Superposition of large objects

[entropy1]

If a buckyball can be in superposition as a whole, why can't bigger objects like (the size of) a human body? Why are macro objects not in superposition (after the due operation)? Or are they?

I am not sure if this question has an official answer, but math to illustrate an answer is appreciated. (Or an article reference)

 

[anuttarasammyak]

Superposition has no restriction of size. However usually large objects tend to make quantum jump or undertake observations by environment, so its superposition state is fragile, I think.

 

[f95toli]

You might want to have a look at the various experiments on NEMS/MEMS resonators in the "quantum regime".

There is no upper limit for the size of an object. The "ideal" quantum system is not connected to its environment since any coupling causes decoherence.
In real-life we can isolate small things like ions extremely well which makes it "easy" to observe quantum effect in say an ion trap, but achieving enough isolation tends to get progressively harder as sizes increase.

This does not mean that it can't be done; some quantum effects can be seen in very large objects.
See recent results on the movement of the LIGO mirrors.
https://www.nature.com/articles/s41586-020-2420-8

 

[PeterDonis]

a buckyball can be in superposition as a whole

"Superposition" is not a good term since it is basis dependent. Please be more specific about what, exactly, you mean by "superposition"--what specific quantum state, or better yet, experimental procedure, do you have in mind?

 

[entropy1]

Please be more specific about what, exactly, you mean by "superposition"--what specific quantum state, or better yet, experimental procedure,

Ok. A quick search on Google suggests a buckyball can interfere with itself in a double split experiment.

 

[PeterDonis]

A quick search on Google suggests a buckyball can interfere with itself in a double split experiment.

So then your question would be, why can't we make a much larger object like a human body or a rock interfere with itself in a double slit experiment?

As far as actually trying the experiment is concerned, the answer is simple: in order to make anything interfere with itself in a double slit experiment, you have to maintain its quantum coherence--you have to be able to put it in a precisely controlled quantum state and design your experiment so it will stay in that state from the source to the detector. This is easy to do with light. It is reasonably easy to do with something like electrons. It is much harder to do with buckyballs, but possible--but take a look sometime at how carefully the experimental apparatus had to be controlled and what precautions they had to take (for example, cooling everything down to an extremely low temperature to avoid random thermal excitations messing things up).

It is impossible to do with a macroscopic object, now and for the foreseeable future, simply because there are so many, many orders of magnitude more degrees of freedom. A buckyball is still just 60 carbon atoms; at most it has a few hundred degrees of freedom. A macroscopic object like a human body or a rock has something like $10^{25}$ degrees of freedom. You would have to precisely control all of them to see quantum interference effects in an experiment with such an object, and that's just not possible.

 

[f95toli]

It is impossible to do with a macroscopic object, now and for the foreseeable future, simply because there are so many, many orders of magnitude more degrees of freedom.

Although I agree that it is unlikely that you would be able to do a double slit experiment with a large object I would like to point out that the experiments on nano- and micro-scale mechanical resonators I referred to above does involve putting a large (visible in an optical microscope, I would class them as macroscopic) object into a superposition of two different mechanical modes. Or, in other words, you have a drum (albeit small) that is producing two different "sounds at once".

There is an old (2011) Ted talk where the student (I believe) who carried out the first experiment describes this quite well for a general audience.

 

[vanhees71]

Sure, there are some demonstrations of quantum behaviour of very large objects. There's no strict physical limit for quantum behavior. As said already above, it's only pretty difficult to keep even not too large objects isolated enough from the environment to keep it in a sufficiently coherent state.

The experiment with the bucky balls by Zeilinger et al. demonstrated this nicely: If the buckyballs are cold enough such as that it's unlikely that they radiate off thermal photons, you could keep them coherent enough such as to demonstrate diffraction fringes when going through a double slit. As soon as they are at some temperature, where it becomes likely that just a few photons are radiated off from the bucky balls, the interference fringes are gone. That's a typical example of what Bohr called "complementarity". In this case the complementarity is between coherence of the wave packet and thus uncertainty about the buckyballs position vs. knowledge about their position on the way through the slits due to the irradiation of some photons. In the old-quantum theory language it's an example for "wave-particle dualism", but that's a bit misleading since the true description since 1925 is modern quantum theory.

 

[Halc]

Although I agree that it is unlikely that you would be able to do a double slit experiment with a large object I would like to point out that the experiments on nano- and micro-scale mechanical resonators I referred to above does involve putting a large (visible in an optical microscope, I would class them as macroscopic) object into a superposition of two different mechanical modes. Or, in other words, you have a drum (albeit small) that is producing two different "sounds at once".

They've done it to objects purported to be barely visible to the naked eye. Yes, it needs to be cooled to next to nothing to get the superposition state, often of vibrating and not, but of course not producing any sound. The state is demonstrated to last for a few nanoseconds. I'd like to know what sort of measurement is taken that demonstrates this superposition state (interference of some kind) as distinct from simply not knowing. Perhaps the Ted talk gets into that, but I hate getting my info from videos.

 

[akhmeteli]

It is impossible to do with a macroscopic object, now and for the foreseeable future, simply because there are so many, many orders of magnitude more degrees of freedom. A buckyball is still just 60 carbon atoms; at most it has a few hundred degrees of freedom. A macroscopic object like a human body or a rock has something like $10^{25}$ degrees of freedom. You would have to precisely control all of them to see quantum interference effects in an experiment with such an object, and that's just not possible.

This sounds strange. In Nature Physics volume 15, pages 1242–1245(2019), they show interference of molecules containing about 2000 atoms. I don't think they can control all degrees of freedom. In Nat Commun. 2011 Apr; 2: 263 they write: " We show that even complex systems, with more than 1,000 internal degrees of freedom, can be prepared in quantum states that are sufficiently well isolated from their environment to avoid decoherence and to show almost perfect coherence." So it looks like it is not a matter of control, but of isolation.

 

[PeterDonis]

So it looks like it is not a matter of control, but of isolation.

Isolation is what I mean by "control". The more degrees of freedom an object has, the harder it is to control everything that happens to the object in order to keep all of those degrees of freedom sufficiently isolated. For example, such experiments are typically done in vacuum chambers with opaque walls to avoid interactions with stray air molecules or photons.

In fact, the more degrees of freedom an object has, the more you have to worry about internal interactions between the degrees of freedom. This is why, for example, objects typically have to be cooled to a tiny fraction of a degree above absolute zero for quantum interference effects to be observable--so that internal excitations are frozen out.

 

[akhmeteli]

Isolation is what I mean by "control". The more degrees of freedom an object has, the harder it is to control everything that happens to the object in order to keep all of those degrees of freedom sufficiently isolated. For example, such experiments are typically done in vacuum chambers with opaque walls to avoid interactions with stray air molecules or photons.

In fact, the more degrees of freedom an object has, the more you have to worry about internal interactions between the degrees of freedom. This is why, for example, objects typically have to be cooled to a tiny fraction of a degree above absolute zero for quantum interference effects to be observable--so that internal excitations are frozen out.

In Nature Physics volume 15, pages 1242–1245(2019), they don't seem to cool anything at all. They say: "The delocalized molecules in our experiment are each roughly the mass of the green fluorescent protein25 (27 kDa) or a small BEC, while exceeding the temperature of a BEC by more than nine orders of magnitude. High-contrast quantum interference persists despite the thousands of excited vibrational levels and billions of structural and conformational isomers present in the molecular beam. This is because we probe the centre-of-mass motion, and can thus discount internal degrees of freedom as long as the internal temperature is kept at a level where thermal radiation does not provide which-path information18. With advances in beam sources for biomolecules and metal clusters26,27, techniques to cool the particles below 80 K (refs. 28,29), and refined grating26 and imaging technologies30, our experiment is scalable and will push matter-wave interference and macroscopicity tests by another order of magnitude24." (my emphasis)
In their experiment, the grating period is 266 nm, it means that the transferred momentum corresponds to a quantum with the energy of 4.66 eV, which is much greater than the room temperature.

 

[PeterDonis]

they don't seem to cool anything at all

Yes, but as they say:

we probe the centre-of-mass motion, and can thus discount internal degrees of freedom as long as the internal temperature is kept at a level where thermal radiation does not provide which-path information

I believe that the more internal degrees of freedom there are, the lower the temperature at which thermal radiation will provide which-path information.

Also, probing only the center of mass motion is a very limited form of quantum interference detection.

That's not to say these experiments aren't very interesting and worthwhile; they are. It's just good to be cautious about how much they demonstrate.

 

[akhmeteli]

I believe that the more internal degrees of freedom there are, the lower the temperature at which thermal radiation will provide which-path information.

Maybe so, but could you explain why? Their quote does not seem to suggest they worry about the number of dof. I would say it is mostly the mass that is important, not the number of dof (of course, the mass and the number of dof are related, but I don't feel the dof are directly relevant, as the results of two-slit interference do not seem to reveal the number of dof).

Also, probing only the center of mass motion is a very limited form of quantum interference detection.

Yes, but the OP explained, when you asked him/her, what kind of superposition he/she had in mind: " interfere with itself in a double split experiment. "

 

[PeterDonis]

Their quote does not seem to suggest they worry about the number of dof.

They don't say so, but that's because they are implicitly assuming that the number of internal degrees of freedom is small enough that they can get away with ignoring them. They certainly don't seem to be offering any kind of actual proof, or even plausibility argument, for that assumption, let alone an argument that it will continue to be valid for objects with many orders of magnitude more internal degrees of freedom.

the results of two-slit interference do not seem to reveal the number of dof

The results of two-slit interference measure just one degree of freedom (roughly, momentum in the "horizontal" direction with respect to the slits and the detector screen). So of course those results by themselves can't tell you anything about the total number of degrees of freedom present; the measurement is ignoring all other degrees of freedom besides the one it is measuring.

However, the fact that the measurement only measures one degree of freedom does not necessarily mean the other degrees of freedom have no effect at all on the results.

 

[akhmeteli]

They don't say so, but that's because they are implicitly assuming that the number of internal degrees of freedom is small enough that they can get away with ignoring them. They certainly don't seem to be offering any kind of actual proof, or even plausibility argument, for that assumption, let alone an argument that it will continue to be valid for objects with many orders of magnitude more internal degrees of freedom.

I don't see arguments for importance of the number of dof either.

The results of two-slit interference measure just one degree of freedom (roughly, momentum in the "horizontal" direction with respect to the slits and the detector screen). So of course those results by themselves can't tell you anything about the total number of degrees of freedom present; the measurement is ignoring all other degrees of freedom besides the one it is measuring.

However, the fact that the measurement only measures one degree of freedom does not necessarily mean the other degrees of freedom have no effect at all on the results.

But it seems to mean that quantum effects can be demonstrated in spite of roughly a hundred thousand dof.

 

[vanhees71]

They don't say so, but that's because they are implicitly assuming that the number of internal degrees of freedom is small enough that they can get away with ignoring them. They certainly don't seem to be offering any kind of actual proof, or even plausibility argument, for that assumption, let alone an argument that it will continue to be valid for objects with many orders of magnitude more internal degrees of freedom.
The results of two-slit interference measure just one degree of freedom (roughly, momentum in the "horizontal" direction with respect to the slits and the detector screen). So of course those results by themselves can't tell you anything about the total number of degrees of freedom present; the measurement is ignoring all other degrees of freedom besides the one it is measuring.

However, the fact that the measurement only measures one degree of freedom does not necessarily mean the other degrees of freedom have no effect at all on the results.

It's about the number of relevant degrees of freedom. The temperature has to be low enough such that not too many of the very many internal degrees of freedom like vibrations are relevant. E.g., it must be avoided to irradiate thermal photons which can provide "which-way information" to avoid decoherence.

It's also about the energy of the excitations. That's why, e.g., there are stable entangled states between the vibrational modes of macroscopic (mm-sized) diamonds at room temperature:

https://www.scientificamerican.com/article/room-temperature-entanglement/
https://science.sciencemag.org/content/334/6060/1253.abstract

 

[Stephen Tashi]

So then your question would be, why can't we make a much larger object like a human body or a rock interfere with itself in a double slit experiment?

Using a whimisical question to motivate a serious question:

If the each human body was a living human, each might know which slit it passed it passed through. Would these observations destroy the interference pattern - in a similar way to having an outside observer detect which slit a body went through?

In a more serious vein:

If the objects used in the double slit experiment undergo a change when they pass through the slits and the nature of that change is different depending on which slit they pass through, does this necessarily destroy the interference pattern?

 

[PeterDonis]

I don't see arguments for importance of the number of dof either.

See post #17 by @vanhees71. The more degrees of freedom there are, the higher the probability that more of them will be excited.

 

[PeterDonis]

If the objects used in the double slit experiment undergo a change when they pass through the slits and the nature of that change is different depending on which slit they pass through, does this necessarily destroy the interference pattern?

"Change" is too vague. You would need to be more specific.

 

[akhmeteli]

See post #17 by @vanhees71. The more degrees of freedom there are, the higher the probability that more of them will be excited.

What I see in #17 by @vanhees71 looks more like statements than arguments. Your quote above looks more interesting.

So we are now talking about the tails of Bose/Fermi/Maxwell-Boltzmann distributions. Yes, with 10^25 dof, a small part of them can be significantly excited, but one can expect that the probability of their de-excitation with energy transfer specifically into the center-of-mass velocity degrees of freedom may be small, ironically, because the number of dof is very high.

Let me also note that the rate of de-excitation would depend on the temperature relaxation rate. Maybe this is why the authors of the article I quoted mentioned "isolation".

 

[PeterDonis]

one can expect that the probability of their de-excitation with energy transfer specifically into the center-of-mass velocity degrees of freedom may be small

A likely mode of de-excitation of such degrees of freedom is into thermal interactions with the environment, such as emission of thermal radiation. Another possible outcome is transfer into another internal mode, but as long as the object is at a higher temperature than its environment, internal degrees of freedom will eventually de-excite into thermal interactions with the environment. (If the object is at a lower temperature than its environment, thermal interactions with the environment will excite internal degrees of freedom rather than de-excite them.)

The probability of de-excitation of an internal degree of freedom into the center-of-mass motion is zero, since it would violate conservation laws.

 

[akhmeteli]

A likely mode of de-excitation of such degrees of freedom is into thermal interactions with the environment, such as emission of thermal radiation.

We need to compare the characteristic time of such de-excitation with the pretty short time of flight. If the interfering object is isolated enough, there will be no de-excitation due to environment during the time of flight.

Another possible outcome is transfer into another internal mode, but as long as the object is at a higher temperature than its environment, internal degrees of freedom will eventually de-excite into thermal interactions with the environment. (If the object is at a lower temperature than its environment, thermal interactions with the environment will excite internal degrees of freedom rather than de-excite them.)

Again, we don't care about "eventually", we care about what happens during the time of flight.

The probability of de-excitation of an internal degree of freedom into the center-of-mass motion is zero, since it would violate conservation laws.

I am not sure, as the object interacts with the grating.

 

[PeterDonis]

We need to compare the characteristic time of such de-excitation with the pretty short time of flight.

Yes. Have you done the math to show that the time of flight is always much, much shorter than the characteristic time of thermal de-excitation, no matter how many internal degrees of freedom the object has? Or do you have a reference that gives such a demonstration?

the object interacts with the grating

That is an external interaction, not an internal one. External interactions can of course change the energy and momentum of the object, as long as the total energy and momentum of object plus whatever it is interacting with is conserved.

 

[akhmeteli]

Yes. Have you done the math to show that the time of flight is always much, much shorter than the characteristic time of thermal de-excitation, no matter how many internal degrees of freedom the object has? Or do you have a reference that gives such a demonstration?

No, I don't think I am going to do the mathematics or look for a reference. However, you made a statement about the importance of the number of dof, I asked for arguments, your arguments (and some of them are interesting) did not use mathematics or references, so my objections (or rather doubts) to your arguments were equally qualitative.

 

[PeterDonis]

I don't think I am going to do the mathematics or look for a reference.

Then we have probably taken this particular subthread as far as it can go.

 

[physika]

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If a buckyball can be in superposition as a whole, why can't bigger objects like (the size of) a human body? Why are macro objects not in superposition (after the due operation)? Or are they?

I am not sure if this question has an official answer, but math to illustrate an answer is appreciated. (Or an article reference)

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http://www.tequantum.eu/

"test of the quantum superposition principle on macroscopic objects to establish the ultimate bounds to the validity of the quantum framework"

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https://cordis.europa.eu/project/id/766900

"This roadmap will enable the test of quantum effects for systems whose mass is orders of magnitude larger than that employed in the most successful quantum experiments to date, thus closing the gap with the macroscopic world"

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