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April 4

Special relativity. Simultaneity 2

Question

Remark

Ok. There is no observers, just clocks showing something on their faces. In Special relativity. Simultaneity we showed : in frame ε clock from ε shows on its face: at start $0$ when light reaches hind end of ε' coach $\tau _{1}={\tfrac {L/2}{c+u}}$, when light reaches front end of ε' coach $\tau _{2}={\tfrac {L/2}{c-u}}$; in frame ε clocks from ε' show on their faces (from left to rigth): at start $\theta _{0}^{[}$, $0$, $\theta _{0}^{]}$, when light reaches hind end of ε' coach $\theta _{1}^{[}$, $\theta _{1}=\tau _{1}{\sqrt {1-u^{2}/c^{2}}}$, $\theta _{1}^{]}$; when light reaches front end of ε' coach $\theta _{2}^{[}$, $\theta _{2}=\tau _{2}{\sqrt {1-u^{2}/c^{2}}}$, $\theta _{2}^{]}$. Suppose, when light reaches walls, clocks on walls are reseted to zero, so $\theta _{1}^{[}=\theta _{2}^{]}=0$. Reseting of clocks is the result , so must be seen from all frames, so in all frames clocks on walls must show zero if light reaches them. Then: $\theta _{1}^{[}=\theta _{0}^{[}+\tau _{1}{\sqrt {1-u^{2}/c^{2}}}$ and $\theta _{2}^{]}=\theta _{0}^{]}+\tau _{2}{\sqrt {1-u^{2}/c^{2}}}$. $0=\theta _{0}^{[}+\tau _{1}{\sqrt {1-u^{2}/c^{2}}}$ and $0=\theta _{0}^{]}+\tau _{2}{\sqrt {1-u^{2}/c^{2}}}$. $\theta _{0}^{[}=-\tau _{1}{\sqrt {1-u^{2}/c^{2}}}$ and $\theta _{0}^{]}=-\tau _{2}{\sqrt {1-u^{2}/c^{2}}}$. $\theta _{0}^{[}=-{\tfrac {L/2}{c+u}}{\sqrt {1-u^{2}/c^{2}}}$ and $\theta _{0}^{]}=-{\tfrac {L/2}{c-u}}{\sqrt {1-u^{2}/c^{2}}}$. So at start in frame ε clocks from ε' show on their faces (from left to rigth): $-{\tfrac {L/2}{c+u}}{\sqrt {1-u^{2}/c^{2}}}$, $0$, $-{\tfrac {L/2}{c-u}}{\sqrt {1-u^{2}/c^{2}}}$. How to check this? I have tried to use Lorentz transformations for time , but got absolutely different result. Hind clock when shows $\theta _{0}^{[}$, is situated in ε in point $(x,t)=(-L/2,0)$ and also in ε' in point $(x',t')=(-L'/2,\theta _{0}^{[})$, but also it can be represented as $(x',t')=({\tfrac {x-ut}{\sqrt {1-u^{2}/c^{2}}}},{\tfrac {t-xu/c^{2}}{\sqrt {1-u^{2}/c^{2}}}})$ $=({\tfrac {-L/2-u\cdot 0}{\sqrt {1-u^{2}/c^{2}}}},{\tfrac {0-(-L/2)u/c^{2}}{\sqrt {1-u^{2}/c^{2}}}})$ $=({\tfrac {-L/2}{\sqrt {1-u^{2}/c^{2}}}},{\tfrac {{\tfrac {+L/2}{c^{2}}}u}{\sqrt {1-u^{2}/c^{2}}}})$. So $\theta _{0}^{[}={\tfrac {{\tfrac {+L/2}{c^{2}}}u}{\sqrt {1-u^{2}/c^{2}}}}\neq -{\tfrac {L/2}{c+u}}{\sqrt {1-u^{2}/c^{2}}}$. Why? Or backwards: $(x',t')=(-L'/2,\theta _{0}^{[})$; $(x,t)=({\tfrac {x'+ut'}{\sqrt {1-u^{2}/c^{2}}}},{\tfrac {t'+x'u/c^{2}}{\sqrt {1-u^{2}/c^{2}}}})$. By subsituting $x'=-L'/2=-L/2{\sqrt {1-u^{2}/c^{2}}}$, $t'=\theta _{0}^{[}=-{\tfrac {L/2}{c+u}}{\sqrt {1-u^{2}/c^{2}}}$: $(x,t)=((-L/2)(1+{\tfrac {u/c}{1-u^{2}/c^{2}}}),...)$. Why $x\neq L/2$? But I don't want to use coordinate. I like to imagine that time in moving frame is slowing down through explanation by primitive clock made from vertical rod and mirror https://upload.wikimedia.org/wikipedia/commons/8/8f/Reference_desk_Science160404140000.PNG . Is there same intuitive explanation for desynchronization?

https://en.wikipedia.org/w/index.php?title=Wikipedia:Reference_desk/Science&action=edit&oldid=711458491 Light path analysis and consequences https://en.wikipedia.org/w/index.php?title=Wikipedia:Reference_desk/Science&action=edit&oldid=711808143 Null result of Michelson–Morley experiment extrapolation https://en.wikipedia.org/w/index.php?title=Wikipedia:Reference_desk/Science&action=edit&oldid=713271286 Special relativity. Derivation of t' formula https://en.wikipedia.org/w/index.php?title=Wikipedia:Reference_desk/Science&action=edit&oldid=713271421 Special relativity. Simultaneity

37.53.235.112 (talk) 05:49, 4 April 2016 (UTC)

Time in a moving frame is not "slowing down", it is proceeding at the "normal" rate. From an inertial frame that is moving relative to the original moving frame (or "stationary" by some ad-hoc definition), time is observed to be running more slowly, but this effect is symmetrical because time in the "stationary" frame is observed to be running more slowly when observed from the moving frame. It is only when one frame (either of them) accelerates to match the speed of the other that a twins paradox appears. Perhaps someone else can explain how your equations work out? Dbfirs 11:02, 4 April 2016 (UTC)

Symmetry of time is certainly claimed by special relativity, however general relativity lays claim to an asymmetry that exists (and it's an asymmetry that I view as being much more important and fundamental). For instance, if on one hand, a rogue twin planet Krypton, which is like our own, was moving very near the speed of light, their communication systems hibernate with, say, just one computation per week and therefore incapable of processing any interactive communication data we may wish to share with them during their brief passage with us though our inner Solar System (within the orbit of Pluto). They would be "dead on arrival". On the other hand, we could interactively observe them, probe their planet with radar, etc. in excruciating detail during the brief encounter because we are unaffected and are almost at rest with respect to the CMB rest frame, which is likely the ultimate arbitrator of what constitutes the fastest clocks. -Modocc (talk) 13:08, 4 April 2016 (UTC)

I follow http://www.feynmanlectures.caltech.edu/I_15.html . Please, write answers using materials which do not go beyond sections 15-1 ... 15-6.37.53.235.112

[after edit conflict]Alas, according to SR, your intuition is incorrect for a very simple reason: you are incorporating classical velocity addition with your primitive photon clock and not the relativistic temporal and spacial transforms which are derived independently. Not a bad idea though and consistent with absolute simultaneity and distances :-), but it is very much inconsistent with the reference frame invariant lightspeed of your photon, which according to Einstein, requires relativity of simultaneity as well as length contracted distance (length contraction) that the light travels and is frame dependent. Thus relativity goes well beyond the classical paradigm. The book "Einstein's Theory of Relativity" by Max Born may be a bit dated, but from it I learned the basics of how its nonEuclidean worldlines were developed many years ago. -Modocc (talk) 16:08, 4 April 2016 (UTC)

you are incorporating classical velocity addition We can use classical velocity addition for approach velocity and we should use relativistic velocity addition for object velocity. Just write what formulas are wrong in my 1st question. 37.53.235.112 (talk) 16:40, 4 April 2016 (UTC)

@Modocc: Your explanation is confusing at best. The whole idea of relativity is there's no difference between how we see Krypton and they see us (how we see the CMB is something else!). We see their clocks ticking slowly and they see our clocks ticking slowly. The solution to this staring contest is that sooner or later, one party accelerates and comes back again, and is revealed to be the "true" slowed party. Or else both parties keep moving apart and their record of each other's light just keeps getting more and more out of date. There's a graphic in Twin paradox - the "simultaneity planes" change angle when you accelerate, i.e. "the same time back on Earth" takes as abrupt a jump forward as your rocket engines will allow (could be backward if you accelerate away faster). But of course, unless you're in possession of an ansible, those simultaneity planes don't really physically exist - they don't mean anything because no information or substance can follow any of those spacetime paths. Wnt (talk) 15:34, 4 April 2016 (UTC)

Whatever reference frame one wants to invoke to solve the paradox involving time doesn't actually matter. The fact is that when we accelerate matter, particles' contract and their lifetimes increase, but with consequences. Do that to a rocket or planet so it is fast enough then with regard to a staring contest then the rocket or Krypton cannot interact with us while it is in close proximity to us, its computers are simply aging too slow with respect to the laser light we can bounce off it and that we observe as it passes us by. The fact that such asymmetry exists is the whole point of the paradox. --Modocc (talk) 16:28, 4 April 2016 (UTC)

That's why I wrote above that the twins paradox appears whichever frame is accelerated to match the other. There is still symmetry, because the "rest frame" could be accelerated to match the velocity of the "moving frame" and the same paradox will appear except that the age difference will be reversed. Dbfirs 18:21, 4 April 2016 (UTC)

Krypton is nearby from Earth's perspective for the same amount of time as Earth is nearby from Krypton's perspective. They can investigate us as much as we can investigate them. It's a symmetric situation. You seem to be suggesting that we have longer than they do because we're moving at a slower speed relative to the CMB. That's incorrect. -- BenRG (talk) 06:22, 5 April 2016 (UTC)

In case I wasn't clear, I assumed that Krypton was initially accelerated relative to our Milky Way when it was hypothetically created and that it is now moving almost, but not quite, at the speed of light (this is just a thought experiment. I'm not saying that it even possible, but its something to think about) when we encounter it. Now we know that our computers can process a few serial computations per clock cycle, so lets figure ten gigahertz to give us a benchmark here. It takes about 33,000 seconds of elapsed time for light to traverse the orbit of Pluto and in that time our computers can do a lot of data crunching during our encounter with weak short-range signals (such as with our land-based radar) that are aimed at the rogue planet as it passes us by. Now let Krypton's velocity be such that its 10 gigahertz computers are time dilated to only 1/30,000 clock cycles per second. Then at this speed, during our 33,000 second encounter, their computers' clocks can cycle only once and their weak signals will be fewer in number too. -Modocc (talk) 07:28, 5 April 2016 (UTC)

Similarly, Krypton's observations of Earth will be hopelessly distorted, with our computers appearing to run ridiculously slowly. Dbfirs 08:32, 5 April 2016 (UTC)

A stark uncompromising asymmetry would exist however, for real time computations are required by the radio telescopes' tracking computers and their computers could barely perform a single computation during the entire crossing of our solar system and both our ability to perform and their inability to do likewise are reference frame invariant. Modocc (talk) 04:44, 6 April 2016 (UTC)

I don't understand the lack of symmetry that you claim. Krypton's computers run at normal speed in their reference frame. Dbfirs 19:11, 6 April 2016 (UTC)

@Modocc: you've specified a time dilation factor of γ = 10 GHz / (1/30000 Hz) = 3×10¹⁴, which corresponds to a speed of √(1 - 1/γ²) ≈ (1 − 6×10⁻³⁰) c. Assuming Pluto is around 16,500 light seconds away from us, and Krypton passes close to Earth, Earth-bound telescopes won't see Krypton pass the orbit of Pluto until 16500(c−v) ≈ 0.1 yoctosecond before it passes Earth. (They will see it in the form of a concentrated beam of gamma rays that will probably sterilize the Earth, but never mind.) If Earth scientists send a radar beam to probe Krypton's surface a nanosecond after it passes us, the beam will return to us about 10 trillion years later, and will be redshifted by a factor of about 4×10²⁹.

So it is not true that Earth-bound scientists will have lots of time to investigate Krypton. Of course, they will most likely spot Krypton's arrival before it gets to Pluto. If they notice it 1 second before it passes us, they'll have seen it at 10²⁵ times the distance of Pluto, which seems implausible but maybe not. That would give them 1 full second to send radar signals to it which will all bounce back within that second (blueshifted by a factor of 4×10²⁹).

Krypton will have exactly the same opportunity to investigate us, since this is a completely symmetric situation. The symmetry of reference frames is the most important thing about special relativity. -- BenRG (talk) 19:25, 6 April 2016 (UTC)

Well, yes, detection of Krypton's existence is also important before we would be making any observations at all: thus simply let Krypton emit significant electromagnetic radiation ahead of it (we can do the same for them) and then we will get to track them and observe them for the full range of our active radars, but their radars will be dysfunctional with regard to the task. [see a better strategy below] This is because we are the stay-at-home twin for most of the inertial mass around us has been nearly at rest for billions of years and so our watches differ from theirs and time in physics is what clocks measure. If my own twin takes a trip and returns he will have completed fewer tasks than I have, perhaps only a few weeks worth compared to my years worth, thus our performances are asymmetric even though the naive Lorentz transformation preserves spacetime symmetry. --Modocc (talk) 21:16, 6 April 2016 (UTC)

But if you accelerate to match your fast-moving twin's inertial frame, it will be you who has completed fewer tasks because you will be younger than your twin. I still insist that the situation is symmetrical. Dbfirs 21:38, 6 April 2016 (UTC)

If Krypton is the stay-at-home twin that would be true, but since I specified that Krypton was accelerated initially then I would simply be rejoining joining him for the first time as an older man (although we are physically the same, we would have to be born in different places) when I crash land on his planet in a hail of gamma rays. :-) BenRG made a really good point about the lead distance involved and although the numbers can be tweaked (I'm not a big fan of playing with them much) a more robust strategy to recording their passage I suppose would be to have numerous active pulsed radars that continuously cover the sky much like we do with our weather radars. It is a very large volume of space to cover, but perhaps more feasible and likely than the origin of a massive Krypton (which, being our twin, would have their own matrix of radars). -Modocc (talk) 00:50, 7 April 2016 (UTC)

Suppose Earth knows in advance that Krypton is coming and starts sending out radar beams 33000s before Krypton reaches Earth, so that the first beam bounces off Krypton just as it crosses Pluto's orbit. Those beams are sent over a period of hours, but since they travel at c just like any other light, they all arrive back in the 0.1 ys interval between seeing Krypton cross Pluto's orbit and Krypton passing Earth. Of course, no equipment could record the signal in that time, but we could imagine faster computers (or a less ridiculous gamma factor).

To be fair, you must allow Krypton to start sending signals 33000s before the meeting by its proper time. For large γ the Doppler shift factor is roughly 2γ. So those signals will reflect off Earth over a period of about 33000s / 2γ ≈ 55 picoseconds (of Earth proper time), and will be received by Krypton over a period of 55ps / 2γ ≈ 0.1 ys (of Krypton proper time), just before the planets pass each other.

The fact that Krypton accelerates and we don't is an asymmetry in your scenario. But it only accelerates when it's far away, and by assumption, it can only investigate us (and we it) when it's nearby. Physics is local; the universe doesn't remember who accelerated in the past. When Earth and Krypton are near each other, an exact symmetry of nature (Lorentz/Poincaré symmetry) exchanges them, so the situation is symmetrical. -- BenRG (talk) 03:09, 7 April 2016 (UTC)

"To be fair, you must allow Krypton to start sending signals 33000s before the meeting by its proper time"? It takes precisely 33000 times a gigahertz number of computer cycles for that to happen, thus those signals would have to begin at a far greater distance from us than Pluto which is but approximately one half of their cycles away by my earlier calculation above and since they are just about almost physically identical to us and are therefore sending similar signals they should be considerably weaker upon arrival.. or am I missing something important here? -Modocc (talk) 03:52, 7 April 2016 (UTC)

Yes, it starts long before they reach Pluto's orbit (the trip from there to Earth takes only 55ps by their clocks), but the light doesn't travel farther in any Lorentz-invariant sense. With respect to Earth's rest frame, you could say that relativistic beaming prevents the light from spreading as much as you'd otherwise expect over such a long distance. With respect to Krypton's rest frame, Earth is 33000 light seconds away when they send the first signal, and Pluto's orbit is only 16mm closer.

(If there is background dust comoving with Earth, Krypton's signals will travel through a lot more of it and be attenuated more by that. But if there is background dust then the relativistic dust bombardment will destroy Krypton long before it reaches Earth anyway. This scenario only works in a perfect vacuum.) -- BenRG (talk) 05:27, 7 April 2016 (UTC)

The relativistic Doppler is symmetrically invariant with respect to spacetime's worldlines, thanks for clarifying that. As for the destruction of Krypton, that is most certainly why we inhabit our frame and not Krypton's frame. Krypton is a myth. --Modocc (talk) 08:47, 8 April 2016 (UTC)

and also in ε' in point $(x',t')=(-L'/2,\theta _{0}^{[})$ – I think everything before this is correct, and this is wrong. In the original setup the primed clocks showed t' on their faces, but in your revised setup they show an offset from that (specifically $t'-L'/2c$), so you should have $(x',t')=(-L'/2,\;\theta _{0}^{[}+L'/2c)$. That should agree with the result from the Lorentz transform (with $L'=L/{\sqrt {1-u^{2}/c^{2}}}$). -- BenRG (talk) 23:48, 4 April 2016 (UTC)

I think I'm hopelessly misled. Why $\theta _{0}^{[}\neq \theta _{0,self}^{[}$? How to calculate them (suppose light flash never occurred , so no synchronization was ever made)? Why in all frames result of experiment is same, but indication of clocks (which also is result of some processes inside clock) are not? 37.53.235.112 (talk) 18:04, 5 April 2016 (UTC)

You wrote "hind clock when shows $\theta _{0}^{[}$, is situated [...] in ε' in point $(x',t')=(-L'/2,\theta _{0}^{[})$". This means that at $t'=\theta _{0}^{[}$, the clock reads $\theta _{0}^{[}$.

The clock is at rest wrt ε', so it ticks at the same rate as the coordinate time of ε'. So if it shows $\theta _{0}^{[}$ at $t'=\theta _{0}^{[}$, then it must show $t'$ at every time.

But you also wrote "in all frames clocks on walls must show zero if light reaches them". So the hind clock shows $0$ when the light arrives. So $t'=0$ when the light arrives. But this is clearly wrong: the light is emitted at $(x',t')=(0,0)$ and doesn't travel infinitely fast.

So there is an internal contradiction in the assumptions you made about the behavior of the clock (or in the assumptions I made when reading). Which part is wrong depends on what thought-experiment you meant to describe. I think what's wrong is the idea that at $t'=\theta _{0}^{[}$, the hind clock reads $\theta _{0}^{[}$. This was true in your previous Ref Desk thread, when that clock was set to show $t'$ on its face at all times. But now it is set to show $0$ when the light arrives. Since it has the same worldline and ticks at the same rate as in your previous thread, the time it shows in this thread differs by a constant offset from the time it showed in the last thread. The offset is $L'/2c$. In the last thread it showed $0$ at $t'=0$ and $L'/2c$ at $t'=L'/2c$ when the light arrived, but now it shows $-L'/2c$ at $t'=0$ and $0$ at $t'=L'/2c$when the light arrives. In the last thread it showed $\theta _{0}^{[}$ at $t'=\theta _{0}^{[}$, but in this thread it shows $\theta _{0}^{[}$ at $t'=\theta _{0}^{[}+L'/2c$. -- BenRG (talk) 00:44, 6 April 2016 (UTC)

Question	Remark
Ok. Then we have next ε' frame ε frame time coordinate clock reading time coordinate clock reading $t'=0$ $\theta _{0}^{[}=-{\tfrac {L'}{2c}}$ $\theta _{0}^{]}=-{\tfrac {L'}{2c}}$ $t=0$ $\theta _{0}^{[}=-{\tfrac {L'}{2c}}$* $\theta _{0}^{]}=-{\tfrac {L'}{2c}}$ $t'=-{\tfrac {L'}{2c}}$ $\theta _{1}^{[}=0$ $\theta _{1}^{]}=\theta _{2}^{]}=0$ $t=\tau _{1}={\tfrac {L/2}{c+u}}$ $\theta _{1}^{[}=0$ $t=\tau _{2}={\tfrac {L/2}{c-u}}$ $\theta _{2}^{]}=0$ * because θ is not variable, θ is just literal representation of digits.	You wrote "hind clock when shows $\theta _{0}^{[}$, is situated [...] in ε' in point $(x',t')=(-L'/2,\theta _{0}^{[})$". This means that at $t'=\theta _{0}^{[}$, the clock reads $\theta _{0}^{[}$. The clock is at rest wrt ε', so it ticks at the same rate as the coordinate time of ε'. So if it shows $\theta _{0}^{[}$ at $t'=\theta _{0}^{[}$, then it must show $t'$ at every time. But you also wrote "in all frames clocks on walls must show zero if light reaches them". So the hind clock shows $0$ when the light arrives. So $t'=0$ when the light arrives. But this is clearly wrong: the light is emitted at $(x',t')=(0,0)$ and doesn't travel infinitely fast. So there is an internal contradiction in the assumptions you made about the behavior of the clock (or in the assumptions I made when reading). Which part is wrong depends on what thought-experiment you meant to describe. I think what's wrong is the idea that at $t'=\theta _{0}^{[}$, the hind clock reads $\theta _{0}^{[}$. This was true in your previous Ref Desk thread, when that clock was set to show $t'$ on its face at all times. But now it is set to show $0$ when the light arrives. Since it has the same worldline and ticks at the same rate as in your previous thread, the time it shows in this thread differs by a constant offset from the time it showed in the last thread. The offset is $L'/2c$. In the last thread it showed $0$ at $t'=0$ and $L'/2c$ at $t'=L'/2c$ when the light arrived, but now it shows $-L'/2c$ at $t'=0$ and $0$ at $t'=L'/2c$when the light arrives. In the last thread it showed $\theta _{0}^{[}$ at $t'=\theta _{0}^{[}$, but in this thread it shows $\theta _{0}^{[}$ at $t'=\theta _{0}^{[}+L'/2c$. -- BenRG (talk) 00:44, 6 April 2016 (UTC)
When do clocks show proper time $\theta _{i,self}^{[]}$?

37.53.235.112 (talk) 05:00, 6 April 2016 (UTC)

$t=0$ and $t'=0$ are lines in spacetime. The reading of a clock at $t=0$ is its reading at the intersection of its worldline and the line $t=0$.

The lines $t=0$ and $t'=0$ intersect only at the origin $(x,t)=(x',t')=(0,0)$, so the only way a clock can show the same reading at $t=0$ and $t'=0$ is if it passes through $(0,0)$. The two "middle" clocks in this setup do pass through $(0,0)$, but the hind and front clocks don't. The hind clock passes through $t'=0$ before $t=0$, and the front clock passes through $t=0$ before $t'=0$.

In your table, the clock readings at $t'=0$ are correctly given as $-{\tfrac {L'}{2c}}$, and the clock readings at $t=0$ are correctly given as $\theta _{0}^{[}$ and $\theta _{0}^{]}$. But $\theta _{0}^{[}\neq -{\tfrac {L'}{2c}}\neq \theta _{0}^{]}$.

I don't understand what you mean by $\theta _{i,self}^{[]}$. -- BenRG (talk) 18:06, 6 April 2016 (UTC)

I don't understand what you mean by $\theta _{i,self}^{[]}$ -- It's clock's proper time. E.g. $\theta _{0,self}^{[}$ -- proper time of hind clock at start, $\theta _{1,self}^{[}$ -- proper time of hind clock when light reaches it. Also I don't know what is worldline, so don't understand this part. Clock shows something when it is situated in some place in space. When clock is situated in some place , it can be in point $(x,t)$ or $(x',t')$. So it must have same readings. As I wrote readings are such letters as $\theta$ and $\tau$. But absolutely unclear for me which readings must be equal what other readings and when. E.g. you wrote that $\theta _{0}^{[}=-{\tfrac {L'}{2c}}$ when $t'=0$ . What time $t$ corresponds with this? $t=0$? Why then reading of hind clock does not coincide? 37.53.235.112 (talk) 18:54, 6 April 2016 (UTC)

I never wrote $\theta _{0}^{[}=-{\tfrac {L'}{2c}}$, or if I did it was a typo. You defined (I think) $\theta _{0}^{[}$ to be the hind clock's reading at t=0. It's not the hind clock's reading at t'=0, because the hind clock crosses t'=0 at a different time (an objectively different point in spacetime, and also a different proper time).

The best way to understand this sort of thing is with a spacetime diagram. I'll attempt one in ASCII.

  rear of train    front of train
(and hind clock)  (and front clock)
          v           v                 ^
          /           /                 |
         /           /,,  <-- t'=0    later
        /         ,,/’                
       /      ,,’’ /                 earlier
   .../.....@...../....  <-- t=0        |
     /,,’’       /                      v
    ’’

The point marked @ is $(x,t)=(x',t')=(0,0)$. The lines $t=0$ and $t'=0$ are angled differently (relativity of simultaneity). The clocks read $\theta _{0}^{[]}$ on the line $t=0$, but not on the line $t'=0$. There is no single well-defined "time at the start" because there is no single well-defined "start" of this experiment. Does that help? -- BenRG (talk) 19:42, 6 April 2016 (UTC)

Does that help? No because it's rotatings. As I wrote, I did not study rotatings yet and I will not study rotating specially.

You defined (I think) $\theta _{0}^{[}$ to be the hind clock's reading at t=0. Yes, it's reading of hind clock of moving coach ε' in coordinate system of ε. So reading in coordinate system of ε' must be $\theta _{0,self}^{[}$. But you use same notation $\theta _{0}^{[}$ just saying it's different (but it's impossible as $\theta _{0}^{[}$ is number e.g. $13$, and $13$ cannot be sometimes $11$). It is confusing. And one more thing is unclear: if hind clock is situated in some place of space, it's no matter what coordinate system is applied, so in both systems readings must be same (coordinates may be different). Yes or no? 37.53.235.112 (talk) 05:46, 7 April 2016 (UTC)

Yes, the readings are the same, the coordinates are different.

My diagram is just a picture of the scenario you set up. (Except that I left out the light beams because the diagram was cluttered enough already.) The horizontal and vertical axes are x and t respectively. I didn't introduce any new rotating. I did say the Lorentz transformation is like a rotation, but you are already doing Lorentz transformations (and doing them correctly).

The reading on a clock at some particular spacetime point doesn't depend on reference frames. For example, I could add numbers to the diagram showing the readings on the clocks:

                  /           /
                 /           /,,  <-- t'=0
                /         ,-10
               /      ,,’’ /
           ..-7.....@....-13...  <-- t=0
             /,,’’       /
           -10          /

and those numbers are objectively correct. They wouldn't change if I drew this diagram using x' and t' instead:

             |             |
             |             |
           ˙-7.            |
             | ˙˙..        |
           ,-10,,,,,@,,,,,-10,,  <-- t'=0
             |        ˙˙.. |
             |            -13.  <-- t=0

The numbers aren't in exactly the same places but all of the relationships are the same. The readings on the t=0 line are −7 and −13, the readings on the t'=0 line are both −10, and −10 is above −13, and so on.

Yes, it's reading of hind clock of moving coach ε' in coordinate system of ε. – That doesn't really make sense. "The reading of the hind clock at t=0" makes sense (it's −7). "The reading of the hind clock when the light reaches it" makes sense (it's 0, not shown on this diagram). But "the reading of the hind clock in the coordinate system of ε" doesn't make sense. You need to be more specific about what time you're talking about—for example, by giving a value of t.

I think that with these numbers, you'd say $\theta _{0}^{[}=-7$ and $\theta _{0}^{]}=-13$. But I'm still not sure what you mean by $\theta _{0,self}^{[}$. Is it $-10$? -- BenRG (talk) 06:28, 7 April 2016 (UTC)

Yes, it's reading of hind clock of moving coach ε' in coordinate system of ε. – That doesn't really make sense. I imagine $\theta _{0}^{[}$ as reading on hind clock seen from ε at start (start in ε is $t=0$) and virtual observer's eye is almost touching hind clock (but of course this eye is not moving with hind clock). $\theta _{1}^{[}$ is reading on hind clock seen from ε at moment light reaches hind clock ($t=\tau _{1}$) and again virtual observer's eye is almost touching hind clock. I understand that difference between $\theta _{0}^{[}$ and $\theta _{1}^{[}$ equals $\tau _{1}{\sqrt {...}}$, but I'm not sure how to calculate $\theta _{0}^{[}$ independently from $\theta _{1}^{[}$, and what other readings (besides $\theta _{1}^{[}$) influenced by $\theta _{0}^{[}$.

But I'm still not sure what you mean by $\theta _{0,self}^{[}$. Is it $-10$? Yes, for this numeric example. This is what is called "proper time", right? I imagine $\theta _{0,self}^{[}$ as reading on hind clock seen from ε' coach at start (start in ε' is $t'=0$) and virtual observer's eye is almost touching hind clock (but eye IS moving with hind clock). In first thread https://en.wikipedia.org/w/index.php?title=Wikipedia:Reference_desk/Science&action=edit&oldid=713271421 Special relativity. Simultaneity I thought $\theta _{0,self}^{[}=\theta _{0,self}^{]}=\theta _{0,self}=0$ -- all 3 clocks in ε' coach were synchronized at start. 37.53.235.112 (talk) 10:04, 7 April 2016 (UTC)

Okay, I think I understand all of your symbols now. In the previous thread, indeed $\theta _{0,self}^{[}=\theta _{0,self}^{]}=\theta _{0,self}=0$. But in this thread you changed the rules by saying "when light reaches walls, clocks on walls are reseted to zero". I assume you don't mean that they were literally rewound to 0 from whatever higher value they were showing (if so, all your other calculations are wrong). I think you meant that they counted down from a negative value to 0. In that case, $\theta _{0,self}^{[}=\theta _{0,self}^{]}=-L'/2c$, since the elapsed proper time from t'=0 until the light arrives is $L'/2c$.

In any case, I still think my first comment in this thread was correct. You said the hind clock, when it shows the numerical value $\theta _{0}^{[}$ on its face, is at $t'=\theta _{0}^{[}$. And that isn't true. It was true with the clocks set as they were in the previous thread. It isn't true with the clocks set as they are in this thread.

The clocks are in the same places in spacetime in this thread as in the last thread. Only the values they show on their faces are different. And they are always different by exactly L'/2c. The clocks tick at the same rate, they are just set to different initial values, $-L'/2c$ in this thread versus $0$ in the other one. In the previous thread, the hind clock showed $\theta _{0}^{[}$ on its face at $t'=\theta _{0}^{[}$. In this thread, it shows $\theta _{0}^{[}-L'/2c$ on its face at $t'=\theta _{0}^{[}$, and it shows $\theta _{0}^{[}$ on its face at $t'=\theta _{0}^{[}+L'/2c$. Behind all the complicated symbols, it's a very simple situation. -- BenRG (talk) 07:19, 8 April 2016 (UTC)

Question

Remark

You said the hind clock, when it shows the numerical value $\theta _{0}^{[}$ on its face, is at $t'=\theta _{0}^{[}$. It was not statement , but assumption as I'm not sure it's true (even for previous thread). I've taken it from previous thread (see Remark). So, we shall heve next situation: ε' frame ε frame time coordinate clock reading time coordinate clock reading $t'=0$ $\theta _{0,self}^{[}=-{\tfrac {L'}{2c}}$ $\theta _{0,self}^{]}=-{\tfrac {L'}{2c}}$ $t=0$ $\theta _{0}^{[}=\theta _{1}^{[}-\tau _{1}{\sqrt {...}}$ $=-\tau _{1}{\sqrt {1-u^{2}/c^{2}}}$ $\theta _{0}^{]}=\theta _{2}^{]}-\tau _{2}{\sqrt {...}}$ $=-\tau _{2}{\sqrt {1-u^{2}/c^{2}}}$ $t'=+{\tfrac {L'}{2c}}$ $\theta _{1,self}^{[}=\theta _{2,self}^{[}=0$ $\theta _{2,self}^{]}=\theta _{1,self}^{]}=0$ $t=\tau _{1}={\tfrac {L/2}{c+u}}$ $\theta _{1}^{[}=0$ $t=\tau _{2}={\tfrac {L/2}{c-u}}$ $\theta _{2}^{]}=0$ $t'=\theta _{0}^{[}+{\tfrac {L'}{2c}}$ $\theta _{3,self}^{[}=\theta _{0}^{[}$ $\theta _{3,self}^{]}=\theta _{0}^{[}$ ... $t'=A$ $\theta _{(t'=A),self}^{[}=A-{\tfrac {L'}{2c}}$ $\theta _{(t'=A),self}^{]}=A-{\tfrac {L'}{2c}}$ $t=A$ $\theta _{(t=A)}^{[}=(A-\tau _{1}){\sqrt {..}}$ $\theta _{(t=A)}^{]}=(A-\tau _{2}){\sqrt {..}}$ Correct? Let's check. Hind clock at start is situated in ε in point $(x,t)=(-L/2,0)$ and in ε' in point $(x',t')=(-L'/2,0)$. $(x',t')=({\tfrac {x-ut}{\sqrt {1-u^{2}/c^{2}}}},{\tfrac {t-xu/c^{2}}{\sqrt {1-u^{2}/c^{2}}}})$; $(x,t)=({\tfrac {x'+ut'}{\sqrt {1-u^{2}/c^{2}}}},{\tfrac {t'+x'u/c^{2}}{\sqrt {1-u^{2}/c^{2}}}})$. What's next? What to substitute in and what should be compared with result?

https://en.wikipedia.org/w/index.php?title=Wikipedia:Reference_desk/Science&action=edit&oldid=713271421 Special relativity. Simultaneity. In your problem, say the light is emitted at (0,0) (in either coordinate system). It reaches the walls at $(x',t')=(\pm L/2,L/2c)$, or equivalently $(x,t)=({\tfrac {\pm Lc}{2(c\pm u)}},{\tfrac {L}{2(c\pm u)}})$. Your first clock has the parametric equation (x,t)(τ) = (0,τ), which you can plug into the Lorentz transformation to find (x',t')(τ). To find the digital reading of that clock at a particular (x,t) or (x',t'), you just solve for τ. Your other three clocks have the parametric equations (x',t')(θ) = (0, θ) and (x',t')(θ[]) = (±L/2, θ[]), and you can plug those into the Lorentz transformation to find (x,t)(θwhatever). Any question you have about what someone sees at a given (place,time) can be answered in this way. They are simple questions about coordinate geometry. -- BenRG (talk) 19:58, 29 March 2016 (UTC)

37.53.235.112 (talk) 12:02, 8 April 2016 (UTC)

OK. According your suggestions we have:

$(x';t')(A)=(-{\tfrac {L'}{2}};A-{\tfrac {L'}{2c}})$;

$(x,t)=({\tfrac {x'+ut'}{\sqrt {1-u^{2}/c^{2}}}},{\tfrac {t'+x'u/c^{2}}{\sqrt {1-u^{2}/c^{2}}}})$;

we will substitute x' and t' and should get next

$\color {red}{(x;t)(A)=(-{\tfrac {L}{2}}+uA;(A-\tau _{1}){\sqrt {1-u^{2}/c^{2}}})}$.

After substitution:

$(x,t)(A)=({\tfrac {(-{\tfrac {L'}{2}})+u(A-{\tfrac {L'}{2c}})}{\sqrt {1-u^{2}/c^{2}}}},{\tfrac {(A-{\tfrac {L'}{2c}})+(-{\tfrac {L'}{2}})u/c^{2}}{\sqrt {1-u^{2}/c^{2}}}})$;

$(x,t)(A)=({\tfrac {uA}{\sqrt {1-u^{2}/c^{2}}}}-{\tfrac {L/2}{1-u/c}},{\tfrac {A}{\sqrt {1-u^{2}/c^{2}}}}-{\tfrac {L/2}{c+u}})$.

Why result doesn't match with highlighted equation? 37.53.235.112 (talk) 18:02, 9 April 2016 (UTC)

Composition of Antarctic tephra

This block of tephra is located at Brown Bluff, Tabarin Peninsula, Antarctica. The dark specks appear to be Alkali basalt (per Skilling, 1994). Can anyone help identify the composition of the matrix material? Many thanks in advance.--Godot13 (talk) 17:30, 4 April 2016 (UTC)

Hard be to certain, but the deposits at Brown Bluff and other locations within the James Ross Island Volcanic Group are mainly formed in lava deltas topped by subaerial lava flows Skilling (2002) erupted into an englacial lake. If this block is part of that, then we're looking at a lump of hyaloclastite breccia, with both clasts and matrix made up of shattered basaltic glass. Mikenorton (talk) 17:50, 4 April 2016 (UTC)

Mikenorton- Many thanks!--Godot13 (talk) 17:56, 4 April 2016 (UTC)

Shadows

Is it true that a shadow is a tangible representation of nothing? Meaning that a shadow is not a thing but it exists independent of humans. A shadow can travel faster than the speed of light, and besides the particles occupying the space of a shadow, the shadow itself has no mass/energy? 2601:204:C003:57A5:B517:938E:2F62:3EA0 (talk) 20:25, 4 April 2016 (UTC)

A shadow is an area of reduced light due to some object blocking some of the light source(s). ←Baseball Bugs ^{What's up, Doc?} carrots→ 20:30, 4 April 2016 (UTC)

Yep, I've always wondered about a shadow being able to travel faster than the speed of light, due to the angle at which a shadow can be caused. Apologies for the previous answer which has nothing at all to do with your question. The Rambling Man (talk) 20:36, 4 April 2016 (UTC)

I don't think shadows are things in and of themselves but the manifestation of other things that are things in and of themselves (ie light/objects)...does this make sense??68.48.241.158 (talk) 20:41, 4 April 2016 (UTC)

Shadows are a product of light and objects, so it doesn't make sense that a shadow would "travel" faster than the light that's accompanying it. ←Baseball Bugs ^{What's up, Doc?} carrots→ 20:51, 4 April 2016 (UTC)

It can sometimes be useful to look at the speed of "negative reality", like how quickly an electron hole can travel, or how quickly "coolth" spreads from a cold object. In the case of looking at how quickly a shadow moves, this could be important for things like a sundial. StuRat (talk) 21:13, 4 April 2016 (UTC)

There is a lot of very wrong science wrapped up in such a very short quantity of discussion here!

Shadows do not "travel faster than the speed of light." Maybe the best place to start reading is our article on propagation delay; but I think it would be helpful to go back and read our article on light, wave, and shadow to help you re-center your understanding around the way scientists actually study these topics.

The original question also touches on more philosophical ideas about the absence of substance (in this case, rather, the absence of photons...) Well, you might also enjoy reading about horror vacui - but you should understand up front that this is a pre-scientific philosophical idea that is largely refuted by careful study of modern theory and experiment. As you have arrived to the science reference desk, you should follow up that reading by looking at our article on the vacuum, and on electromagnetic radiation, which we now know may propagate in a vacuum. This concept can be a bit baffling, but pay careful attention to the way scientists define their terms, and you will find that the modern explanation is very consistent with experiment.

Nimur (talk) 21:21, 4 April 2016 (UTC)

A "shadow", like the dot made by a laser pointer, isn't an object. It's, well, a concept. You can take a laser pointer and wiggle it across the surface of the moon, and in theory, if it's perfectly collimated, that little dot might break the lightspeed barrier. But of course "that dot" is different photons from one instant to the next. They say you can never step in the same river twice ... same about a laser pointer dot, or a shadow, since the one is different photons each time, and the other is the lack of different potential photons each time.

Inevitably group velocity and phase velocity will come up, though they're not very directly related. The concept though is that there are things that aren't things that can go faster than light. Wnt (talk) 22:06, 4 April 2016 (UTC)

TANGIBLE (adj.) means capable of being touched, from Latin tangere "to touch". The OP has surely never touched a shadow and may not have read Shadow#Propagation speed in the article they already cited. Since there is no actual communication between points in a shadow that projects over a large surface, the shadow's edge cannot convey information between those distances at any speed. AllBestFaith (talk) 13:29, 5 April 2016 (UTC)

Consider a star that's, say, ten light years distant. It is constantly emitting photons. Any photons hitting us were emitted about ten years ago. Now suppose some large, dark object passes between us and the star, maybe hallway between us, i.e. five light years away from each of us. The photons already more than five light years away from the star will continue on their merry way toward us. The dark object will, at least temporarily, block that stream of photons, thus putting the star in shadow from our perspective. But we won't observe that phenomenon until about five years after it happened. So, NO, shadows do not "travel" faster than light. ←Baseball Bugs ^{What's up, Doc?} carrots→ 13:53, 5 April 2016 (UTC)

• The answer above by Wnt is correct and informative, but let me enlarge on it slightly. It is thought to be impossible for matter to travel faster than the speed of light, but there is no prohibition whatsoever against a phenomenon traveling faster than the speed of light. For an easy-to-visualize example, think of a wave on the water making contact with a straight shoreline. The smaller the angle between the wave and the shoreline, the faster the contact point will move. There is no upper limit to its speed: as the angle approaches zero, the propagation speed of the contact point increases without bound. Looie496 (talk) 13:57, 5 April 2016 (UTC)
  • No, it isn't correct. A shadow can't "travel" any faster than the photons it's blocking. ←Baseball Bugs ^{What's up, Doc?} carrots→ 14:11, 5 April 2016 (UTC)

I think you're using that term differently than most people. For example, most people would say that the shadow of a hawk travels across the ground, or the shadow of the Moon travels across the Earth during a solar eclipse. But your use of "travel" is that a shadow travels only away from the Sun in these cases. Wnt (talk) 14:46, 5 April 2016 (UTC)

I don't follow. Shadows "travel" only in relation to the light source and the object causing the shadow. ←Baseball Bugs ^{What's up, Doc?} carrots→ 19:27, 5 April 2016 (UTC)

The technical term for gathering in special buildings to look at moving shadows is cinematography from Greek kinein "to move" + graphein "to write". AllBestFaith (talk) 21:55, 5 April 2016 (UTC)

What about THIS???? you only have to watch the first 2-3 minutes or so 199.19.248.20 (talk) 00:43, 6 April 2016 (UTC)

OK - speed of movement of a shadow. Let's put together a thought-experiment. Let's take a laser with a pencil-thick beam - and let's put an opaque black dot onto the exit window of the laser so that it casts a circular beam of light with a 'shadow' in the center of the beam. The laser is on a stand that allows us to rotate it really quickly. If I place this contraption vertically above my (infinitely large and perfectly flat) desk, shining the laser downwards, I'll see a shadow on my desk cast by that black dot. As we rotate the light from the vertical towards the horizontal, the center of the shadow moves from being vertically below the laser to being infinitely far away to the side. Since we can rotate the light from vertical to horizontal in a fraction of a second - but the shadow moves from being right in front of me to being infinitely far away in just a couple of seconds - it's tempting to say that it moves faster than the speed of light.

But that's not true.

The light from the laser is what defines the edges of the the shadow - and that light can't travel faster than light. So no matter how fast I rotate the lamp to "move the shadow" from right in front of me to being a million miles off to my right - the light from the laser can't travel that million miles to define the edges of the shadow at anything faster than the speed of light. The shadow moves at speeds approaching (but never exceeding) the speed of light.

OK - so we need another thought experiment. Instead of projecting the shadow onto a flat desk, let's project it onto the inside of a vast sphere...an entire light-second in radius. If I'm standing in the center of the sphere - then I see the light reflected back at me from the sphere with a two second delay. If I suddenly move the laser from shining on the sphere to my right - to shining on the sphere to my left - then two seconds later, I see the light disappear from my right side and a fraction of a second later, it'll reappear on my left...and the shadow moved with it. So the "shadow" did indeed track all the way across the sphere in that tiny fraction of a second (albeit with a two second delay). It travels a distance of pi light-seconds in the time it took me to spin the laser around...which is *way* faster than the speed of light.

But the problem here is that this shadow isn't a constant 'thing' - it's the absence of photons, but it's the absence of different photons when it's pointing in one direction versus pointing in the other direction. It's like driving along a freeway with a beige Volvo estate wagon a mile ahead of you. Suddenly it turns off of the freeway, out of sight. Simultaneously, you notice in your rearview mirror, a different beige Volvo estate wagon drives onto the freeway a mile behind you. Do you now conclude that the absence-of-a-Volvo travelled faster than the speed of light?

SteveBaker (talk) 16:36, 6 April 2016 (UTC)

Tigers smarter than lions?

This might be just a bit of useless and potentially wrong trivia, but when people claim that tigers are smarter than lions, could it be that they are right? If yes, how could that be measured? AFAIK, brain size alone won't let us conclude about the intelligence of an animal. But where could the information bit come from?--Scicurious (talk) 20:58, 4 April 2016 (UTC)

One of the predictors of intelligence is the degree of social integration, as social structures require a lot of intelligence to navigate (when to act submissive, when to dominate, when to fight). Since lions are social animals and tigers are not, that would seem to mean more intelligence is required of lions. StuRat (talk) 21:10, 4 April 2016 (UTC)

hard to say, all kinds of philosophical problems involved....is a dog smarter than a tiger because it can be trained to do things for humans but tigers can't?? or are tigers smarter because they can't be conned into doing things for humans?? you can look at behavior and behavior differences but the interpretation of smartness is inherently subjective...look at controversy over IQ....ants might be the smartest if look at how successful they are in terms of numbers etc...humans might be the dumbest..or the smartest as can use tools like crazy...but maybe dumb as the use of these tools may lead to their demise...idk...68.48.241.158 (talk) 21:15, 4 April 2016 (UTC)

There are lots of ways of assessing animal intelligence, but usually scientists don't make claims about animals being "smarter" than another or terms like "intelligence" which is very broad and poorly defined. Rather, they talk about memory, learning, path finding and many other more specific things that are slightly more amenable to experimental or observational quantification. Our article Animal_cognition has some info and refs on methods. Here are a few books that give overviews of how we measure intelligence in animals, why animals are intelligent, etc. [1] [2] [3]. They are not feline specific, but we do have cat intelligence which gives this [4] scholarly article comparing the brains of lions to tigers. I might search a bit more later for more specific refs. You may also enjoy ref 3 and others at Portia_fimbriata, which describe how this spider can do things that smart lions do, like breaking line of sight to make a detour around prey, so as to approach it from a better angle. In the mean time, I suspect user:Snow Rise might have something helpful to add. SemanticMantis (talk) 21:17, 4 April 2016 (UTC)

Also, a strike against tiger intelligence is that they refuse to jump over a wall of white fabric, even when cornered and facing death. For some reason they have a very strong instinct not to jump into something unfamiliar, even when doing so could save their life. StuRat (talk) 21:21, 4 April 2016 (UTC)

Heh, I wonder how much evolution prepared them for the whole "cornered and facing death" thing. It doesn't sound like a tiger kind of problem. :) Wnt (talk) 22:08, 4 April 2016 (UTC)

I wonder where you get this information from StuRat. I always do. Scicurious (talk) 22:24, 4 April 2016 (UTC)

"Nepalese aristocrats developed a technique later adopted by British hunters in which roles of white cloth, which tigers reportedly will not cross, where laid out to funnel tigers to an area where hunters waited." [5]. StuRat (talk) 23:58, 4 April 2016 (UTC)

StuRat to his credit quotes accurately from a source that is rife with spelling mistakes. A good convention in such quotations is to insert sic in brackets at misspellings; it stands for sic erat scriptum "thus was it written" and is a way to be scrupulously fair to both the present reader and original writer. Example: "...roles of white cloth...where[sic] laid out..." AllBestFaith (talk) 13:07, 5 April 2016 (UTC)

Sounds apocryphal to me, but who knows. But what you said was "For some reason they have a very strong instinct not to jump into something unfamiliar, even when doing so could save their life." Which sounds doubtful to me. I think if the tiger felt under stress, it would go over (or through) the fabric if that were the only option. This source makes it sound more like they bounded the an area such that it made it more convenient for the the tiger to take another path, to where they lay in wait. Two very different images, if you ask me, even if we assume either to be accurate.. Snow ^{let's rap} 06:23, 5 April 2016 (UTC)

The original source I saw was a very old video, showing the tigers being funneled in as described above. The fabric was only high enough that they couldn't see over it, they could have easily jumped over it. StuRat (talk) 16:24, 5 April 2016 (UTC)

(ec)But they had no reason to do so.--TMCk (talk) 17:00, 5 April 2016 (UTC)

A "virtual grid" near Lone Pine, California

Animals can sometimes be fooled relatively easily - for example, these painted "cattle grids". I suspect that if the tigers were sufficiently motivated, they would have jumped over the cloths. It was probably very skillful animal handling that allowed this method to be used. DrChrissy ^(talk) 16:57, 5 April 2016 (UTC)

Yes, the virtual cattle grids are another good example of what I mean. A smarter animal would notice they aren't quite the same as real cattle grids, and test them out with just one hoof. When they determined that they could walk on it, they would then have learned the difference and remember it. Getting back to the Q, lions do seem confused by the wild stripes on zebras, so that might be a mark against them. StuRat (talk) 17:21, 5 April 2016 (UTC)

But do we know whether tigers are similarly confused by the motion dazzle of the zebra stripes - it's just not black and white (sorry, could not resist that!). More seriously, because the zebra is able to confuse the lion, does that mean the zebra is more intelligent than the lion? Obviously not, (because the stripes are not part of any conscious effort) but I think it indicates the lack of usefulness of trying to apply "intelligence" to species other than humans. DrChrissy ^(talk) 17:45, 5 April 2016 (UTC)

@DrChrissy: and @StuRat:, you're both a bit out of date on your Zebra thinking. See this 2014 Nature Communications paper concluding "there is no consistent support for camouflage, predator avoidance, heat management or social interaction hypotheses" [6]. Rather, they conclude there is strongest support for the stripes being useful in avoiding ectoparasitism. Obviously this is not the be-all, end-all answer, but it's hard to get more authoritative than a comprehensive Nature paper from just a few years ago. SemanticMantis (talk) 19:19, 5 April 2016 (UTC)

Actually, I am well aware of that hypothesis. The function of the stripes is, in my opinion, not yet settled. I actually think they might be multi-functional, but you are correct to point out to other readers that motion-dazzle is not the only possibility. DrChrissy ^(talk) 19:42, 5 April 2016 (UTC)

I'm fairly confused though. If you accept there is no consistent support that zebra stripes even help with lions, why do you think it confuses tigers. I'm sure someone has fooled around with tigers and zebras, but if we can't even get enough evidence that it helps with lions, it seems unlikely we have anything even close to useful for tigers. (I believe there are some who suggest tigers may also use motion dazzle, but even if that's true I'm not sure there's any reason to think it's for other tigers as opposed to their prey.) Nil Einne (talk) 07:28, 6 April 2016 (UTC)

I've just read the Nature paper and I am not convinced it discredits the motion-dazzle hypothesis. The paper really has only one comment on this.

Across contemporary ecosystems in Africa, where lions have been subjects of repeated detailed study, lions capture zebra in significantly greater proportions to their abundance

but this leaves the question - what proportion would be captured if the zebra did not have stripes? Regarding the insect deterrent hypothesis, I am also left with another question. If this is so effective, why have no other animals (e.g. antelope) evolved something similar? DrChrissy ^(talk) 13:32, 6 April 2016 (UTC)

By the way, did you know that some sheep in the valleys of Wales completely trump lions and tigers in intelligence. They have learned to curl themselves into a ball (like a hedgehog) and roll over cattle grids to get to the more luscious grass on the other side. Please note, I meant to post this 4 days ago.  ;-) DrChrissy ^(talk) 17:04, 5 April 2016 (UTC)

"Measures" of intelligence (please note the scary quotes) are totally, totally dependent on the questions you ask and the way in which this is investigated. What would you like to know? Is the hunting behaviour of the tiger more plastic than that of the lion? Can tigers solve human derived puzzles quicker than lions? Do circus tigers learn "tricks" more quickly than circus lions? It all depends on the question asked and the way we try to determine the answer. Unfortunately, so many studies on animal "intelligence" are clearly locked firstly within an anthropocentric world, and then secondly our own limitations of trying to investigate this. How do we objectively measure whether a tiger is more intelligent than an earthworm? If we can not answer that, then we can not measure whether a tiger is more intelligent than a lion. DrChrissy ^(talk) 23:11, 4 April 2016 (UTC)

As others have noted already, the question is problematic as phrased because "intelligence" is not an empirically quantifiable value. That is to say, despite the way we idiomatically reference it (especially with regard to our own species) it's not a substance or unidimensional quality or process that lends itself to measurement. Part of this is innate; to the extent that "intelligence" is seen as a desirable quality, there will always be a propensity towards reductionism in order that it can be seen as a uniform quality that is more present in some than others. But this mistaken concept got kicked into overdrive in the pre-modern and early modern history of the biological sciences, in order to justify the hierarchical structures that many "learned" men wanted to presume, particularly with regard to racist and gendered notions of innate superiority. I don't mention this just as a general aside either--these beliefs were central to the development of notions like IQ, and the tests that purported to evaluate a "general intellect". Proponents of this variety of psychometrics have tried hard to excise the bias from these tests since, but many cognitive scientists believe the very concept upon which they are predicated (a general measure of intelligence) is flawed beyond repair and based in a lack of understanding of the modular mind.

Now, bringing this back around to animal behaviour, the complexities become even more pronounced when we try to compare species. You can test for performance on certain tasks, but then your are necessarily bringing your value judgments into what intelligence is best typified by when you select the tasks for "general" intelligence. That's not to say you can't measure changes in the concept of general intelligence; if a given individual or generation raises in performance on all kinds of task, largely across the board, you know that intelligence has become "superior" in the sense. But there are too many different types of behaviours and faculties when it comes to cognition to say which is going to prove most vital or advantageous to a given individual in the longterm, in an open system like an eco-system or a social system. And to compare the needs and environment of two different animals that are alike only that both are cats and apex predators misses the functional meaning of intelligence. cognitive researchers (and sometimes social psychologists) call this "situated intellect" (and also a principle of environmental psychology), while sociobiologists (and EP and sociobiology really are the same fields as seen from either the anthropocentric/narrow or zoocentric/broad lens) call this the animal's "behavioural niche". You might even say that all animals with substantially developed brains have a "cognitive niche", but that term is already applied to in a related but distinct sense to describing ones of the ecological niches that humanity fills.

But it goes further than the species level, because what turns out to be "smart" behaviour varies not just by the species but by the individual and their circumstances. What is the "intelligent" solution in the aggregate? If its the type of decision that leaves the animal best off in the long run, the animal doesn't know what that's going to be--even if we, or it, could even put together an accurate or concrete notion of what "best off" would be for it. Indeed, most species won't even necessarily ever recognize the long-term consequences of its actions, especially if the "decision" and the outcome are separated by a bit of time. But the decisions that the animal makes are tailored to ecological/environmental demands the members of its heritage during its evolutionary past. But even if you are asking which species is more "intelligent" with regard to adapting to unexpected circumstances, you'd have to qualify the conditions very carefully to decide which was "more intelligent" in this regard. Ultimately you'd have to have a lot of experience studying the ethological nature of both species just have an informed decision, and even then you'd have to pass your opinion along subjectively; there'd be no one empirical measure you could use. If they naturally cohabitated in a certain region, you could at least measure their success in their survival rates, but you can't even do that here. Snow ^{let's rap} 06:11, 5 April 2016 (UTC)

Which species is closer to extinction? ←Baseball Bugs ^{What's up, Doc?} carrots→ 13:45, 5 April 2016 (UTC)

There are different (sub)species of each, but according to the infoboxes at lion and tiger, the tigers are currently more threatened. While I appreciate a little teleological thinking, that does not tell us much of anything about intelligence, though it may tell us something about their Ecological_resilience. SemanticMantis (talk) 14:06, 5 April 2016 (UTC)

But not even much about that, since both species live in drastically different ecological contexts, with different degrees and forms of habitat displacement, prey reduction, interruption of reproductive habits and other population stressors. The populations of asiatic lions and most tiger species are so reduced now, I don't think they co-exist anywhere in the world, making comparison of their circumstances an apples and oranges affair. That line of inquiry raises another issue, actually--namely that you get substantial variation of behaviour between subspecies. Snow ^{let's rap} 20:15, 5 April 2016 (UTC)

@BBB: That's a ridiculous point of comparison. Which are closer to extinction, Polar Bears or House Flies? Your conclusion: House flies are more intelligent than polar bears? That's meaningless. Turn brain on before posting! SteveBaker (talk) 20:49, 5 April 2016 (UTC)

The trouble with direct comparison of intelligence is that behavior is often evolved to match environment. Why won't a tiger jump a white sheet? Well, maybe it's just stupid - but maybe it's evolved to avoid jumping into hidden snow banks for some deep and subtle reason that we've failed to comprehend? It's easy to label weird behaviors like this as "stupid" - when in reality, we just don't have the intelligence to understand them ourselves.

Why is it that your stupid dog spins around in a circle before (s)he poops? It turns out that dogs prefer to face North or South when they poop - and spinning around helps them sense the earth's magnetic field more easily [7]. Are dogs stupid for doing this - or is there something they know that we don't? Maybe they are smarter than we random-direction-pooping humans?

The root problem here is that we simply do not have a reasonable definition for the word "Intelligence" - and the closest we ever get to having a means to measure this vague thing is the IQ test - which more or less defines "Intelligence" as "The ability to get a high score on an IQ test".

So when it comes to animals, not only would it be hard to compare different species against some fixed standard - but it's also impossible to come up with a fixed standard that has much real-world significance.

So how do we define as "intelligence"? "That which humans have but other animals and computers have less of!"

For example, we'd say that humans were more intelligent than chimpanzees. But teach a chimpanzee to the digits 1 through 9, then place those digits in random order on a computer screen and have the subjects remember the positions of each digit and to recall them in numerical order. Sounds easy - but chimpanzees are much better at playing this game than people are[8]! If this is a measure of intelligence then chimpanzees are smarter than humans - and at a game that we invented! I'm old enough to remember when beating a human at chess was regarded at the pinnacle of intelligence...until Deep Blue beat Kasparov...then it was winning Jeopardy! (well, Watson nailed that one pretty effectively)...and then playing Go...but since a week or two ago, computers beat us all at that too. We have the Turing test - but to pass that, the computer has to adequately pretend to be a human...which takes us back to "Intelligence is that thing that humans have" - which is cheating! Computers are fast edging towards passing the Turing test - so now we're looking for another reason why we can't call them "intelligent".

Consider the Clark's nutcracker - which can hide tens of thousands of nuts around it's territory - then, nine months later, flawlessly retrieve them as needed and without hesitation...even when they are buried under feet of snow. Humans can't manage to hide more than a dozen or two without losing track. Over short-term memory, even cats have better memories than we do! These things are mental capabilities that are beyond what humans can do...yet we persist in moving the goal posts to preserve our feelings of superiority!

Clearly humans DO have a breadth and depth of skills and mental capabilities that no other animal (nor machine) can come close to matching - but defining what that thing is eludes us.

So asking whether a Lion or a Tiger has more of some indefinable thing is entirely meaningless. First define what the word means, and how to measure it - then we'll tell you who has the most of it.

SteveBaker (talk) 20:49, 5 April 2016 (UTC)

Surprised no one here has mentioned Encephalization or Brain-to-body mass ratio. Our page has the ratio for Lion (1:550) but I can't find Tiger after a brief search. Yes it's imperfect and has glaring exceptions, but as a "starting point" it's better that "the question is meaningless".. Surely we CAN compare 2 animals and decide a Raven is smarter than a housefly, the question is a tiger smarter than a lion might be much "harder" to resolve, but doesn't mean it's meaningless. Ultimately, the animals might be similar enough to say there is more overlap then we can't reliably distinguish between the two for that metric. Vespine (talk) 23:30, 5 April 2016 (UTC)

Well yes, of course we might all be inclined to agree, as an impressionistic matter, that the raven is "smarter" than a house fly. Certainly we can see that it has a vastly more complex CNS and has something much closer to the kind of problem-solving capabilities we recognize as more similar to human cognitive capabilities. But that's not what the OP asked about; he wanted to know if there were specific and concrete measures by which two relatively closely related (at least when compared against the raven-fly scenario) could be judged with regard to "intelligence". And the short answer is, no not really, though you could (theoretically) get performance measures if you narrow the question to a specific behavioural task in a specific environmental context. That said, brain to body mass ratio is an interesting phenomena, but once again, it only makes sense as a vaguely defined trend; when you look at the particulars of this supposed correlation, it breaks down all over the place. Snow ^{let's rap} 01:48, 6 April 2016 (UTC)

What is the evidence that a raven is "smarter" than a housefly? Can a raven land upside down on a ceiling? Rather than looking at brain ratios etc, we first need to define what "smarter" means. Once we agree on that (Ha!) We can devise questions and studies to answer those. DrChrissy ^(talk) 13:09, 6 April 2016 (UTC)

I'd go with "the ability to reason a solution to a novel problem". Crows/ravens seem able to figure out how to use tools (sticks) to fish for food they can't reach, even to the extent of first fishing for a bigger stick with a smaller stick. StuRat (talk) 16:44, 6 April 2016 (UTC)

What is the evidence that a raven is "smarter" than a housefly? I think this kind of statement is bordering on solipsism, how could we possibly know anything? Oh the despair. IMHO it's actually not that hard. For example, it doesn't take "intelligence" to land on a ceiling, in fact, a study was done which examined how a fly does it, and all it has to do is reach up with it's front legs and sticky feet do the rest. Vespine (talk) 22:27, 6 April 2016 (UTC)

Yes, of course I already knew how houseflies managed this - I was asking the question in a way that would indicate how the question posed about "intelligence" determines the answer and therefore the futility of asking the question. StuRat has now posed the suggestion that tool-use indicates intelligence. Tool use by animals tells us that ants will drop stones down the burrows of rival colonies. And there are other examples of tool-use by invertebrates, but again very dependent on the definition of "tool-use". DrChrissy ^(talk) 22:42, 6 April 2016 (UTC)

No, you misquoted me. I did not state that tool use indicates intelligence, I stated that "the ability to reason a solution to a novel problem" does. That solution may, or may not, involve tool use. In ants, presumably any tool use is an evolved instinctive behavior, and not to a novel situation, as competing any colonies have existed as long as ants have. StuRat (talk) 17:21, 7 April 2016 (UTC)

@StuRat Apologies for misquoting you - it was not intentional. With regards to ant responses to novel situations, you might care to look at this problem solving in leafcutter ants, Atta colombica.

Other examples of invertebrates responses to novel situations include include -

• Social transmission of information during the waggle dance of honeybees.
• Idiothetic orientation by spiders, i.e. they memorize information about their previous movements.
• Detour behaviour in which spiders choose to take an indirect route to a goal rather than the most direct route, thereby indicating flexibility in behaviour and route planning, and possibly insight learning.
• Conceptualisation in the honeybee, Apis mellifera.
• Numeracy in the yellow mealworm beetle, Tenebrio molitor, and honeybee.

References

DrChrissy ^(talk) 17:48, 7 April 2016 (UTC)

How are any of those novel problems ? For example, bees have encountered food sources as long as they've existed, and needed to communicate that info to the hive, so that would be an evolved instinctive behavior, not requiring intelligence. StuRat (talk) 15:35, 9 April 2016 (UTC)

"I'd go with" ≠ "empirical measure". We're not talking about whether anyone has a right to a "reasonable" subjective impulse as to what constitutes remarkable intelligence, relative or otherwise, especially if it meshes with with the semantics of their impressionistic/fuzzy logic definition for the term. The OP was inquiring about empirical measurement. And the answer, notwithstanding the question being steeped in a deeply complex cognitive inquiry, is that no, there is no real way to determine with scientific clarity that a tiger is smarter than a lion or vice versa. Nor indeed that a raven is smarter than a housefly. If that makes me sound solipsistic, well I understand what Vespine means to say by that, but coming from a scientific perspective, I don't know of a single sociobiologist who I think would make the claim that they could "prove" that. They might talk about the relative complexity of the nervous system or the behaviour itself, or they might talk about whether the task was accomplished with working memory or by a previously observed instinctive reaction, whether it required novel pattern analysis or was a conditioned response, whether the animal could (or had to) learn the behaviour socially, or whether it could add a new step to the process to meet new necessities, ect, ect. But no serious researcher is going to say "this animal is X order of magnitude or Y% greater than this other species in terms of intelligence."

Again, just avoid running this circle one more time, the argument is not that "you shouldn't say, as reasonable shorthand, that an iguana is smarter than an ant." But if you want to prove that statement as empirical fact...well you better be a revolutionary in the understanding of animal and human make-up on par with Charles Darwin in his day, with a bit of Carl Sagan's gift of gab mixed in, because you're going to have to advance our understanding of the mind and the brain lightyears in order to be able to come up with one unified measure that defines "intelligence" such that great thinkers all over the world, greatly divided over basic questions about the nature of cognition and intelligence all nod and go "Yup, that's it, alright. Oh, what do you know, Johnson, looks like I've an intelligence rating of 354.7 Vesps. You're only 320.1. So....now we know that, don't we Mr. Nobel laureate?!" <------"Vesps" used in good humour! :) Snow ^{let's rap} 04:45, 7 April 2016 (UTC)

THIS paper takes a reasonable stab at a mathematically solid definition of intelligence. However, it depends on a few uncomputable measures - so it's not something that can be practically tested - and a lot of people who work in the field do not agree with it. SteveBaker (talk) 15:18, 7 April 2016 (UTC)