Do all objects really have a de Broglie wavelength?

[Robert100]

When I was learning about gravity, I was taught that F = [G(m1)(m2)]/r^2, and that this equation was valid for r (the distance between mass 1 and mass 2) at all distance scales. However I now know better: Physicists today admit that we do not know that this relationship is true at all scales, and that it hasn't even been properly tested on any scales less than 1mm, or greater than 1 galaxy diameter. In fact a small but growing number of physicists now hold that the existence of dark matter is not a given, but only appears to exist if we assume that our understanding of gravitational force works the same on all scales. Hence new hypotheses such as MOND.

I always wondered if the same was true with matter having de Broglie wavelengths. As bizarre as this idea is, I accept the experimental results that matter, from the scale of electrons up to atoms, does have a fullerene wavelength. If I understand correctly, experiments have been carried out that demonstrate de Broglie wave diffraction of C60 fullerenes, which really blows my mind. (But my mind does not constrain reality!)

First question: Is it controversial that we are detecting wave like properties of a large molecule? Wouldn't that imply that "large" objects like molecules don't have any physical existence without an observation? Yet we exist, and we are made of molecules. What causes us to appear as classical objects when we are not being observed? Decoherence? (That would be an acceptable answer, IMO.) Or is anyone claiming that the results of this experiment have been misunderstood, and we are not seeing wavelike diffraction in C60 in the same way that electrons diffract?

In fact, does QM obligate us to believe that large objects (say, larger than a human cell) actually have any de Broglie wavelength at all? After all, many physicists are now holding that there may be fundamental limits on length, the Plack scale, and that space itself may be quantized. So if an object is massive enough to have a wavelength less than Plack scale, doesn't that imply that it may not have a de Broglie wavelength?

I add for clarification a discussion from Wikipedia, from the Wave-Particle Duality article. Any thoughts?

--- begin quote ---

In 1999, the diffraction of C60 fullerenes by researchers from the University of Vienna was reported1. Fullerenes are rather large and massive objects, having an atomic mass of about 720. The de Broglie wavelength is 2.5 picometers, whereas the diameter of the molecule is about 1 nanometer, i.e. about 400 times larger. As of 2005, this is the largest object for which quantum-mechanical wave-like properties have been directly observed. The interpretation of the experiment remains controversial because these experimenters have assumed the arguments of wave-particle duality and have assumed the validity of de Broglie's equation in their argument.

Whether objects heavier than the Planck mass (about the weight of a large bacterium) have a de Broglie wavelength is theoretically unclear and experimentally unreachable. The wavelength would be smaller than the Planck length, a scale at which current theories of physics may break down or need to be replaced by more general ones.

--- end quote ---

Thoughts?


Robert

 

[ZapperZ]

When I was learning about gravity, I was taught that F = [G(m1)(m2)]/r^2, and that this equation was valid for r (the distance between mass 1 and mass 2) at all distance scales. However I now know better: Physicists today admit that we do not know that this relationship is true at all scales, and that it hasn't even been properly tested on any scales less than 1mm, or greater than 1 galaxy diameter.

I'll just pick on ONE of such point that is VERY out of date. There are experimental results that have verified this at the MICRON scales[1,2]. This in addition to the earlier report from the U. of Washington group of sub-millimeter verification of the Newtonian gravitational laws (PRL 86 , 1418 (2001))There is also a good review of the progress in such measurement so far:

http://physicsweb.org/articles/world/18/4/6

So you really need to update your knowledge on this. And this is just ONE of the errors that I find just scanning your post rather quickly.

Zz.

[1] J. Chiaverini, et al., PRL v.90, p.151101 (2003).
[2] J.C. Long et al., Nature v.421, p.922 (2003)

 

[Robert100]

Zz writes:
> So you really need to update your knowledge on this. And this is just
> ONE of the errors that I find just scanning your post rather quickly.


Um, I didn't make any errors. I'm not proposing any new theories, and I am not offering any data. I'm only asking a question.

Sure, I didn't know that peer-reviewed, uncontested reliable sub millimeter measurements vis-a-vis the gravitational force had been made. But not knowing about this isn't a reason to insult me. (And by your answer I assume that these results you refer me to must be generally accepted as accurate.)

I notice that no one has yet tried to answer the question. Does this silence mean that the Wikipedia article is correct in stating that physicists have no idea whether or not macroscopic objects (larger than a cell, say) have a DeBroglie wavelength? I assume that if no one says otherwise, then the answer must be "Yes, most physicists would agree that this assertation may be correct."

I'm not debating or offering any theories: I am merely asking what the mainstream view on this issue is.

The idea that space may be quantized (in some way) on the Planck scale is now a mainstream, respectable idea. (Not proven, but a reasonable position to investigate.) As such, I am only asking if this implies that it is literally impossible to have such tiny de Broglie wavelengths? And if it isn't impossible, how do we reconcile this seeming dilemma?


Robert

 

[ZapperZ]

Zz writes:
> So you really need to update your knowledge on this. And this is just
> ONE of the errors that I find just scanning your post rather quickly.


Um, I didn't make any errors. I'm not proposing any new theories, and I am not offering any data. I'm only asking a question.

Sure, I didn't know that peer-reviewed, uncontested reliable sub millimeter measurements vis-a-vis the gravitational force had been made. But not knowing about this isn't a reason to insult me. (And by your answer I assume that these results you refer me to must be generally accepted as accurate.)

I didn't insult you. I contested your claim. It wasn't a question. This is what you said:

Physicists today admit that we do not know that this relationship is true at all scales, and that it hasn't even been properly tested on any scales less than 1mm, or greater than 1 galaxy diameter.

I didn't see any question there. If you had asked, you would have been given a number of citations on such experimental evidence. And it isn't just one, there have been at least 3 different experimental evidence done by different groups using different techniques. How much more convincing can you get?

Zz.

 

[Robert100]

> I didn't see any question there. If you had asked, you would have been
> given a number of citations on such experimental evidence. And it isn't
> just one, there have been at least 3 different experimental evidence
> done by different groups using different techniques. How much more
> convincing can you get?


I am sorry that I misinterpreted your reply. It's too easy to misinterpret text in the absence of face-to-face interaction.

However, I am not really asking about gravity; I was only using that as an example of things I was taught in the 80s that weren't tested at all length scales, and which are only now being more fully explored.

My real question is about the de Broglie wavelength of macroscopic objects: objects much larger than Buckyballs. I know that we can calculate the wavelength of a fast moving baseball, but since the calculated wavelength is less than Planck scale widths, what physical meaning does this wavelength have?

Since space may be quantized at Planck scale [* and then again, it may not. *], what would that imply about the wavelengths of macroscopic objects? Are they non-existent, and only appear in our calculations as a result of a limitation of our understanding of quantum mechanics?

Lord knows that QM is the most iron clad theory we've ever come across, but then again we simply can't do any direct measurements on Planck scale phenomenon.

Think about how tiny the "wavelength" of Earth itself is. Is there any discussion (in the mainstream physics community) of minimum size limits on this phenomenon? Smallest possible wavelengths?

Come to think of it, are there largest possible wavelengths? The size of the universe might be a practical size barrier. Might there exist fundamental limits on wavelengths on large scales as well?

Thanks for any ideas you may have,

Robert

 

[vanesch]

>
My real question is about the de Broglie wavelength of macroscopic objects: objects much larger than Buckyballs. I know that we can calculate the wavelength of a fast moving baseball, but since the calculated wavelength is less than Planck scale widths, what physical meaning does this wavelength have?

de Broglie wavelength is an approximate notion, which only makes sense for essentially single free particles ; the correct notion is the one of quantum state (and in said case of a single, free particle, those states can be analysed as a sum over plane harmonic waves, which each then have a wavelength, and that's the de Broglie wavelength). So the full, correct description of a system in quantum theory is through a "quantum state" which is an element (a ray in fact) in a Hilbert space.

So your actual question is: "does it make sense to assign a quantum state to a macroscopic object ?"

The answer to this question is in fact a matter of opinion and interpretation, and there are two main schools of thought over this: one school says "yes" and the other says "no". (I belong to the "yes" school, and there are many respectable physicists who belong to the "no" school ; in fact the founding fathers of quantum theory belonged to the "no" school ; it is only in the 50-ies and 60-ies that the "yes" school came into existence and is known as all the different variants on the "many worlds views" - but I'm SO tired to write this out here each time that I won't - which must be a relief to ZapperZ and a lot of other people ).

So pick your choice ! It doesn't change much - or anything - to the actual physics you can do. It's purely conceptual.

 

[Hans de Vries]

>
My real question is about the de Broglie wavelength of macroscopic objects: objects much larger than Buckyballs. I know that we can calculate the wavelength of a fast moving baseball, but since the calculated wavelength is less than Planck scale widths, what physical meaning does this wavelength have?

I'm from the "no" school. I do not believe in a deBroglie wavelength for
arbitrary large objects. The reason is, in my opinion, that this would
implicitly involve an intervention from the consciousness of the observer:
OK, a gedankenexperiment and a question: We use a very small golden
chain with 7 pieces for an interference experiment, how will the inter-
ference pattern look like:

1) The deBroglie wavelength is determined by the total mass of the
chain and this wavelength determines the interference pattern.

2) The seven pieces do not even need to touch each other during
the experiment. The pieces thus interfere individually and the fringe
pattern is 7 times wider.

3) The chain is actually two chains of 4 and 3 pieces each. We get
two different interference patterns 3 and 4 times wider.

4) All above patterns are possible plus all other permutations. It just
depends on the consciousness of the observer. Whatever the observer
defines as an object will have its deBrogle wave length according to
the mass of that object and will interfere as such.
Now, since I do not believe in interventions from the consciousness of
the observer I have a problem in believing in deBroglie wavelengths for
arbitrary large objects. I want to see some physical reason independent
of the observer.

Pretty complex objects like atomic nuclei show a very clear deBroglie
behavior if you shoot them into a thin metal foil and look at the defrac-
tion pattern. OK, now here we can indeed imagine a physical reason
that might group all sub-particles (quarks,gluons, hundreds of them)
together, for instance: The entire nucleus fits into the Compton radius
of each and every sub-particle.

I can't see such a physical reason for larger objects like buckyballs, let
alone a virus in a space-capsule as proposed for future Talbot-Lau
interference experiments. All claims made for large objects stem from
these Talbot-Lau experiments. Quite a while ago I spend some time
looking at this type of experiment and came to the conclusion that
they can not distinguish between interference patterns and simple
shadow patterns from a beam of particles. For more on this plus lots
of references:

https://www.physicsforums.com/showthread.php?t=42169Regards, Hans

 

[vanesch]

Hans,

what you write is an illustration of the fact that the concept of "de Broglie" wavelength is an approximation in the case of single particles in a state which is a monochromatic plane wave; for composed objects (or for more involved states of motion), one needs to work with a genuine quantum state.
Your chain which you can split up in different parts or not, should be described by a state in a tensor product of the 7 pieces, and exactly how it will behave will depend on what was the initial state, and exactly what's being done to them. So it is difficult to replace this by a single monochromatic wave to which one could give a de Broglie wavelength: the quantum state (if it exists) would be way more involved.

 

[Hans de Vries]

Your chain which you can split up in different parts or not, should be described by a state in a tensor product of the 7 pieces, and exactly how it will behave will depend on what was the initial state, and exactly what's being done to them.

The argument holds independent of different initial states. You can
prepare the thought experiment so that the pieces form a straight
line and have zero relative motion so they will stay in a straight line.
You're still left with the same choice of how to subdivide the chain.
(subdivide by pieces, or by smaller parts)Regards, Hans.

P.S: There's an interesting link to Galileo’s old experiment in Pisa to
show that the acceleration from gravity is independent of the mass of
the object. If heavier objects would fall faster, then the chain of 7
pieces would need to fall faster then it's individual pieces.

 

[reilly]

As long as we consider QM to be valid, then everything subject to QM's strictures has a deBroglie wavelength -- that's nothing more than saying the free particle wave function can be written as a superposition of plane waves, which, of course, are the waves of de Broglie. (Don't forget that for human-scale macroscopic objects, superposition is often not a problem, in the sense that the superimposed states are virtually identical-- even if there are millions of them. And, any way, we see averages, based on detection schemes that cannot get down to atomic dimensions, many molecular dimensions as well -- we do not see the molecular structure of air nor water.

Yes, it is formally quite reasonable to assign a deBroglie wavelength to the moon. But why bother? Using QM to compute the lunar orbit, is, if you will pardon the expression, sheer lunacy. But, it could be done. This kind of issue is not unfamiliar in nuclear and atomic physics, when dealing with heavy elements like uranium, for which some special techniques have been developed, like the Fermi_Thomas model or the liquid drop model.

As far as Hans de Vries's experiment: tell me what the initial condition is, what are the physical dimensions and masses involved and the dynamics of the chain elements -- can they exchange energy, does the chain have more than one energy state, is Wigner's Compound Nucleus approach valid? -- and what you are measuring?

You do this, and I'll tell you what to expect when you measure.

Regards,
Reilly Atkinson

 

[vanesch]

As long as we consider QM to be valid, then everything subject to QM's strictures has a deBroglie wavelength -- that's nothing more than saying the free particle wave function can be written as a superposition of plane waves, which, of course, are the waves of de Broglie.

Yes, but how do you assign ONE WAVELENGTH to a *superposition*, or to a compound system ? That was my point: de Broglie wavelengths correspond to monochromatic plane waves. Once the quantum state is more involved than this (because it is in a superposition of such waves, or because it is composed of subsystems), you cannot have ONE de Broglie wavelength, in fact, you have many of them in your quantum state.
And the original "contradiction" was derived from the fact that one could derive two ways of reasoning, which arrived at two different de Broglie wavelengths. But that's no surprise!

Imagine I mix a 1250Hz with a 1400Hz signal: what's the wavelength ? According to one reasoning, one might arrive at the one that corresponds to 1250Hz, and according to another, one might arrive at the one corresponding to 1400Hz, and then at their sum, or their difference, or whatever. But this, in itself, is not a contradiction.