Honey, I Shrunk the Ferrari

Not many people know this, but my dad has a magical garage; it has a door on the front, and a door on the back, and these 2 doors can be opened or closed instantly (within zero seconds).
Since my parents are away and I’m extremely bored, this is how I wanna spend my afternoon:
My friend will open the front door of our 4 meter long garage, and I shall speed with my dad’s 4 meter long Ferrari into the open garage; as soon as the back of the car will go through the front door, my friend will close the door (for a split second the whole car will be trapped inside the closed garage) and then immediately open the back door allowing me to come out from the other side. Since me and my friend both have hyper-sharp reflexes, we should have no problems pulling this off and no explaining to do when my dad gets back home.

Do you know how can we complete this stunt with a 2 meter long garage (and the same 4 meter long Ferrari) without damaging the expensive paint job? Hint: Lorentz Factor. Extra kudos for explaining both points of view (my friend in the garage and me in the car).

* Actually, the truth is that my dad drives a modest Hyundai Accent and I don't live at my parents' house, but I think this riddle sounds cooler as an expensive teenage prank.

EDIT: I've posted the solution as a comment to this post.

p.s. It’s all about motivation; I say put Angelina Jolie on the fifth row, and Conway’s Soldiers will get there.


tzvook said...

this stuff was part of the 3rd physics class I took. It was the most interesting one, but I hardly passed it (which says a lot about the other 2...)

Nature Nut /JJ Loch said...

What a GREAT photo and post.


Cheers! JJ

Uri Kalish said...

OK, since it’s been a few days and no one posted any solution…

Yes. I can pull this stunt with a 4 meter long Ferrari and a 2 meter long garage; it comes down to speed.

The Theory of Relativity teaches us that a moving object will “appear” shorter to a “stationary” observer. I put quotes around the word “stationary” since there is nothing stationary in Einstein’s world; all the reference frames are moving in relative speeds to one another. I put quotes around the word “appear” since this is not just an optical illusion; the moving car really becomes shorter if measured by someone on another reference frame (i.e. not in the moving car), although the driver will not detect any change to the car’s length. As you can probably guess, the faster the car moves – the shorter it becomes.

One of the superstars of The Theory of Relativity is the Lorentz Factor which can help us out here figuring out the required speed in order to make an object half its length. The Lorentz Factor formula is 1/(sqrt(1-(v^2/c^2))), where c is the speed of light and v is the object’s speed. In this case The Lorentz Factor equals 2 when the speed is 0.866*c which is about 260,000 kilometers per second. So if I’ll drive a 4 meter long Ferrari at a speed of about 260,000 kilometers per second, I can fit into a 2 meter long garage. My friend in the garage will see a short Ferrari speeding into the garage; when it’s completely inside the garage, he will close the front door and open the back door. No harm’s done and no paint job needed.

But how can this be explained from my point of view? From my point of view in the car, the car is not moving so it’s still 4 meters long. To make things worse, it is the rest of the world (including the garage) which is moving towards me and therefore getting shorter. So in my reference frame, a 1 meter long garage (as I apply the Lorentz Factor to the length of the garage) is speeding towards my not moving 4 meter long Ferrari. The two points of view are obviously different, but the outcome must be the same. When my dad comes home, will he be mad or not? As it turns out, simultaneous events on one reference frame are not simultaneous on another frame. I would see the back door opens before the front door closes, and my car will go through without a problem.

So, to sum it up: From my friend’s point of view in the garage: The 2 meter long Ferrari enters the 2 meter long garage. He closes the front door and opens the back door allowing me to come out from the other side unharmed. From my point of view: The 1 meter long garage is speeding towards my 4 meter long Ferrari. The back door opens first, the car advances and only later the front door closes – again no harm to the car. Different stories, but just one harmless outcome; just don’t tell my dad!

notedscholar said...

There are other ways. You can have the garage door stop moving. And this wouldn't be cheating, because time is just motion.

Bet you didn't think of that loophole!


roentarre said...

This car is soooo cute and I prefer this one than Ferrari!!

Small, compact and easy to park !!

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kaden said...

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May said...

Nothing better than popular science! Keep it up!

MrNiceGuy said...

nice post you have... keep it up... i like the pic... cheer

Bruno R.Ramos said...

I liked the text so mush. The picture is a project to the future. little space to the people won't be problem...Hehehehe...

TatianaV said...

I so loved the photo and the solution to the riddle ;) But where have you gone for so long? Hope all is OK with you and family

Garg the Unzola said...

Your dad's magical garage has some pretty well oiled doors.

Quran Learning Classes said...

Nothing better than popular science! It's great picture. keep it up!

mihai said...

hi, i like your blog very much, and i like the way you explain in easy to understand terms such interesting things. i whould like to know however, regarding this post, if the necessary speed of the car is in km/s or m/s, because i know that "c" is in m/s. thank you very much for sharing all these things with us.

Uri Kalish said...

Thanks :)
The Lorentz Factor equals 2 when the speed is 0.866*c which is about 260,000 kilometers per second.
The speed of light can be specified in many units (km/s, m/s, cm/s, mm/s, etc.) - it doesn't matter - only the RATIO between your speed and the speed of light determines the amount of contraction in length.
Hope that was clear.