Because the mirrors are not perfect reflectors. Every time a photon strikes the mirror, there is a chance it will be absorbed, rather than reflected. The result is that when you reopen the box there are no free photons left to come out as light.
The other theory, of light travelling in electromagnetic waves, presents a problem. The light's amplitude fades over distance and even though they can travel for immense distanced in a vacuum, they can not be completely kept. However, if you are talking about in a human lifetime, then they wouldn't lose their amplitude then, or even for millions of years. This is why we can still see stars, even galaxies on the other side of the universe today.
If you were looking to store the light in a mirror box solution, then you would have to diffract the light around, which wouldn't be easy as the gap would have to be shorter than the wavelength of the light itself. As the beams aren't naturally polarised, only a select few waves would diffract the first few hundred times, with less and less over time. A mirror could be used, but only 99% of the light is reflected back.
Due to this problem, it would be extremely difficult to store the raw light.
While I agree with the foregoing replies, I have a reservation. You can store light. It actually gets done in ceertain data storage devices, though I am not aware that any of them have been used commercially. They are versions of the technological strategy known as delay line storage. The trick is to send information-bearing beams of light down a suitable channel, typically by repeated reflection, then to capture them before they fade, and re-project them as long as needed. This stores the data for as long as required, though no one beam of light lasts longer than a small fraction of a millisecond.
But then you did ask about storage, not indefinite storage. For longer-term storage, consider optic fibres. It is now possible to store a beam in a fibre for several milliseconds. For light that is not bad going at all. It would be ungracious to complain about its shelf life. You don't say that we cannot store a drinkable cup of coffee, just because it goes off its best in less than an hour, do you?
If we can manage a suitably high refractive index in a clear medium, we could store light for much longer. Bob Shaw wrote some science fiction on that theme. He did a pretty creative job of it too.
Ah, but what does it mean to "store"? Presumably to keep in one location in space for an indefinite time. Photons, in their raw form, cannot exist without movement (from our perspective). A photon has no concept of time: while it may seen to us that it has traveled from the middle of the universe to us in 13B years, to the photon, it got there the instant it was created. From the photon's perspective, that vast distance is exactly zero meters, so of course it took zero time. From the photon's perspective, it was very well stored.
There have been successes in slowing light down, stopping it, and even getting it to move backwards, but this is traveling in a medium while the medium moves. (look up Dr. Lena Hau) I would not call this light in it's raw form
Your point has merit of course, but it is not really cogent. The semantics of the word "storage" are largely arbitrary, but I suggest that the most nearly essential attribute is that one begins with some entity and eventually recovers that entity.
Consider a tent for example: among many possible definitions we could call it a dwelling, in particular, a portable dwelling. So let's port it! First, we knock it down, fold it up, and in doing so reduce it to anything but a dwelling except possibly for a few enclosed cockroaches. When we reach our destination we unfold it and re-erect it.
Now, would you deny that we had stored the tent, on the grounds that during its storage it had not been a dwelling? I think that is rather special pleading.
In a delay line storage device a modulated beam of light is ideally not changed at all, either in frequency or in modulation. The fact that it is moving does not seem to me a persuasive argument for its not being stored. Certainly the data, the information, is stored, unless you have some argument to the effect that moving data is not stored data. Suit yourself on that point, but it is just possible that you might be in the minority in insisting on any such convention.
It certainly is true that stationary light is something of a contradiction in terms, much as warm ice would be. Where I come from, ice, on being warmed, turns into liquid and putting it into a glass to prepare say, whiskey on the rocks, would not satisfy most clients. Accordingly, although I could store the water content of ice, if I did not store the ice cold, I could hardly claim to have ice in store.
Similarly, although I could store either the data from a modulated beam of light, or its energy, or even both, permitting me to regenerate a reasonably equivalent facsimile, to claim that I was storing the light itself would be a rather peculiar argument if the light were not moving, any more than the ice would be ice if it were molten.
In short, I don't see why storing something in a mode that maintains appropriate aspects of its nature should not be called storage simply because it is not static.
But by all means, if this does not strike you as reasonable, please do not feel constrained to adopt my personal preferences.
Theres No Option to Post My Design of how to Tempoarily store light until it becomes vibrant. but I will tell you the Design.
Light Off Glass or a Crystal needs points that refect without Absorbing the the Photon first off, So Dark Reflector of anykind must mot be used.
Do this test, Get a Glass, Preferably an Semi Oval Glass, and Fill it with water to 1cm short from the brim. If you have a Spotlight then hold the Glass directly under it to a distance that the glare doesnt hurt your eyes....
Now Look under the bottom of the Oval Upwards towards the Brim. You will Notice that The Spot light itself doesnot pass the Brim due to the Thin Layer Slighly curving the Brim inwards. Now Look at the Bottom of the Handle where the base is, look through the base of the wine glass. You will see the Light From the Spot Light...
Design. You Need a Clear Sphere, wiih Dents like a Golf Ball On It. But The Flat Surface Inbetween needs to be covered with a Clear Refector, Not dark though, the Refector neeeds to be White.... And it needs to be a White mirror if there is such a Thing. The Dents need to remain Clear.... On the Parellel Opposite of a Dent in the Sphere the White Refector Must Be Present to Block The Beam Back Into the Sphere.
So the Spheres Design and the Dents would not be Exactly like a Gold ball as the Not One Dent on the Sphere should have a Dent on Its Opposite side.... Opposite each dent needs to be the White reflector surface....
In the Centre Of The Sphere there Needs to Be an Inverted Sphere, Which Means The Curves Of the Centre must Curve into the Centre... For example, You would need Nana Sized Dents In the Hollow Core Maybe Created by A Lazer. The Dents must move in the Same Direction and the dont need a Reflector surface in the Core. The Core Would be Small Also to Catch the Ray That Would be Created by one Beam, But Obviously There will be as Many Beams depending on the Dents Stucture on the Out Surface of the Sphere. I Believe the Sphere would need to be, 9.99mm and the Hollow Core be 0.99 mm also,
The Outer Dents will Vary Depending on what size the beam should be before it hits the Centre of the Sphere, The Dents in the Hollow Core should also Seperate the Outbeam into a Series of Smaller Beams. Even if some light Rays escape the Core the White Relecter Should already Repell them back. Not all the Nano Beans will Stay inside but a Good Percentage Will. Also note exposure to a Constant light Source will Gradually Increase the Vibrancy of light in the Core. Without the Source of Light Eventually The Light Will Escape Until a Better Model of the Sphere can be Designed. The More Vibrant the Light In the Core, The Bigger the Core will Look. Even though its the Light Source that Growing. This is How In the Beginning The Universe can Into Existance, Because a Void must exist at first before the Void Inverts into Energy. So The Core needs the Void in the Centre to Collapse the Nano Beams as they Pass Through it. although i dont know how much the beam will collaps before it slows down.
I thought for some reason The Core Could also Be Filled With Liquid Plamsa below - 100 and kept in a room of that Temperature, A Photon would Be Absorbed by the Plamsa and then Added to The Plasma. The Plamsa would become more Vibrant to a Point that It Grows outside of the Sphere, And Builds Up On It. Then Solid Light Would Surround The Sphere.
I know This Can Be Used for Quantum Dimention Designs, To Slow Down Quantum Particles in a Suspended state, Seen as Particles maintain there Stucture though Light. All You would need to do is Allow for A Partcle to Pass though Frozen Light And that Should Suspend The Particle. But If that Particle Is Connected to Multi Posistions in the Quantum World then It Could Alter Space Fabric on a Low Scale. Sometimes One Particle Is Invovled In Billions of Super States of The Quantum World and If Trapped From Being in Multi Positions then it will Also Suspend the Billions Of Super Positions it would be in. In some way Braking down the Quantum Dimention its One With. In a Way Freezinga Quantum Super Position is Like Freezing The Past and Future, And if you Pass Information From One Point In the Past or Future though a Superposition and You HAve That Frozon Superposition, all you would need to do if Recieve the Information passing through it. But Like I Said, Freezing a Superpostion from fuctioning in Billions Of States, Brakes down Reality. So Within Moments Of Recieving the Data Transfer within Nana Seconds, you need to Allow The Super Position to Fuction As Normal...
The Quantum idea, Can Be Down In Another Way without the Sphere, But The Sphere Idea Is About Suspening Light Into a Storage Mechanism.
I know Many Things in Relation, for I have also Tapped into a Quantum Consious State. In a way The Mind also Has Many Superpostions, but not easily Accessible in High Wave Forms Of Consiousness. The State Needs to Slow Down to A Point Of Nothing, Because when A Nothing State Occures, The Many Superpositions Leak into Nothing, Nothing Allows For More Possibilities.
I may Update this with The Designs, But for now Give this the Benefit of the Dought and Test it...