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It’s like imaginary numbers are fake and don’t exist, but many calculations for electric circuits are easily done using these numbers. Sting theory is that to t

It’s like imaginary numbers are fake and don’t exist, but many calculations for electric circuits are easily done using these numbers. Sting theory is that to the nth degree. And, when done well it allows you describe the largest distances and the smallest particles using one mathematical principle. It’s useful in a sense that we can explain the existing observations. Though the predictions will be (currently) impossible to verity because where we have working theories in easy domain, planet scale -1g -1atm, nothings gets disproven. It’s that larger scale at insane conditions we may conclude something interesting. Though testing it will take another possibly larger hydrogen collider, or gravity wave measurement device. The quote They fight you and call you crazy, until your not them you are a genius — has never been more true. I say let the ideas be worked out, and the market place of ideas will solve if it’s relevant. The authors assumption that particle theoretical physics is dead is imo completely wrong, there are still many great people working on it.

mgamache 5y ago
Eventually it will sort out yes. There's a cost to beating a dead horse in time and resources. We've been stuck for 40 years: Physicists today can happily make career by writing papers about things no one has ever observed, and never will observe. This continues to go on because there is nothing and no one that can stop it. https://iai.tv/articles/why-physics-has-made-no-progress-in-50-years-auid-1292 https://iai.tv/articles/why-physics-has-made-no-progress-in-...
- throwaway81523 5y ago
  Nobody has ever observed the interior of a black hole and reported the results to the outside, and nobody ever will (unless GR is drastically wrong). And yet we consider our theory of BH interiors to be basically valid except at the center, where it breaks down. That's perfectly good physics, so deal with it.
sorokod 5y ago
> imaginary numbers are fake and don’t exist, In what relevant sense do imagenary numbers differ from real numbers? Being a mathematical abstraction they are in no way required to help approximate phisical reality. That they do is a source of wonder to many, but that is beside the point.
katmannthree 5y ago
> It’s like imaginary numbers are fake and don’t exist It's even better than that. Working from the other side, we generally take the natural numbers N = {0, 1, 2, 3, ...} to be "real" in a philosophical sense as we have an implied mapping of x in N fundamentally describing possession of discrete quantities of goods. This get a little more tricky when you generalize it to the integers Z = {..., -2, -1, 0, 1, 2, ...}, but we still consider these physically grounded as you can "owe" a discrete quantity of goods to someone. This is an incomplete mapping to reality as possession of y goods where y is in Z- doesn't actually describe where your y goods go to, but it's useful enough that we ignore that. Now that's all good and well for discrete quantities of goods, but what about fractional quantities? We need a new system to describe more numbers between the numbers we already have. Thus we defined the set of rational numbers Q = {n | n = p/q where p, q are in Z and q is not 0}. This lets us compactly describe almost any number we want between the existing integers. Most still consider these to be physically grounded, because we created these to describe concrete things in our reality which they do very compactly. You can claim that at least some of these are physically grounded in reality as using 1/3 a cup of flour or buying 1/2 a watermelon is certainly something one can very clearly and explicitly do. The rationals have some issues though, namely that they still have holes in them. Suppose you want to describe the relationship between the diameter of a circle and its circumference. The constant you use to transform one to the other, π, does not exist in Q. You can get as close as you like, but you can't actually reach it. That's a bit of a problem for people whose job it is to make sure that the things math says are correct are actually fully correct. There are other problems, suppose you want to make a rectangular plot of land whose area is 2 square miles. How long does each side need to be? You can get as close as you like by using rational numbers, but the actual length of that side (sqrt(2)) is not in Q. To fix this, we then very delicately construct the set of real numbers R = {x | where x is in {Q and all of the numbers described above which are missing from Q}}. This is where the physical grounding of the numbers starts to get ugly, because as it turns out that just like for some numbers in Q (consider 22/7, which does not evaluate to a fixed number of digits but rather goes on forever) these are uncountable and most of them unrepresentable, i.e. if you tried to write the number out completely on a piece of paper the universe isn't big enough to hold it (and in some cases, you can't even specifically refer to the number in constructive terms as with π). This turns into a whole philosophical debate which IMO is silly but some people do take pretty seriously. But wait, there's more! The field of real numbers is closed under addition and multiplication (and thus subtraction and division), but it's _not_ closed under some other operations. Suppose you're an EE trying to represent physical signals that very much do exist in reality, and you need to take the root of a negative real number because that is a meaningful quantity in context of the still physically grounded thing you're modeling. Well you can take the root of a negative real number, but that number is not itself a real number. Thus we must define the imaginary numbers to hold those negative roots and then the complex numbers to join the imaginary numbers back to the reals. In every single one of these steps, the new numbers were created to describe aspects of our observed physical reality. The break from the common definition of "numbers are real because I can go buy 24 tangerines and 24 is a number" happened way back at the integers where we added a reflection around the end of the natural numbers. From a perfectly reasonable perspective then, the real and imaginary numbers are both "real" in that they describe actual physical things that exist even though you can not in fact buy -1 apples or 22/7 cats or π bananas or sqrt(-1) movie tickets.
tim333 5y ago
>many calculations for electric circuits are easily done using these numbers. String theory is that to the nth degree. Not really. Imaginary numbers work really well for calculating real physics behaviour, string theory not at all pretty much. Unless n=0 in your analogy.
- pa7x1 5y ago
  What's your background to make such a claim? Are you aware that String theory has made contributions to condensed matter physics and mathematics? Not to speak of its applications to quantum gravity, for example, being able to calculate the entropy of a black hole from counting microstates.
  - adrian_b 5y ago
    You are too optimistic about the contributions of the string theory. A lot of papers and books have been published about the string theory and all claim to calculate something. As an interesting mathematical model, string theory certainly qualifies. On the other hand, as a mathematical model usable in physics, a theory like string theory must pass 3 criteria: 1. It should be able to calculate some numerical values of physical quantities that can be measured. 2. Those measurements must be made and the results must be as predicted, with a reasonable accuracy. 3. It should not be possible to compute the same numerical values that have been validated by measurements using other simpler mathematical models. I have browsed through many research papers and a few books about string theory and I have never seen any results even remotely approaching the fulfillment of these 3 criteria.
    - pa7x1 5y ago
      I think you misunderstand how physical theories work. All physical theories we know have free variables that need to be fixed before being able to make any numerical predictions. In classical electrodynamics it's the permittivity and permeability of the vacuum. In Newton's theory is G. In General Relativity is G and \lambda. In QED is the fine-structure constant, \alpha. And the Standard Model of particle physics has 20 free parameters that have to be set by hand using input from the experiment before being able to use it to make precise numerical computations and having any predictive power. If you don't fix these inputs you don't have a theory, you have a family of theories and you cannot discern which one is the correct one. On top of that, Quantum Field Theory (QFT) the "theory" (continue reading to see why the word theory is a misnomer) that underlies the Standard Model is not constraining enough and you still need to pick the right gauge theories that model our universe. So QFT is better understood as a framework, from which we build a model of reality by hand-picking some theories that seem to suit our universe, then we fix their free parameters using experiments and only then we can predict everything else. String Theory is much the same as QFT in this regard. It's a framework for building physical theories. It arguably has less free-parameters (it has only 1), the string tension. Buy you still need to pick the right models within the framework, here again String Theory is arguably more constraining but you still have an immense amount of options, commonly referred as the String Theory landscape (or vacua) and relate to how you compactify the extra dimensions. So if you applied the same criteria to Quantum Field Theory you would come to the conclusion that is "an interesting mathematical model" but a "useless physical theory". Disclaimer: I studied Theoretical Physics. I do not work in academia or in physics, for that matter. My sustenance does not depend on money flowing into High Energy physics.
adrian_b 5y ago
The comparison with the imaginary numbers is not the best, because the imaginary numbers are as real as the real numbers. While the real number 2.0 can represent the scaling of a vector by 2, the imaginary unit is the rotation of the same vector by a right angle. Any oscillation is equivalent with the projection of a rotation on an axis. Because it is easier to make computations with rotations, all the calculations for electric circuits use rotations to model the oscillations, therefore they use imaginary numbers. This name of "imaginary" numbers should better be abandoned, or at least their meaning should be much better explained in school, because they are not some mathematical abstraction used only in seldom cases, but it is almost impossible to design a device that does not use rotations either in the actual space or in an abstract space, thus needing imaginary numbers for mathematical modelling. On the other hand, string theory and a few other theories that are explored by some physicists are completely artificial mathematical models about which nobody has proven yet that they have any relationship with the real world.

mgamache 5y ago

Eventually it will sort out yes. There's a cost to beating a dead horse in time and resources. We've been stuck for 40 years: Physicists today can happily make career by writing papers about things no one has ever observed, and never will observe. This continues to go on because there is nothing and no one that can stop it. https://iai.tv/articles/why-physics-has-made-no-progress-in-50-years-auid-1292 https://iai.tv/articles/why-physics-has-made-no-progress-in-...

throwaway81523 5y ago
Nobody has ever observed the interior of a black hole and reported the results to the outside, and nobody ever will (unless GR is drastically wrong). And yet we consider our theory of BH interiors to be basically valid except at the center, where it breaks down. That's perfectly good physics, so deal with it.

sorokod 5y ago

> imaginary numbers are fake and don’t exist, In what relevant sense do imagenary numbers differ from real numbers? Being a mathematical abstraction they are in no way required to help approximate phisical reality. That they do is a source of wonder to many, but that is beside the point.

katmannthree 5y ago

> It’s like imaginary numbers are fake and don’t exist It's even better than that. Working from the other side, we generally take the natural numbers N = {0, 1, 2, 3, ...} to be "real" in a philosophical sense as we have an implied mapping of x in N fundamentally describing possession of discrete quantities of goods. This get a little more tricky when you generalize it to the integers Z = {..., -2, -1, 0, 1, 2, ...}, but we still consider these physically grounded as you can "owe" a discrete quantity of goods to someone. This is an incomplete mapping to reality as possession of y goods where y is in Z- doesn't actually describe where your y goods go to, but it's useful enough that we ignore that. Now that's all good and well for discrete quantities of goods, but what about fractional quantities? We need a new system to describe more numbers between the numbers we already have. Thus we defined the set of rational numbers Q = {n | n = p/q where p, q are in Z and q is not 0}. This lets us compactly describe almost any number we want between the existing integers. Most still consider these to be physically grounded, because we created these to describe concrete things in our reality which they do very compactly. You can claim that at least some of these are physically grounded in reality as using 1/3 a cup of flour or buying 1/2 a watermelon is certainly something one can very clearly and explicitly do. The rationals have some issues though, namely that they still have holes in them. Suppose you want to describe the relationship between the diameter of a circle and its circumference. The constant you use to transform one to the other, π, does not exist in Q. You can get as close as you like, but you can't actually reach it. That's a bit of a problem for people whose job it is to make sure that the things math says are correct are actually fully correct. There are other problems, suppose you want to make a rectangular plot of land whose area is 2 square miles. How long does each side need to be? You can get as close as you like by using rational numbers, but the actual length of that side (sqrt(2)) is not in Q. To fix this, we then very delicately construct the set of real numbers R = {x | where x is in {Q and all of the numbers described above which are missing from Q}}. This is where the physical grounding of the numbers starts to get ugly, because as it turns out that just like for some numbers in Q (consider 22/7, which does not evaluate to a fixed number of digits but rather goes on forever) these are uncountable and most of them unrepresentable, i.e. if you tried to write the number out completely on a piece of paper the universe isn't big enough to hold it (and in some cases, you can't even specifically refer to the number in constructive terms as with π). This turns into a whole philosophical debate which IMO is silly but some people do take pretty seriously. But wait, there's more! The field of real numbers is closed under addition and multiplication (and thus subtraction and division), but it's _not_ closed under some other operations. Suppose you're an EE trying to represent physical signals that very much do exist in reality, and you need to take the root of a negative real number because that is a meaningful quantity in context of the still physically grounded thing you're modeling. Well you can take the root of a negative real number, but that number is not itself a real number. Thus we must define the imaginary numbers to hold those negative roots and then the complex numbers to join the imaginary numbers back to the reals. In every single one of these steps, the new numbers were created to describe aspects of our observed physical reality. The break from the common definition of "numbers are real because I can go buy 24 tangerines and 24 is a number" happened way back at the integers where we added a reflection around the end of the natural numbers. From a perfectly reasonable perspective then, the real and imaginary numbers are both "real" in that they describe actual physical things that exist even though you can not in fact buy -1 apples or 22/7 cats or π bananas or sqrt(-1) movie tickets.

tim333 5y ago

>many calculations for electric circuits are easily done using these numbers. String theory is that to the nth degree. Not really. Imaginary numbers work really well for calculating real physics behaviour, string theory not at all pretty much. Unless n=0 in your analogy.

pa7x1 5y ago
What's your background to make such a claim? Are you aware that String theory has made contributions to condensed matter physics and mathematics? Not to speak of its applications to quantum gravity, for example, being able to calculate the entropy of a black hole from counting microstates.
- adrian_b 5y ago
  You are too optimistic about the contributions of the string theory. A lot of papers and books have been published about the string theory and all claim to calculate something. As an interesting mathematical model, string theory certainly qualifies. On the other hand, as a mathematical model usable in physics, a theory like string theory must pass 3 criteria: 1. It should be able to calculate some numerical values of physical quantities that can be measured. 2. Those measurements must be made and the results must be as predicted, with a reasonable accuracy. 3. It should not be possible to compute the same numerical values that have been validated by measurements using other simpler mathematical models. I have browsed through many research papers and a few books about string theory and I have never seen any results even remotely approaching the fulfillment of these 3 criteria.
  - pa7x1 5y ago
    I think you misunderstand how physical theories work. All physical theories we know have free variables that need to be fixed before being able to make any numerical predictions. In classical electrodynamics it's the permittivity and permeability of the vacuum. In Newton's theory is G. In General Relativity is G and \lambda. In QED is the fine-structure constant, \alpha. And the Standard Model of particle physics has 20 free parameters that have to be set by hand using input from the experiment before being able to use it to make precise numerical computations and having any predictive power. If you don't fix these inputs you don't have a theory, you have a family of theories and you cannot discern which one is the correct one. On top of that, Quantum Field Theory (QFT) the "theory" (continue reading to see why the word theory is a misnomer) that underlies the Standard Model is not constraining enough and you still need to pick the right gauge theories that model our universe. So QFT is better understood as a framework, from which we build a model of reality by hand-picking some theories that seem to suit our universe, then we fix their free parameters using experiments and only then we can predict everything else. String Theory is much the same as QFT in this regard. It's a framework for building physical theories. It arguably has less free-parameters (it has only 1), the string tension. Buy you still need to pick the right models within the framework, here again String Theory is arguably more constraining but you still have an immense amount of options, commonly referred as the String Theory landscape (or vacua) and relate to how you compactify the extra dimensions. So if you applied the same criteria to Quantum Field Theory you would come to the conclusion that is "an interesting mathematical model" but a "useless physical theory". Disclaimer: I studied Theoretical Physics. I do not work in academia or in physics, for that matter. My sustenance does not depend on money flowing into High Energy physics.

adrian_b 5y ago

The comparison with the imaginary numbers is not the best, because the imaginary numbers are as real as the real numbers. While the real number 2.0 can represent the scaling of a vector by 2, the imaginary unit is the rotation of the same vector by a right angle. Any oscillation is equivalent with the projection of a rotation on an axis. Because it is easier to make computations with rotations, all the calculations for electric circuits use rotations to model the oscillations, therefore they use imaginary numbers. This name of "imaginary" numbers should better be abandoned, or at least their meaning should be much better explained in school, because they are not some mathematical abstraction used only in seldom cases, but it is almost impossible to design a device that does not use rotations either in the actual space or in an abstract space, thus needing imaginary numbers for mathematical modelling. On the other hand, string theory and a few other theories that are explored by some physicists are completely artificial mathematical models about which nobody has proven yet that they have any relationship with the real world.