a cloaking device

In a vacuum the speed of light is exactly 299,792,458 meters per second.  It is also constant in a vacuum so it can be used as a length - stars are multiple light years away, the moon is about one and a quarter light seconds out, and if you're six feet tall it takes light about six billionths of a second to travel your length.¹  It travels more slowly when moving through matter, but for most materials the speed is also constant if somewhat lower.   

 

Jheri wrote and asked for a simple explanation of some recent physics that was interesting, but didn't require a deep physics background.  So this one is for Jheri - let's build something that may seem impossible on first blush and let's only use the fact that the speed of light is constant.  Let's build a cloaking device.

 

In the past year or so there have been a number of exotic schemes that use nano materials to make temporal cloaking devices.  Some have been built, but explaining them without some serious physics is very difficult.  But it turns out you can build a cloaking device with mirrors and it is easy to explain.  The only physics you have to worry about is that light travels at a constant speed.  You'll need four very flat mirrors and four special mirrors than can quickly change from being a mirror to a transparent window.  You'll need a light source, an object to illuminate and something to view the scene with - your eye or a camera for example.

 

There are a few impractical issues, but we're just after the basic physics.  Physicists go into a play mode with an idealized apparatus that only occurs in thought and is usually called a gedanken experiment (gedanke is German for thought).  

 

Here is a sketch of the apparatus we'll be using.²  

 

 

The mirrors A, D, E and H are very flat and can be quickly switched from being a mirror to a transparent pane.  Mirrors B, C, F and G are just very flat normal mirrors.  The odd shape in the center is an object that will be cloaked - perhaps a very valuable diamond.  

 

If the switching mirrors were set to transparent light would travel from the light source on the left through A and D, illuminating the diamond and then passing through E and H to the observer.   Just what an unwitting observer might expect...

 

but we'll be a bit more clever.

 

The mirrors are set at 45° angles and the path length for A, B, C and D is the same as that of E, F, G and H. 

 

We'll consider two interesting paths.  

 

path I  Mirrors A and D are set to transparent and E and H are set to mirror  The light path from the source to the observer is A, D, diamond, E, F, G, H.  It is longer than the simple "straight through" path where all of the switching mirrors are transparent, but the observer doesn't know.

path II  Now switch A and D to mirror and E and H to transparent.  The path is now A, B, C, D, diamond, E, H.  The path length is exactly the same as that of path I and the observer can't distinguish between the two.

 

OK - now for some fun.  I recommend pencil and paper at this point so you can sketch out what is happening.

 

Start with the apparatus set up as path I.  Now let's start the cloak.

 

° switch mirror A to its reflective state.  As this is a gedanken experiment it happens instantly.  A bit of light is traveling from A towards D, but the light immediately after the switch is now traveling towards B.  

° when the little bit of light traveling towards D has gone through D, switch it to its reflective state

you have now created a gap equal to the time it takes light to go on path ABCD minus the time it would take to directly go from A to D.  As time advances a segment of light is traveling from D to the diamond, but it suddenly stops - the light that should have followed it is on the ABCD circuit.  

When the gap reaches the diamond you have the duration ABCD-AD to do something with the diamond in total darkness (no light would make it to the observer) - for example you could remove it.  If the path ABCD was long - say AD was very short compared to ABCD, but AB was very long (put mirrors B and C on the moon for example) - you would have a long window to work with.

° Light continues to move along the ABCD path and as it leaves D and illuminates the diamond (or where the diamond was:-), the cloaking period has ended.  Now E and H are set to their transparent state.

° The light passes through E and H and then to the observer. From the observer's point of view there is always light - we've just played with its path.

 

Now imagine putting a clock in place of the diamond.  Let's say the ABCD-AD light path time is very long - five minutes.  If you were watching the cloak and started the cloak at 5:00 PM the clock would suddenly jump from 5:00 PM to 5:05 for the observer.  If you want to get fancy, think about how you might reset the device as a more challenging case.³   (update - August 15 ...  Jheri solved the reset case and posted her solution as a comment.  Don't look at the comments if you want the challenge.) 

 

Simple in concept, but it pays to draw the light paths for each of the steps to sort out what is going on.  And, although this is a gedanken experiment, there are very fast switching mirrors and you can perform the experiment in the real world.  There are some tricks to match intensities as mirrors aren't perfect and switching mirrors double so, but these are do-able details ...  at least on a small scale.

 

 

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¹ The meter is defined as 1/299792458 of a light second in a vacuum, so with refined measurements of the speed of light we get the meter to better precision too. 

Colleen is very tall at 2.00 meters.  People constantly are asking for her height, so for variety she can tell them she's six and two thirds of a nanosecond tall ...  at least in a vacuum or in our atmosphere...

² Based on an idea from Miguel Lerma.  Very elegant.  The physics existed to have worked this out over 110 years ago, but no one thought about cloaking devices using mirrors until recently.

 ³ hint: you have to combine two beams for awhile... this means you need some way to deal with the intensity change and possible interference if you use a laser.

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Recipe Corner

 

This is based on a recipe by David Lebovitz.  I had to make a vegan ice cream and it was great.  For extra richness you could replace 1/2 cup or thereabouts of coconut milk with heavy cream.

 

Vegan Avocado Ice Cream

Ingredients

 

° 2 ripe Haas avocados

° 1-1/2 cans (about 600g) coconut milk (full fat)  (or 1 can coconut milk and 125g heavy cream for dairy friendly folks)

° 100g white cane sugar

° 1/2 tsp vanilla extract (rum should work too)

° pinch of finely ground sea salt

° squeeze of fresh lime juice

 

Technique

 

° Scoop out the avocado  put it in a food processor

° Add coconut milk, sugar, vanilla, salt, lime juice and puree until completely smooth. Chill in a refrigerator for at least four hour

° churn freeze

 

Comments

[Jheri]

So clear Steve!

This sounds impractical. How big could you make it and what would you use it for? Is it possible to change network communications by using delays and switches, or would you notice slow clocks that are set on other paths?

[Jheri]

I think I figured out the reset!

It is starting with mirrors A and D reflecting and E and H transmitting.

To reset turn A transparent. For the length of the obscurity gap light going from A to D will combine with the light that is taking the ABCD path. I don't see any way around the double brightness.

When the light from the ABCD path leaves D, turn D to transparent.

For the time the double intense light is striking E, E must be half transmission and half reflection. I don't see any other way to make this reset work without this halfway state. Does this make sense? I thought about it for a long time:-) Half of the split light travels EFGH and the other half goes from E to H.

As the double light finishes striking E, turn E to full reflection and in the time it takes light to go from E to H, H is turned to full reflection.

My head is spinning:) Does this work? Is there any way to do it without the mirror being half and half transmission? Let me know and I will celebrate with a treat:-)

[steve]

Outstanding Jheri - you nailed it!

I didn't mention the fact that you need one of the mirrors to be a beamsplitter (half transmission and half reflection), but figured it out. I'm impressed! The next time we get together I'll buy you the pint of gelato at L'Arte del Gelato .. what you normally have:-) In the meantime you have cause for celebration. This is a bit tricky.

As to your earlier comment. Yes - you can do this with any form of communication where the speed of light - or an electric signal - is constant. It would be easier in the case you mention, but perhaps not as visually dramatic.

[Jean Russell]

Unfortunately the mirror of G and C are observable unless they are also cloaked. If they are cloaked, than their version of G and C are visible to the observer looking in their direction instead of toward the light source. I forget the math for calculating the angle opposite GH, but that would define the limitation to the view of the observer. We can add appropriate blinders in the thought experiment and restrict the observer from turner her head. Also, to cloak (make invisible) the diamond or clock, wouldn't C and F have to become transparent, making the light path ABGH?

[steve]

There are a two types of cloaks - one cloaks objects and the other events. This is a temporal cloak (thanks to Jean for pointing out the confusion!).

You may or may not be able to see the mirrors, but the point is the observer is looking at the object that is being illuminated by the light source. The apparatus can insert a cloaking time that can't be detected without observing and understanding the apparatus. To the observer looking on the source-A-D-object-E-H path the cloak is a true cloak. It is just a gedanken experiment:-)

Consider the periscopes AB and CD -- together they are just a periscope pair. In a gedanken experiment the mirrors can be perfect. Assume that A and D can switch to transparent. There is no way an observer can determine if the light path is ABCD or AD unless some sort of travel time experiment can be conducted. The only light available is traveling along the path. The mirrors, by themselves, are invisible as no external light is provided. But even if they were visible the observer couldn't determine the path without some extra information.