The photon - the particle which makes up light - is probably one of the best known elementary particles. Nonetheless, everything can be made more involved. Thus, we studied a more complicated version of it in our most recent paper.
"Why in the world should we do this?" is a valid question at this point. That proceeded in multiple stages. I have written quite some time ago that for a particle physicist it is baffling that chemistry works. Chemistry works, among other things, because the electric charge of nuclei and electrons are perfectly balanced. Well, as perfect as we can measure, anyhow. In the standard model of particle physics there is no reason why this should be the case. However, the standard model is mathematical consistent only if this is the case. In fact, only if the balance is really perfect. Mathematical consistency is not a sufficient argument why a theory needs to be correct. Experiment is. So people have investigated this baffling fact since decades. In this process, the idea came up that there is a reason for this. And that reason would be that the standard model is only a facet of an underlying theory. This underlying theory enforces the equality of the electric charges by combining the weak, strong, and electromagnetic forces into one force. Such theories are called grand-unified theories, or short GUTs.
Such GUTs use a single gauge theory to combine all these forces. This is only possible with a certain kind, which is fundamentally different from the one we use for electromagnetism alone. It is more similar to the ones of the strong and weak force. We have investigated this type of theories for a long time. And one central insight is that in such theories none of the elementary particles can be observed individually. Only so-called bound states, which are made from two or more elementary particles, can be. That is very different from the ordinary photon of electromagnetism, which is, essentially, elementary.
The central question was therefore whether any such bound state could have the properties of the photon which we know from experiment. Otherwise a GUT would (very likely) not be a possible candidate to explain the balance of electric charges in chemistry. The photon has three important features. It does not carry itself electric charge. It is massless. And it has one unit of so-called spin.
Thus we needed to build a bound state in a GUT with these properties. The spin and absence of charge is actually quite simple, and you get this almost for free in any GUT. It is really the fact that it should not have mass which makes it so complicated. It is even more complicated to verify that it has no mass.
We had some ideas from our previous work, using pen-and-paper calculations, how this could work. There had also been some numerical simulations looking into similar questions in the early 1980ies, though they were, given resources back then, very exploratory. So we set up our own, modern-day numerical simulations. However, it is not yet possible to simulate a full, realistic GUT. For this all computing power on earth would not suffice, if we want to be done in a lifetime. So we used the simplest possible theory which had all the correct features relevant to a true GUT. This is an often employed trick in physics. One reduces a problem to the absolutely essential features, throwing away the rest, which has no or little impact on the particular question at hand. And by this getting a manageable problem.
So we did. And due to some ingenious ideas of my collaborators, especially my PhD student Vincenzo Afferrante, we were able to perform the simulations. There was a lot of frustrating work for the first few months, actually. But we persevered. And we were rewarded. In the end, we got our massless photon in exactly the way we hoped! We thus demonstrated that such a mechanism is possible. We got a massless photon made up out of elementary particles! A huge success for the whole setup. In addition, the things which make up the photon are (partly) very massive. That a bound state can be lighter than its constituents is an amazing consequence of special relativity. For us, this is an added bonus. Because you cannot see the fact that a particle is made up of other particles if you have not enough energy available to create the constituents. Again, this comes from the theory of relativity. In this scenario one of the constituents is indeed so heavy that we would not be able to produce it in experiments yet. Hence, with our current experiments, we would not yet detect that the photon is made up from other particles. And this is indeed what we observe. So everything is consistent. Very reassuring. Unfortunately, it is so heavy that also none of the currently planned experiments would be able to do so. Hence, we will not be able to test this idea directly experimentally. This will need to resort to indirect evidence.
Of course, I gloss over a lot of details and technicalities here, which took most of our time. Describing them would fill multiple entries.
Now, the only thing we need to do is to figure out whether anything we neglected could interfere. None of it will at a qualitative level. But, of course, we have very good experiments. And thus to make the whole idea a suitable GUT to describe nature, we also need to get it quantitatively correct. But this will be a huge step. Therefore we broke it down in small steps. We will do them one by one. Our next step is now to get the electron right. Let's see if this also works out.
Showing posts with label GUT. Show all posts
Showing posts with label GUT. Show all posts
Tuesday, April 21, 2020
Monday, January 22, 2018
Finding - and curing - disagreements
The topic of grand-unified theories came up in the blog several times, most recently last year in January. To briefly recap, such theories, called GUTs for short, predict that all three forces between elementary particles emerge from a single master force. That would explain a lot of unconnected observations we have in particle physics. For example, why atoms are electrically neutral. The latter we can describe, but not yet explain.
However, if such a GUT exists, then it must not only explain the forces, but also somehow why we see the numbers and kinds of elementary particles we observe in nature. And now things become complicated. As discussed in the last entry on GUTs there maybe a serious issue in how we determine which particles are actually described by such a theory.
To understand how this issue comes about, I need to put together many different things my research partners and I have worked on during the last couple of years. All of these issues are actually put into an expert language in the review of which I talked in the previous entry. It is now finished, and if your interested, you can get it free from here. But it is very technical.
So, let me explain it less technically.
Particle physics is actually superinvolved. If we would like to write down a theory which describes what we see, and only what we see, it would be terribly complicated. It is much more simple to introduce redundancies in the description, so-called gauge symmetries. This makes life much easier, though still not easy. However, the most prominent feature is that we add auxiliary particles to the game. Of course, they cannot be really seen, as they are just auxiliary. Some of them are very obviously unphysical, called therefore ghosts. They can be taken care of comparatively simply. For others, this is less simple.
Now, it turns out that the weak interaction is a very special beast. In this case, there is a unique one-to-one identification between a really observable particle and an auxiliary particle. Thus, it is almost correct to identify both. But this is due to the very special structure of this part of particle physics.
Thus, a natural question is whether, even if it is special, it is justified to do the same for other theories. Well, in some cases, this seems to be the case. But we suspected that this may not be the case in general. And especially not in GUTs.
Now, recently we were going about this much more systematically. You can again access the (very, very technical) result for free here. There, we looked at a very generic class of such GUTs. Well, we actually looked at the most relevant part of them, and still by far not all of them. We also ignored a lot of stuff, e.g. what would become quarks and leptons, and concentrated only on the generalization of the weak interaction and the Higgs.
We then checked, based on our earlier experiences and methods, whether a one-to-one identification of experimentally accessible and auxiliary particles works. And it does essentially never. Visually, this result looks like
On the left, it is seen that everything works nicely with a one-to-one identification in the standard model. On the right, if one-to-one identification would work in a GUT, everything would still be nice. But a our more precise calculation shows that the actually situation, which would be seen in an experiment, is different. There is non one-to-one identification possible. And thus the prediction of the GUT differs from what we already see inn experiments. Thus, a previously good GUT candidate is no longer good.
Though more checks are needed, as always, this is a baffling, and at the same time very discomforting, result.
Baffling as we did originally expect to have problems under very special circumstances. It now appears that actually the standard model of particles is the very special case, and having problems is the standard.
It is discomforting because in the powerful method of perturbation theory the one-to-one identification is essentially always made. As this tool is widely used, this seems to question the validity of many predictions on GUTs. That could have far-reaching consequences. Is this the case? Do we need to forget everything about GUTs we learned so far?
Well, not really, for two reasons. One is that we also showed that methods almost as easily handleable as perturbation theory can be used to fix the problems. This is good, because more powerful methods, like the simulations we used before, are much more cumbersome. However, this leaves us with the problem of having made so far wrong predictions. Well, this we cannot change. But this is just normal scientific progress. You try, you check, you fail, you improve, and then you try again.
And, in fact, this does not mean that GUTs are wrong. Just that we need to consider somewhat different GUTs, and make the predictions more carefully next time. Which GUTs we need to look at we still need to figure out, and that will not be simple. But, fortunately, the improved methods mentioned beforehand can use much of what has been done so far, so most technical results are still unbelievable useful. This will help enormously in finding GUTs which are applicable, and yield a consistent picture, without the one-to-one identification. GUTs are not dead. They likely just need a bit of changing.
This is indeed a dramatic development. But one which fits logically and technically to the improved understanding of the theoretical structures underlying particle physics, which were developed over the last decades. Thus, we are confident that this is just the next logical step in our understanding of how particle physics works.
However, if such a GUT exists, then it must not only explain the forces, but also somehow why we see the numbers and kinds of elementary particles we observe in nature. And now things become complicated. As discussed in the last entry on GUTs there maybe a serious issue in how we determine which particles are actually described by such a theory.
To understand how this issue comes about, I need to put together many different things my research partners and I have worked on during the last couple of years. All of these issues are actually put into an expert language in the review of which I talked in the previous entry. It is now finished, and if your interested, you can get it free from here. But it is very technical.
So, let me explain it less technically.
Particle physics is actually superinvolved. If we would like to write down a theory which describes what we see, and only what we see, it would be terribly complicated. It is much more simple to introduce redundancies in the description, so-called gauge symmetries. This makes life much easier, though still not easy. However, the most prominent feature is that we add auxiliary particles to the game. Of course, they cannot be really seen, as they are just auxiliary. Some of them are very obviously unphysical, called therefore ghosts. They can be taken care of comparatively simply. For others, this is less simple.
Now, it turns out that the weak interaction is a very special beast. In this case, there is a unique one-to-one identification between a really observable particle and an auxiliary particle. Thus, it is almost correct to identify both. But this is due to the very special structure of this part of particle physics.
Thus, a natural question is whether, even if it is special, it is justified to do the same for other theories. Well, in some cases, this seems to be the case. But we suspected that this may not be the case in general. And especially not in GUTs.
Now, recently we were going about this much more systematically. You can again access the (very, very technical) result for free here. There, we looked at a very generic class of such GUTs. Well, we actually looked at the most relevant part of them, and still by far not all of them. We also ignored a lot of stuff, e.g. what would become quarks and leptons, and concentrated only on the generalization of the weak interaction and the Higgs.
We then checked, based on our earlier experiences and methods, whether a one-to-one identification of experimentally accessible and auxiliary particles works. And it does essentially never. Visually, this result looks like
On the left, it is seen that everything works nicely with a one-to-one identification in the standard model. On the right, if one-to-one identification would work in a GUT, everything would still be nice. But a our more precise calculation shows that the actually situation, which would be seen in an experiment, is different. There is non one-to-one identification possible. And thus the prediction of the GUT differs from what we already see inn experiments. Thus, a previously good GUT candidate is no longer good.
Though more checks are needed, as always, this is a baffling, and at the same time very discomforting, result.
Baffling as we did originally expect to have problems under very special circumstances. It now appears that actually the standard model of particles is the very special case, and having problems is the standard.
It is discomforting because in the powerful method of perturbation theory the one-to-one identification is essentially always made. As this tool is widely used, this seems to question the validity of many predictions on GUTs. That could have far-reaching consequences. Is this the case? Do we need to forget everything about GUTs we learned so far?
Well, not really, for two reasons. One is that we also showed that methods almost as easily handleable as perturbation theory can be used to fix the problems. This is good, because more powerful methods, like the simulations we used before, are much more cumbersome. However, this leaves us with the problem of having made so far wrong predictions. Well, this we cannot change. But this is just normal scientific progress. You try, you check, you fail, you improve, and then you try again.
And, in fact, this does not mean that GUTs are wrong. Just that we need to consider somewhat different GUTs, and make the predictions more carefully next time. Which GUTs we need to look at we still need to figure out, and that will not be simple. But, fortunately, the improved methods mentioned beforehand can use much of what has been done so far, so most technical results are still unbelievable useful. This will help enormously in finding GUTs which are applicable, and yield a consistent picture, without the one-to-one identification. GUTs are not dead. They likely just need a bit of changing.
This is indeed a dramatic development. But one which fits logically and technically to the improved understanding of the theoretical structures underlying particle physics, which were developed over the last decades. Thus, we are confident that this is just the next logical step in our understanding of how particle physics works.
Wednesday, January 18, 2017
Can we tell when unification works? - Some answers.
This time, the following is a guest entry by one of my PhD students, Pascal Törek, writing about the most recent results of his research, especially our paper.
Some time ago the editor of this blog, offered me to write about my PhD research here. Since now I gained some insight and collected first results, I think this is the best time to do so.
In a previous blog entry, Axel explained what I am working on and which questions we try to answer. The most important one was: “Does the miracle repeat itself for a unified theory?”. Before I answer this question and explain what is meant by “miracle”, I want to recap some things.
The first thing I want to clarify is, what a unified or a grand unified theory is. The standard model of particle physics describes all the interactions (neglecting gravity) between elementary particles. Those interactions or forces are called strong, weak and electromagnetic force. All these forces or sectors of the standard model describe different kinds of physics. But at very high energies it could be that these three forces are just different parts of one unified force. Of course a theory of a unified force should also be consistent with what has already been measured. What usually comes along in such unified scenarios is that next to the known particles of the standard model, additional particles are predicted. These new particles are typically very heavy and thus makes them very hard to detect in experiments in the near future (if one of those unified theories really describes nature).
What physicists often use to make predictions in an unified theory is perturbation theory. But here comes the hook: what one does in this framework is to do something really arbitrarily, namely to fix a so-called “gauge”. This rather technical term just means that we have to use a mathematical trick to make calculations easier. Or to be more precise, we have to use that trick to even perform a calculation in perturbation theory in those kinds of theories which would be impossible otherwise.
Since nature does not care about this man-made choice, every quantity which could be measured in experiments must be independent of the gauge. But this is exactly how the elementary particles are treated in conventional perturbation theory, they depend on the gauge. An even more peculiar thing is that also the particle spectrum (or the number of particles) predicted by these kinds of theories depends on the gauge.
This problem appears already in the standard model: what we call the Higgs, W, Z, electron, etc. depends on the gauge. This is pretty confusing because those particles have been measured experimentally but should not have been observed like that if you take the theory serious.
This contradiction in the standard model is resolved by a certain mechanism (the so-called “FMS mechanism”) which maps quantities which are independent of the gauge to the gauge-dependent objects. Those gauge-independent quantities are so called bound states. What you essentially do is to “glue” the gauge-dependent objects together in such a way that the result does not depended on the gauge. This exactly the miracle I wrote about in the beginning: one interprets something (gauge-dependent objects as e.g. the Higgs) as if it will be observable and you indeed find this something in experiments. The correct theoretical description is then in terms of bound states and there exists a one-to-one mapping to the gauge-dependent objects. This is the case in the standard model and it seems like a miracle that everything fits so perfectly such that everything works out in the end. The claim is that you see those bound states in experiments and not the gauge-dependent objects.
However, it was not clear if the FMS mechanism works also in a grand unified theory (“Does the miracle repeat itself?”). This is exactly what my research is about. Instead of taking a realistic grand unified theory we decided to take a so called “toy theory”. What is meant by that is that this theory is not a theory which can describe nature but rather covers the most important features of such kind of theory. The reason is simply that I use simulations for answering the question raised above and due to time constraints and the restricted resources a toy model is more feasible than a realistic model. By applying the FMS mechanism to the toy model I found that there is a discrepancy to perturbation theory, which was not the case in the standard model. In principle there were three possible outcomes: the mechanism works in this model and perturbation theory is wrong, the mechanism fails and perturbation theory gives the correct result or both are wrong. So I performed simulations to see which statement is correct and what I found is that only the FMS mechanism predicts the correct result and perturbation theory fails. As a theoretician this result is very pleasing since we like to have nature independent of a arbitrarily chosen gauge.
The question you might ask is: “What is it good for?” Since we know that the standard model is not the theory which can describe everything, we look for theories beyond the standard model as for instance grand unified theories. There are many of these kinds of theories on the market and there is yet no way to check each of them experimentally. What one can do now is to use the FMS mechanism to rule some of them out. This is done by, roughly speaking, applying the mechanism to the theory you want to look at, count the number of particles predicted by the mechanism, compare it to the number particles of the standard model. If there are more the theory is probably a good candidate to study and if not you can throw it away.
Right now Axel, a colleague from Jena University, and myself look at more realistic grand unified theories and try to find general features concerning the FMS mechanism. I am sure Axel or maybe myself keep you updated on this topic.
Some time ago the editor of this blog, offered me to write about my PhD research here. Since now I gained some insight and collected first results, I think this is the best time to do so.
In a previous blog entry, Axel explained what I am working on and which questions we try to answer. The most important one was: “Does the miracle repeat itself for a unified theory?”. Before I answer this question and explain what is meant by “miracle”, I want to recap some things.
The first thing I want to clarify is, what a unified or a grand unified theory is. The standard model of particle physics describes all the interactions (neglecting gravity) between elementary particles. Those interactions or forces are called strong, weak and electromagnetic force. All these forces or sectors of the standard model describe different kinds of physics. But at very high energies it could be that these three forces are just different parts of one unified force. Of course a theory of a unified force should also be consistent with what has already been measured. What usually comes along in such unified scenarios is that next to the known particles of the standard model, additional particles are predicted. These new particles are typically very heavy and thus makes them very hard to detect in experiments in the near future (if one of those unified theories really describes nature).
What physicists often use to make predictions in an unified theory is perturbation theory. But here comes the hook: what one does in this framework is to do something really arbitrarily, namely to fix a so-called “gauge”. This rather technical term just means that we have to use a mathematical trick to make calculations easier. Or to be more precise, we have to use that trick to even perform a calculation in perturbation theory in those kinds of theories which would be impossible otherwise.
Since nature does not care about this man-made choice, every quantity which could be measured in experiments must be independent of the gauge. But this is exactly how the elementary particles are treated in conventional perturbation theory, they depend on the gauge. An even more peculiar thing is that also the particle spectrum (or the number of particles) predicted by these kinds of theories depends on the gauge.
This problem appears already in the standard model: what we call the Higgs, W, Z, electron, etc. depends on the gauge. This is pretty confusing because those particles have been measured experimentally but should not have been observed like that if you take the theory serious.
This contradiction in the standard model is resolved by a certain mechanism (the so-called “FMS mechanism”) which maps quantities which are independent of the gauge to the gauge-dependent objects. Those gauge-independent quantities are so called bound states. What you essentially do is to “glue” the gauge-dependent objects together in such a way that the result does not depended on the gauge. This exactly the miracle I wrote about in the beginning: one interprets something (gauge-dependent objects as e.g. the Higgs) as if it will be observable and you indeed find this something in experiments. The correct theoretical description is then in terms of bound states and there exists a one-to-one mapping to the gauge-dependent objects. This is the case in the standard model and it seems like a miracle that everything fits so perfectly such that everything works out in the end. The claim is that you see those bound states in experiments and not the gauge-dependent objects.
However, it was not clear if the FMS mechanism works also in a grand unified theory (“Does the miracle repeat itself?”). This is exactly what my research is about. Instead of taking a realistic grand unified theory we decided to take a so called “toy theory”. What is meant by that is that this theory is not a theory which can describe nature but rather covers the most important features of such kind of theory. The reason is simply that I use simulations for answering the question raised above and due to time constraints and the restricted resources a toy model is more feasible than a realistic model. By applying the FMS mechanism to the toy model I found that there is a discrepancy to perturbation theory, which was not the case in the standard model. In principle there were three possible outcomes: the mechanism works in this model and perturbation theory is wrong, the mechanism fails and perturbation theory gives the correct result or both are wrong. So I performed simulations to see which statement is correct and what I found is that only the FMS mechanism predicts the correct result and perturbation theory fails. As a theoretician this result is very pleasing since we like to have nature independent of a arbitrarily chosen gauge.
The question you might ask is: “What is it good for?” Since we know that the standard model is not the theory which can describe everything, we look for theories beyond the standard model as for instance grand unified theories. There are many of these kinds of theories on the market and there is yet no way to check each of them experimentally. What one can do now is to use the FMS mechanism to rule some of them out. This is done by, roughly speaking, applying the mechanism to the theory you want to look at, count the number of particles predicted by the mechanism, compare it to the number particles of the standard model. If there are more the theory is probably a good candidate to study and if not you can throw it away.
Right now Axel, a colleague from Jena University, and myself look at more realistic grand unified theories and try to find general features concerning the FMS mechanism. I am sure Axel or maybe myself keep you updated on this topic.
Thursday, March 5, 2015
Can we tell when unification works?
Some time ago, I wrote about the idea that the three forces of the standard model, the electromagnetic force, the weak force, and the strong force, could all be just different parts of one unified force. In the group I am building I have now a PhD student working on such a theory, using simulations.
Together, we would like to answer a number of questions. The most important one is, whether such a theory is consistent with what we see around us. That is necessary to make such a theory relevant.
Now, there is almost an infinite number of versions of such unified theories. We could never hope to check each and every one of them. We could pick one. But hoping it would be the right one is somewhat too optimistic. We therefore take a different approach. We aim to get a general criterion such that we can check out many of the candidate theories at the same time.
For this reason, we ignore for the moment that we would like to reproduce experiments. Rather, we ask ourselves what are common traits of these theories. We have done that. What we are currently doing is to construct the simplest possible theory which has as many of these traits as possible. We have almost completed that. This reduced theory will become indeed very simple. Of known physics, it contains the weak force and the Higgs. As with every unified theory, it also contains a number of additional particles. But they are not dangerous, if they will be too heavy to be visible to us. At least, as long as we do not have more powerful experiments. The last ingredient are the interactions between the different particles. That is what we are working on now. Having the simplest possible theory has also another benefit - it demands small enough computer resources to be manageable.
After fixing the theory, how do the questions look like? One of the traits of such theories is that there are many new particles. What is there fate? How is it arranged that we cannot see them? If we think of the theory describing only rather small changes to the standard model, we can use perturbation theory. With this, we would just follow pretty old footsteps, and the answer can essentially be guessed form the experience of other people. The answer will be that all the surplus stuff is indeed very, very heavy. In fact, so heavy that our experiments will not be able to see it in any foreseeable future, except as very indirect effects. We get out what we put in.
But here comes the new stuff. As I have described earlier, there are many subtleties when it comes to the Higgs of the standard model. But in the end, everything collapses to a rather simple picture. Almost a miracle. Almost, but not quite. The reason is the structure of the standard model, which is very special in the number and properties of particles. The other one is that the parameters, things like masses, just fits.
The natural question is hence: Does the miracle repeats itself for this type of unified theory? Is the new stuff really heavy? Is the known stuff light enough? If the almost-miracle repeats itself, the answer is yes. Should it repeat itself? Well, we will test under which conditions it repeats itself, by playing around both with the number of particles, their structures, and the parameters. We assume right now that we can get it to work, but that we can also break it. And we would like to understand very precisely when it breaks and why it breaks. And finally, the most obvious question, do we want that it repeats itself? Probably the most obvious question, arguably the hardest to answer. If it does not repeat itself, a whole class of ideas becomes more problematic. Ideas, which are conceptually pretty attractive. So, in principle, we would like to see it repeating itself. But then, would it not be more interesting if we needed to start afresh? Probably also true. But in the end, our preference should not play a role. After all, nature decides, and we are just the spectators, trying to figuring out what goes on. And our preferences have nothing to do with it, and therefore we should keep them out of the game.
Together, we would like to answer a number of questions. The most important one is, whether such a theory is consistent with what we see around us. That is necessary to make such a theory relevant.
Now, there is almost an infinite number of versions of such unified theories. We could never hope to check each and every one of them. We could pick one. But hoping it would be the right one is somewhat too optimistic. We therefore take a different approach. We aim to get a general criterion such that we can check out many of the candidate theories at the same time.
For this reason, we ignore for the moment that we would like to reproduce experiments. Rather, we ask ourselves what are common traits of these theories. We have done that. What we are currently doing is to construct the simplest possible theory which has as many of these traits as possible. We have almost completed that. This reduced theory will become indeed very simple. Of known physics, it contains the weak force and the Higgs. As with every unified theory, it also contains a number of additional particles. But they are not dangerous, if they will be too heavy to be visible to us. At least, as long as we do not have more powerful experiments. The last ingredient are the interactions between the different particles. That is what we are working on now. Having the simplest possible theory has also another benefit - it demands small enough computer resources to be manageable.
After fixing the theory, how do the questions look like? One of the traits of such theories is that there are many new particles. What is there fate? How is it arranged that we cannot see them? If we think of the theory describing only rather small changes to the standard model, we can use perturbation theory. With this, we would just follow pretty old footsteps, and the answer can essentially be guessed form the experience of other people. The answer will be that all the surplus stuff is indeed very, very heavy. In fact, so heavy that our experiments will not be able to see it in any foreseeable future, except as very indirect effects. We get out what we put in.
But here comes the new stuff. As I have described earlier, there are many subtleties when it comes to the Higgs of the standard model. But in the end, everything collapses to a rather simple picture. Almost a miracle. Almost, but not quite. The reason is the structure of the standard model, which is very special in the number and properties of particles. The other one is that the parameters, things like masses, just fits.
The natural question is hence: Does the miracle repeats itself for this type of unified theory? Is the new stuff really heavy? Is the known stuff light enough? If the almost-miracle repeats itself, the answer is yes. Should it repeat itself? Well, we will test under which conditions it repeats itself, by playing around both with the number of particles, their structures, and the parameters. We assume right now that we can get it to work, but that we can also break it. And we would like to understand very precisely when it breaks and why it breaks. And finally, the most obvious question, do we want that it repeats itself? Probably the most obvious question, arguably the hardest to answer. If it does not repeat itself, a whole class of ideas becomes more problematic. Ideas, which are conceptually pretty attractive. So, in principle, we would like to see it repeating itself. But then, would it not be more interesting if we needed to start afresh? Probably also true. But in the end, our preference should not play a role. After all, nature decides, and we are just the spectators, trying to figuring out what goes on. And our preferences have nothing to do with it, and therefore we should keep them out of the game.
Subscribe to:
Posts (Atom)
