# Infinity Sphere

Discussion in 'Physics & Math' started by Michael, May 28, 2009.

1. ### EnmosValued Senior Member

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Oh no, I didn't want to revive it. It's just that it's kind of the same idea

I don't think one can prevent leakage, but if the light is diffused inside the sphere you can put more light into sphere than comes out of it, until some threshold is reached of course.

3. ### Billy TUse Sugar Cane Alcohol car FuelValued Senior Member

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You are correct. Leakage is impossible, in principle, to prevent if photons are entering the sphere. (If no hole and hot when formed, it might* have the some black boldy radiation in it.)

The entrance to the perfect diffusely reflecting sphere of radius R could be a small hole of radius r (or a window with any transparency you like, not zero). Let's assume a hole as any window is even more complex to fully understand as will soon be clear, I hope.

Then when photons are coming out at the same rate they are going in, then the probablity, P, of one inside the sphere escaping thru the hole instead of reflecting on the next time it is R from the center of the sphere is approximately P = 0.25(r/R)^2. I neglected the area of the hole when computing the area of the sphere as if the hole did not exist. The 0.25 comes for fact that sphere has four times the area of the same radius circle.

Calculating how many photons are in the sphere when they are entering and exiting at E per second is an interesting problem. I am nearly sure the correct answer is NOT just E/P, but that is a crude approximation to the number. To do it correctly is very complex.

If they were no hole, then the trapped photons would have all directions of travel equally probable. I.e. uniformly distributed in angular distribution. However the distribution of difusely reflected photons is not uniform in angle but peaked at the normal. Thus with the hole, those from the far side of the sphere with their last reflection will dominate the escaping photons. I.e. the angular distribution of the almost trapped photons will "have a hole burnt in it" by the hole.

This is very much like the distribution of atomic velocities of the excited atoms in a laser, which would resemble the Doppler profile of the line when not lasing, has a "hole burnt in it" by the laser action. Note the "se" in laser is for "Stimulated Emission." - I.e. those atoms that happend to be traveling so that their Doppler speed is resonate with them much narrower laser radiation line are stimulated to give their excitation energy to the laser and selectively removed from the Doppler velocity distribution. I.e. the laser is burning a hole in the velocity distribution of the exceited atoms it is using. This is a major factor in determining how much power the laser beam has.

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*It would not even have the wall temperature black body IR in it as the assumption that r = 1 means e = zero as r + e = 1. (Here r is the reflection and e the emission coefficients of the wall) What ever radiation field in it at the time the two hemispheres were joined to make the difuse sphere is the eternal distribution, except for its energy loss due to scattering by the vacuum virtual particle pairs I mentioned in an early post of this thread.

Last edited by a moderator: Jun 9, 2009

5. ### PandaemoniValued Senior Member

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What is a "perfectly" reflective surface. No mirror is perfectly reflective. In that sense it's like asking about the substance from which angels are made.

Second, do you have a point particle bouncing around a surface composed of an infinite number of points for an infinite amount of time? Perhaps the "particles" are strings? Perhaps we believe in loop quantum gravity so that "space" itself (and the interior of our sphere) is quantized. Then again, who said time was infinite?

7. ### Billy TUse Sugar Cane Alcohol car FuelValued Senior Member

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I am sure you know it is the, non existent, non achievable, limit on reflection coefficient, r = 1, which is much better defined and understood than anything about "angels" so your comparison is very weak.

8. ### grimaceBannedBanned

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as a matter of fact i am now sure of it.

9. ### DRZionTheoretical ExperimentalistValued Senior Member

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No mirror is perfectly reflective, but total internal reflection reflects 100% of light if the angle is below a certain threshold. This is the mechanism behind fiber optics, which leaves losses mostly due to absorption by the glass as well as pulse broadening. However the reflection is 100%.

10. ### Billy TUse Sugar Cane Alcohol car FuelValued Senior Member

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That is correct but note the pulse broading can be avoided (and a few, long, high-data-rate optical fiber lines do this) via making the data pulses solitons. (My college friend, L.M., developed the soliton optical pulse while at Bell Labs.)

11. ### PandaemoniValued Senior Member

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There is in fact a large literature on the physical substance of angels, dated from the middle ages, when they felt very sure that they did know quite a lot obout the physical substance of angels (hence the somewhat misstated old saw "How many angels can dance on the head of a pin?") My point is that first the poster needs to tell us what the properties of the perfectly reflective substance are (just as the philosophers needed to tell us the basic properties of spiritual matter before moving on to the specific properties of angels, like their ability to occupy every point in space simultaneously).

If he is talking about what amounts to fiber optic system, for example, then we need to know that the photon will be fires at an angle greater than the critical angle (and, incidentally, that the glass used has no impurities whatsoever, or else the photon will eventually be absorbed and cease tro be reflected). But that is a very specific set up.

He then needs to consider the nature of the photon, as point particle or something else, and then they nature of space, as an infinitely divisible background or made of discrete units or made of indefinable unites since "measurement" of lengths smaller than the Planck Length are not meaningful (according to some).

Without constraints on the properties of the parts, you can reach any answer your heart desires on te outcome of the question, just as the certain philosophers could in discussing their angels.

12. ### DRZionTheoretical ExperimentalistValued Senior Member

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Storing photons in this kind of device for even several minutes or even seconds could be very useful. One could use these as photon bombs that release all stored energy upon impact. Or, it could be a very high powered capacitor/battery for laser light. I know that in the new NIF fusion testing laser device most of the room is taken up by capacitors to hold the enormous amount of energy that is released in each pulse of the laser. An infinity sphere could perhaps be used to store some of this energy.

13. ### Billy TUse Sugar Cane Alcohol car FuelValued Senior Member

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I think that the problem does not require your level of details. There is an object trapped inside a sphere which when inside the sphere always travels in straight lines at the speed of light. We need not know more about it if we assume that it only interacts with a point on the surface of the sphere (not the “perfect” vacuum inside the sphere); however, we need to know the nature of this interaction, which has the following properties:

(1) Reflection without loss of energy or absorption - i.e. after the interaction is over, the object is again traveling within the sphere at the speed of light and still has the same energy as before wall reflection. If the object has a non-zero length, (as photons do) then the “head” (leading part in its direction of travel) begins the new (post reflection) direction of travel before the “tail” does. Thus, post reflection, the straight line of travel has changed and we need to tell how. Two cases have been suggested:

(2a) Specular reflection. Then the trajectory of the object is always in a plane containing the center of the sphere. I.e. the problem has been reduced to a 2D problem with the trajectory confined by a circle with each wall reflection having the approach and exit straight trajectory lines making the same angle with the radius line to the point of reflection.
(2b) Diffuse reflection. Now the object will eventually pass by any point inside the sphere with miss distance arbitrarily small and thus remains a 3D problem. The angle of approach and exit now usually differ with diffuse reflection. Diffuse reflection can be modeled as specular reflection for a “bumpy surface” (one with randomly located hills and valleys but very small compared to the radius of the sphere) I.e. the sphere is slightly imperfect. Usually the shape and size of these hills is taken to be such that a set of many randomly selected radius line approaches to the surface reflection points will result in a set of exit from the surface rays (or lines of travel) distributed as follows:

P = 1+ cos(e)
Where “e” is the angle the exiting ray makes with the object’s approaching travel line (which is one of the radius lines when the effect of shape and size of the hills is being defined). Note, e < 90 degrees is required. P is the un-normalized or relative probability of various exit directions. For example reflection back to the center of the sphere is twice as probable as nearly tangential to the surface reflection. Both are of course zero (0 = 2x0) so one compares a small range of variation in e such that the total solid angles are the same if one wants to measure the relative intensities. This particular formulae is often found to be representative of “diffuse reflection” for flat “rough” surface (such as aluminized fine sand paper) with normally incident light, so is often taken as the definition n of “diffuse reflection.”

Few if any posters have been concerned with the distribution of reflected rays in the diffuse case, so giving a common standard model for that is “over kill” but I do so as we are discussing what is needed to define the problem. If you still think the problem is ill defined, tell what is lacking. Note, however all agree that r =1 is an unachievable idealization, so real world properties of photons need not be considered in this idealized problem.

There has been some discussion of how the object (photon) got inside the sphere which I have contributed to. I suggested a small whole and noted some of the complexities that creates in the diffuse reflection wall case, if one then wants to know how many objects are inside the “sphere” when they are both enter and leaving at the same rate.

14. ### EnmosValued Senior Member

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What about a few lightmicroseconds of nano-tubes before the light enters a sphere with a reflective inner-coating ?

Last edited: Jun 11, 2009
15. ### Billy TUse Sugar Cane Alcohol car FuelValued Senior Member

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I do not understand your question. - Are you suggesting a multitude of very short U shaped nano-tubes covering the interior of the sphere's surface with the photon entering one open end and exiting the other? If so I think they would need to infinitely thin walled, hexagonal in cross section* and in contact. Please be a little more discriptive and I probably will give my opinion.

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*Not sure one can cover the surface of a sphere with regular hexaons, especially it they are U shaped tube end and all the same size. I.e. although r = 1 and perfect specular reflections are unachievable idealizations from reality, they are not self contradictory, but I stongly suspect U shapped nano tubes covering a sphere are self contradictory conceptually.

Also if U tube light pipes were in mutal contact, they would not function as light pipes. Optical fibers light pipes must have a non-absorbing, transparent, jacket outside the core, with lower index of refraction than the core to function. This is because total internal reflection occurs inside the optically denser of two contacting non absorbers. However, the E field of the photon does actually go into the outter jacket material but none remains there. I.e. the photon "samples" what is outside the core and "knows" the index of that material is lower so it returns.** These jackets would need to be infinitely thin if the hexagonal cores are to cover the spherical surface, but then their index of refraction is at best il defined, probably a nonsensical self contradiction.

**This is inaccurate, just my way, given my macro experiences, of speaking. Photons are not macro objects that fit easily into descriptive terms derived from my macro experiences. Photons do what photons do, and need not conform to my limited set of experiences with things like particles and waves. Many photons are much longer than most think of them as being - some are meters long*** when their energy is well defined. I have measured the length of some yellow (sodium D) lines. From the modest pressure lamp I was using they were about 30 cm long.

***When produced by isolated atom, the QM uncertainlty principle and the radiative decay lifetimes of their upper state to their lower state sets their length. Alternatively after they are "born" the length can also be viewed as a result of the Fourier analysis of the number of cycles required to define their frequency / energy. Well defined energy photons come from long lived excited state, have many cycles and are long physically to fit all the cycles in them. If many for same sorce are examined by high wavelength resolution instrument (like a Fabry Perot interferometer) their "spectral lines" are very narrow.

16. ### EnmosValued Senior Member

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No, I meant using nano-tubes to create a delay so that the light won't be able to 'leak' through the 'feeding hole'.

Edit: Ok, maybe I was a bit (very) sloppy in the wording. What I meant was using a sort of microscopic glass fiber (and very very long) to guide the photons to the sphere.

17. ### Billy TUse Sugar Cane Alcohol car FuelValued Senior Member

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That is an interesting idea, or at least when I expand it a little. At any location along the tube when light can go one way, the same wavelength can also go the other way, but because light travels more slowly in glass etc than air or vacuum it might, contrary to my initial expectations, be possible to make a "one-way" light valve.

A concentric metal tube with air between it and the axial light pipe could have a microwave propagating along it (and the axial light pipe fiber). Not glass (significantly) but some materials do have their in index of refraction and other optical properties changed by and electric field. Ideal would be a material that became opaque. Then one could imagine a long section of transparent light pipe with two moving opaque regions. If the opaque regions could be made to move with actual speed of the photons and photons were between these two opaque regions then the photons could continue to enter the sphere, yet photons trying to go the other way would encounter at least one of the traveling opaque regions.

This would not prevent the photons from leaving the sphere, only absorb those that do in the opaque regions. There is no light value possible that can let photons in but reflect or return those that try to escape. I am sure of this as if there were thermodynamic laws would be violated as one could grow infinite energy density inside the sphere.

18. ### PandaemoniValued Senior Member

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Before I start considering the rest of your post, this one intrigued me, in what sense do you feel photons have a length? I can conceive of a photon with a length but only under peculiar interpretations of models that I happen to use in my head, that I do not trust to be accurate models of "reality" when it comes to such a measurement. Do you mean to suggest the uncertainty about the current location of the actual photon?

Edit: A kindred spirit, in that regard: http://www.rp-photonics.com/spotlight_2008_05_05.html

Last edited: Jun 12, 2009
19. ### EnmosValued Senior Member

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Yes, but if you are able to make the tubes long enough you can put a hell of a lot of photons in there.

Now what would happen if you were to throw this sphere (with massive amounts of photons stored in it) to the ground, breaking it ?
Would you see a flash of light ?

What would be the maximum photon density (if there is a maximum) ? And what would happen if that maximum is reached ?

20. ### Billy TUse Sugar Cane Alcohol car FuelValued Senior Member

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There is a maximium photon content for any fixed rate of photon injection but it is not easy to calculate - See my comments in post 22.
When the max is achieved there would be a steady state with photons leaving at the same rate they enter. Not actually an equlibrium state but nearly that.
Yes the light would come out. If the walls were diffuse reflectors, approximately uniformaly in all directions. What happens with specular walls would depend upon the planes the photon were confined to be fore breaking and also the last refection off the now falling / bouncing pieces of the sphere.

21. ### EnmosValued Senior Member

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Ah yes, but that's not what I meant.
What is the maximum amount of photons that can occupy, for example, 1 cm[sup]3[/sup] ?

22. ### Billy TUse Sugar Cane Alcohol car FuelValued Senior Member

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If you mean that the photon is entirely inside a cube 1 cm on the edge, probably the answer is zero, as I do not think any photons are that short, at least optical or longer wave length photons are not. Possibly some gamma rays photons might fit inside a 1 cm cube.

Most photons, at least from gases,* have a well defined energy. This means that they are many cycles of an electromagnetic wave and because they travel so fast their is quite a separation between their "head" and "tail." To make short photons you need them to come from atoms that are experiencing many strong collisons during the period in which the photon is be generated. These collisions are dynamically changing the energy levels of the emitting atom. Thus the wavelength of the photon's "head" can differe significantly from the wavelength of it "tail." I.e. Its frequency and energy are not well defined so if Fourier analysis were done on this smear of wavelengths, it would not have a well defined frequency content or peak in the distribution. Such a "smear" can be the result of only a relative few cycles of a pure frequency but I do not know if the photon is actually short. If one measures its length by the technique I have used, one would think that it is short, but that may be more a flaw in the measurement technique used than the fact that the photon is actually short.

I will not go into details, but my technique used an interferometer with two different paths, one could be made longer than the other. As photons only interfer with themselves, when you make the difference in length of the two paths sufficiently large, the tail of the photon wave using the short path has already arrived at the screen before the head of that same photon using the longer path so there is no interference pattern. - This is one way to try to understand the faiding out of the interference pattern as the path difference of the intererometer is increased and leads to the idea you have measured the length of the photon. However an alternative interpretation is that the photon head and it tail are simply with different wavelengths so of course the interference pattern has faided away - you did not measure the length of the photon you only found the length in which it wave length changed significantly. Really neither POV is correct as human experience based discription or understanding of this "measurement." - Photons are photons, not objects describable in terms of human language that has developed to describe human experieces.

With either POV, I think that all optical or longer wavelength photons are much too long to fit entriely inside a cube only 1 cm on an edge so I will stick by my answer of zero.

*I know very little about the photons that come from hot solids. There are so many of them it is hard to isolate one and study it. We just know how the total energy is distributed.

Last edited by a moderator: Jun 13, 2009
23. ### EnmosValued Senior Member

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Huh ? I'm confused..
Light in the visible spectrum has wavelengths ranging from 380 nm to 750 nm.
I'm also pretty sure that a photon either doesn't have a size or that its size is way smaller than 1 cm.
Perhaps I just don't get what you are saying though..