7 ms·

Lost Causes of Theoretical Physics (2003)

98 points by scottlocklin 9y ago

sgillen 9y ago
The many worlds interpretation is just that, and INTERPRETATION, not a predictive theory. The article seems really upset by that, but is it any reason to label it a lost cause? I guess you can’t really study it or preform experiments on it but that shouldn’t be any suprise for any interpretation of quantum mechanics. I might be missing something here...
- ajkjk 9y ago
  After skimming the whole thing, I was relieved to see that the argument against Many Worlds was the only one I considered invalid. It took the form of "It's not even a testable theory", rather than "it has mathematical deficiencies". Well, of course, no one's saying it's testable necessarily, but for various aesthetic and intuitive reasons it still seems valid. Just don't expect predictions from it and you'll be fine.
  - whatshisface 9y ago
    Valid and true are two very different things - and we've seen from history that the human brain can be lead into believing that essentially anything is intuitive or aesthetic.
    - ajkjk 9y ago
      Sure, hence the reason physicists tend to say MWI is valid and good, rather than 'true'.
  - naasking 9y ago
    > After skimming the whole thing, I was relieved to see that the argument against Many Worlds was the only one I considered invalid. You should consider the Bohmian criticisms invalid as well then. Many have argued that de Broglie-Bohm is "many worlds in disguise", so if the criticisms the author levels against Bohmian mechanics are true, then they apply to MWI, but if they don't apply to MWI, then they don't apply to Bohmian mechanics either. Not because they are the same theory, because they are not ontologically the same, but the formalisms are interchangeable.
    - ajkjk 9y ago
      Oh yeah. Probably, yeah. I glossed over that one because its criticisms were strangely technical for a theory that, iirc, just rephrases regular quantum theory.
- IntronExon 9y ago
  From other sections it seems clear that the author is a devout adherent of The Copenhagen Interpretation, aka objective wavefunction collapse; this is a close relative of the baseline non-Interpretation “Shut Up And Calculate.” People like that are generally utterly unmoved by anything short of a rigorous mathematical formulation, which works for them in QM where “rigorous mathematical formulation” is pretty much all of what matters. While I respect the adherence to formalism, the notion that our imperfect view of QM (it doesn’t mesh with GTR after all) represents an ontology to hang your hat on is less respectable. Wavefunction collapse seems like a massive cop-out, and it won’t satisfy anyone except the most rigid logical positivist. Something like MWI is on the other end of the philosophical spectrum, so the hostility is not surprising. At the end of the day though, it comes down to this: If you want to build something based on QM, you need someone like this guy. If you want to satisfy your human need for an ontology, he won’t help you.
  - Retra 9y ago
    I would argue that expecting QM to satisfy a human need for ontology is about as useful as expecting general relativity to satisfy a human need for sexual gratification. It's easy to find a way to be dissatisfied: just want more out of things. But it doesn't make sense to always expect to get what you want. Some things simply won't provide. As long as QM is providing a means to achieve accurate predictions and precise language, it is doing its job perfectly. It is not responsible for satisfying a (potentially irrational) need for ontological interpretation.
    - IntronExon 9y ago
      And if QM and GTR agreed in their predictions I’d be right there with you, telling people to suck it up. I’m a bit there with you anyway, because nature has no obligation to us, and the predictive power of QM is just incredible. But... in the absence of a complete theory including gravity, there are huge gaps. It’s just human nature to try and fill those gaps, for better or worse. For worse when people stuff those gaps with god, but for better when they’re uncomfortable with overly pat explanations like objective collapse.
- omazurov 9y ago
  > The many worlds interpretation is just that, and INTERPRETATION, not a predictive theory. How does the many worlds interpretation INTERPRET the Born rule? Shouldn't that be a key feature of any QM interpretation?
- whereismypwd 9y ago
  His argument is that it's useless as a research topic because you cannot perform experiments about it. You can still believe it if you like, but its slightly less useful than trying to convince everyone to replace pi with tau..
  - hawkice 9y ago
    I mean, the pi/tau thing is _purely_ aesthetic. That's a big waste of time for sure. Having a more coherent metaphor for the evolution of quantum systems might help with physical insight, though. If e.g. the universe isn't differentiable across spacetime, we need a better understanding of GR. Many worlds insists it is differentiable (and local), so thinking that way could help integrate the two. It isn't an important thing, but pi/tau is an unrealistically silly thing to compare it to.
  - gizmo686 9y ago
    QM is a mathematical model. Many worlds is an intuition to understand that model. There is a pedagogical question on if many worlds is a useful mental model to have. There is also a philosophical question of if many worlds better captures the essence of the model relative to Copenhagen. We can also flip it around. Why should we think of QM in terms of the Copenhagen when it makes to testable predictions.
    - millstone 9y ago
      Wouldn't you consider the Born rule to be a testable prediction (though in an admittedly weak sense of simply being postulated)? If the Born rule were found to be violated, it would invalidate Copenhagen but not MWI, which IMO means Copenhagen is more falsifiable.
      - naasking 9y ago
        > If the Born rule were found to be violated, it would invalidate Copenhagen but not MWI, which IMO means Copenhagen is more falsifiable. All quantum mechanical interpretations depend upon the Born rule. A violation of the Born rule would rule them all out, except perhaps Bohmian mechanics which allows the possibility of non-equilibrium states, but we have no idea if those can be created.
- zombieprocesses 9y ago
  If a theory isn't predictive, it isn't falsifiable. If it isn't falsifiable, then the theory isn't truly scientific. This is a major issue/concern in advanced theoretical physics. Is it really physics if you can't experiment or is it just mathematics? The foundation of science is falsiability within the scientific method. It's the core tenet.
  - sgillen 9y ago
    For sure, I’m by trying to say it’s a real theory, it’s just a way to interpret the quantum mechanics that we can test in a way that provide us with some sort of intuition when working with the physics.
  - jamesrcole 9y ago
    But what if, after spending more time working on and thinking about it, someone does find a way to make predictions based on it or on an extension/modification of it? If that's a possibility (I can't say, I'm not a physicist) then I'd be a mistake to discard it on the basis that it's just not predictive now.
  - TheOtherHobbes 9y ago
    But you need to do a lot of speculative work before falsifiability becomes possible. And that speculative work is going to involve groping around in the dark being guided by mathematical logic (and a certain amount of politics, fashion, and wishful thinking.) Considering physics as if MWI could be true has the potential to lead to mathematical elaboration and eventual falsifiability. Considering physics as if there's no need to interpret QM because there's nothing to interpret (because Copenhagen is the correct interpretation) is a statement of faith, not rigour - because as a position, it's no more falsifiable than MWI, or Bohm, or any of the other interpretations. The point of mathematical physics is to generate new falsifiable predictions. It's still science, it's just embryonic proto-knowledge - which is why it's called research, not teaching.
  - naasking 9y ago
    > If a theory isn't predictive, it isn't falsifiable. If it isn't falsifiable, then the theory isn't truly scientific. That's an overly anemic view of science. Scientific theories have both predictive and explanatory power. Interpretations of QM don't change the former, but they do change the latter. Copenhagen, favoured by this article's author for some unfathomable reason, has little explanatory power. Many worlds and Bohmian mechanics have excellent explanatory power, and their predictive power equals Copenhagen.
- akvadrako 9y ago
  It does make different predictions though. WMI essentially says there is only unitary evolution and nothing like a physical collapse. That means everything unitary evolution predicts will happen, unlike other "interpretations". This matters in at least two cases: (1) In a finite system (perhaps our universe, but doubtful), those other worlds will eventually come back into contact. They never go away and with only a finite number of states available, the splitting of worlds can't continue forever. (2) From a subjective perspective, there is always a future version of yourself in some "branch". Since you will become all future versions, you are subjectively immortal.
carlob 9y ago
> Aspect, Dalibrand and Roger (1982) Aspect, Dalibard and Roger (1982)
- rubidium 9y ago
  Grad school physics was/is your background I assume. I had the same thought when reading.
  - carlob 9y ago
    Yep, I was a graduate student in physics, but not at all in that field. The reason why I recognize Dalibard's name even misspelled is because I was a student in the same institution and I used to know several of his grad students. Little bit of trivia: he was 23 or 24 when he wrote that paper…
qwerty456127 9y ago
I'm not a physicist but as far as I know the key concept of the Everett interpretation is that you can think of universe states as of vectors and perform mathematical operations on them. IMHO giving up the ability to think this way would be a tragic loss. Many other parts of the list would make a huge pity to forget too.
zakk 9y ago
> Rigorous Feynman Path Integrals It depends on how rigorous you want the treatment to be. The whole machinery of Feynman diagrams is derived from Path Integrals and Wick's Theorem, so they are rigorous, at least as rigorous as standard perturbation theory using operatorial quantum mechanics. A mathematical physicist won't be amused, though, that's correct. But I wouldn't say that Path Integrals are less rigorous than the average technique used in Theoretical Physics, and particularly in many-body theory.
- auntienomen 9y ago
  I think it's incorrect to say that Feynman diagrams are as rigorous as standard perturbation theory. Perturbation theory in QM has a completely rigorous description. It's controlled approximations to known mathematical objects. By contrast, the derivation of perturbation theory in quantum field theory involves applying reasonable well-understood transformations to mathematical objects which are largely _unknown_. Nothing protects you from garbage-in, garbage out. (Perturbation theory turns out perfectly sensible looking answers for theories like 6 dimensional scalar field theory, which doesn't actually exist.) That said, Feynman integrals are something mathematical physicists have a reasonable level of comfort with these days. There's a well-developed theory of Euclidean path integrals which works just the way Feynman integrals are supposed to. The rigorously constructed examples are lower dimensional field theories, like scalar field theory in 3d, but they don't really differ in kind from the 4d theories used in particle physics. It's just that the analysis gets significantly harder in 4d.
- evanb 9y ago
  There's been a lot of progress nonperturbatively defining quantum mechanics and quantum field theory using resurgence lately. See, for example, the very recent https://arxiv.org/abs/1802.10441 https://arxiv.org/abs/1802.10441
evanb 9y ago
There has been an enormous resurrection of the analytic bootstrap. Grep, for example, https://www.icts.res.in/program/NUMSTRINGS2018/talks https://www.icts.res.in/program/NUMSTRINGS2018/talks for bootstrap. The difference is the realization that the bootstrap equations can be solved numerically and can be thought of as a way to test whether certain conformal theories exist at all, rather than as a way to take you from hardly-any-input-at-all to a complete description of the theory.
hliyan 9y ago
Not a physicist, but isn't "Bohmian Mechanics" (1) what's also known as "Pilot Wave Theory", which is now gaining experimental support (2) ? Clarke's First Law: "When a distinguished but elderly scientist states that something is possible, he is almost certainly right. When he states that something is impossible, he is very probably wrong." 1. https://en.wikipedia.org/wiki/De_Broglie–Bohm_theory https://en.wikipedia.org/wiki/De_Broglie–Bohm_theory 2. https://www.quantamagazine.org/pilot-wave-theory-gains-experimental-support-20160516/ https://www.quantamagazine.org/pilot-wave-theory-gains-exper...
- whatshisface 9y ago
  Pilot waves, multiverse and Copenhagen are fundamentally ineligible for experimental support, at least with respect to each other. They lead to the same numbers, meaning than an experiment that agrees with one will also agree with the others. It's something like trying to tell the difference between 2x=2y and x+2=y+2. The "support" in the article is really just a physical system that obeys (as a macroscopic approximation) something like pilot waves: "just like the universe" if pilot waves are right, and "just like those silly nonlocalists" if pilot waves aren't.
  - OscarCunningham 9y ago
    Right. It doesn't provide evidence for pilot wave theory any more than rolling some balls around on a rubber sheet provides support for Glgeneral relativity.
  - John_KZ 9y ago
    While the current formulation details of the pilot wave theory doesn't allow for new predictions, a better formulated one will. I strongly believe we'll see the breakthrough in the coming 10-15 years. Quantum mechanics are statistic predictions and it's about time we treat them as such.
    - naasking 9y ago
      > While the current formulation details of the pilot wave theory doesn't allow for new predictions Actually pilot wave theories do have new predictions, namely quantum non-equilibrium. We just have no idea if we can actually design an experiment for it.
soVeryTired 9y ago
Can anyone explain Feynman path intergrals to a non-physicist? I'm guessing there's a bit more to it than defining a measure on C[0, T] and lebesgue integrating.
dandare 9y ago
Does it say Mach Principle is incorrect? That is good, as a non physicist I could never wrap my head around the distant stars influencing anything.
- akvadrako 9y ago
  The distant stars are important because they make space flat. Remember that general relativity says mass bends space, or more accurately is the same thing as space. So if all the mass was nearby, space would bend inward around the current point and it would fold in on itself - the universe would be like the inside of a sphere. Because the mass is distributed evenly at the largest scales, it instead continues flatly in all directions.
  - posterboy 9y ago
    > the universe would be like the inside of a sphere. The surface of which is "flat"? The interior surface, if that's the right word. Like living on the Event Horizon of a black hole. So we don't and hardly can know what's outside or inside or on the outside or inside.

98 points by scottlocklin 9y ago

The many worlds interpretation is just that, and INTERPRETATION, not a predictive theory. The article seems really upset by that, but is it any reason to label it a lost cause? I guess you can’t really study it or preform experiments on it but that shouldn’t be any suprise for any interpretation of quantum mechanics. I might be missing something here...

ajkjk 9y ago
After skimming the whole thing, I was relieved to see that the argument against Many Worlds was the only one I considered invalid. It took the form of "It's not even a testable theory", rather than "it has mathematical deficiencies". Well, of course, no one's saying it's testable necessarily, but for various aesthetic and intuitive reasons it still seems valid. Just don't expect predictions from it and you'll be fine.
- whatshisface 9y ago
  Valid and true are two very different things - and we've seen from history that the human brain can be lead into believing that essentially anything is intuitive or aesthetic.
  - ajkjk 9y ago
    Sure, hence the reason physicists tend to say MWI is valid and good, rather than 'true'.
- naasking 9y ago
  > After skimming the whole thing, I was relieved to see that the argument against Many Worlds was the only one I considered invalid. You should consider the Bohmian criticisms invalid as well then. Many have argued that de Broglie-Bohm is "many worlds in disguise", so if the criticisms the author levels against Bohmian mechanics are true, then they apply to MWI, but if they don't apply to MWI, then they don't apply to Bohmian mechanics either. Not because they are the same theory, because they are not ontologically the same, but the formalisms are interchangeable.
  - ajkjk 9y ago
    Oh yeah. Probably, yeah. I glossed over that one because its criticisms were strangely technical for a theory that, iirc, just rephrases regular quantum theory.
IntronExon 9y ago
From other sections it seems clear that the author is a devout adherent of The Copenhagen Interpretation, aka objective wavefunction collapse; this is a close relative of the baseline non-Interpretation “Shut Up And Calculate.” People like that are generally utterly unmoved by anything short of a rigorous mathematical formulation, which works for them in QM where “rigorous mathematical formulation” is pretty much all of what matters. While I respect the adherence to formalism, the notion that our imperfect view of QM (it doesn’t mesh with GTR after all) represents an ontology to hang your hat on is less respectable. Wavefunction collapse seems like a massive cop-out, and it won’t satisfy anyone except the most rigid logical positivist. Something like MWI is on the other end of the philosophical spectrum, so the hostility is not surprising. At the end of the day though, it comes down to this: If you want to build something based on QM, you need someone like this guy. If you want to satisfy your human need for an ontology, he won’t help you.
- Retra 9y ago
  I would argue that expecting QM to satisfy a human need for ontology is about as useful as expecting general relativity to satisfy a human need for sexual gratification. It's easy to find a way to be dissatisfied: just want more out of things. But it doesn't make sense to always expect to get what you want. Some things simply won't provide. As long as QM is providing a means to achieve accurate predictions and precise language, it is doing its job perfectly. It is not responsible for satisfying a (potentially irrational) need for ontological interpretation.
  - IntronExon 9y ago
    And if QM and GTR agreed in their predictions I’d be right there with you, telling people to suck it up. I’m a bit there with you anyway, because nature has no obligation to us, and the predictive power of QM is just incredible. But... in the absence of a complete theory including gravity, there are huge gaps. It’s just human nature to try and fill those gaps, for better or worse. For worse when people stuff those gaps with god, but for better when they’re uncomfortable with overly pat explanations like objective collapse.
omazurov 9y ago
> The many worlds interpretation is just that, and INTERPRETATION, not a predictive theory. How does the many worlds interpretation INTERPRET the Born rule? Shouldn't that be a key feature of any QM interpretation?
whereismypwd 9y ago
His argument is that it's useless as a research topic because you cannot perform experiments about it. You can still believe it if you like, but its slightly less useful than trying to convince everyone to replace pi with tau..
- hawkice 9y ago
  I mean, the pi/tau thing is _purely_ aesthetic. That's a big waste of time for sure. Having a more coherent metaphor for the evolution of quantum systems might help with physical insight, though. If e.g. the universe isn't differentiable across spacetime, we need a better understanding of GR. Many worlds insists it is differentiable (and local), so thinking that way could help integrate the two. It isn't an important thing, but pi/tau is an unrealistically silly thing to compare it to.
- gizmo686 9y ago
  QM is a mathematical model. Many worlds is an intuition to understand that model. There is a pedagogical question on if many worlds is a useful mental model to have. There is also a philosophical question of if many worlds better captures the essence of the model relative to Copenhagen. We can also flip it around. Why should we think of QM in terms of the Copenhagen when it makes to testable predictions.
  - millstone 9y ago
    Wouldn't you consider the Born rule to be a testable prediction (though in an admittedly weak sense of simply being postulated)? If the Born rule were found to be violated, it would invalidate Copenhagen but not MWI, which IMO means Copenhagen is more falsifiable.
    - naasking 9y ago
      > If the Born rule were found to be violated, it would invalidate Copenhagen but not MWI, which IMO means Copenhagen is more falsifiable. All quantum mechanical interpretations depend upon the Born rule. A violation of the Born rule would rule them all out, except perhaps Bohmian mechanics which allows the possibility of non-equilibrium states, but we have no idea if those can be created.
zombieprocesses 9y ago
If a theory isn't predictive, it isn't falsifiable. If it isn't falsifiable, then the theory isn't truly scientific. This is a major issue/concern in advanced theoretical physics. Is it really physics if you can't experiment or is it just mathematics? The foundation of science is falsiability within the scientific method. It's the core tenet.
- sgillen 9y ago
  For sure, I’m by trying to say it’s a real theory, it’s just a way to interpret the quantum mechanics that we can test in a way that provide us with some sort of intuition when working with the physics.
- jamesrcole 9y ago
  But what if, after spending more time working on and thinking about it, someone does find a way to make predictions based on it or on an extension/modification of it? If that's a possibility (I can't say, I'm not a physicist) then I'd be a mistake to discard it on the basis that it's just not predictive now.
- TheOtherHobbes 9y ago
  But you need to do a lot of speculative work before falsifiability becomes possible. And that speculative work is going to involve groping around in the dark being guided by mathematical logic (and a certain amount of politics, fashion, and wishful thinking.) Considering physics as if MWI could be true has the potential to lead to mathematical elaboration and eventual falsifiability. Considering physics as if there's no need to interpret QM because there's nothing to interpret (because Copenhagen is the correct interpretation) is a statement of faith, not rigour - because as a position, it's no more falsifiable than MWI, or Bohm, or any of the other interpretations. The point of mathematical physics is to generate new falsifiable predictions. It's still science, it's just embryonic proto-knowledge - which is why it's called research, not teaching.
- naasking 9y ago
  > If a theory isn't predictive, it isn't falsifiable. If it isn't falsifiable, then the theory isn't truly scientific. That's an overly anemic view of science. Scientific theories have both predictive and explanatory power. Interpretations of QM don't change the former, but they do change the latter. Copenhagen, favoured by this article's author for some unfathomable reason, has little explanatory power. Many worlds and Bohmian mechanics have excellent explanatory power, and their predictive power equals Copenhagen.
akvadrako 9y ago
It does make different predictions though. WMI essentially says there is only unitary evolution and nothing like a physical collapse. That means everything unitary evolution predicts will happen, unlike other "interpretations". This matters in at least two cases: (1) In a finite system (perhaps our universe, but doubtful), those other worlds will eventually come back into contact. They never go away and with only a finite number of states available, the splitting of worlds can't continue forever. (2) From a subjective perspective, there is always a future version of yourself in some "branch". Since you will become all future versions, you are subjectively immortal.

carlob 9y ago

> Aspect, Dalibrand and Roger (1982) Aspect, Dalibard and Roger (1982)

rubidium 9y ago
Grad school physics was/is your background I assume. I had the same thought when reading.
- carlob 9y ago
  Yep, I was a graduate student in physics, but not at all in that field. The reason why I recognize Dalibard's name even misspelled is because I was a student in the same institution and I used to know several of his grad students. Little bit of trivia: he was 23 or 24 when he wrote that paper…

qwerty456127 9y ago

I'm not a physicist but as far as I know the key concept of the Everett interpretation is that you can think of universe states as of vectors and perform mathematical operations on them. IMHO giving up the ability to think this way would be a tragic loss. Many other parts of the list would make a huge pity to forget too.

zakk 9y ago

> Rigorous Feynman Path Integrals It depends on how rigorous you want the treatment to be. The whole machinery of Feynman diagrams is derived from Path Integrals and Wick's Theorem, so they are rigorous, at least as rigorous as standard perturbation theory using operatorial quantum mechanics. A mathematical physicist won't be amused, though, that's correct. But I wouldn't say that Path Integrals are less rigorous than the average technique used in Theoretical Physics, and particularly in many-body theory.

auntienomen 9y ago
I think it's incorrect to say that Feynman diagrams are as rigorous as standard perturbation theory. Perturbation theory in QM has a completely rigorous description. It's controlled approximations to known mathematical objects. By contrast, the derivation of perturbation theory in quantum field theory involves applying reasonable well-understood transformations to mathematical objects which are largely _unknown_. Nothing protects you from garbage-in, garbage out. (Perturbation theory turns out perfectly sensible looking answers for theories like 6 dimensional scalar field theory, which doesn't actually exist.) That said, Feynman integrals are something mathematical physicists have a reasonable level of comfort with these days. There's a well-developed theory of Euclidean path integrals which works just the way Feynman integrals are supposed to. The rigorously constructed examples are lower dimensional field theories, like scalar field theory in 3d, but they don't really differ in kind from the 4d theories used in particle physics. It's just that the analysis gets significantly harder in 4d.
evanb 9y ago
There's been a lot of progress nonperturbatively defining quantum mechanics and quantum field theory using resurgence lately. See, for example, the very recent https://arxiv.org/abs/1802.10441 https://arxiv.org/abs/1802.10441

evanb 9y ago

There has been an enormous resurrection of the analytic bootstrap. Grep, for example, https://www.icts.res.in/program/NUMSTRINGS2018/talks https://www.icts.res.in/program/NUMSTRINGS2018/talks for bootstrap. The difference is the realization that the bootstrap equations can be solved numerically and can be thought of as a way to test whether certain conformal theories exist at all, rather than as a way to take you from hardly-any-input-at-all to a complete description of the theory.

hliyan 9y ago

Not a physicist, but isn't "Bohmian Mechanics" (1) what's also known as "Pilot Wave Theory", which is now gaining experimental support (2) ? Clarke's First Law: "When a distinguished but elderly scientist states that something is possible, he is almost certainly right. When he states that something is impossible, he is very probably wrong." 1. https://en.wikipedia.org/wiki/De_Broglie–Bohm_theory https://en.wikipedia.org/wiki/De_Broglie–Bohm_theory 2. https://www.quantamagazine.org/pilot-wave-theory-gains-experimental-support-20160516/ https://www.quantamagazine.org/pilot-wave-theory-gains-exper...

whatshisface 9y ago
Pilot waves, multiverse and Copenhagen are fundamentally ineligible for experimental support, at least with respect to each other. They lead to the same numbers, meaning than an experiment that agrees with one will also agree with the others. It's something like trying to tell the difference between 2x=2y and x+2=y+2. The "support" in the article is really just a physical system that obeys (as a macroscopic approximation) something like pilot waves: "just like the universe" if pilot waves are right, and "just like those silly nonlocalists" if pilot waves aren't.
- OscarCunningham 9y ago
  Right. It doesn't provide evidence for pilot wave theory any more than rolling some balls around on a rubber sheet provides support for Glgeneral relativity.
- John_KZ 9y ago
  While the current formulation details of the pilot wave theory doesn't allow for new predictions, a better formulated one will. I strongly believe we'll see the breakthrough in the coming 10-15 years. Quantum mechanics are statistic predictions and it's about time we treat them as such.
  - naasking 9y ago
    > While the current formulation details of the pilot wave theory doesn't allow for new predictions Actually pilot wave theories do have new predictions, namely quantum non-equilibrium. We just have no idea if we can actually design an experiment for it.

soVeryTired 9y ago

Can anyone explain Feynman path intergrals to a non-physicist? I'm guessing there's a bit more to it than defining a measure on C[0, T] and lebesgue integrating.

dandare 9y ago

Does it say Mach Principle is incorrect? That is good, as a non physicist I could never wrap my head around the distant stars influencing anything.

akvadrako 9y ago
The distant stars are important because they make space flat. Remember that general relativity says mass bends space, or more accurately is the same thing as space. So if all the mass was nearby, space would bend inward around the current point and it would fold in on itself - the universe would be like the inside of a sphere. Because the mass is distributed evenly at the largest scales, it instead continues flatly in all directions.
- posterboy 9y ago
  > the universe would be like the inside of a sphere. The surface of which is "flat"? The interior surface, if that's the right word. Like living on the Event Horizon of a black hole. So we don't and hardly can know what's outside or inside or on the outside or inside.