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[Heliman]

Question for the more physics-minded folks out there:

Breaking c seems relatively simple in a relative frame. You send one observer at 0.55c in one direction. You send another observer at 0.55c in the opposite direction. To each observer's relative frame, the other is moving at 1.1c, correct?

For one, I always wondered what the hell that would look like. Would they be seeing an after-image? Would it be like a Doppler shift from hell?
Second, I haven't read the paper, but did they account in any way for the Earth's orbital/rotational motion and Sol's movement? Maybe neutrinos operate somehow so as to be outside the relative observer frame? If that even makes sense....

They may not have needed to Redking. Any apparatus for testing velocity that could be used would necessarily be just as effected by they earth's rotation and the pull from Sol's movement.

What COULD have happened though is that these neutrinos are partially or totally unaffected by the earth/ Sol's movement. That's would be just as crazy though.

[RedKing]

They'd have to make pretty damn sure they get every single thing possible accounted for, so i'd say yes. They're double-checking everything just in case, but they get paid to not fuck it up like that.

I know, I'm just trying to think "outside the box" (and given my pitiably small schooling in physics, I'm probably so far inside the box that I can't even see the entrance anymore).

I love that the CERN scientists aren't like "Woo! We broke the speed of light!" but rather "Umm...that wasn't supposed to happen. These numbers can't be right. Please, somebody out there tell us what we did wrong." That reluctance is a big part of why I'm more confident than most extraordinary claims that this one is legit.

[Blargityblarg]

They'd have to make pretty damn sure they get every single thing possible accounted for, so i'd say yes. They're double-checking everything just in case, but they get paid to not fuck it up like that.

I know, I'm just trying to think "outside the box" (and given my pitiably small schooling in physics, I'm probably so far inside the box that I can't even see the entrance anymore).

I love that the CERN scientists aren't like "Woo! We broke the speed of light!" but rather "Umm...that wasn't supposed to happen. These numbers can't be right. Please, somebody out there tell us what we did wrong." That reluctance is a big part of why I'm more confident than most extraordinary claims that this one is legit.

Yeah, explaining C as the top speed is pretty much why relativity is there.

[Willfor]

Picard: Warp 11, ensign. Engage.
Ensign: FFFFUUUUU...

It's been a while since I've seen any TNG/read the technical manuals/discussed this with one particularly fine example of the Trekker oevre...  They were on the revised "Warp 10 equals infinite speed" scale, weren't they?  (Whereas TOS, especially in STIV:tVH still had a continual logarithmic thing...)

According to canon, if you pass warp 10 you turn into a horny prehistoric lizard.

Have a video from the writer of the episode disavowing himself of it.

[Logical2u]

Question for the more physics-minded folks out there:

Breaking c seems relatively simple in a relative frame. You send one observer at 0.55c in one direction. You send another observer at 0.55c in the opposite direction. To each observer's relative frame, the other is moving at 1.1c, correct?

G-flex has mentioned this, but I'm unsure of how much detail this topic has been discussed with yet... once you start approaching considerable fractions of C, a change of reference frame no longer obeys Gallilean transformations, but rather Lorentz transformations. Applying these transformations, as byproducts of relativity, results in things like time dilation (a moving clock runs slow) and length contraction (moving rulers are shorter). Velocity, being defined roughly as distance travelled per unit time, is obviously affected by these affects of relativity - since a travelling clock runs slow and is length contracted, its velocity measurement is going to be different!

This is helpfully quantified in something called the Lorentz velocity transformation - if I use that formula, and the information you provided me, one of your observers will see the other observer moving at .844c away from him, rather than 1.1c away from him, in his relative frame. (IE from one .55c rocket ship, it sees the other moving away at .844c)

Basically Lorentz transforms conspire to make any situation where you might see something going faster than light actually turn out to be going slower than light.

Also for other aspiring physicists, I find this site - http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/relcon.html#relcon - very useful.

Edit:Spelling

[USEC_OFFICER]

Question for the more physics-minded folks out there:

Breaking c seems relatively simple in a relative frame. You send one observer at 0.55c in one direction. You send another observer at 0.55c in the opposite direction. To each observer's relative frame, the other is moving at 1.1c, correct?

Amazingly, I have the exact same thing in my physics textbook. And it turns out that only in Newtonian (ie classical) physics would that occur. Therefore they had to create a new equation that would work the same as classical physics at low speeds, but not break Einstein's second postulate (and therefore relativity) at high speeds. They came up with this. Long story short, the two observers actually appear to be moving at 0.84c away from each other. Realitivity, huh?

EDIT: Ninja'd. (Though thanks for the link)

[RedKing]

Question for the more physics-minded folks out there:

Breaking c seems relatively simple in a relative frame. You send one observer at 0.55c in one direction. You send another observer at 0.55c in the opposite direction. To each observer's relative frame, the other is moving at 1.1c, correct?

For one, I always wondered what the hell that would look like. Would they be seeing an after-image? Would it be like a Doppler shift from hell?

Wouldn't the one observer X appear to the other Y as not having left the starting point until just after Y stopped?
...Wait, did you mean sending them away from each other or against each other? Because I was thinking away.

Should apply either way. If towards each other, the opposite observer should (if I'm understanding everything right) be red-shifted like hell but would still be perceptible, because light reflected off of them would still be outracing them. But then, the incoming light itself is travling at 1.55c relative to the observer, isn't it?

If away, then it gets conceptually tricker (for me, at least). The relative velocity would be -1.1c, which would seem to mean that their actual position would be continually outstripping their perceivable position. In short, you'd be seeing a blue-shifted afterimage of where they *were* some time prior. Which is sort of how it works for stellar objects anyways (when we see a distant star, we're seeing the star as it actually was hundreds or thousands of years ago), but only more so.

This is one of those things that I've never understood. It would seem that because virtually nothing in the universe is at total rest, any light traveling in an opposite vector to that of an observer is always ever so slightly greater than 1c, isn't it?

For one, I always wondered what the hell that would look like. Would they be seeing an after-image? Would it be like a Doppler shift from hell?
Second, I haven't read the paper, but did they account in any way for the Earth's orbital/rotational motion and Sol's movement? Maybe neutrinos operate somehow so as to be outside the relative observer frame? If that even makes sense....

They may not have needed to Redking. Any apparatus for testing velocity that could be used would necessarily be just as effected by they earth's rotation and the pull from Sol's movement.

What COULD have happened though is that these neutrinos are partially or totally unaffected by the earth/ Sol's movement. That's would be just as crazy though.

Yeah, that's what I was trying to get at. That maybe neutrinos are somehow "pegged" to the fabric of spacetime and so are still constrained by c, just not in a relative frame (as light itself apparently isn't). That still doesn't explain why light in the relative frame of Earthbound observers still appears to travel slower than these neutrino bursts did, though....unless c isn't a universal constant. And there have been experiments that show c can be heavily modified by environmental conditions (that's probably not the right term, but...) like the guys who slowed light down to 38mph in a vat of hypercooled sodium. Since neutrinos don't seem to interact with matter in the same way that most particles do, it makes a certain amount of sense that this may be because they're.....I dunno, "meta-particles" for lack of a better term?

I'm sorry, I know I'm being a complete physics n00b here but I'm just trying to wrap my brain around it.



EDIT: Okay, thanks for the explanation. I'll have to brush up on Lorentz. All I know of the name is in application to fractals.

[alway]

Breaking c seems relatively simple in a relative frame. You send one observer at 0.55c in one direction. You send another observer at 0.55c in the opposite direction. To each observer's relative frame, the other is moving at 1.1c, correct?

Time dilation and all that. Summary of relativity: nothing can go faster than the speed of light and there is no absolute frame of reference. The reason Einstein came up with relativity was precisely to reconcile those two things, which at the time were pretty much seen as unofficial rules of physics but which were nonetheless counter to one another in Newtonian physics. Relativistic physics put time into the equation, allowing time dilation to keep the peace between the two.

[Starver]

Breaking c seems relatively simple in a relative frame. You send one observer at 0.55c in one direction. You send another observer at 0.55c in the opposite direction. To each observer's relative frame, the other is moving at 1.1c, correct?

Long story short, no.

The longer story, with some unfortunate generalisations, but roughly correct, is that each travelling observer can only consider themselves effectively stationary, once they have attained their cruising speed.  Even their presumably stationary origin point will have to be considered to be travelling away from their own space-platform while they are doing so.  Perhaps at 0.55c, except that various effects come into play to affect this impression, and more so with their opposite number.

If there are "kilometre posts" marking out the space-lane, each traveller can see their opposite number signalling "I have passed 1.65x7^8 kilometre markers over the last second", and even witness (if you have a good view) that they are indeed passing that many during the period that the opposing-number's clock ticks out a second.  But you are witnessing their existence through images that are necessarily conveyed by the light-rays (or equivalent, perhaps a CCTV camera broadcast as a signal), as they take increasingly longer to travel between the parties[1].  And so you see their clock ticking slowly.  Their clock being slow means that they are actually accumulating the count they claim during the second of time that they claim, but this is a higher count than the number of posts you can see them passing in one of your seconds, which is the only type that you can consider meaningful.  So even if you add the number of posts travelling past you (relatively speaking, as they are passing you at the speed that your origin is now apparently receding) to the total you can observe the other guy passing, you won't get more than 3x10^8 in one of your seconds.


That's an explanation excluding spacial distortion, on top of that, of course, and you probably no longer be considering the supposed kilometre-posts to be a kilometre apart, either, as they pass by at 0.55c.


I've cut that down to the bone (by my standards), so I know there are issues to be picked up upon in that explanation, but I think it'll do for now.  And probably someone has already ninjaed me with a better explanation... 

Edit1: It seems doubly ninjaed.
Edit2: And more ninjaed even while typing that I was doubly-ninjaed.  Lost count now.
Edit3: Post, damn you, post..



[1] By most relevent observer's viewpoints, with subtly different interpretations from each.  This includes each of the travelling observers doing their best to keep track of this, the origin-point observers looking at the signals as they pass and a hypothetical fourth-party observer placed way out, perpendicular to the diverging paths, far enough out that parallax can be ignored, and thus able to ignore (or accurately account for) the near-identical delay in signal transit from each observer/the origin to create their own 'true' picture of the situation.  FCVO "true", but arguably as good as any mythical "universal" frame of reference.

[Starver]

But then, the incoming light itself is travling at 1.55c relative to the observer, isn't it?

Everything else being covered by now, I think, another "no" is needed.  Light (in a vacuum) is always seen to travel at the speed of light, regardless of direction of travel, what its source is doing and what you are doing[1].  If you try to contrive for it not to be, by moving either yourself or the measuring tape/clock combo by which you are attempting to measure the speed of light according to a different frame, it subjects your observation of the apparatus to the effects of time/space-dilation meaning that the clock/tape are wrong (or, ultimately, your perception of them) and they still show the light to be travelling at the SoL.

If I've explained that correctly, of course.

[1] In an inertial frame of reference, definitely, and even in accelerating ones, by adding a few effects over and above pure observer/observed effects.

[alway]

When light is supposedly 'slowed down' in various mediums, it actually isn't a decrease in the speed of light; it just starts interacting oddly with the surrounding stuff iirc. As for 'meta-particles', look up Feynman Diagrams and prepare to have your mind blown. Turns out every particle is actually a cloud of an infinite number of virtual particles (which themselves are clouds of their own virtual particles, and so on). Neutrinos are difficult to detect simply because they interact weakly due to lacking a charge and having an extremely low mass.

[RedKing]

But then, the incoming light itself is travling at 1.55c relative to the observer, isn't it?

Everything else being covered by now, I think, another "no" is needed.  Light (in a vacuum) is always seen to travel at the speed of light, regardless of direction of travel, what its source is doing and what you are doing[1].  If you try to contrive for it not to be, by moving either yourself or the measuring tape/clock combo by which you are attempting to measure the speed of light according to a different frame, it subjects your observation of the apparatus to the effects of time/space-dilation meaning that the clock/tape are wrong (or, ultimately, your perception of them) and they still show the light to be travelling at the SoL.

Aha!!! Okay, that makes sense to me now. So (and I'm being fast and loose with the numbers here), if I'm traveling at 0.0001c, so that incoming light in a non-relativistic system would be at 1.0001c, then what I actually experience is time dilation such that perceived time is slowed by a factor sufficient to rebalance the equation so that the light is still going at 1c. At relatively low speeds like that example, the dilation is such that it's not noticeable. At 0.5c, time would be slowed by...a factor of 2? Or something thereabouts, so that light still winds up with a perceived velocity of c.

Heh....this also means that there is some literal truth when people say that running will make you live longer. xD

[PTTG??]

Well, there goes my neat hard science 4x game based on light speed lag in communication. 25,000,000 C just isn't as tactical, since that crosses the galaxy in 35 hours...

[Starver]

At 0.5c, time would be slowed by...a factor of 2? Or something thereabouts, so that light still winds up with a perceived velocity of c.

Not exactly like that, and there's both time and distance (mis)conceptual changes.  (And mass, which should only matter in other contexts.)

The equations involved have (from memory) the key factor of "root(1 - vē/cē)"[1].  Which makes it not just simple multiples for each element, but plug some numbers into that and you'll see how the lower velocities make it an insignificant effect (Newton rules, near as makes no difference), close to the top end (v->c) it's a very significant factor, a velocity actually equal to light gives you a factor of zero (and where that's used as the numerator of a division, gives you an undefined result, already having been rapidly approaching infinity) and a velocity greater than the speed of light (v>c) gives you imaginary results, showing that if you had somehow got past SoL (through all the "diminishing returns" of more energy needed to push more mass, and all the time ship-time slowing so it takes longer from an observer's PoV, and then getting past that "division by zero" bit) you find yourself in very strange territory that you'd probably never need to worry about anyway.

Makes sense?  Probably not.  A lengthier explanation than I intend, but still probably not good enough (in comprehensiveness/accuracy) for those who consider this their bread and butter...

But, yes, I (at least) think you have it right enough to understand the apparent paradox involved.

[RedKing]

Reading up on neutrinos. Mind is sufficiently blown.

1. As something with non-zero mass, surpassing c definitely causes problems with physics, because IIRC it should require an infinite amount of energy to accelerate any object with mass to or past c.
2. Neutrinos seem to be a interesting candidate for "catalyzed nuclear reactors", since they seem to affect rate of fission and radioactive decay rates. I've always thought that if we could find some way to create "catalyzed fusion", where you could get sustainable fusion reactions without requiring the insane heat/pressure of a traditional fusion reactor, you could make fusion practible.
3. Particle physics make my tiny brain go ouchie.

EDIT:
Right...I remember something now about mass increasing with velocity, such that at lightspeed any object with non-zero mass at rest has infinite mass. And this is why it takes infinite energy to accelerate to that degree, which is why it's (supposed to be) impossible. So if neutrinos exceed c, they should theoretically have a mass that is some multiple of i. At which point you broke all the physics.

Wow....today is turning out to be far more educational than I expected.