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According to the De Broglie hypothesis, wavelength equals to h/mv(m-mass, v-velocity, h-Planck constant), so by moving at a slow speed, that is reducing the v(velocity factor) can human beings with such high masses(m) have a wavelength that is long enough to interfere?

alst
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1 Answers1

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If we assume that the human body can be treated as a single particle at the centre of mass, then we can tackle this problem. Optimal diffraction occurs when the wavelength is equal to the size of the aperture.

The average male shoulder width is .465m, so we can take the width of the aperture to be $.5$m. This would give a wavelength of $.5$m. So, $\lambda=0.5=\frac{h}{mv}$

The average male body weight is 81.9kg, which we can take as 80kg. Then, using $h=6.626 \times 10^{-34}$, we get:

$v=\frac{h}{m\lambda}=\frac{6.626 \times 10^{-34}}{40}$

This gives a velocity of $1.6565 \times 10^{-35}$ metres per second. If we then take a door to be $.3$m deep, it would take you $1.8 \times 10^{34}$ seconds, or $5.7 \times 10^{26}$ years. That's pretty slow.

Of course, all of this assumes that we could take the human body as a single particle - which we can't.

Noah P
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  • http://physics.stackexchange.com/questions/57390/validity-of-naively-computing-the-de-broglie-wavelength-of-a-macroscopic-object But this explains that the de Broglie wavelength formula is valid to a non-fundamental (many body) object. – alst Sep 01 '16 at 07:47
  • If you look at John Rennie's answer, it states that all the particles are required to be coherent. Considering the complexity of the human body, and all the fluids, and the fact that it's almost impossible for a bullet, then the formula is not valid for a human. Though, if it were, then I have given the times involved. – Noah P Sep 01 '16 at 08:14
  • So is that means David Bar Moshe's answer is wrong? – alst Sep 01 '16 at 08:20
  • No, but it requires all the particles to be coherent, which would not be possible. – Noah P Sep 01 '16 at 08:25
  • I've read John Rennie's answer, he also said that we can prepare a bullet in a coherent state in principle, what does this mean? Can a human be in coherent state in principle too? – alst Sep 01 '16 at 09:07
  • @alst You clearly didn't read it all - He also states that the bullet would immediately reduce to an incoherent state, and that the upper limit for the size of an object would be comparable to the size of a buckyball. – Noah P Sep 01 '16 at 09:19
  • Actually... I read it all. He also mentioned it's the interactions with environment causes incoherent, so I guess we can suppose the people in a coherent state is in a universe without anything else. But I don't understand why there is a upper limit? – alst Sep 01 '16 at 09:33
  • It's the upper limit for a system that can remain in a coherent state, with environmental influences – Noah P Sep 01 '16 at 09:39
  • But why can't we make something bigger to remain it in a coherent state? – alst Sep 01 '16 at 10:06
  • Only small objects exhibit quantum behaviour – Noah P Sep 01 '16 at 10:08
  • Maybe I didn't say it clearly, John Rennie said we can prepare a bullet in a coherent state,in principle, so that means we can make every particle of the bullet be in coherent state. Then he mentioned there is a upper limit, so I want to know since we can make a macroscopic object coherent, why its size can influence this? – alst Sep 01 '16 at 10:34
  • Because larger objects do not exhibit quantum behaviour – Noah P Sep 01 '16 at 10:35
  • Let us continue this discussion in chat. – Noah P Sep 01 '16 at 10:35