How do two interfering EM waves conserve energy in all cases? | AskScience Blog

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Saturday, August 13, 2016

How do two interfering EM waves conserve energy in all cases?

How do two interfering EM waves conserve energy in all cases?


How do two interfering EM waves conserve energy in all cases?

Posted: 13 Aug 2016 01:35 AM PDT

Intro below, question in bold at the bottom.

Hey guys! I'm a molecular electronics PhD student at Leiden university, and before that did a nanoscience MSc at Groningen university. I've asked this question to my fellow students and also some postdocs and professors. We have not yet found a satisfactory answer.

The problem is a gedankenexperiment where two laser beams or more specifically: two electromagnetic waves meet each other and interfere perfectly destructively or constructively. So we have two (for example) laser beams that cross paths. Now, each laser sends out an oscillating electromagnetic field with a certain power (say 100 watts). We set up the system in such a way that they interfere constructively completely. When the two beams cross and in, we can add the beams vectorially and end up with an EM-field with twice the amplitude. Since the energy density of an EM-field goes with the amplitude squared, we suddenly have four times the output power.

Now, I know that this cannot be. We could simply use quantum mechanics and say: well, we just have twice the amount of photons now, and photons do not interfere with each-other, only with themselves. Therefore, you just have twice the power, not four times. However, this answer sounds unsatisfactory to me. I think that the answer should be simpler and should not require quantum mechanics, or anything other than the laws of Maxwell.

Furthermore, I'm not interested in answers along the lines of: "Well, you can never make a laser like that, since the laser linewidth is never infinitely sharp". I think that the solution should not be practical one, but a principle one.

I have looked at this thread. However, the answers here are among the lines of: well, the intensity goes somewhere else. So that means that whatever interferes destructively somewhere, should interfere constructively somewhere else. This sounds like the most valid answer, but I don't see how this is a fundamental and not a practical issue.

For example: we could take a laser beam with a width of half the wavelength (I now this is not practical, but I don't see why we cannot do this fundamentally), and at 90 degrees cross another identical laser beam, so that they interfere constructively. Twice the field amplitude, four times the power. We could also interfere destructively and end up with no power.

So my question is: how do we solve this problem? And if it has to do with constructive interference in one place, destructive interference in the other, why should this not depend on the geometry if the setup, eg. the width and angle of the two beams?

submitted by /u/Blokshibe
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How do dung beetles extract nutrients from waste product?

Posted: 12 Aug 2016 07:59 PM PDT

Is there any meaning to rotation around the time axis in spacetime?

Posted: 12 Aug 2016 04:30 PM PDT

If spacetime is a four-dimensional object, and you can rotate around the three spatial axes, how would you interpret rotation around the time axis?

submitted by /u/ergotist
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Why are electric fields additive?

Posted: 13 Aug 2016 07:49 AM PDT

In undergraduate physics, you are taught that if you add the individual forces that a set of electrically charged particles put on another, that sum will be equal to the force experienced by the particle.

But let's say you have 3 particles in a line. Apparently this rule still holds. However, forces are supposed to be carried by particles in QM, the photon specifically here. If you shine a light, which is made of photons, on two inline objects, it won't hit the farther back one, because that is in shadow.

So if electric force is additive for inline particles, that makes it sound like the photons from the far left reach the particle on the far right, when the shadow example makes me think it shouldn't. How does that work?

submitted by /u/Bananawamajama
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A photons wavelegth increases because of cosmic expansion. Does the same happen to the (De Broglie) wavelegth of matter-wavefuntions? Does this mean all matter, not only photons, lose energy/momentum?

Posted: 12 Aug 2016 05:42 PM PDT

Is it feasible to completely eradicate mosquitoes without devastating the ecosystem?

Posted: 12 Aug 2016 09:22 AM PDT

Is there a research-backed process to create a healthier gut biome, particularly for achieving a healthy weight?

Posted: 12 Aug 2016 02:15 PM PDT

I've read about an individual receiving a fecal transplant and becoming obese because the donor was overweight. Given the obesity epidemic, has there been a recommended diet that helps create a gut biome that actually helps achieve a healthy weight?

submitted by /u/cisco55
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Why do the bubbles in Latte foam periodically pop in waves?

Posted: 12 Aug 2016 12:59 PM PDT

Here I am doing science at my desk and I find myself periodically distracted by the (very quiet) sound of the foam in my latte popping. Desperate for any distraction, I investigated.

Periodically (every 2-3 minutes) the popping sounds get louder for a second and then die back down. It's these periods of higher intensity that distracted me (not that it's hard to). I observed the foam for a bit and realised that the increased intensity coincided with a 'wave' of bubbles popping.

I set up a makeshift camera stand by stacking two cans of soda and recorded the effect with my phone: https://youtu.be/57ZlEtC5iAU (wave starts near the south-east of the mug, near where the white foam touches the wall of the mug).

What causes these periodic waves to occur? Intuitively I would have thought that the timing of the bubbles popping would be stochastic enough to avoid these sorts of effect, but I can see that if there are a sufficient number of 'about to pop' bubbles that a wave could be started.

Some (interesting?) observations:

  • The wave starts from the same are of the cup each time
  • The wave travels around the streak of white foam in the center, never through the white foam (as far as I can tell)
  • If I take a sip the effect is accelerated (happens only a few seconds after a sip consistently)
  • If I wiggle the mug just enough to cause small waves in the liquid but not enough to make the foam move from where it's attached to the side of the mug, the timing of the waves seems to be unaffected

Some off the cuff questions:

  • Since the wave tends to start in the same place, and in this case the wave starts near a patch of white foam, does the 'type' of foam affect the wave? It seems to since the wave goes around the white foam.
  • Do other 'foamy' systems exhibit this behaviour (beer, bubble tea, sea foam, etc.)?

Thanks for any insight :D

submitted by /u/jmct
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Why does an alternator turn slower, or resist turning more when under load?

Posted: 12 Aug 2016 01:51 PM PDT

I noticed this in my car when I would activate something that draws electricity like window motors, the engine RPMs would drop slightly until I let off the window motor button. Is this a stupid question and I'm totally wrong about what's actually happening to cause the engine RPMs to dip while there's an electrical load? Thank you for any useful input!!

submitted by /u/knivesngunz
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Why do fish when they die artificially float to the top of the water, but don't appear to in any other case?

Posted: 12 Aug 2016 11:11 AM PDT

Why does it seem like when fish die artificially (be it from the lack of oxygen due to thick ice or eutrophication, or some poisonous substances) they almost always float to the top of the water, but when they die in any other way(from old age, if that is even possible, or from disease) they don't float to the top?

submitted by /u/fjellhus
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Is listening to relaxing meditative music during study a help or a hindrance?

Posted: 12 Aug 2016 09:49 AM PDT

I've heard two schools of thought on this:

(1) It helps focus attention, bully out distracting thoughts from the mind and create a sense of relaxation to calm the anxiety of impending exams.

(2) You should study in exam conditions so that you don't need a certain external stimulus such as a chair, sound or smell to trigger off the memories in your mind.

Obviously, whatever works for the individual is best but I was wondering if there is a scientific consensus on the topic.

submitted by /u/VeterinaryStudentK9
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What are the technical differences between amylose and cellulose and can we turn one form to another?

Posted: 12 Aug 2016 02:16 PM PDT

They're both built with D-glucose units, however one is wood, and the other is bread. Why do they differ so much?

We throw away alot of paper, cardboard etc. Is there any industrial process that we could say recycle cellulose? turn it into amylose for animal feed? perhaps even decompose it into glucose for use in making bio-fuel?

submitted by /u/aortm
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How many satellites is needed for locating via GPS?

Posted: 12 Aug 2016 03:09 PM PDT

And why is more better? Is it only because of more possibilities to get right data?

submitted by /u/Dokans
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How does the pressure at the lowest point of the Mariana Trench compare to the pressure in space?

Posted: 12 Aug 2016 04:45 PM PDT

Can the barycenter of a two-body system be a Lagrange point?

Posted: 12 Aug 2016 07:26 AM PDT

First let me say that I'm a total novice, so I may be using these terms incorrectly, and I definitely have no grounding in the mathematics that describe these sorts of scenarios. Let me clarify what I mean: Barycenter: the center of mass of a system of celestial bodies, and therefore (if I'm interpreting Kepler's laws correctly) one of the foci in all elliptical orbits in the system. Lagrange Point: a gravitationally neutral point in a system that may or may not move based on the constituent orbits in the system. If these definitions are wrong, please tell me. But insofar as the underlying wrongness does not disallow my question being compatible with reality, I would love to learn more in this area.

submitted by /u/139mod70
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What are some intuitive applications of eigenvalues/eigenvectors in engineering?

Posted: 12 Aug 2016 08:34 AM PDT

I somewhat understand the concepts, but I have a hard time understanding how they are applied or what they represent in the physical world, so some examples would really help me.

submitted by /u/Rimio
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How does a neutrino detector work?

Posted: 12 Aug 2016 10:18 AM PDT

Could the "bionic leaf" technology be used to trap or convert CO2 on a large scale in a way that would help reduce (and hopefully reverse) the effects of CO2 emissions on the environment?

Posted: 12 Aug 2016 08:26 AM PDT

I just saw an article on utilizing a bionic leaf that can collect CO2 in the air to use as fuel. Could the same technology be used to trap or convert CO2 on a large scale in a way that would help reduce (and hopefully reverse) the effects of CO2 emissions on the environment?

submitted by /u/GandalfTheWhey
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How much pressure is needed to compress water?

Posted: 12 Aug 2016 09:10 AM PDT

Solids are compressible to the extent with enough force you could lessen the amount of space a solid occupies, is this also possible with water?

submitted by /u/shercroft
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What's something considered basic/common, that we still have little to no understanding of?

Posted: 12 Aug 2016 12:47 PM PDT

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