How to diffract a bowling ball

[Ivan Seeking]

This is a distant cousin to my question about the wave function of atoms in a solid. If I were to construct some apparatus that allows me to cool a bowling ball to near absolute zero, and to then cause the ball to roll through a doorway at a speed of say 10^-35 meters per second, then, since the low temp reduces atomic motion in the ball, and since the ball's speed yields a DeBroglie wavelength of macroscopic proportions, about a meter, will the ball diffract when as passes through the doorway? [?]

 

[MrCaN]

No, because it is rolling, and making contact with the ground.

 

[Ivan Seeking]

Originally posted by MrCaN
No, because it is rolling, and making contact with the ground.

Speaking in a purely theoretical sense of course, we could set this experiment up in space and give the ball a quantum sized nudge. Then all that we have to do is to wait about 10^34 years and the ball should diffract as it passes through an appropriately sized aperture. No?

 

[jeff]

Originally posted by Ivan Seeking
This is a distant cousin to my question about the wave function of atoms in a solid. If I were to construct some apparatus that allows me to cool a bowling ball to near absolute zero, and to then cause the ball to roll through a doorway at a speed of say 10^-35 meters per second, then, since the low temp reduces atomic motion in the ball, and since the ball's speed yields a DeBroglie wavelength of macroscopic proportions, about a meter, will the ball diffract when as passes through the doorway? [?]

Whether quantum theory is needed to predict the behaviour of a physical system depends not only on the debroglie wavelengths h/mv (by 'h' I mean h/2pi, i.e. h-bar) of the various objects involved, but on their size and the size of the intervals of time or distance over which the system is allowed to evolve before measurement. All of this information is captured in a mathematical quantity called the "action" of the system, and it's size relative to h - they both have units of angular momentum - determines whether classical theory is sufficient (this is why h is often referred to as the "quantum of action"). In the case of a non-relativistic point-particle of mass m moving at speed v(t) and allowed to travel over some time interval T, the action is basically the kinetic energy of the particle integrated over the time interval T and is thus of order mv^2T (where v can be viewed as some sort of average speed). So even if h/mv is large, unless mv^2T is of order h or smaller, you'll observe no quantum effects. If instead of a point-particle we have some extended object, the geometrical distribution of mass throughout it must be accounted for which means it's size enters the fray increasing the size of the action and requiring T be even smaller to produce non-classical behaviour.

 

[MrCaN]

Talking purely theoreticaly, you could diffract any object through a door way with the correct speed.

 

[MrCaN]

And as a side note, DeBroglie got his doctorite, by writing a paper less than a page long, predicting the difraction of objects, without ever even attempting to prove it. Unfair I say.

 

[Ivan Seeking]

Originally posted by steinitz
Whether quantum theory is needed to predict the behaviour of a physical system depends not only on the debroglie wavelengths h/mv (by 'h' I mean h/2pi, i.e. h-bar) of the various objects involved, but on their size and the size of the intervals of time or distance over which the system is allowed to evolve before measurement. All of this information is captured in a mathematical quantity called the "action" of the system, and it's size relative to h - they both have units of angular momentum - determines whether classical theory is sufficient (this is why h is often referred to as the "quantum of action"). In the case of a non-relativistic point-particle of mass m moving at speed v(t) and allowed to travel over some time interval T, the action is basically the kinetic energy of the particle integrated over the time interval T and is thus of order mv^2T (where v can be viewed as some sort of average speed). So even if h/mv is large, unless mv^2T is of order h or smaller, you'll observe no quantum effects. If instead of a point-particle we have some extended object, the geometrical distribution of mass throughout it must be accounted for which means it's size enters the fray increasing the size of the action and requiring T be even smaller to produce non-classical behaviour.

You seem to allow but also ignore the v->0 condition. Am I missing something? Does something fundamentally limit our smallest v? Do you and MrCan disagree or is my theoretical condition too broad somehow. Also, thanks for the enlightenment. This question has bugged me for years.

Edit: I realize that mv^2T goes as mv^S/v, where S is the path length of the ball over the interval T. However, in order to get to the root of my question, do we actually have to run the experiment over the entire length of the ball's diameter? One question that comes to mind for me is: When and how does the ball diffract? What force acts to change the ball's direction? When does this force act; as soon as one atom of the ball moves into the aperature, or when the ball is completely through the aperature? If we can even start to cause action on the ball, don't we have a paradox? Somehow we seem to avoid this problem with photons and other quantum sized objects, but this example seems to drive the "paradox" of diffraction to the core. Insights? [?]

 

[Ivan Seeking]

Originally posted by MrCaN
Talking purely theoreticaly, you could diffract any object through a door way with the correct speed.

Do you and steinitz disagree or am I missing something?

Edit: Also, I knew a radiation physicist in Los Angeles who actually received a Ph.D. based on one paper done shortly after he graduated. It seems that no one has previously studied the effects of cables and other topological considerations on the output of a medical/diagnostic type X-Ray tube. He did such a good job that he was awarded his doctorate based solely on this paper.

 

[jeff]

Originally posted by Ivan Seeking
You seem to allow but also ignore the v->0 condition. I realize that mv^2T goes as mv^S/v, where S is the path length of the ball over the interval T.

I think your question may in part stem from my failure to more clearly distinguish between action and debroglie wavelength, and my attempt to finesse the subject of path-integrals (by describing v in the expression mv^2T not simply as the average speed but as "some sort of" average speed). So...

Reflecting the fact that they have zero debroglie frequency, bodies at rest produce no diffraction patterns for the obvious reason that they don't pass through gratings. Of course the point at which they're resting will be unknown.

On the other hand, the probability of a non-relativistic point-particle being measured to have position x at t=0 and x' at t=T may be given in terms of a path-integral which is a sort of action-weighted sum over all possible paths beginning at x and ending at x' and thus over the speeds v(t) of the particle along these paths. Notice that the need to integrate over a range of values of v(t) is by the uncertainty principle a result of determining the positions of the particle at x and x'.

Because in the path-integral v(t) is not fixed - and in particular may approach arbitrarily small values - the characteristic size of the action is determined by the fixed values of m and T (and in the case of extended bodies, they're size as well) and not by v(t). In particular - and this is the point - the "average speed" v in mv^2T is a somewhat misleading (appologies) fiction introduced for pedagogical reasons.

Originally posted by Ivan Seeking
However, in order to get to the root of my question, do we actually have to run the experiment over the entire length of the ball's diameter? One question that comes to mind for me is: When and how does the ball diffract? What force acts to change the ball's direction? When does this force act; as soon as one atom of the ball moves into the aperature, or when the ball is completely through the aperature? If we can even start to cause action on the ball, don't we have a paradox? Somehow we seem to avoid this problem with photons and other quantum sized objects, but this example seems to drive the "paradox" of diffraction to the core. Insights?

Given that your question is one of principle, I think it suffices to say that the quantum signatures produced by bodies of finite size will in general reflect the geometry of their spatial extension in complicated ways that depend on the details of the experiments performed.

 

[MrCaN]

I guess I'm missing the point, the limit on v is zero, or not moving, if it is moving, even the slightest, then it is considered moving.

Note: Yes PHd's are given for work done, i.e. a paper based on research, or experiments, but De'Brolie basicly had a paper 1 sentence long, that wasn't backed up by researc or experiments, due to, his own reasoning, lack of ability.

 

[HallsofIvy]

MrCan "And as a side note, DeBroglie got his doctorite, by writing a paper less than a page long, predicting the difraction of objects, without ever even attempting to prove it. Unfair I say"

Not only unfair, untrue: the published version had 106 pages=

"Research on the quantum theory, Faculty of Science of Paris, 1924, Thesis of doctorate supported in Paris on November 25, 1924 (Annals of Physics, l0-2nd series, { \bf III }, 1925, p. 22-128; German translation, Akademische Verlagsgesellschaft, Leipzig, 1927)."

I haven't seen the original copy of of the doctoral dissertation but most dissertations get cut sharply before they are published in a journal.

Also MrCaN: "Also, I knew a radiation physicist in Los Angeles who actually received a Ph.D. based on one paper done shortly after he graduated."

MrCaN cleverly didn't give the name so no one can check up on this. I started to say that any reputable University includes a minimum amount of course work and tests as well as a dissertation but that is "reputable" (and MrCaN also didn't give the name of the university). Recently I received an e-mail offering a doctorate based on just sending them a check. (and a list of "life experiences" for which they would give credit but I suspect it is the check that is important!) They did say it was from a "well-known unaccredited university"!

 

[Ivan Seeking]

Originally posted by HallsofIvy
MrCaN: "Also, I knew a radiation physicist in Los Angeles who actually received a Ph.D. based on one paper done shortly after he graduated."

MrCaN cleverly didn't give the name so no one can check up on this. I started to say that any reputable University includes a minimum amount of course work and tests as well as a dissertation but that is "reputable" (and MrCaN also didn't give the name of the university). Recently I received an e-mail offering a doctorate based on just sending them a check. (and a list of "life experiences" for which they would give credit but I suspect it is the check that is important!) They did say it was from a "well-known unaccredited university"!

Actually that was me. This person was someone that I worked with in Los Angeles...I don't normally give out private names on the net. I can only say for sure that he was employed and well known as having a Ph.D. in radiation physics. I also knew him personally and this is what he told me. I don't know for a fact that this is true, but, knowing Tim, I never even considered that he would lie. Of course this could be possible [that he lied] but I really doubt it.

Edit: I guess I'm OK to tell you that the university was UCLA.

 

[MrCaN]

Originally posted by HallsofIvy

Also MrCaN: "Also, I knew a radiation physicist in Los Angeles who actually received a Ph.D. based on one paper done shortly after he graduated."

MrCaN cleverly didn't give the name so no one can check up on this. I started to say that any reputable University includes a minimum amount of course work and tests as well as a dissertation but that is "reputable" (and MrCaN also didn't give the name of the university). Recently I received an e-mail offering a doctorate based on just sending them a check. (and a list of "life experiences" for which they would give credit but I suspect it is the check that is important!) They did say it was from a "well-known unaccredited university"!

Yes it is true, I didn't give his name, or the University he attended, of course I also didn't say that, so that is probably the reason that I didn't give that information, but thanks for think of me when you quote other people.

Originally posted by HallsofIvy

I like to wear lady's underwear.

Hey, that's your poragitive. Have a good day.

 

[eNtRopY]

That's kind of a cool game... completely fabricating a quote from nowhere.

Originally posted by MrCaN
I fvcked my uncle last night.

 

[MrCaN]

Originally posted by eNtRopY
That's kind of a cool game... but my ass hurts after words

hehe good one

 

[eNtRopY]

Seriously, a theoretical bowling ball could in diffract through a perfectly rigid door way providing the doorway was narrower than the bowling ball and the bowling ball was very cold.

Another fun question to ask is, "could a theoretical rabbit diffract through a fence with evenly spaced rungs?"

eNtRopY

 

[jeff]

Originally posted by eNtRopY Seriously, a theoretical bowling ball could in diffract through a perfectly rigid door way providing the doorway was narrower than the bowling ball and the bowling ball was very cold.

As I've already explained, the bowling ball is to big to diffract. Also, causality precludes perfectly rigid objects.

 

[Ivan Seeking]

Originally posted by jeff
As I've already explained, the bowling ball is to big to diffract. [and from earlier]Given that your question is one of principle, I think it suffices to say that the quantum signatures produced by bodies of finite size will in general reflect the geometry of their spatial extension in complicated ways that depend on the details of the experiments performed

So, again it sound like nature taunts us with implicit paradoxes that can never be observed? I hate it when that happens. I think god invented physics just to toy with my head.

Also, causality precludes perfectly rigid objects.

How? This is an extremely interesting statement.

 

[Ivan Seeking]

Originally posted by eNtRopY
Seriously, a theoretical bowling ball could in diffract through a perfectly rigid door way providing the doorway was narrower than the bowling ball and the bowling ball was very cold.

Another fun question to ask is, "could a theoretical rabbit diffract through a fence with evenly spaced rungs?"

eNtRopY

I used to really worry about this when walking slowly through a forest on a cold day.

Also, the answer is that no. Even under idealized circumstances, Jeff has explained why this experiment would never work. But, even if it could, the width of the doorway would need to be about equal to the wavelength of the ball; not smaller than the ball.