What are the implications of this experiment?

[Demystifier]

AFAIK, if Steinberg et al would have added calculated Bohmian photon trajectories for the experiment – that paper would have been a real blockbuster (and cover on various science magazines etc)...

Perhaps, but for those who understand WHY Bohmian trajectories are expected to coincide with weak trajectories, it wouldn't make much difference.

So what is it?

• Completely Impossible task
• Completely useless information – because die-hard believers already know the result
• Stupid question by ignorant laymen – there’s no relation at all between experiment and theory in this case
• Not worth the time because ignorant laymen wouldn’t understand it anyway

A combination of second and fourth answer:
- To specialists, it is already clear from equations written in the paper (or in the papers cited therein) that weak and Bohmian trajectories mathematically coincide (up to the experimental errors), so there is no point in showing Bohmian trajectories explicitly.

 

[Varon]

An explanation: http://scienceblogs.com/principles/2011/06/watching_photons_interfere_obs.php

As early as message #9 in page 1 of this thread, the website above shared by Truecrimson already explained clearly what seemed to be the case. Have we missed this? It states that:

"In the Bohmian picture, you take an average because you start with a distribution over all the possible starting positions and momenta, even though each particle follows a well-defined path at all times. In the more orthodox interpretations, you take an average because the final position and momentum that you measure is chosen from a rage of possible values determined from a probability distribution, and the only way to find probabilities is by taking averages."

Is this correct? Do all agree with it? If correct and true. It is all there is to it. And end of story.

 

[Ken G]

Do you think Steinberg's claim is false in some way?

I think weak measurement is fine, the problem is the concept of an "average trajectory." There doesn't seem to be anything quantum mechanical to me in that concept, I see it as a purely classical concept that is easily computed classically, so the fact that it can also be built up one photon at a time is a simple example of the correspondence principle and doesn't have anything particularly profound to say about the Bohm interpretation.

 

[Demystifier]

I think weak measurement is fine, the problem is the concept of an "average trajectory." There doesn't seem to be anything quantum mechanical to me in that concept, I see it as a purely classical concept that is easily computed classically, so the fact that it can also be built up one photon at a time is a simple example of the correspondence principle and doesn't have anything particularly profound to say about the Bohm interpretation.

So, are you saying that nonlocality appearing in calculation of trajectories for 2 or more particles is also purely classical?

(Simultaneous weak measurement of trajectories for many particles also yields Bohmian trajectories.)

 

[IllyaKuryakin]

I think weak measurement is fine, the problem is the concept of an "average trajectory." There doesn't seem to be anything quantum mechanical to me in that concept, I see it as a purely classical concept that is easily computed classically, so the fact that it can also be built up one photon at a time is a simple example of the correspondence principle and doesn't have anything particularly profound to say about the Bohm interpretation.

Well, it's interesting to think about. I haven't seen anyone produce the same average trajectories through classical means either, but that isn't a falsification. Since the experiment paper appeared in a reputable peer reviewed journal, I expect it's been carefully reviewed by specialists in the field and they would have considered alternate explanations.

On the question of what does this experiment prove? It seems to prove just what it claims to prove, that photons passing through a double slit have a measureable average trajectory, compatable with Bohmian predictions. I don't see that the author claims it proves anything more, so I can't really assume more or question Steinberg's claim. Under QM, it's possible, even probable, that some photons take a very different path from the average, but that isn't the subject of the experiment. It would make an interesting follow-up experiment.

 

[IllyaKuryakin]

True, I hope you saw my (painful ) 'withdrawal' in post #199...


AFAIK, if Steinberg et al would have added calculated Bohmian photon trajectories for the experiment – that paper would have been a real blockbuster (and cover on various science magazines etc)...

Or is it my ignorance? There is no way to make any use, and compare, average experimental trajectories with deterministic theoretical Bohmian trajectories??

Bohmian Mechanics provides all the information necessary to calculate these average trajectories. Given specific trajectory predictions of Bohmian Mechanics, the average trajectory is easily calculated. Of course, as many have pointed out to me here, it doesn't work the other way arround. I would have loved to see those average trajectories presented with the paper, but the reader is left to draw their own conclusions. Perhaps the author just didn't want to go that far in "choosing sides" in a very controversial subject.

 

[IllyaKuryakin]

No, that is not correct. There is nothing involving interactions of "one photon with another photon" in this experiment. The photons go through one at a time.

A classical "local" way to look at the experiment. In fact, the whole ensemble of photons are corrolated in a non-local (partially) hidden way, if you accept the Bohmian Mechanics explanation of the results.

 

[IllyaKuryakin]

They do not say it explicitly. Yet, in their theoretical derivation of trajectories they use only orthodox QM. But to see that, it's not enough to read what they say. You need to UNDERSTAND it. Or if your understanding of QM is not good enough, the best you can do is to trust someone else (not necessarily me, of course). In any case, it's up to you to choose what you will believe. For me it is better that more people believe that this experiment proves that Bohmian interpretation is right, because it makes my own professional research on Bohmian mechanics more relevant in the scientific community.

This is just incorrect. Nowhere in the cited papers do the authors claim the same average trajectories can be calculated via only using orthodox QM. In fact, the claim is quite the opposite, that the trajectories can be calculated by Bohmian Mechanics and it's variants that meet certain criteria. I agree, this is not about what you believe. It's about what the papers say. You are insistent on injecting something into the papers that is not there. If you can quote a section of the papers that specifically states that the same trajectories can be calculated using only orthodox QM, you can justify your belief. In that case, I'd have to say you are correct and I just missed it. But I've been through them twice now, and I don't see it?

 

[Ken G]

So, are you saying that nonlocality appearing in calculation of trajectories for 2 or more particles is also purely classical?

I don't know what you mean by nonlocality. You mean like the nonlocality in the streamlines of a sound wave flowing through a musical instrument, or are you talking about some kind of entanglement, of which there is none in this experiment?

I agree with you there is nothing fundamentally Bohmian going on here. I merely add that there is nothing fundamentally "quantum" going on here either, except in the way they have chosen to measure what is fundamentally a purely classical wave effect. Not only is this orthodox QM, it is orthodox wave mechanics.

 

[IllyaKuryakin]

This is just incorrect. Nowhere in the cited papers do the authors claim the same average trajectories can be calculated via only using orthodox QM. In fact, the claim is quite the opposite, that the trajectories can be calculated by Bohmian Mechanics and it's variants that meet certain criteria. I agree, this is not about what you believe. It's about what the papers say. You are insistent on injecting something into the papers that is not there. If you can quote a section of the papers that specifically states that the same trajectories can be calculated using only orthodox QM, you can justify your belief. In that case, I'd have to say you are correct and I just missed it. But I've been through them twice now, and I don't see it?

Let me say this another way. Much of the math of Bohmian Mechanics is identical to orthodox QM, but just because you recognize an identical treatemnt of schrodingers wave equation does not mean the authors are specifically saying that orthodox QM produces the same specific trajectory information that can be sampled through weak measurements to produce average trajectories. It's not a matter of beliefs, it's simply a matter of Bohmian Mechanics providing deterministic solutions that orthodox non-deterministic QM simply cannot. Of course you can say you don't believe that, but what is the specific basis of your belief?

 

[Ken G]

This experiment has nothing to do with Bohmian mechanics, except to say that it doesn't discredit it, and of course it couldn't without discrediting all of QM. Why do people want so badly to find evidence the universe is deterministic, when Bohmian mechanics does not increase anyone's predictive power? The real value of the trajectory concept, and this is exactly why it fails in QM, is that it is predictive in classical physics. Get over it people-- the Bohm picture is just a mental mnemonic you can use if you like to imagine the universe is deterministic. It's philosophy, not physics, though it dovetails perfectly well with physics, as does many-worlds, as does CI.

 

[Demystifier]

If you can quote a section of the papers that specifically states that the same trajectories can be calculated using only orthodox QM, you can justify your belief. In that case, I'd have to say you are correct and I just missed it. But I've been through them twice now, and I don't see it?

Fair enough!

See
http://xxx.lanl.gov/pdf/0808.3324v1

the top of page 5:
"(3) Bohmian mechanics and the variants referred to in (2) are empirically equivalent
to each other—and to standard quantum mechanics. In particular, for
all of them the result of a “weak measurement of velocity” is given by the
Aharonov-Albert-Vaidman formula given above, and hence by the formula for
velocity in Bohmian mechanics."

And later on the same page:
"However (3) is well established, and true."

 

[unusualname]

Ok, apparently the "trajectories" can be calculated by classical EM analysis, although it's only a qualitative match since the calculation is necessarily simplified:

The Interpretation of Diffraction and Interference in Terms of Energy Flow Prosser 1976 (pdf download)

The Ghose et al paper (Bohmian trajectories for photons) mentions this but says it is only a coincidence in the single photon case (!), but they also calculate two photon trajectories which should not admit to classical analysis.

So now someone needs to weakly measure the average trajectories for the two-photon case!

Back to the labs guys.

 

[Demystifier]

So now someone needs to weakly measure the average trajectories for the two-photon case!

Back to the labs guys.

Yes, that would really be a cool experiment.

Of course, theoreticians already know the result, but who cares what theoreticians say?

 

[Demystifier]

I don't know what you mean by nonlocality. You mean like the nonlocality in the streamlines of a sound wave flowing through a musical instrument, or are you talking about some kind of entanglement, of which there is none in this experiment?

I mean the later.

I agree with you there is nothing fundamentally Bohmian going on here. I merely add that there is nothing fundamentally "quantum" going on here either, except in the way they have chosen to measure what is fundamentally a purely classical wave effect. Not only is this orthodox QM, it is orthodox wave mechanics.

I could agree with you on the level of one particle case, which does not involve entanglement. But "genuinely quantum" effects appear when entanglement is present.

 

[Ken G]

Ok, apparently the "trajectories" can be calculated by classical EM analysis, although it's only a qualitative match since the calculation is necessarily simplified:

The Interpretation of Diffraction and Interference in Terms of Energy Flow Prosser 1976 (pdf download)

Thank you for finding that reference, I thought it was obvious! But that's not the same as being true.

The Ghose et al paper (Bohmian trajectories for photons) mentions this but says it is only a coincidence in the single photon case (!), but they also calculate two photon trajectories which should not admit to classical analysis.

What I see as the fundamental problem is that any time you are going to use a statistical aggregate, you are going to get a classical result, and if you want to employ "weak" measurement, how are you going to avoid using statistical aggregates? I think it will have to be something a lot more subtle than a figure with lines on it-- to be interesting, it will need to be some kind of Bell's inequality that deals with predictive power, not after-the-fact reconstructions.

 

[Ken G]

I could agree with you on the level of one particle case, which does not involve entanglement. But "genuinely quantum" effects appear when entanglement is present.

There is no entanglement in this thread.

 

[unusualname]

Thank you for finding that reference, I thought it was obvious! But that's not the same as being true.
What I see as the fundamental problem is that any time you are going to use a statistical aggregate, you are going to get a classical result, and if you want to employ "weak" measurement, how are you going to avoid using statistical aggregates? I think it will have to be something a lot more subtle than a figure with lines on it-- to be interesting, it will need to be some kind of Bell's inequality that deals with predictive power, not after-the-fact reconstructions.

Yes but there's no way you could calculate the two-photon "trajectories" by classical calculations, so in that case the only alternative to a dBB calculation would be what I expect is an extremely difficult and tedious one using standard quantum mechanics. If that were the case (it may not be) then dBB would at least have some claim to be a effective calculational tool, not just another interpretation.

 

[DevilsAvocado]

Perhaps, but for those who understand WHY Bohmian trajectories are expected to coincide with weak trajectories, it wouldn't make much difference.

A combination of second and fourth answer:
- To specialists, it is already clear from equations written in the paper (or in the papers cited therein) that weak and Bohmian trajectories mathematically coincide (up to the experimental errors), so there is no point in showing Bohmian trajectories explicitly.

You dBB guys need to book a meeting with some PR-guru... immediately!

Let’s pretend that Eddington decide not to publish the photograph of the 1919 solar eclipse, because he and Einstein already knew the result. What would have happened to relativity then?

My guess is that of course it would have been successful – but it would have taken much longer time!

 

[Ken G]

Yes but there's no way you could calculate the two-photon "trajectories" by classical calculations, so in that case the only alternative to a dBB calculation would be what I expect is an extremely difficult and tedious one using standard quantum mechanics. If that were the case (it may not be) then dBB would at least have some claim to be a effective calculational tool, not just another interpretation.

True, though I'm not clear on just what an "average two-particle trajectory" even means. If it involves statistical aggregations, it might indeed translate into some kind of classical correlation function. I guess I'd have to see just what kind of experiment is being discussed as a means of addressing a two-particle trajectory, and maybe there is some way that it could indeed support a Bohmian calculation that could not be done classically. Seems pretty hypothetical at the moment-- my own inclination would be to suspect that it is impossible to gain predictive power from a Bohmian calculation that you can't do classically (if it relates to average properties) or quantum mechanically (if it relates to quantum correlations).

 

[zenith8]

Yes but there's no way you could calculate the two-photon "trajectories" by classical calculations, so in that case the only alternative to a dBB calculation would be what I expect is an extremely difficult and tedious one using standard quantum mechanics. If that were the case (it may not be) then dBB would at least have some claim to be a effective calculational tool, not just another interpretation.

You dBB guys need to book a meeting with some PR-guru... immediately!

This http://www.tcm.phy.cam.ac.uk/~mdt26/raw_movie.gif" on Mike Towler's site is nice enough.. (wait for it to finish downloading, then everything will flow smoothly). It's the evolution of the deBB particle density for a single-particle in a box calculated directly from the trajectories of an ensemble.

Look at the little hurricanes where it is 'stirred' by the nodal points of the wave function. These mix things up to such an extent that an initial particle density not equal to the square of the wave function becomes so over the course of time and stays there - hence demonstrating why the Born rule is true. Well, I was impressed when I first saw it. Though I wish he would produce a double video showing the evolution of the wave function alongside it - with the two becoming more and more similar.

 

[DevilsAvocado]

Bohmian Mechanics provides all the information necessary to calculate these average trajectories. Given specific trajectory predictions of Bohmian Mechanics, the average trajectory is easily calculated.

And I’m almost shocked that this 'elementary' graph is not in the paper...

Of course, as many have pointed out to me here, it doesn't work the other way arround.

I don’t quite understand... "the other way around"...? If we put in the exact same setup into calculated Bohmian trajectories, we should get something very similar to the physical experiment, right?

 

[unusualname]

This http://www.tcm.phy.cam.ac.uk/~mdt26/raw_movie.gif" on Mike Towler's site is nice enough.. (wait for it to finish downloading, then everything will flow smoothly). It's the evolution of the deBB particle density for a single-particle in a box calculated directly from the trajectories of an ensemble.

Look at the little hurricanes where it is 'stirred' by the nodal points of the wave function. These mix things up to such an extent that an initial particle density not equal to the square of the wave function becomes so over the course of time and stays there - hence demonstrating why the Born rule is true. Well, I was impressed when I first saw it. Though I wish he would produce a double video showing the evolution of the wave function alongside it - with the two becoming more and more similar.

In deterministic dynamical systems it is not unusual to see a system evolve towards an invariant probability density, and for schrodinger evolution the invariant probability density is the square of psi.

 

[zenith8]

In deterministic dynamical systems it is not unusual to see a system evolve towards an invariant probability density, and for schrodinger evolution the invariant probability density is the square of psi.

Well, obviously. But it beats introducing the Born rule as a postulate doesn't it? (especially because they claim potentially-testable experimental consequences of allowing the particles to have a 'non-equilibrium' different probability distribution to the square of the wave function).

Anyway, that wasn't really my point. It's just a pretty video showing an average density from an ensemble of trajectories, in response to the request for Eddington-like PR...

 

[DevilsAvocado]

This http://www.tcm.phy.cam.ac.uk/~mdt26/raw_movie.gif" on Mike Towler's site is nice enough..

Thanks! :!)

 

[Varon]

Funny.

1) IllyaKuryakin is claiming only Bohmian Mechanics can explain the trajectories
2) Demystifier is claiming Quantum Mechanics is sufficient to explain the trajectories
3) Ken G is claiming that Classical Wave Mechanics is sufficient to explain the trajectories.

How many pages is the original paper "Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer"? I'm thinking if it's worth getting at $15. Is the paper full of equations or is there many descriptions that non-physicists could follow too?

 

[Ken G]

That does seem like an accurate summary of the situation. What's more, I would add that since I'm the one saying all three are the same, I feel the burden of proof is on anyone who claims they are not. Certainly we have three ways to make trajectory plots, and certainly they all attempt to say something physical about the average motions of the particles, so why wouldn't the default expectation be that they are all the same? And isn't the burden on the people who did the experiment and claimed to learn something new to establish just what is new about it, rather than give it to the popular media and let them run with it in all kinds of overblown directions?

 

[Varon]

That does seem like an accurate summary of the situation. What's more, I would add that since I'm the one saying all three are the same, I feel the burden of proof is on anyone who claims they are not. Certainly we have three ways to make trajectory plots, and certainly they all attempt to say something physical about the average motions of the particles, so why wouldn't the default expectation be that they are all the same? And isn't the burden on the people who did the experiment and claimed to learn something new to establish just what is new about it, rather than give it to the popular media and let them run with it in all kinds of overblown directions?

Something confused me about the Sacha Kocsis paper "Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer". It says:

"In our experiment, we sent an ensemble of single photons through a two-slit interferometer
and performed a weak measurement on each photon to gain a small amount of information about its momentum, followed by a strong measurement that postselects the subensemble of photons arriving at a particular position [see (22) for more details]. We used the polarization degree of freedom of the photons as a pointer that weakly couples to and measures the momentum of the photons. This weak momentum measurement does not appreciably disturb the system, and interference is still observed. The two measurements must be repeated on a large ensemble of particles in order to extract a useful amount of information about the system. From this set of measurements, we can determine the average momentum of the photons reaching any particular position in the image plane, and, by repeating this procedure in a series of planes, we can reconstruct trajectories over that range. In this sense, weak measurement finally allows us to speak about what happens to an ensemble of particles inside an interferometer."

Question. When the above says "performed a weak measurement on each photon to gain a small amount of information about its momentum". Is it talking of the photon in terms of particle, wave, or field?

Ken, in your view, you were saying that they just performed weak measurement on a portion of the wave and no particle is necessary. Is this what you meant? Pls. elaborate.

 

[Ken G]

Question. When the above says "performed a weak measurement on each photon to gain a small amount of information about its momentum". Is it talking of the photon in terms of particle, wave, or field?

A measurement is a measurement-- there is no need for any theoretical picture of the photon at all. Remember they sent photons through one at a time, so they were performing the measurement on individual photons. The measurement was a location, and a polarization. They then averaged together subpopulations of photons that ended up at the same place, to use the average polarization to get a kind of direction out of that photon ensemble. It sounds about as classical as classical gets, if you ask me.

Ken, in your view, you were saying that they just performed weak measurement on a portion of the wave and no particle is necessary. Is this what you meant?

They definitely performed their measurements on photons, not waves. Then they averaged a whole bunch of those measurements together. Adding up a whole bunch of quanta is exactly the classical limit of a wave. I feel they are stuck between a rock and a hard place-- a weak measurement doesn't tell them much of anything about a single photon, so they have to add up a whole bunch, but that doesn't tell them much of anything about a single photon either-- it tells them something about a wave, and you can get that information with classical wavelike measurements. This is the point: it's the same information, just obtained in a much more difficult way.

 

[DevilsAvocado]

Certainly we have three ways to make trajectory plots, and certainly they all attempt to say something physical about the average motions of the particles, so why wouldn't the default expectation be that they are all the same?

In some sense, I’m buying what you’re saying, but what has Classical Wave Mechanics to say about particles??

I mean, every kid can jump in the pool and create that interference pattern, or a professor playing with water in the lab:

https://www.youtube.com/watch?v=-8a61G8Hvi0

But not many kids know about http://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality" , and this is what it’s all about...

 

[vanhees71]

But not many kids know about http://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality" , and this is what it’s all about...

To say it friendly, the Wikipedia article on "wave-particle duality" is somewhat misleading. "Wave-particle duality" was a notion of the socalled "old quantum mechanics", which is full of such paradoxes and leads in almost all cases to wrong predictions. E.g., the Bohr-Sommerfeld model of the hydrogen atom by chance predicts the correct energy levels (using an ad hoc hypothesis on how to select the "allowed trajectories of the electron in phase space") but it totally fails to predict the shape of hydrogen atoms, which are in their ground state spheres, not little circular disks. Old quantum theory cannot explain atoms with one than more electrons without introducing new "rules". That's not what physicists call a fundamental theory.

For this reason, they were looking all the time since 1900 (when Planck discovered the law describing the black-body spectrum) for a fully selfconsistent theory, and this has been found by Heisenberg in 1925 and then worked out by Born, Jordan, Heisenberg, Pauli and many others. A bit later the same theory has been discovered independently by Schrödinger ("wave mechanics") and by Dirac (the most general form). This is what is today called "quantum theory", and there you don't need any "wave-particle dualism", but you have a general framework to describe the behavior of particles and fields. In a sense particles and fields are unified to one fundamental principle, called quantum fields.

Quantum theory makes only predictions about probabilities (Born's probability interpretation of the quantum theoretical states of a system). This has caused a lot of concern in the older generation of physicists like Einstein and Schrödinger (who even regretted to have found one manifestation of modern quantum theory because of the non-deterministic nature of the theory).

Since even today many people feel uneasy about an "uncertain world", a whole plethora of socalled interpretations has been invoked. However, all you need is the "minimal statistical interpretation" (with Ballentine as its prime advocate) to use quantum theory in everyday-physics work, i.e., to describe observations in nature, including all high-precision measurements done to check quantum theory.

This new hype about "trajectories of photons" measured in socalled weak measurements is a bit unjustified since the findings, while quite interesting, do not contradict quantum theory at all. What's called "trajectory" here is not that of a single photon but an average one for a large ensemble of photons. As massless particles with spin 1 there's not even a well-defined position observable at all! Thus, one can not find a limit where to interpret a photon as a quasiclassical particle.

 

[Demystifier]

There is no entanglement in this thread.

Now there is.

 

[Demystifier]

1) IllyaKuryakin is claiming only Bohmian Mechanics can explain the trajectories

I expect him to withdraw this claim when he sees my post #222.

2) Demystifier is claiming Quantum Mechanics is sufficient to explain the trajectories

Not only me. As can be seen in post #222, this is also said by certain well-recognized experts for Bohmian mechanics.

3) Ken G is claiming that Classical Wave Mechanics is sufficient to explain the trajectories.

As he gives no equations supporting his claims, his claims are not even wrong.

 

[Varon]

A measurement is a measurement-- there is no need for any theoretical picture of the photon at all. Remember they sent photons through one at a time, so they were performing the measurement on individual photons. The measurement was a location, and a polarization. They then averaged together subpopulations of photons that ended up at the same place, to use the average polarization to get a kind of direction out of that photon ensemble. It sounds about as classical as classical gets, if you ask me.

When you mention "classical". Does that include "photon"? Because Young proposed the wave nature of light.. it was Einstein who proposed the photon and here it was no longer classical.

They definitely performed their measurements on photons, not waves.

This is very important. If they indeed performed measurements on photons and it is between emitter and detector. Then it is already Bohmian in spirit! Because in Copenhagen.. what happens between emission and detection is close door or invalid. So if a photon is indeed detected. Then it's no longer Copenhagen even if position is not well defined like full blood Bohmian pilot wave and particle ontology!

Then they averaged a whole bunch of those measurements together. Adding up a whole bunch of quanta is exactly the classical limit of a wave. I feel they are stuck between a rock and a hard place-- a weak measurement doesn't tell them much of anything about a single photon, so they have to add up a whole bunch, but that doesn't tell them much of anything about a single photon either-- it tells them something about a wave, and you can get that information with classical wavelike measurements. This is the point: it's the same information, just obtained in a much more difficult way.

 

[Varon]

I expect him to withdraw this claim when he sees my post #222.


Not only me. As can be seen in post #222, this is also said by certain well-recognized experts for Bohmian mechanics.


As he gives no equations supporting his claims, his claims are not even wrong.

I wonder if the following is the case.

1. The experiment satisfies Standard Quantum Mechanics.
2. But the experiment doesn't satisfy Copenhagen (which in its purest form is about
having no trajectory of any kind even for ensembles)
3. But Modern Standard QM already embedded Copenhagen and Bohmian in the Trajectory
4. Hence the experiment satisfies Standard Quantum Mechanics but not Copenhagen.

Which part do you agree and don't.
I wonder which part IllyaKuryakin agrees and doesn't.
It's possible we are all having some semantic mismatch in the agreements.