Would a particle exhibiting non-linear acceleration due to gravity violate the laws of physics? Regardless of whether this is true or not, a linear function is a "pure math" term, as you state it. Something being mathematical doesn't render it totally separate from physics.
The accelerating particle has nothing to do with math. This isn't a math problem. Math is merely used to describe the motion. Now if you laid out the acceleration due to gravity equation and plugged in the particles velocity, trying to reconcile it would be mathematically impossible. However, once again, the equation itself is merely used as a description. The equation can exist just fine without the physics, and physics only needs the equation to help us understand it. The more we know about physics, the more accurate the equations (from Newton to Einstein to quantum, etc). But a math problem remains a math problem only.
As far as NP-completeness, first come up with an algorithm to solve an NP-complete problem in polynomial time. That's pure math. The physics come when it's time to implement that algorithm. k.ovaska's comment states that such an algorithm exists, but a non-deterministic Turing machine (which I take is physically impossible) is necessary. If that's true, that means the algorithm is physically impossible to implement.
Besides, I thought that "NP-complete" was a pure math term. Since when has pure math had anything to do with physics? I can understand that solving an NP-complete problem in polynomial time could be mathematically/logically impossible, but calling it "violating the laws of physics" should be a misnomer. Would a number that's greater than 2 and less than 1 violate the laws of physics? How about a triangle with 4 sides?
However, I got tired of seeing fiction that tried to make me believe things that could not be true due to the laws of physics, or due to other aspects of reality.
To your current understanding of the laws of physics and reality you mean.
Well we can't wait for Titan's puppet master overlords to make it over here and start taking us over, can we? Gotta fight 'em over there so we don't have to fight them over here!
Besides, the Titanians will welcome us as liberators.
Yes, you'll never see any light that it emits _now_. But you are seeing the light that it emitted 18 billion years ago, a time when it was moving close, but not faster than, the speed of light, relative to us.
I'm guessing you mean 12.8 billion years ago. In any case this makes your comment of "The spacetime on which it sits is moving 3 or 4 times the speed of light, relative to us. Even if it was moving really quite fast, it wouldn't affect the redshift by all that much." invalid because the redshift is based on the time when the galaxy was much closer and the relative speed due to expansion much lower.
The spacetime on which it sits is moving 3 or 4 times the speed of light, relative to us.
Seems a bit circular. "We know galaxy is far away because the redshift is caused by expansion. We know redshift is caused by expansion because galaxy is far away."
And maybe I don't understand relativity, but it seems to me that if our galaxy and that one were moving away from each other (due to expansion) at 3 or 4 times the speed of light at the time that the light was emitted, we'd never see that light. I'm pretty sure I read that somewhere too.
What if the redshift is caused by a much closer galaxy moving away from us normally (i.e. not through universal expansion). It could be a mere billion light years away, but with enough relative velocity it would "look" more distant. Or am I misunderstanding something?
upload, post, transmit, share, store or otherwise make available content that would constitute, encourage or provide instructions for a criminal offense, violate the rights of any party, or that would otherwise create liability or violate any local, state, national or international law
Haha, is there anything that could be posted without violating some law somewhere?
And even if one such machine managed to suck all the free energy out of the universe.... then what? Energy still can't be created or destroyed. It's still there, just have to get to it.
This in itself is a very strong blow against perpetual motion machines, since if they could exist, it's likely that one would have appeared naturally, and sucked all the (free) energy available to them.
And how do you know these accidental "natural" machines haven't appeared all over the place? They could've sucked the free energy out of immidiate surroundings, and then stopped. Seems to me that the ability to even measure the amount of free energy directly (instead of calculating it) would imply the ability to harness it (no matter how inefficiently). So how would you know if there was suddenly a lot less free energy in your vicinity.
And, yet, you haven't managed to describe Linux. So your point is?
I wasn't trying to describe Linux. My point is that you can't say "All that's important is that the OS supports the HW/SW I want" because 100% functionality and 0% usability just won't cut it.
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Or just use her name and apply ROT4 encryption. Let her parents try to guess that.
Photons aren't supposed to have mass (otherwise they couldn't travel at light speed), so how are they affected by gravity?
Don't forget, terrorists also have training videos.
If there's no supervision, the Church of Scientology could delete your iPod auction because it thinks you're an incarnation of Xenu.
I'm getting ########### myself.
Would a particle exhibiting non-linear acceleration due to gravity violate the laws of physics? Regardless of whether this is true or not, a linear function is a "pure math" term, as you state it. Something being mathematical doesn't render it totally separate from physics.
The accelerating particle has nothing to do with math. This isn't a math problem. Math is merely used to describe the motion. Now if you laid out the acceleration due to gravity equation and plugged in the particles velocity, trying to reconcile it would be mathematically impossible. However, once again, the equation itself is merely used as a description. The equation can exist just fine without the physics, and physics only needs the equation to help us understand it. The more we know about physics, the more accurate the equations (from Newton to Einstein to quantum, etc). But a math problem remains a math problem only.
As far as NP-completeness, first come up with an algorithm to solve an NP-complete problem in polynomial time. That's pure math. The physics come when it's time to implement that algorithm. k.ovaska's comment states that such an algorithm exists, but a non-deterministic Turing machine (which I take is physically impossible) is necessary. If that's true, that means the algorithm is physically impossible to implement.
Besides, I thought that "NP-complete" was a pure math term. Since when has pure math had anything to do with physics? I can understand that solving an NP-complete problem in polynomial time could be mathematically/logically impossible, but calling it "violating the laws of physics" should be a misnomer. Would a number that's greater than 2 and less than 1 violate the laws of physics? How about a triangle with 4 sides?
It's a million-to-one chance, but it might just work!
There, now if you're exactly right about the odds, it will happen.
Side effects include eye irritation, and death. Then there will be cake.
Jonathan? Is that you?
However, I got tired of seeing fiction that tried to make me believe things that could not be true due to the laws of physics, or due to other aspects of reality.
To your current understanding of the laws of physics and reality you mean.
Well we can't wait for Titan's puppet master overlords to make it over here and start taking us over, can we? Gotta fight 'em over there so we don't have to fight them over here!
Besides, the Titanians will welcome us as liberators.
You're joking now, but when it turns out that those molecules really are sentient....
Yes, you'll never see any light that it emits _now_. But you are seeing the light that it emitted 18 billion years ago, a time when it was moving close, but not faster than, the speed of light, relative to us.
I'm guessing you mean 12.8 billion years ago. In any case this makes your comment of "The spacetime on which it sits is moving 3 or 4 times the speed of light, relative to us. Even if it was moving really quite fast, it wouldn't affect the redshift by all that much." invalid because the redshift is based on the time when the galaxy was much closer and the relative speed due to expansion much lower.
Wouldn't that be like comparing the relative velocity of Alpha Centauri to that of a star on the opposite edge of the Milky Way?
The spacetime on which it sits is moving 3 or 4 times the speed of light, relative to us.
Seems a bit circular. "We know galaxy is far away because the redshift is caused by expansion. We know redshift is caused by expansion because galaxy is far away."
And maybe I don't understand relativity, but it seems to me that if our galaxy and that one were moving away from each other (due to expansion) at 3 or 4 times the speed of light at the time that the light was emitted, we'd never see that light. I'm pretty sure I read that somewhere too.
What if the redshift is caused by a much closer galaxy moving away from us normally (i.e. not through universal expansion). It could be a mere billion light years away, but with enough relative velocity it would "look" more distant. Or am I misunderstanding something?
Imagine buying a 12 cylinder Lamborguini, getting on a highway, and then realizing that if its speed drops below 55mph it will explode.
Reactivate your account and "update" the email address.
upload, post, transmit, share, store or otherwise make available content that would constitute, encourage or provide instructions for a criminal offense, violate the rights of any party, or that would otherwise create liability or violate any local, state, national or international law
Haha, is there anything that could be posted without violating some law somewhere?
If every slashdotter could get a TV for every 6 months of no sex, you'd quickly be out of business.
Glad to see I'm not the only one who immediately thought of that. Never seen the "Try to be more original" error on slashdot before!
And even if one such machine managed to suck all the free energy out of the universe.... then what? Energy still can't be created or destroyed. It's still there, just have to get to it.
This in itself is a very strong blow against perpetual motion machines, since if they could exist, it's likely that one would have appeared naturally, and sucked all the (free) energy available to them.
And how do you know these accidental "natural" machines haven't appeared all over the place? They could've sucked the free energy out of immidiate surroundings, and then stopped. Seems to me that the ability to even measure the amount of free energy directly (instead of calculating it) would imply the ability to harness it (no matter how inefficiently). So how would you know if there was suddenly a lot less free energy in your vicinity.
And, yet, you haven't managed to describe Linux. So your point is?
I wasn't trying to describe Linux. My point is that you can't say "All that's important is that the OS supports the HW/SW I want" because 100% functionality and 0% usability just won't cut it.