Vanishing Pencil: Math/Physics Mystery from High School Teacher

[chasrob]

This is a math/physics question, although it concerns an SF story I’m working on, so I thought I’d post it here.

Years ago, my high school physics teacher related this--concerning (if I remember correctly) “random motions--quantum fluctuations or brownian motions "or something similar. He said “Take an ordinary box with a removable lid. Ok, take a pencil (not a chicken) and put it in the box and close the lid. Then, open the lid and observe the pencil.

“After you open and see the pencil a sufficient, gargantuan number of times, you will open the box and viola, the pencil will be gone.” If I recall, he said what the approximate number of times was, or a lower bound number of openings. Which now I forget.

Anyone hear of such a thing? Is it similar in magnitude to 10^(10^33), the odds against a beer can spontaneously tipping over, according to Richard Crandall*, "The Challenge of Large Numbers", in a Scientific American. Or 10^(10^42), what mathematician John Littlewood of Cambridge calculated as the probability of a mouse surviving on the surface of the sun for a period of one week? In other words, something like a googolplex?

*Richard E. Crandall received his Ph.D. in physics from the Massachusetts Institute of Technology.

 

[PeroK]

“After you open and see the pencil a sufficient, gargantuan number of times, you will open the box and viola, the pencil will be gone.”

It's nonsense, IMO. Ironically, QM explains why the box and the pencil are solid. The implication of your teacher's remarks is that in solid, reliable classical mechanics it's all nice and sensible and pencils stay in boxes and in weirdo QM, pencils can spontaneously disappear out of boxes.

The reality is that the experiment will fail on a calculable basis for mundane reasons. For example, you'll think you've put the pencil in the box, but have carelessly dropped it. If you do the experiment enough times, then eventually the pencil will not be in the box, but not because of QM, but because of experimental error on your part.

Note that a viola is a stringed musical instrument larger than a violin. Voilà is the word you're looking for.

 

[PeroK]

Anyone hear of such a thing? Is it similar in magnitude to 10^(10^33), the odds against a beer can spontaneously tipping over, according to Richard Crandall, "The Challenge of Large Numbers", in a Scientific American.

Beer cans tip over all the time. How would you know it's spontaneous? And, if you watch it long enough, it biodegrades (in a calculable timescale). It's 80-100 years for an aluminium can. That's science. Watching a beer can until it spontaneously tips over due to "quantum fluctuations" is garbage, IMO.

 

[chasrob]

It's nonsense, IMO. Ironically, QM explains why the box and the pencil are solid. The implication of your teacher's remarks is that in solid, reliable classical mechanics it's all nice and sensible and pencils stay in boxes and in weirdo QM, pencils can spontaneously disappear out of boxes.

The reality is that the experiment will fail on a calculable basis for mundane reasons. For example, you'll think you've put the pencil in the box, but have carelessly dropped it. If you do the experiment enough times, then eventually the pencil will not be in the box, but not because of QM, but because of experimental error on your part.

Note that a viola is a stringed musical instrument larger than a violin. Voilà is the word you're looking for.

 

[chasrob]

Just a l’accent aigu difference? Did not know that.

 

[PeroK]

Just a l’accent aigu difference? Did not know that.

Different spelling. Viola/voila.

 

[chasrob]

Different spelling. Viola/voila.

My bad.

 

[chasrob]

... For example, you'll think you've put the pencil in the box, but have carelessly dropped it.

You don't touch the pencil, you just open the lid, see--yeah it's there, close the lid, repeat.

 

[PeroK]

You don't touch the pencil, you just open the lid, see/observe, close the lid, repeat.

The box will wear away and decompose long before the pencil vanishes through quantum fluctations. You could calculate that scientifically - how long a wooden box would last if it is repeatedly opened.

You'll be long dead, the Earth and Sun gone and the universe will have suffered a heat death long before anything remotely strange will happen to the pencil.

 

[chasrob]

I don't understand. Because the box will never last long enough, that falsifies the premise?

 

[Nik_2213]

Should you, with a merely human life-time, open box and find it empty, I'd suggest searching where your cat usually leaves play-things...

Yes, we have 'Poltercats': If neither stuck down nor in a clip-locked lunch-box, consider it moved...

 

[chasrob]

That's science as well, eh?

 

[Nik_2213]

IMHO, cats embody one of the many corollaries to Murphy's Implacable Law...

 

[chasrob]

Computing these probabilities must be a complex affair, e.g., what is the probability that sometime in your life you will suddenly find yourself standing on planet Mars, reassembled and at least momentarily alive? Making sweeping assumptions about the reassembly of living matter, Dr. Crandall estimated the odds against this event to be 10^(10^51) to 1!

 

[Hornbein]

This is a math/physics question, although it concerns an SF story I’m working on, so I thought I’d post it here.

Years ago, my high school physics teacher related this--concerning (if I remember correctly) “random motions--quantum fluctuations or brownian motions "or something similar. He said “Take an ordinary box with a removable lid. Ok, take a pencil (not a chicken) and put it in the box and close the lid. Then, open the lid and observe the pencil.

“After you open and see the pencil a sufficient, gargantuan number of times, you will open the box and viola, the pencil will be gone.” If I recall, he said what the approximate number of times was, or a lower bound number of openings. Which now I forget.

Anyone hear of such a thing? Is it similar in magnitude to 10^(10^33), the odds against a beer can spontaneously tipping over, according to Richard Crandall*, "The Challenge of Large Numbers", in a Scientific American. Or 10^(10^42), what mathematician John Littlewood of Cambridge calculated as the probability of a mouse surviving on the surface of the sun for a period of one week? In other words, something like a googolplex?

*Richard E. Crandall received his Ph.D. in physics from the Massachusetts Institute of Technology.

Yes.

 

[PeroK]

I don't understand. Because the box will never last long enough, that falsifies the premise?

Experimentally, yes. More fundamentally, predicting and measuring the decay of an object is science. Ignoring entirely what happens in an experiment and hypothesising some bizarre outcome is fantasy.

For example, if you try to push your hand through a wall, then gradually you'll wear the wall away. That's what happens. Eventually, your hand will go through the wall because the wall has been sufficiently worn away and not because of the "random quantum fluctations".

Also, why would these random quantum fluctuations apply to the pencil as a whole? Why would we either see the pencil as it is or nothing? Why wouldn't just a little bit of the pencil disappear? Why wouldn't the pencil spontaneously split in two? Transmute into a column of ants? Start dancing on its point?

 

[pinball1970]

You don't touch the pencil, you just open the lid, see--yeah it's there, close the lid, repeat.

Got it, give the pencil a quantum eraser.