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Contents

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This demonstration is designed to explain Gardner's Paradox.

But first, what are all the sliders and labels for?

Press the RIGHT ARROW button below to continue throughout the lesson.

 O_g#(

The first thing you should do is adjust the slow motion dial until everything is moving at a speed you feel comfortable with.

Some computers are faster than others. This slider is here so you can make things faster on your computer.

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The slow motion dial goes from 4 to 100.

If you set it at 4, the photons go from point A to point B in 4 frames.

If you set it at 100, the photons go from point A to point B in 100 frames.

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When you move the Hidden Details slider up, this text fades out and exposes the "Behind-The-Looking-Glass" world.

Although there is really nothing behind the mirror, we can simulate the reflection most easily by

creating a virtual image behind it.

The circles are shown in the hidden details so that you can tell where each photon came from,

and realize that they are all moving at the same speed.

 <RN^#(

The velocity slider controls the velocity of the light emitter.

.99 times the speed of light is the fastest we go here.

 JS^#(

You may think that just one photon is emitted, but actually THREE photons are emitted.

The Angle slider adjusts the angle between them.

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Now bring the velocity and the Angle both down to zero.

You should see a blue A showing where the photon is emitted,

and a blue B showing where the photon reflects off the mirror.

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Now bring the velocity up a little.

You will see a two new symbols, a blue C, and a red A with a bar over it.

Let's call that symbol "ABar"

ABar shows the place on the Emitter Line where the photon "comes from" and where it "goes to" from the Emitter's perspective..

A and C shows where the photon "comes from" and "goes to" from our perspective.

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ABar and A are in the same place when the Photon shoots out!

ABar and C are in the same place when the Photon hits!

Does this seem like what should happen?

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Well yes, I think so.

The guy at the emitter certainly sees the photon come from the emitter and return to the emitter.

If we saw something different it would be very weird.

 !X#(

Now bring the velocity down to zero and bring the angle up.

Now you see points B1 and B2 where the photons strike the mirror

and points C1 and C2 where the photons come back to the Emitter Line.

The question is, when does the guy at the Emitter KNOW that the Emitter Line has been struck by

the photons at points C1 and C2?

 Ys#(

Any time we wanted, we could cover the mirror with a blanket,

so the photons wouldn't be reflected back to him.

Would he know this as soon as we stopped the photon at point B1?

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Did you say WRONG!! If so, good for you!

He has to wait until he receives the signal at point A!

The signal has to travel the complete circuit from A-->B1-->C1-->A

before he knows for sure we haven't blocked the photon.

This signal can't travel faster than the speed of light.

 ]y#(

Okay, now let's get to the complicated stuff.

Bring BOTH the Angle and the Velocity up so you can see point C1.

Now there are ELEVEN different labels on the screen!

(A, ABar), where lights are emitted,

(B, B1, B2), where lights strike the mirror

(C, C1, C1Bar, C2, C2Bar), where lights hit the Emitter Line

and D where the signals reach the Emitter.

!^p텀`9p 2'qXΈw8(VkcǍOAs you change the velocity, things look a lot different from our perspective, they still look the same to the guy at the Emitter. But lets look at the things that we see that are the same.

1. He sees photons strike at C1Bar, C2Bar. and ABar. We see the same thing.

2. He sees the signals strike him simultaneously at point ABar=D. We see the same thing.

3. Though not shown here, he sees the photons striking our mirrors at (B, B1, and B2). We see the same thing.

What do all of these three things have in common?

W`x $ Z'q_(Vky9"D0Vu[N(%VxyYf^C!xΈw'5CxµkWЪV…yむǕPFA vKK:!x&uK)5xw as#(

So, now, I'll explain Gardner's Paradox.

It involves the photon going from point A to B1 to C1 to D.

Gardner found that if the guy at the Emitter released a Photon

at an angle backwards

while moving forward,

an observer will see the light returning to the Emitter Line more quickly.

This agrees with the Theory of Special Relativity.

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