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Comment by cool-RR | Hacker News Reader

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.)

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Until physicists can solve a problem like this, they can take their time with quantum gravity and string theory.

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I think you were referring to the 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.

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.

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.

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 - add in 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.

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?

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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 )

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.

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

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.

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

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.

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.

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.

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.

Well, it isn't, and no, I haven't confused General with Special Relativity, trust me on that :) Maybe you confused Quantum Mechanics with Quantum Field Theory?

I think I meant QED, sorry.

Ah OK then yes, QED is relativistic and in the classical limit it should become classical electrodynamics.

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.

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.)

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?

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.

Assume we do this experiment. We can do it as many times as we wish, changing the positions, velocities, etc. of the bodies as we wish, until we have as many cases as we want.

Do you believe we will not succeed in detecting a pattern and predicting how any such system will behave?

You mean, assume we take a bunch of charged particles with relativistic speeds and see what happens when they interact? That's what physicists do using accelerators. (Except they don't really observe the positions of particles at all times, they just see what goes in and what comes out, which is OK because as I mentioned that is all we can compute anyway.) When the velocities, and therefore energies, involved are really high you can't talk of any classical approximation because the quantum-field-theoretic effects take over and you observe phenomena like particle creation and annihilation etc. When the velocities are low you will probably observe non-relativistic two-body Coulomb scattering, which is mathematically no different from the Newtonian interaction between a planetoid and the Sun.

I think you are complicating this too much.

Firstly, I don't mean particles; Just small enough bodies. And near-lightspeed velocities are not necessary; Maybe 5% of lightspeed will do.

When the velocities are low you will probably observe non-relativistic two-body Coulomb scattering, which is mathematically no different from the Newtonian interaction between a planetoid and the Sun.

Dude, what does that mean? Can you solve the problem I raised or not?

Dude, what does that mean?

Dude, google it if you want to know: http://www.google.com/search?q=coulomb+scattering

Can you solve the problem I raised or not?

This I believe I have already answered above.

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