes lenses or glasess reflective or transmissive based on the
wavelength.  Same matrix algebra is used.

---

Request for Answer Clarification by deeptimer-ga on 09 Mar 2005 13:59 PST

If I somehow offended you, hedgie, I apologize but don't know what I
did.  I posted just one request to clarify, and (...I thought...) made
clear (by asking for a *brief* follow up) that I respect the value of
your time.  The follow up questions were solely intended to remove the
parable-nature of your response, and fit it into my original question
explicitly.

This being my first GA experience, in fact I did review GA's pricing
guidelines, and many example Q&As from the site, before posting my
question.  The URL to answers made by you also shows that the $10 is
in line with many past sessions you've elected to participate in. 
Further, many of your answers (even to low fee questions) demonstate a
high degree of thoughfulness, and I compliment you for those.

As we seem to be talking more about the $10 and less about the
physics, I conclude that we're done with the question, and that your
answer is the same as the #2 answer I posted originally.

Please keep in mind that you elected to answer the question and take
the fee, vs. e.g., posting a preliminary comment seeking to establish
a "fairer" fee and consensus on the work product, etc.  I did not
force you into this action: you did it voluntarily.  The voluntary
interaction of a seller and a buyer is (by definition) "fair" or one
of the parties simply elects not to take part in the transaction in
the first place.

I have been careful herein to state no further questions and consider
the matter closed.

---

Clarification of Answer by hedgie-ga on 09 Mar 2005 16:37 PST

My answer is indeed similar to your point 2:

" I am really asking what would happen if the technology were
 'theoretically perfect' .."

but adds  a)  ".. the mirror then would be perfect"
     and b) corrects 'the mirrors is at the point of interference'
 (where of course you may have to place a real mirror) to the beam-splitter". 

I am under obligation to answer your RFCs, after I choose to answer
the question. Sorry about that. To avoid continuation of this charade,
perhaps
-if you need to keep clarifying- ou may  use just the comment area?

 BTW - the problem with your question is that it was not a question.
 Apparently you know the answer:
  " Some get it right "   and know it best then anyone else.
   May be the service you want  would be called Questions and not Answers?
   May be that would be in even  greater demand.

Hedgie

The response was similar in scope and depth to others I have received
of a similar nature, suggesting a rating of 3.  However, post facto
criticisms of the offered fee are unprofessional and should have been
clarified (by use of the comments feature) before formally answering
and accepting payment; thus a rating of 2 is given.

Ist das nicht für 10 Dollar (mickerige 7 ?) viel verlangt?  Und dann
hört es sich wie eine Uni-Aufgabe an (Homework).

I earned my degree back in 1981.

I'll expand on my remarks a little.  I am a retired engineer who loves
to ponder physics questions, and this one has been on my mind for
years.  I assure the readership this is no "homework assignent."  I
simply love to ponder such thought experiements, and seek others with
the same enthusiasm (hence the offer is only $10: it is more for the
enjoyment of the thought process and less so for those who just want
the gold).  I've had occassion during my career to ask several
physicists this question, and have never gotten the same answer twice.
 Some of the answers I've heard are:

1. Second order effects cause incomplete beam recombination and the
energy is lost thusly.  The argument is essentially that it is
*theoretically* impossible to split the beam then later recombine it
*perfectly*.  What one means by *theoretical* and *perfect* of course
depends on ones perspecttive, either classical or quantum.  I ask for
the Maxwellian reply because the 19th century physics community was
fond of viewing its knowledge as nearly complete, and so one should be
able to address this question in purely classical terms, and have the
answer make reasonable sense.

2. The point of destructive interference acts like a reflector, vs. an
energy sink, causing standing waves in the beams and energy losses
elsewhere in the system, such as at the imperfect laser mirrors.  But
I am really asking what would happen if the technology were
"theoretically perfect" in either the classical or QM sense?

3. The point of beam recombination "gets hot."  I don't know if this
answer is correct, but I like its straightforward boldness,
simplicity, and above all, it testability.

Okay now, no more dodging the question with criticisms of homework!

Regards.

My apologies!  I hope you find someone who knows what you're talking about,
               I sure don't.  Good luck!

Your comments are thought provoking.  By way of testing my
understanding of them, I'll translate them back into my experimental
setup, again assuming ideal components and so forth.  In essence I
believe your point is that the entire beam path stores energy until no
more can be accepted (for some ancilliary reason).  Thus, the point of
recombination must be acting as a perfect reflector of the beams'
energy (and so must the energy source, I guess).

Certainly I do not expect a mathematically rigorous answer for $10! 
Merely an explanation as one might direct to an educated lay audience,
but of sufficient intellectual depth to convey the ring of truth and
clarity.  I am open to raising the offer, if the reasoning for the
price adjustment is logical.

The question is interesting in part because it is (on the one hand)
simple to state, and thus "should" take just a few moments thought and
typing to answer.  Prorated to an hourly rate, under such an
assumption, the $10 extrapolates to a handsome rate!  But then again,
despite the question's apparent simplicity, there are all these
differing answers coming "off the top of one's head" from those to
whom I've posed in the past.  Thus, ipso facto, the question is
non-obivous and interesting, and it would appear a valid one to put to
the physics community.  In that sense I admit I may be undervaluing
it.

Dunno why your intriguing question got so emotionally messy. Ah well.

Regardless of the practicalities of such an experiment because they
are of no concern in a ?though experiment?, the situation is
equivalent of total reflection. Easiest to think in terms of VSWR or
even reflection from a mirror. Yes one can analyse in terms of Maxwell
field equations (and others) but it helps to ?feel? before
mathematical analysis. Grasping the concept of superposition (as I
think you do) also helps.

So as others have advised, the waves are returned to from whence they
came. There have also been amusing experiments on sound noise
cancellation. Some get it right with adaptive DSP and appreciate that
cancellation can only occur over limited areas. Others however
neglected the obvious that the energy has to go somewhere. It?s like
wearing a tight girdle -- as you wisely implied, it ends up elsewhere.

Best

Guzzi,

Your comments, "Some get it right with adaptive DSP and appreciate that
cancellation can only occur over limited areas" reminds me of a great
(albeit whimzical) short story by Arthur C. Clarke about the dangers
of attempting to workaround this fact.  It is his 1950 piece, "Silence
Please".

Oh wow deeptimer, what a mind hit that was. Read the compilation
decades ago and hadn?t thought about those stories for years. --
?Tales from the white hart?

http://technovelgy.com/ct/AuthorSpecAlphaList.asp?BkNum=184

Did it not finally ?explode?!?

Many thanks for reminder. Must search it out and read again.

Best

Indeed so, Guzzi.  If you enjoyed Clarke's short stories, they have
been recently re-released all in a single volume, "The Collected
Stories of Arthur C. Clarke."  About $20 at Amazon, and at nearly a
kilopage, plenty of enjoyment!  I highly recommend it.

Regards