7 ms·

Physicists are ridiculous. Here's an unsolved problem for you: Given the positions, velocities, masses and charges of a set of macroscopic bodies moving in vac

by cool-RR 17y ago

Physicists are ridiculous. Here's an unsolved problem for you: Given the positions, velocities, masses and charges of a set of macroscopic bodies moving in vacuum, (in speeds which may be relativistic,) calculate the position of each of these bodies after a specified amount of time `t` has passed. (Neglect gravity.) (All quantities are given numerically, and the answers should be numeric too, allowing for a specified margin of error.) --------- Until physicists can solve a problem like this, they can take their time with quantum gravity and string theory.

tome 17y ago
There's a big difference between having a verifiable theory for something which is computationally hard, and having no theory at all!
- cool-RR 17y ago
  I'm sorry, I didn't understand what you are saying. Are you saying that the problem I gave was computationally hard? I only want the algorithm, regardless of how computationally hard it is.
jlefo7p6 17y ago
I think you were referring to the n-body problem (http://en.wikipedia.org/wiki/N-body_problem http://en.wikipedia.org/wiki/N-body_problem). If so, I suggest not neglecting gravity. Without gravity (and either assuming these guys don't run into each other or can somehow pass through each other), the position of each body is independent, and can be found through the following equation: Position = Initial + (Velocity * Time) Blah blah vector components blah blah, but you get my point.
- ars 17y ago
  He included "charge" which (mathematically) is identical to gravity. Plus he said relativistic, so the very concept of "position" (and time) is not so simple.
  - trjordan 17y ago
    If you're assuming a fixed viewer, it's actually pretty easy to define position and time. There are just relativistic corrections to a bunch of the terms.
    - ars 17y ago
      Only if you assume no acceleration on the objects. But he said charge, so they do accelerate. You'd have to figure out the position and velocity of each one relative to the others to figure would what the effect of the charge will be. And don't forget to include the propagation delay of the charge field. This is by far not a simple problem. Much much harder than the N-body problem. If the top poster had only left out "Physicists are ridiculous." it would have been quite an insightful post, instead it was an inciteful one. Look up http://en.wikipedia.org/wiki/Einstein_field_equations http://en.wikipedia.org/wiki/Einstein_field_equations - add in http://en.wikipedia.org/wiki/Stress-energy_tensor http://en.wikipedia.org/wiki/Stress-energy_tensor and you'll see that the motion of relativistic bodies is barely understood. I'm upmoding him, because I think -7 is more than enough.
DarkShikari 17y ago
Mathematicians are ridiculous. Here's an unsolved problem for you: Take a positive number n. If n is odd, triple it and add 1. If n is even, halve it. Repeat the process ad infinitum but stop if n reaches 1. For all numbers n, will this series converge to 1? --------- Until mathematicians can solve a problem like this, they can take their time with the Riemann Hypothesis and Axiom of Choice. ;) ( http://en.wikipedia.org/wiki/Collatz_Conjecture http://en.wikipedia.org/wiki/Collatz_Conjecture )
- cool-RR 17y ago
  Nice parody. I think it's not a valid comparison though. Proving the Collatz Conjecture is not essential for understanding the Riemann Hypothesis, or any other such subject. It will probably not advance the proof of RH at all. On the other hand, knowledge of the problem I raised, motion of charged macroscopic objects, is crucial to understanding Classical Electromagnetism, which is crucial to understand QM, which is crucial to understand most of modern physics.
schtog 17y ago
I think we should close all hospitals. Those stupid doctors can't cure all diseases therefore medicine is complete useless.
- cool-RR 17y ago
  I don't think your analogy is valid: Knowing how to cure all diseases would be a very high goal that stands above what doctors accomplished up to the present time. The challenge that I gave is below what physicists "know" today. When a physicist studies Qunatum Mechanics, he knows that on the macroscopic scale, QM will behave like classical electromagnetism. The problem that I raise, is that physicists don't know classical electromagnetism well enough in the first place. They can't calculate motion of macroscopic objects. I don't think it's wise to try to study QM before they solved that challenge, the same way it won't be wise to start learning Special Relativity before you studied Newtonian Mechanics.
  - schtog 17y ago
    Fair enough, I stand corrected, I commented as I did because I interpreted it as a typical "science can't explain everything therefore it is useless" or "your theory isn't perfect therefore my theory must be correct" rant.
  - pfedor 17y ago
    When a physicist studies Qunatum Mechanics, he knows that on the macroscopic scale, QM will behave like classical electromagnetism. Why do you say this? Quantum Mechanics in the classical limit does not become classical electrodynamics. How could it? QM is non-relativistic. Classical electrodynamics is relativistic. QM in the classical limit becomes classical (Newtonian) mechanics.
    - cool-RR 17y ago
      I admit I haven't studied QM, but I believe that it's relativistic. Maybe you have confused General Relativity with Special Relativity? QM is incompatible with GR, but I think it's based on SR.
cool-RR 17y ago
I apologize for saying physicists are ridiculous. I hope that people who reply to post will state what they think is the status of the problem I raised. Do you think it's solved (give a solution)? Unsolved? Unimportant? Explain.
- pfedor 17y ago
  So for starters, if by "macroscopic" you mean a object that has a finite size (as opposed to point objects), then the problem is underspecified, because you didn't give a model of the finite size objects' behavior under the action of external forces (the model typically used in classical mechanics is that of a rigid body, which means we assume a bunch of points which act on one another with forces necessary to keep the distances between points constant; but it cannot be used for relativistic systems.) If we're talking about points, then the problem cannot be solved in classical electrodynamics because the classical electrodynamics doesn't address the issue of a charge interacting with its own field (for example, an accelerating charged particle emits radiation which slows it down, so called Bremsstrahlung; this phenomenon is not fully tractable withing the framework of classical electrodynamics; it is solved in quantum electrodynamics, to the extent that anything is.)
  - cool-RR 17y ago
    I am talking about point-sized bodies, or at least bodies small enough so their size can be neglected. You say "the problem cannot be solved in classical electrodynamics". Firstly, I'm not sure I agree. Secondly, can it be solved at all? Can you give me an algorithm that will solve this problem?
    - pfedor 17y ago
      You say "the problem cannot be solved in classical electrodynamics". Firstly, I'm not sure I agree. I would be happy to be proven wrong, but that's what I remember from studying physics many years ago. You can calculate the motion of a charged pointlike particle in given fields, and you can calculate the fields produced by charged pointlike particles following any motions, but you can't calculate the effects of the interaction of a particle with its own field. This said, I vaguely remember some tricks that involved arbitrary dropping of some infinite terms, a bit like renormalization in QED only not precisely defined in any way. Perhaps with those tricks you can arrive to some kind of solution. Secondly, can it be solved at all? Can you give me an algorithm that will solve this problem? The interaction of a particle with its own field is tractable in quantum electrodynamics or so I was told. However, as you are no doubt aware, the state of a quantum-mechanical system is not really defined in terms of positions and velocities of a set of particles, so your problem taken literally doesn't make sense in this framework. And even if you re-stated it in an appropriate language, quantum field theory won't give you the precise evolution in time of any system, typically the best you can hope for is a transition amplitude between non-interacting particles in time minus infinity and non-interacting particles in time plus infinity.

by cool-RR 17y ago

tome 17y ago

There's a big difference between having a verifiable theory for something which is computationally hard, and having no theory at all!

cool-RR 17y ago
I'm sorry, I didn't understand what you are saying. Are you saying that the problem I gave was computationally hard? I only want the algorithm, regardless of how computationally hard it is.

jlefo7p6 17y ago

I think you were referring to the n-body problem (http://en.wikipedia.org/wiki/N-body_problem http://en.wikipedia.org/wiki/N-body_problem). If so, I suggest not neglecting gravity. Without gravity (and either assuming these guys don't run into each other or can somehow pass through each other), the position of each body is independent, and can be found through the following equation: Position = Initial + (Velocity * Time) Blah blah vector components blah blah, but you get my point.

ars 17y ago
He included "charge" which (mathematically) is identical to gravity. Plus he said relativistic, so the very concept of "position" (and time) is not so simple.
- trjordan 17y ago
  If you're assuming a fixed viewer, it's actually pretty easy to define position and time. There are just relativistic corrections to a bunch of the terms.
  - ars 17y ago
    Only if you assume no acceleration on the objects. But he said charge, so they do accelerate. You'd have to figure out the position and velocity of each one relative to the others to figure would what the effect of the charge will be. And don't forget to include the propagation delay of the charge field. This is by far not a simple problem. Much much harder than the N-body problem. If the top poster had only left out "Physicists are ridiculous." it would have been quite an insightful post, instead it was an inciteful one. Look up http://en.wikipedia.org/wiki/Einstein_field_equations http://en.wikipedia.org/wiki/Einstein_field_equations - add in http://en.wikipedia.org/wiki/Stress-energy_tensor http://en.wikipedia.org/wiki/Stress-energy_tensor and you'll see that the motion of relativistic bodies is barely understood. I'm upmoding him, because I think -7 is more than enough.

DarkShikari 17y ago

Mathematicians are ridiculous. Here's an unsolved problem for you: Take a positive number n. If n is odd, triple it and add 1. If n is even, halve it. Repeat the process ad infinitum but stop if n reaches 1. For all numbers n, will this series converge to 1? --------- Until mathematicians can solve a problem like this, they can take their time with the Riemann Hypothesis and Axiom of Choice. ;) ( http://en.wikipedia.org/wiki/Collatz_Conjecture http://en.wikipedia.org/wiki/Collatz_Conjecture )

cool-RR 17y ago
Nice parody. I think it's not a valid comparison though. Proving the Collatz Conjecture is not essential for understanding the Riemann Hypothesis, or any other such subject. It will probably not advance the proof of RH at all. On the other hand, knowledge of the problem I raised, motion of charged macroscopic objects, is crucial to understanding Classical Electromagnetism, which is crucial to understand QM, which is crucial to understand most of modern physics.

schtog 17y ago

I think we should close all hospitals. Those stupid doctors can't cure all diseases therefore medicine is complete useless.

cool-RR 17y ago
I don't think your analogy is valid: Knowing how to cure all diseases would be a very high goal that stands above what doctors accomplished up to the present time. The challenge that I gave is below what physicists "know" today. When a physicist studies Qunatum Mechanics, he knows that on the macroscopic scale, QM will behave like classical electromagnetism. The problem that I raise, is that physicists don't know classical electromagnetism well enough in the first place. They can't calculate motion of macroscopic objects. I don't think it's wise to try to study QM before they solved that challenge, the same way it won't be wise to start learning Special Relativity before you studied Newtonian Mechanics.
- schtog 17y ago
  Fair enough, I stand corrected, I commented as I did because I interpreted it as a typical "science can't explain everything therefore it is useless" or "your theory isn't perfect therefore my theory must be correct" rant.
- pfedor 17y ago
  When a physicist studies Qunatum Mechanics, he knows that on the macroscopic scale, QM will behave like classical electromagnetism. Why do you say this? Quantum Mechanics in the classical limit does not become classical electrodynamics. How could it? QM is non-relativistic. Classical electrodynamics is relativistic. QM in the classical limit becomes classical (Newtonian) mechanics.
  - cool-RR 17y ago
    I admit I haven't studied QM, but I believe that it's relativistic. Maybe you have confused General Relativity with Special Relativity? QM is incompatible with GR, but I think it's based on SR.

cool-RR 17y ago

I apologize for saying physicists are ridiculous. I hope that people who reply to post will state what they think is the status of the problem I raised. Do you think it's solved (give a solution)? Unsolved? Unimportant? Explain.

pfedor 17y ago
So for starters, if by "macroscopic" you mean a object that has a finite size (as opposed to point objects), then the problem is underspecified, because you didn't give a model of the finite size objects' behavior under the action of external forces (the model typically used in classical mechanics is that of a rigid body, which means we assume a bunch of points which act on one another with forces necessary to keep the distances between points constant; but it cannot be used for relativistic systems.) If we're talking about points, then the problem cannot be solved in classical electrodynamics because the classical electrodynamics doesn't address the issue of a charge interacting with its own field (for example, an accelerating charged particle emits radiation which slows it down, so called Bremsstrahlung; this phenomenon is not fully tractable withing the framework of classical electrodynamics; it is solved in quantum electrodynamics, to the extent that anything is.)
- cool-RR 17y ago
  I am talking about point-sized bodies, or at least bodies small enough so their size can be neglected. You say "the problem cannot be solved in classical electrodynamics". Firstly, I'm not sure I agree. Secondly, can it be solved at all? Can you give me an algorithm that will solve this problem?
  - pfedor 17y ago
    You say "the problem cannot be solved in classical electrodynamics". Firstly, I'm not sure I agree. I would be happy to be proven wrong, but that's what I remember from studying physics many years ago. You can calculate the motion of a charged pointlike particle in given fields, and you can calculate the fields produced by charged pointlike particles following any motions, but you can't calculate the effects of the interaction of a particle with its own field. This said, I vaguely remember some tricks that involved arbitrary dropping of some infinite terms, a bit like renormalization in QED only not precisely defined in any way. Perhaps with those tricks you can arrive to some kind of solution. Secondly, can it be solved at all? Can you give me an algorithm that will solve this problem? The interaction of a particle with its own field is tractable in quantum electrodynamics or so I was told. However, as you are no doubt aware, the state of a quantum-mechanical system is not really defined in terms of positions and velocities of a set of particles, so your problem taken literally doesn't make sense in this framework. And even if you re-stated it in an appropriate language, quantum field theory won't give you the precise evolution in time of any system, typically the best you can hope for is a transition amplitude between non-interacting particles in time minus infinity and non-interacting particles in time plus infinity.