What if the Bohmian model turned out to be correct?

[Ken G]

Can you summarize that essence, with the intention of interesting me (or others) in it enough to go look it up and dig deeper?

 

[akhmeteli]

Even if you are not saying it, from your interpretation it follows that pair creation without field interactions is possible.

Not really, for the simple reason that, as I said, there are always field interactions, even if they are somewhat hidden in one-particle theories.

Therefore, the predictions resulting from your interpretation are necessarily different from those of the conventional information, without regard whether you say this or not.

Not really, because there can be no predictions of the conventional interpretation (I guess that's what you meant?) for the case of the absence of field interactions - again, for the simple reason that there are always field interactions.

... your interpretation, just like mine, can, in principle, be distinguished from the conventional interpretation.

It may be so, but I am not aware of any convincing specific arguments.

 

[akhmeteli]

But you must agree that measurement involves a (unitary) change of the wave function, so the trajectories must be different from those without the measurement.

Whether I must agree with that or not, I fail to see what this is supposed to prove. If you believe this proves that the predictions of BI and CI differ in the relativistic case, I just cannot imagine how your argument can prove that, as the argument is, on the face of it, equally correct or wrong both for the relativistic and the nonrelativistic case, and I believe you agree that in the nonrelativistic case the predictions of BI and CI coincide.

Are you familiar with the theory of quantum measurements in Bohmian mechanics? Do you understand how an effective wave function collapse takes place due to interaction with the measuring apparatus? If not, then you do not understand the essence of BM.

No offence, but my knowledge or lack thereof is irrelevant, unless you believe I wrote something terribly wrong because of my ignorance. If you do believe that, could you please indicate what it is? So far you just said that my interpretation, while also logical, predicts something different from what CI does (I don't exactly disagree, but neither do I see reasons to agree) and does not appeal to you (and this is a matter of opinion, not of me being ignorant or knowledgeable). Again, all I'm saying is your arguments fail to convince me, and I tried to explain why.

 

[Demystifier]

Can you summarize that essence, with the intention of interesting me (or others) in it enough to go look it up and dig deeper?

I have presented a short review in the Appendix of
http://xxx.lanl.gov/abs/quant-ph/0208185 [Found.Phys.Lett. 17 (2004) 363]
For more details see also the references cited at the beginning of this Appendix.

 

[Demystifier]

Whether I must agree with that or not, I fail to see what this is supposed to prove.

It is supposed to explain why the dotted trajectories are ignored, or better to say, why they are modified by the position measurement, in a manner that forbids them to join the dashed trajectories. As it is essential, I will not comment other points until we clear this up.

 

[Demystifier]

Not really, for the simple reason that, as I said, there are always field interactions, even if they are somewhat hidden in one-particle theories.

The predictions that depend on the value of the interaction constant cannot be the same as those that do not depend on it. I do not see how the interaction (except the mass and wavefunction renormalization that cannot explain particle creation) could be "hidden" in one-particle theories. Do you?

 

[Schrodinger's Dog]

http://arxiv.org/abs/quant-ph/0303156

S. Goldstein, working with D. Dürr, R. Tumulka, and physicist N. Zanghi of the University of Genoa in Italy.

http://arxiv.org/abs/0707.3487

W. Struyve and H. Westman.

2 recent papers on Bohm interpretation.

This may also be of interest.

http://arxiv.org/abs/hep-th/0610032

A. Valentini

Here's a brief excerpt from the article that set me to thinking about Bohmian mechanics. Like I said at the start I'm not convinced like many people but it did get me to looking into this model.

http://www.newscientist.com/article/mg19726485.700-quantum-randomness-may-not-be-random.html"

Quantum randomness may not be random

AT ITS deepest level, nature is random and unpredictable. That, most physicists would say, is the unavoidable lesson of quantum theory. Try to track the location of an electron and you'll find only a probability that it is here or there. Measure the spin of an atom and all you get is a 50:50 chance that it is up or down. Watch a photon hit a glass plate and it will either pass through or be reflected, but it's impossible to know which without measuring it.

Where does this randomness come from? Before quantum theory, physicists could believe in determinism, the idea of a world unfolding with precise mathematical certainty. Since then, however, the weird probabilistic behaviour of the quantum world has rudely intruded, and the mainstream view is that this uncertainty is a fundamental feature of everything from alpha particles to Z bosons. Indeed, most quantum researchers celebrate the notion that pure chance lies at the foundations of the universe.

Until now, that is. A series of recent papers show that the idea of a deterministic and objective universe is alive and kicking. At the very least, the notion that quantum theory put the nail in the coffin of determinism has been wildly overstated, says physicist Sheldon Goldstein of Rutgers University in New Jersey. He and a cadre of like-minded physicists have been pursuing an alternative quantum theory known as Bohmian mechanics, in which particles follow precise trajectories or paths through space and time, and the future is perfectly predictable from the past. "It's a reformulation of quantum theory that is not at all congenial to supposedly deep quantum philosophy," says Goldstein. "It's precise and objective - and deterministic."

If these researchers can convince their peers, most of whom remain sceptical, it would be a big step towards rebuilding the universe as Einstein wanted, one in which "God does not play dice". It could also trigger a search for evidence of physics beyond quantum theory, paving the way for a better and more intuitive theory of how the universe works. Nearly a century after the discovery of quantum weirdness, it seems determinism may be back.

 

[Demystifier]

Here's a brief excerpt from the article that set me to thinking about Bohmian mechanics. Like I said at the start I'm not convinced like may people but it did get me to looking into this model.

http://www.newscientist.com/article/mg19726485.700-quantum-randomness-may-not-be-random.html"

A larger part of this paper recently published in New Scientist is copied here:
http://www.groupsrv.com/science/post-2760759.html

 

[Schrodinger's Dog]

A larger part of this paper recently published in New Scientist is copied here:
http://www.groupsrv.com/science/post-2760759.html

Hehe that neatly avoids the legal complications by passing the buck. Thanks Demystifier.

 

[akhmeteli]

It is supposed to explain why the dotted trajectories are ignored, or better to say, why they are modified by the position measurement, in a manner that forbids them to join the dashed trajectories. As it is essential, I will not comment other points until we clear this up.

Now that you mentioned the dashed trajectories, I understand that I mixed up the dotted and the dashed trajectories, saying that "I am not enthusuastic about "ignoring the dotted trajectories" in your paper." I should have said that "I am not enthusuastic about the phrase "The dashed one is unphysical because it is assumed that only one particle exists" in your paper." I do apologize for this mix-up. However, this does not mean that now I find the arguments convincing. Specifically, I am not ready to accept the assumption that one-particle relativistic quantum equations, such as the Klein-Gordon equation, describe just one particle (however natural and even tautological that assumption may look, on the face of it), as I believe that travel-back-in-time trajectories describe pair creation.
Also, I am not sure that it is important whether the dotted lines join the dashed lines after measurement.

 

[akhmeteli]

The predictions that depend on the value of the interaction constant cannot be the same as those that do not depend on it. I do not see how the interaction (except the mass and wavefunction renormalization that cannot explain particle creation) could be "hidden" in one-particle theories. Do you?

Actually, I do. The mass and wavefunction renormalization that you mention are a direct result of particle creation. Maybe they cannot "explain" particle creation, but for the same reason that an effect cannot "explain" its own cause. Anyway, particle creation does take place in one-particle theories, if only through wave function/mass renormalization. On the other hand, a particle mass is created (whether partially or totally, is not important here), by the particle's field, and thus depends "on the value of the interaction constant". So there are always field interactions, whether explicit or implicit. And again, if an experiment yields a result incompatible with the predictions of, say, the Dirac equation, but compatible with those of QED, that will not be very exciting.

 

[Demystifier]

1. Specifically, I am not ready to accept the assumption that one-particle relativistic quantum equations, such as the Klein-Gordon equation, describe just one particle (however natural and even tautological that assumption may look, on the face of it), as I believe that travel-back-in-time trajectories describe pair creation.

2. Also, I am not sure that it is important whether the dotted lines join the dashed lines after measurement.

1. In my view, these are merely two ways to say the same thing. As long as there is only ONE CONTINUOUS CURVE in spacetime, it does not matter whether we call it one particle that can move backwards in time, or many particles that can be created and destructed.

2. Well, if they don't join, then you have a problem.
Assume first that they do. Then, even with your many-particle interpretation, the positions of all these particles are determined by ONLY ONE initial particle position. This differs from the n-particle state in the usual sense, which (in the Bohmian interpretation) requires n initial particle positions.
Now assume that they don't. If these two parts of the curve are not joined, then how do you know that they actually belong to the same curve? If you simply say that they do not belong to the same curve, which indeed is in the spirit of your many-particle interpretation, then how do you know that one particle must be accompanied with another one?

I hope you see that the arguments in 2. show that a single-particle interpretation has certain advantages (even if you are still not completely convinced).

 

[Demystifier]

The mass and wavefunction renormalization that you mention are a direct result of particle creation.

In a sense you are right, but the theoretical origin of this "particle creation" differs significantly from "particle creation" in relativistic Bohmian mechanics. The former is related to virtual particles that make sense only in the perturbative method of calculation based on Feynman diagrams. The latter makes sense only in the Bohmian interpretation, irrespective of the method of the calculation. If two things look similar (though not identical), but have different theoretical origins, then it does not seem very likely that they are actually the same.

 

[Demystifier]

And again, if an experiment yields a result incompatible with the predictions of, say, the Dirac equation, but compatible with those of QED, that will not be very exciting.

As far as we know, all effects of QED on the single-particle Dirac equation is a renormalization of the parameters of the Dirac equation. An example is a correction of g, which for free Dirac equation is g=2. The QED correction of this value is one of the most remarkable triumphs of QED.

 

[Demystifier]

Akhmetely, one additional remark. At the beginning, I was also hoping, using similar arguments that you do, that motions backwards in time could be related to genuine particle creation. Nevertheless, by using arguments that I presented above, I have concluded that it was not possible (or at least very unlikely).

However, a truly amazing result was when I recently realized that the Bohmian motions backwards in time ARE related to genuine particle creation - in string theory.
See my preprints arXiv:hep-th/0702060 and arXiv:0705.3542 (I am not giving the direct links because ZZ does not allow to do that for papers that are not yet published). See in particular Fig. 1 in the first paper that summarizes various views of particle creation.

 

[akhmeteli]

As far as we know, all effects of QED on the single-particle Dirac equation is a renormalization of the parameters of the Dirac equation.

I guess you mean the free Dirac equation? Because the Lamb shift does not look like a renormalization of parameters of the Dirac equation.

An example is a correction of g, which for free Dirac equation is g=2.

I am not sure g is a parameter of the free Dirac equation. So what parameter is renormalized in this case?

 

[Demystifier]

Akhmetely, see also the most convincing argument that motions backwards in time of particles cannot be sufficient to explain particle creation. It certainly cannot explain the creation of new kinds of particles, that is, kinds of particles that were not present in the initial state. For example, there are no particle trajectories of electrons that could explain the creation of photons.
Note also that this problem is elegantly avoided in string theory, because in string theory different kinds of particles are nothing but different states of the same object - the string. Therefore, a string can continuously transit from an electron to a photon. A particle cannot do that. See also Fig. 1 mentioned in my previous post.

 

[Demystifier]

I guess you mean the free Dirac equation? Because the Lamb shift does not look like a renormalization of parameters of the Dirac equation.

I am not sure g is a parameter of the free Dirac equation. So what parameter is renormalized in this case?

You are right: strictly speaking g has an operational physical meaning only when the interaction with the magnetic field is also present. Nevertheless, when the magnetic field is treated classically, g (or more precisely the magnetic moment mu) can be viewed as a parameter of the Dirac equation in a classical magnetic field, but a parameter that can be expressed in terms of other parameters (mass and charge). But this is not really important for our main discussion, is it?

 

[akhmeteli]

You are right: strictly speaking g has an operational physical meaning only when the interaction with the magnetic field is also present. Nevertheless, when the magnetic field is treated classically, g (or more precisely the magnetic moment mu) can be viewed as a parameter of the Dirac equation in a classical magnetic field, but a parameter that can be expressed in terms of other parameters (mass and charge). But this is not really important for our main discussion, is it?

I fully agree, it is not important for the discussion.

I cannot reply to your other post(s) now, I'll try to do it in the evening (Pacific time). Take care.

 

[Demystifier]

I cannot reply to your other post(s) now, I'll try to do it in the evening (Pacific time). Take care.

I am looking forward!

 

[Schrodinger's Dog]

Isn't a photon even in QM the most fundamental of particles. I always thought the reason everything would end up under an infinitely expanding universe as photons and then as the fundamental sea of the vacuum because, that form of energy is the lowest common denominator of all matter. A particle and antiparticle pair is as far as it goes, excluding string theory, which I'm not a fan of anyway atm.

 

[Demystifier]

Isn't a photon even in QM the most fundamental of particles. I always thought the reason everything would end up under an infinitely expanding universe as photons and then as the fundamental sea of the vacuum because, that form of energy is the lowest common denominator of all matter. A particle and antiparticle pair is as far as it goes, excluding string theory, which I'm not a fan of anyway atm.

Well, that is wrong. A photon is not more (and not less) fundamental than an electron. The standard model of elementary particle contains a LOT of equally elementary particles (photons, gluons, W bosons, Z bosons, electrons, muons, tau, e-neutrinos, mu-neutrinos, tau-neutrinos, 6 types of quarks, Higgs). In fact, one of the main motivations for string theory is to derive all these seemingly "elementary" particles from a SINGLE elementary object - the string.

 

[Schrodinger's Dog]

Well, that is wrong. A photon is not more (and not less) fundamental than an electron. The standard model of elementary particle contains a LOT of equally elementary particles (photons, gluons, W bosons, Z bosons, electrons, muons, tau, e-neutrinos, mu-neutrinos, tau-neutrinos, 6 types of quarks, Higgs). In fact, one of the main motivations for string theory is to derive all these seemingly "elementary" particles from a SINGLE elementary object - the string.

By that I meant ultimately (under the infinitely expanding model) all matter in the Universe will end up as photons and then vacuum energy, and without strings the idea that a photon can become an electron is meaningless. Rather than it was more elementary than an electron. If I'm getting this straight though your points only make sense if you believe string theory to be more than a hypothesis, if not then they are meaningless, yes? If so carry on, I won't interfere again unless the subject changes.

I'm well aware quarks are more fundamental, that wasn't my point.

 

[Demystifier]

1. By that I meant ultimately (under the infinitely expanding model) all matter in the Universe will end up as photons and then vacuum energy,

2. and without strings the idea that a photon can become an electron is meaningless.

1. Even if that was true (which wasn't), so what? I do not understand your point at all.

2. It is not meaningless if you allow quantum jumps (whatever that means). But if all changes are continuous and if particles are pointlike objects, which is what Bohmian mechanics claims, then yes, it becomes meaningless.

 

[Demystifier]

If I'm getting this straight though your points only make sense if you believe string theory to be more than a hypothesis, if not then they are meaningless, yes?

Let me put it this way. If string theory is wrong, then Bohmian mechanics has problems that cannot be solved in a simple way (but can in a complicated, ugly way). If string theory is correct, then these problems of Bohmian mechanics are resolved automatically, in a simple way.

 

[Schrodinger's Dog]

1. Even if that was true (which wasn't), so what? I do not understand your point at all.

2. It is not meaningless if you allow quantum jumps (whatever that means). But if all changes are continuous and if particles are pointlike objects, which is what Bohmian mechanics claims, then yes, it becomes meaningless.

I'm sorry but yes it is.

The Big Freeze is a scenario under which continued expansion results in a universe that is too cold to sustain life. It could, in the absence of dark energy, occur only under a flat or hyperbolic geometry, because such geometries then are a necessary condition for a universe that expands forever. With a positive cosmological constant, it could also occur in a closed universe. A related scenario is Heat Death, which states that the universe goes to a state of maximum entropy in which everything is evenly distributed, and there are no gradients — which are needed to sustain information processing, one form of which is life. The Heat Death scenario is compatible with any of the three spatial models, but requires that the universe reach an eventual temperature minimum.

http://en.wikipedia.org/wiki/Big_Freeze

The Dark Age - from 10100 years until 10150 years

All Black Holes now Disintegrated: 10150 years

The remaining black holes evaporate: first the small ones, and then the supermassive black holes. All matter that used to make up the stars and galaxies has now degenerated into photons and leptons.

[edit] The Photon Age - 10150 years and Beyond

The Universe Achieves Low-Energy State: 1010³ years and beyond

The Universe now reaches an extremely low-energy state. What happens after this is speculative. It's possible a Big Rip event may occur far off into the future, or the Universe may settle into this state forever, achieving true heat death. Extreme low-energy states imply that localized quantum events become major macroscopic phenomena rather than negligible microscopic events because the smallest perturbations make the biggest difference in this era, so there is no telling what may happen to space or time. It is perceived that the laws of "macro-physics" will break down, and the laws of "quantum-physics" will prevail.

In this scenario where the Universe continues to expand more and more rapidly.

I agree with your second point.

It is meaningless if you accept string theory also I don't see what relevance it has to BM, not least because its a theory without any evidence and thus it shouldn't really be used to extrapolate except in philosophical terms . Personally I'd rather go with whatever theory is the most robust atm. String theory is a bit of a dead end IMO, unless something turns up soon, I think I'm personally going to consign it to the waste bin of nice ideas with no evidence. It's getting quite full actually.

 

[Demystifier]

I'm sorry but yes it is.

Oh, now I see the argument. OK, it is, provided two assumptions:
1. That Hawking radiation really exists (there is no proof yet).
2. That there are no other free massless particles except photons. (If, which is very likely, gravitons also exist, then Hawking radiation will produce gravitons as well.)

 

[Schrodinger's Dog]

Oh, now I see the argument. OK, it is, provided two assumptions:
1. That Hawking radiation really exists (there is no proof yet).
2. That there are no other free massless particles except photons. (If, which is very likely, gravitons also exist, then Hawking radiation will produce gravitons as well.)

Granted but at least we have some inferred evidence of black holes, so I'm willing to speculate on that. And actually knock your self out with string theory, pardon me being grumpy. This thread isn't exactly the least speculatory of threads anyway.

 

[akhmeteli]

1. In my view, these are merely two ways to say the same thing. As long as there is only ONE CONTINUOUS CURVE in spacetime, it does not matter whether we call it one particle that can move backwards in time, or many particles that can be created and destructed.

It took me quite some time to decide whether I should agree with this or not:-). OK, let us assume that I agree.

2. Well, if they don't join, then you have a problem.
Assume first that they do. Then, even with your many-particle interpretation, the positions of all these particles are determined by ONLY ONE initial particle position. This differs from the n-particle state in the usual sense, which (in the Bohmian interpretation) requires n initial particle positions.

Sorry, Demystifier, you just cannot have it both ways. You have just said that in this case "As long as there is only ONE CONTINUOUS CURVE in spacetime, it does not matter whether we call it one particle that can move backwards in time, or many particles that can be created and destructed."

Now assume that they don't. If these two parts of the curve are not joined, then how do you know that they actually belong to the same curve? If you simply say that they do not belong to the same curve, which indeed is in the spirit of your many-particle interpretation, then how do you know that one particle must be accompanied with another one?

I don't know (that they actually belong to the same curve), and I don't care. But it seems important to me that along with the first particle there is the second and the third ones, which are also real and can affect the first particle (as they are very close to it), so I 'm not over-enthusiastic when they are announced "unphysical" without bullet-proof arguments. How do I "know that one particle must be accompanied with another one"? I just take solutions of wave equations very seriously, and you are considering one of such solutions.

I hope you see that the arguments in 2. show that a single-particle interpretation has certain advantages (even if you are still not completely convinced).

You see, come to think of it, I don't really care whether the single-particle or multi-particle interpretation is correct. I can even tolerate the Wheeler's idea that there is just one electron in the Universe. I just cannot see any advantages in deeming that part of the trajectory unphysical. You may say that the advantage is that difference then arises between predictions of BI and CI. I think this can be an advantage only if experiments confirm that you are right. If, however, that does not happen, BI will suffer through no fault of its own. Ultimately, your arguments cannot convince me just because they contradict my physical intuition. I understand, however, that your arguments can eventually prove right, and my intuition - wrong. But that would surprise me immensely.

Another thing. In thirties, Landau and Peierls wrote that the achievable accuracy of coordinate measurement is even further limited in the relativistic case, as a hard enough photon used for such measurement can generate pairs, so you'll never know the coordinate of which particle you are measuring (by the way, maybe this is the ultimate source of the uncertainty relation even in the non-relativistic case). This is actually the case that we are considering.

 

[akhmeteli]

Akhmetely, one additional remark. At the beginning, I was also hoping, using similar arguments that you do, that motions backwards in time could be related to genuine particle creation. Nevertheless, by using arguments that I presented above, I have concluded that it was not possible (or at least very unlikely).

However, a truly amazing result was when I recently realized that the Bohmian motions backwards in time ARE related to genuine particle creation - in string theory.
See my preprints arXiv:hep-th/0702060 and arXiv:0705.3542 (I am not giving the direct links because ZZ does not allow to do that for papers that are not yet published). See in particular Fig. 1 in the first paper that summarizes various views of particle creation.

Again, no offence, but, as you admit in your article, the experimental status of string theory is problematic, to put it mildly, so no arguments based on string theory can convince me. Sorry.

 

[Demystifier]

Again, no offence, but, as you admit in your article, the experimental status of string theory is problematic, to put it mildly, so no arguments based on string theory can convince me. Sorry.

But the experimental status of Bohmian mechanics is also problematic. So how arguments based on BM can convince you?

 

[Demystifier]

1. Sorry, Demystifier, you just cannot have it both ways. You have just said that in this case "As long as there is only ONE CONTINUOUS CURVE in spacetime, it does not matter whether we call it one particle that can move backwards in time, or many particles that can be created and destructed."

2. How do I "know that one particle must be accompanied with another one"? I just take solutions of wave equations very seriously, and you are considering one of such solutions.

3. I just cannot see any advantages in deeming that part of the trajectory unphysical.

4. Another thing. In thirties, Landau and Peierls wrote that the achievable accuracy of coordinate measurement is even further limited in the relativistic case, as a hard enough photon used for such measurement can generate pairs, so you'll never know the coordinate of which particle you are measuring (by the way, maybe this is the ultimate source of the uncertainty relation even in the non-relativistic case). This is actually the case that we are considering.

1. We cannot discuss it without drawings. Therefore, please see the picture in my
http://xxx.lanl.gov/abs/quant-ph/0208185 [Found.Phys.Lett. 17 (2004) 363].
Is it 1 particle or 3 particles?

2. The particle trajectories are not solutions of the wave equations. Perhaps you meant something else?

3. You missed the point. The dotted part is unphysical because this part is actually NOT a solution of the particle-trajectory equation of motion. This is because the interaction with the measuring apparatus changes the wave function. (Sorry, but I must suspect again that you are not familiar with the measurement theory in Bohmian mechanics. Please inform me, by PM if you want, if this is the case. It is essential for the efficiency of further discussion.) Now the dashed part is unphysical because it is no longer joined with the solid part, so it is NOT a part of the same trajectory.

4. Can you give me an appropriate reference in which this was shown? I've seen books with similar statements, but such claims were based on hand waving, not on serious calculations based on principles of quantum field theory.

 

[Schrodinger's Dog]

But the experimental status of Bohmian mechanics is also problematic. So how arguments based on BM can convince you?

I'm willing to buy into the idea that you can have a particle representation in non relativistic QFT. Although the maths is somewhat above me, I can follow it well enough to see what they are driving at. But I think you've hit the nail on the head there: how can arguments on BI (Bohmian Interpretation) convince you if the experimental status of BM (Bohmian Mechanics) is problematic. It's kind of the same with CI (Copenhagen Interpretation) isn't it? Why doesn't CI convince some people, doesn't this again boil down to a measurement problem? Isn't the same problem with CI present in BI.

I think the best you can hope for is to convince people that both a particle and wave model are possible in QFT (and that so far CI has a better track record) since that is already self evident given the nature of photons, that's not exactly controversial. I don't think you can say much more or indeed expect people to be convinced much more than that, after all people aren't that convinced by CI either.

Pardon me if I'm way off the beaten track here, just trying to follow your discussion before it disappears off my radar.

 

[Demystifier]

Schrodinger's Dog, but what IF I have a theory that naturally unifies BM and string theory? Not much if one does not find BM or strings (or both) convincing.

But what IF, in addition, my theory predicts something new that can be tested by experiments, but cannot be predicted without BM or without strings? Then someone who finds this theory "elegant" (whatever that means) could be motivated to make the experimental test in a laboratory.

Finally, what IF the experiment turn out to agree with this prediction? Then we have an experimental proof that both BM and string theory are correct.

Indeed, this is how science (a dialog between theories and and experiments) works.

Just for the record, the first two "IF's" are actually "yes". What remains is to do an experimental test.

 

[Schrodinger's Dog]

Schrodinger's Dog, but what IF I have a theory that naturally unifies BM and string theory? Not much if one does not find BM or strings (or both) convincing.

But what IF, in addition, my theory predicts something new that can be tested by experiments, but cannot be predicted without BM or without strings? Then someone who finds this theory "elegant" (whatever that means) could be motivated to make the experimental test in a laboratory.

Finally, what IF the experiment turn out to agree with this prediction? Then we have an experimental proof that both BM and string theory are correct.

Indeed, this is how science (a dialog between theories and and experiments) works.

Just for the record, the first two "IF's" are actually "yes". What remains is to do an experimental test.

Well that's a no brainer, in that case, that is science. If you can validate it experimentally then it becomes a matter of determining if your underlying principles are valid, just like in CI. If you managed that through experimentation - although it might be inferred not directly proved - your hypothesis is more than, well, a mere hypothesis, then you'd be talking. I'm sure if you could do that, then funding would follow.

I see what you are saying.