Gamma Ray Bursts From Black Holes *May* Exceed Speed Of Light

[all41]

Now that you repeat it...

Note that both the receding galaxy and the moon-laser thing is not about objects moving through space and do not in any way refute c as a limit for latter. In the first, space itself expands, and in the latter no object on the moon moves from left to right; individual photons travel simply still with c from laser to moon; what moves is a rapid succession of different photons.

I didn't grasp the laser across the moon concept--photons still confirm to c
How does the sweep change that?

[rene]

It doesn't, but the point of the "paradox" is that the movement of the image of the laser on the moon exceeds the speed of light as it moves from one side of the moon to the other; 6000 km or so in the very little time it takes to flick one's wrist. However, as said, that image is nothing but an image, and its movement is caused by different photons striking the moon at successive positions.

It's one of the most famous faster-than-light paradoxes, https://en.wikipedia.org/wiki/Lighthouse_paradox. Like all other such paradoxes, none in fact are.

[all41]

I suppose considering a round-trip scenario would stymie this

[rene]

Not sure I follow. In the sense of you contemplating using the image-movement for superluminal transfer of information? Because, yes, any transfer on the moon would involve a round-trip back to the earthbound wrist-flicker, denying that possibility...

[all41]

I'm thinking if the laser was monitored on one visible edge of the moon, and again with another sensor on the other edge, would not c still be the determinate factor in both locations? Certainly halfway between you could expect different results, just can't grasp the movement thing, it still conforms to c.

[rene]

Well, "monitored" is the key phrasing there as to denying superluminal information exchange. I am not sure though what you intend to say as you say "would not c still be the determinate factor". Yes, it would. Note how the Wikipedia page explains how this is NOT in fact a valid paradox and how no object moves with superluminal velocity.

The idea of the supposed paradox were we to mistake the image for an object is simple though. If the image on the moon "moves" from one side of the moon 6000 km across to the other side in s < 6000 km / c seconds then v = 6000 km / s > c. Seeing as how 6000 km / c ~= 0,02 seconds this is possible not even just as a thought experiment (and if we'd struggle, we'd just take mars, or ...)

But once again, the paradox is not in fact a paradox and indeed no object is moving faster than c.

[Portreve]

I don't remember if it was PBS Space Time or Fermilab, but they talked about the Moon laser light paradox thing in one of their videos, too. To be honest, I thought it was pretty stupid, and I never really got why anyone would have considered it a legit thing to begin with. Oh well...

[Flemur]

Rather than using the moon, the light will move much faster when you swing the beam across Jupiter. Or another galaxy.

Another way to visualize something apparently moving faster than anything is actually moving: put down two sheets of paper, turn the top one a few degrees, then slide it over the lower sheet; the speed of the crossing point is faster than the speed of the physical paper (e.g. move the upper paper, say 1/4", and the crossing point moves 8" ...):

Phase_Velocity.png (12.02 KiB) Viewed 1643 times

The "phase velocity" -> infinity as the angle -> zero.

Edit: the "speed of paper" velocity vector (the arrow on the paper) is supposed to be fixed to the top paper which is moving, not the bottom paper, so it should have been rotated slightly CCW in the pic (I rotated and collapsed layers in the wrong order).

[rene]

As far as I can see that sin() needs to be a tan() (which doesn't change the conclusion as long as angle < 45deg) but nice.

[Pippin]

Just to add more info:
https://www.youtube.com/watch?v=SZ5ZWbVWMBU

[rene]

And, like the previous time, I then have to warn unsuspecting users that "the thunderbolts project" is a gathering of the psychologically disadvantaged, obsessed with how "the man is keeping you down". To Pippin's credit, the video is in fact this time pretty explicit about being exactly that, but still, note so before you even try and watch it.

[Pippin]

Would rather warn for group think...
More about speed of light:
https://www.youtube.com/watch?v=73mZMcV-OgU

[rene]

Would rather warn for group think...

Oh, but that's exacty what I'm doing, dear chap. I'm warning against the very large group of people that hold that if they don't understand something it must be wrong.

[Pippin]

I'm warning against the very large group of people that hold that if they don't understand something it must be wrong.

Exactly

[rene]

Ah, darn it, you have won the discussion. So perhaps we may now get back to an exchange based on evidence and/or mathematical proof rather than on feelings of personal inadequacy. I was sort of enjoying Flemur's thing...

[Portreve]

This video by vsauce seems oddly appropriate for this thread; its discussion most of the way through the video about the Dunning-Kruger effect seems extremely appropriate right this second.

Personally, I think there is a correlation (if not an actual connection) between believing something someone does not understand to be wrong, and fear of the unknown.

[Flemur]

As far as I can see that sin() needs to be a tan() (which doesn't change the conclusion as long as angle < 45deg) but nice.

No, it's sin;
V'(angle --> 0) -> infinty.
V'(45) = V * 1.41
V'(90) = V = the speed of the top paper, moving perpendicular to the other paper.

With tan
V'(45) = V (!!)
V'(90) = 0.

[rene]

I am afraid it really is tan(). It of course depends a bit on which angle we take as "the angle" as to how things work out exactly, but it'll never be sin(). Specifically for 45deg, V'=V is precisely right. Mind you, not meant as an argument-from-authority but only in hopes of communicating that I'm not merely guessing, I am trained as a mathematician. I've in fact a nice proof done here showing the tan() but it's a pain to do over a forum. Let me draw something and scan or some such and get back to you...

[Flemur]

I am afraid it really is tan(). It of course depends a bit on which angle we take as "the angle" as to how things work out exactly, but it'll never be sin(). Specifically for 45deg, V'=V is precisely right.

At 90 degrees, the top paper moves horizontally and the contact point moves at the same speed as the paper.

With tan(), V' -> zero as you get to 90 degrees; but try it with two pieces of paper: move the top one horizontally (angle =90 degrees) and contact point obviously moves at the same speed as the paper. Or try it at 89 degrees and you'll see that the speed is very close to the speed of the moving paper, but not close to zero.

The contact point never moves more slowly than the top paper.

Mind you, not meant as an argument-from-authority but only in hopes of communicating that I'm not merely guessing, I am trained as a mathematician.

Me too.

Let me draw something and scan or some such and get back to you...

OK.

Edit: in my picture the original V direction is supposed to be oriented in the same direction as the top paper, not the bottom paper, like an arrow drawn on the top paper and fixed to the top paper, but it looks like I drew it wrong (rotate and collapse image layers in the wrong order). I think this is why we're getting different answers!

Edit2: like this:

Phase2.png (5.85 KiB) Viewed 1469 times

[Portreve]

I am afraid it really is tan(). It of course depends a bit on which angle we take as "the angle" as to how things work out exactly, but it'll never be sin(). Specifically for 45deg, V'=V is precisely right. Mind you, not meant as an argument-from-authority but only in hopes of communicating that I'm not merely guessing, I am trained as a mathematician. I've in fact a nice proof done here showing the tan() but it's a pain to do over a forum. Let me draw something and scan or some such and get back to you...

Not for my own personal benefit because the math you're talking about is completely above my head, but if you want to put in a proof, you could just wrap it in CODE tags, and that way it's handled as monospaced text which will let you maintain formatting integrity with spaces, and if it's long (which I suspect it is) it will be just a small, scrollable field instead of turning your post into something really massive.

For example:

Code: Select all

0 CLS
5 KEY OFF
10 PRINT "What is your name?"
15 INPUT A$
20 PRINT : PRINT "Hello, "A$". What is your best friend's name?"
25 INPUT B$
30 PRINT : PRINT "What is your favorite color, "A$"?"
35 INPUT C$
40 PRINT : PRINT "What is your least favorite color?"
45 INPUT D$
50 PRINT : PRINT "Are you ready for a story? Press [ENTER] to continue."
55 INPUT Z$
60 CLS
65 PRINT A$" was walking along the street one day, minding his own business,"
70 PRINT "when suddenly a "D$"-colored monster with "C$"-colored eyes jumped out"
75 PRINT "from nowhere and attacked him."
80 PRINT
85 PRINT "Fortunately for "A$", his best friend, "B$", was just around the corner."
90 PRINT B$" immediately ran over, and "A$" and "B$" together were able to fight off"
95 PRINT "the "D$"-colored beast, and escape."
100 KEY ON
105 END

Incidentally, the code above illustrates my total programming knowledge and game-writing "skill".