Science desk | ||
---|---|---|
< June 21 | << May | June | Jul >> | June 23 > |
Welcome to the Wikipedia Science Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
Would it be theoretically possible for a pair of binary stars to orbit a planet that sat between them? For that planet to be Earth-like? Neon Merlin 01:25, 22 June 2009 (UTC)
Is there any conversion factor between horsepower and cc of a motor car?? can these be relation in any such numerical figure?? or are these two different things?? —Preceding unsigned comment added by 119.153.21.132 ( talk) 06:22, 22 June 2009 (UTC)
Is time finite or infinite? Bus stop ( talk) 07:41, 22 June 2009 (UTC)
Why the pressures within an inverted vertical tube manometer is being substracted..? —Preceding unsigned comment added by Sreekanth awh ( talk • contribs) 08:26, 22 June 2009 (UTC)
Is there an angle that you could cast light at (in a beam) where the circle iluminated would appear the same size at all distances? Say if you shon it at a wall a foot away from you and held a ruler a couple of inches away from your eye the circle of light would appear 4" wide, and it would also appear that if you stood 10 feet away from the wall, due to perspective. Gunrun ( talk) 08:43, 22 June 2009 (UTC)
I would think so. The apparent radius of a circle goes like 1/d with d the distance between you and the circle. The actual radius of the illuminated circle is proportional to d. You might want to have a look at http://en.wikipedia.org/wiki/Gaussian_beam
My friends and i are trying to do a project in the summer, which would keep us engaged, and at the same time learn something new. We are all first year undergraduate students. The basic idea is this: You have a (computer) mouse which eats light, that is, goes to the brightest area it can. It can do cool things like following the light from a torch, etc. In addition, whenever it collides with an obstacle, it veers back a couple of meters and then zooms off in some other direction. It isn't wired. This is to be done with basic electronics. We are following this book, and you can find the circuit diagram and other details in the link. But the thing is, we are facing multiple problems, and in need of help. The first problem is the IR emitter thingy. The book says the IR emitters (removed from an old mouse) will sense the incoming light, and hence act like the "eyes" of the mouse. It has given clear instructions on how to desolder the emitters and all. My question is, how can IR emitters possibly detect light? Shouldn't you use detectors? This can't be a printing mistake, he's used it several times. Then comes another problem. According to his illustrations, his emitters have 2 terminals, whereas our emitters have 3. What do we do? Worse, our detectors have four! Are there various types of emitters/detectors used in a mouse pcb,and are we stuck with a different kind? If that is the case, would the correct IR emitters/detectors be available in any electronics shop (The major electronics hub in the city is quite some distance away)? I think we are seriously in need of help... Rkr1991 ( talk) 09:13, 22 June 2009 (UTC)
Where are you, Spinningspark ? I thought you were the resident electronics specialist... Rkr1991 ( talk) 05:22, 23 June 2009 (UTC)
How can we reach the lowest possible temperature? If something is 0 C, I can put something -5C and cool it a little. But since the absolute zero temperature does not exist, how can be cool something until the lowest existent temperature, there is nothing cooler than it...-- Mr.K. (talk) 09:56, 22 June 2009 (UTC)
Bringing an object in contact with a cooler object is not the only way of cooling it. see for example http://en.wikipedia.org/wiki/Laser_cooling
OK, forgive my lack of comprehension of science. As I understand it, because light moves extremely fast, but not infinitely quickly, whatever you see took place a fraction before you actually noticed it. And furthermore, the further away the incident is, logically, the longer ago the incident took place. So I wondered, (Q1) what happened if someone had an improbably powerful telescope and was on the moon, looking at Earth. How long ago would whatever he saw actually have taken place?
Q2 What about if the person with the telescope was even further away, say in some high-tech capsule that allowed him to survive and also get a good view from Alpha Centauri?
Q3 How far away would you need to be to see, say, the Romans invading Britain?
If there's a flaw in my logic, please point it out. -- Dweller ( talk) 10:13, 22 June 2009 (UTC)
It's probably impossible to see the romans invade britain now though, unless you're at the planet already, because to get there to see it you'd have to travel faster than than the speed of light. The invasion of the romans is moving away from our planet at light speed! Gunrun ( talk) 10:46, 22 June 2009 (UTC)
According to the article on Thymine, the molecular formula of this nucleoside is C5H6N2O2. However, in the image to the right I can only see two hydrogens and no carbons at all. Where are the four missing hydrogens and the five missing carbons? -- 83.34.187.22 ( talk) 12:00, 22 June 2009 (UTC)
Is there a scientific reason why the East Coast is getting so much rain in the past few weeks? -- Reticuli88 ( talk) 13:23, 22 June 2009 (UTC)
Large-scale movement of the universe is dominated by the metric expansion of space, making further objects recede faster. But what is the farthest object that does actually travel towards us? More generally, what it the object with the largest difference between expected and observed red shift (either way)? -- Stephan Schulz ( talk) 14:59, 22 June 2009 (UTC)
Is there an online database that lists the apparent or observed colours of night sky objects to the human eye using some sort of scientific scale? For example, Mars and Betelgeuse are redder. I know Rigel is blue in absolute terms, but is it blue to the naked eye from a human perspective? I want a version of the Hertzsprung-Russell_diagram using observed data from the human eye on Earth rather than absolute data out there in space. -- Sonjaaa ( talk) 16:53, 22 June 2009 (UTC)
Does a star or planet's B-V colour index represent its apparent colour to a human observer on Earth?-- Sonjaaa ( talk) 00:33, 23 June 2009 (UTC)
I often make spaghetti with different kinds of spaghetti sauces, and it seems that the mushroom sauce gets mold much more often than the tomato-only sauce. I can't imagine why, since both are the same brand, bought in the same amounts, stored in the same type of jar in the same place in the same refrigerator; the only difference between the types is the presence of cooked chunks of mushrooms. Obviously the mushrooms and the mold are different species, so it's not as if the mushrooms are manifesting themselves as mold, but realistically is there any possibility that the mold grows more readily on the mushrooms themselves, and/or that the presence of the mushrooms makes the sauce a better host for mold? Nyttend ( talk) 17:49, 22 June 2009 (UTC)
Are chicken eggs sterile (free of bacteria) before the shell is opened? 65.121.141.34 ( talk) 18:31, 22 June 2009 (UTC)
If we were to create a substantial population in a space station (something like Babylon 5) and ensured that the construction and all people sent there were free of all bacteria/viruses would it remain sterile indefinitely or would the human flora be likely to eventually mutate into forms that cause illness? Thanks :-) -- 87.113.12.133 ( talk) 19:58, 22 June 2009 (UTC)
Thanks all. I'm particularly interested in the fact DNA can spontaneously create a virus, I'll have a further look at that -- 87.113.128.46 ( talk) 22:15, 23 June 2009 (UTC)
Do we know of any stars whose diameter is larger then the orbit Pluto would make (at maximum distance, assuming its eccentricity was 0.0000)? What would be the angle we would be able to see if it was at the distance of Alpha Centari (sp?)? 65.121.141.34 ( talk) 20:53, 22 June 2009 (UTC)
In reading about small stars (due to an earlier question here), I found this quote: "The relatively puny body weighed in at 96 times Jupiter's mass - above the threshold of 75 Jupiter-masses required for a bona fide star, which must also burn hydrogen." So, are there hydrogen-burning planets, considered planets simply because they are less than 75 Jupiter-masses? -- kainaw ™ 22:19, 22 June 2009 (UTC)
There are accumulating unreplied remarks on that page and, of course, there is probably a bunch of you who could answer them. (is mainstream isn't it?) ~ R. T. G 22:32, 22 June 2009 (UTC)
Does an observer move relative to the light cone? Special relativity says "Special relativity incorporates the principle that the speed of light is the same for all inertial observers regardless of the state of motion of the source.", and if an observer moves relative to the light cone, the speed of light is not the same for the observer. And as, if we slide the axis of the path of the observer to enable to regard the observer not moving, then the axis of the light cone is slided accordingly, and it turns out that the speed of light is fixed to the source (like in emission theory). But if an observer does not move relative to the light cone, the plane sharing simultaneity does not seem to tilt. Like sushi ( talk) 23:18, 22 June 2009 (UTC)
(Edit conflict) (indent) The problem is that you can’t just ask if something is "moving", or talk about "the axis" of a light cone, without specifying which inertial frame of reference "motion" is defined relative to, and "the axis" of a light cone is defined in. To use a concrete example, suppose two spacecraft are moving away from each other at some constant speed v, where v is a sizeable fraction of the speed of light. Somewhere in the rough vicinity of the two spacecraft, a flashbulb goes off. Associated with each spacecraft is an inertial frame of reference such that in that frame of reference, the associated spacecraft is stationary, and the flashbulb goes off at the origin of the associated 4-D coordinate system.
The flashbulb going off is an event in spacetime. Associated with the flashbulb going off is a future light cone, which consists of the set of all events in spacetime such that light from the flash reaches that point in space at that point in time. Call the two spacecraft A and B, with associated inertial frames A and B. In inertial frame A, the future light cone associated with the flashbulb going off consists of all events (points in spacetime) such that r=c t, where r is the spatial distance from the flashbulb event as measured in inertial frame A, t is the time since the flashbulb event occurred as measured in inertial frame A, and c is the speed of light. In inertial frame B, the future light cone associated with the flashbulb going off consists of all events such that r’=c t’, where r’ is the spatial distance from the flashbulb event as measured in inertial frame B, t’ is the time since the flashbulb event occurred as measured in inertial frame B, and c again is the speed of light. The speed of light is the same constant value in both frames of reference.
The two observers agree as to which events are on the light cone, but they will disagree as to what the coordinates are of the events on the light cone. E.g., observer A might say that a given event on the light cone occurred 1 second after the flashbulb event, and is 1 light-second away from where the flashbulb event occurred. Meanwhile, observer B might say that the same event on the light cone occurred 2 seconds after the flashbulb event, and is 2 light-seconds away from where the flashbulb event occurred.
More importantly, although observers A and B agree as to which set of events are on the light cone, they do not agree as to which set of events are on the axis of the light cone. Observer A will say that the axis consists of all the events for which r=0, i.e., the world line of an object that was at the flashbulb event, and which is stationary as measured in inertial frame A. In contrast, observer B will say that the axis consists of all the events for which r’=0, i.e., the world line of an object that was at the flashbulb event, and which is stationary as measured in inertial frame B. The only event that observers A and B will agree is on the axis is the origin of the two coordinate systems.
In short, observer A will say that the axis of the light cone is parallel to spacecraft A, i.e, spacecraft A is not moving relative to the axis of the light cone, and spacecraft B is moving relative to the axis of the light cone. In contrast, observer B will say that the axis of the light cone is parallel to spacecraft B, i.e, spacecraft B is not moving relative to the axis of the light cone, and spacecraft A is moving relative to the axis of the light cone. It’s an exactly symmetrical situation, and neither observer is the "correct" one. Red Act ( talk) 05:26, 23 June 2009 (UTC)
No. I think I have found another problem. That is when the observer is out of the light cone and eventually touches its surface. The first question now makes sense? or is it still faulty?
I am confused.
Like sushi (
talk)
10:18, 23 June 2009 (UTC)
I have managed to get out of the confusion. All light cones assume axes parallel to the axis of motion of the observer in the reference frame of him. Like sushi ( talk) 11:10, 23 June 2009 (UTC) Or do they not? Like sushi ( talk) 11:15, 23 June 2009 (UTC)
Sorry,I didn't notice Mr.or Ms. Red Act has written. The axes of all light cones according to that observer are parallel. So the contents of a light cone is always the same for any observer, i.e. the light cone occupies the same spacetime, and only difference is the coordinate system which gives the event the time and location? In fact, I have posted to the math desk to confirm that two points at which observers moving parallel to the source of the cone, are the same distance away, and in a plane with the same y (the spacial axis perpendicular to the direction of motion of the observer) and the light cone meet always make a line of the same tilt, if the velocity of observers are the same (in mathematical form). But I could not be answered somehow. (About for what reference frame, I think I didn't specify. I was thinking only in one reference frame.) If all planes sharing simultaneity is inclined at the same rate in any one reference frame, no matter from what plane you start, the resulting planes are the same if any numbers of observers travel for the same time in their common reference frame, and as such, with the same velocity. Is it that it does not matter if it's the section with the light cone or not, but "from and onto the same plane" and "along parallel lines", and if not we can not simply compare them? Like sushi ( talk) 12:28, 23 June 2009 (UTC)
I think, in one reference frame, a tilted world line (I am not used to this term) of another observer moving relative to you which shows another axis of the light cone goes through the center of the ellipse which is the section of the light cone and the plane of simultaneity for that observer in the first reference frame. If that distorted cone (it is not distorted in outer cone though) can be transformed in to the right cone, making the right cone the distorted cone, then the reciprocity is shown. Like sushi ( talk) 13:27, 23 June 2009 (UTC)
I have noticed that the diagonal lines (the edges of the light cone in the plane y=z=0),are not affected by the transformation. And the outer cone is the same with and without the transformation. As I think (if it is arbitrarily set) the axis of the cone or the world line of the observer moving in respect to the right coordinate system goes through the center of the ellipse which is the section of the light cone and the plane of simultaneity for the distorted coordinate system, it just need to adjust the x-axis to make the distorted cone (of which the surface is not distorted) right.
But does the transformation to make the distorted cone the right one makes the right cone the distorted one with the opposite tilt? And does the y- or z- width of the ellipse section of the transformed light cone appears to be small than the radius of the circle section of the right cone with the centers at the same time in the reference frame of the right coordinate system? (I think that means if the observer regarding himself stationary measures the travel distance of light for the other observer moving relatively to him, in y or z in his right coordinate system, at the same time in his reference frame, it is less than his.)
(I think I have managed to understand , with the help of all of you, that the light cone is always the same if the coordinate system is adjusted to the right one, though the distance to the origin of the light cone in spacetime is different. The questions I am asking now is on the side of the original one, which was about if the shape of light cones, and thus the speed of light are always the same in all (right) coordinate systems, or for all observers who regard themselves at rest.)
Thank you very much for all of you! And I hope you will answer the side questions. Like sushi ( talk) 23:39, 23 June 2009 (UTC)
Alhough it is difficult to imagine, caliculating Lorentz transformation,
for t and x gives
.
So coordinate system A from perspective of B is coordinate system B from perspective of A just with the opposite v. It seems a light cone for A from perspective of B has just the opposite tilt of the light cone for B from perspective of A. (I changed the way of describing coordinate systems and light cones, accoring to (I hope) Mr. or Ms. Red Act's comment below. In the former way of writing, "the transformation to make the distorted cone the right one makes the right cone the distorted one with the opposite tilt.") Like sushi ( talk) 06:42, 25 June 2009 (UTC)
Science desk | ||
---|---|---|
< June 21 | << May | June | Jul >> | June 23 > |
Welcome to the Wikipedia Science Reference Desk Archives |
---|
The page you are currently viewing is an archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages. |
Would it be theoretically possible for a pair of binary stars to orbit a planet that sat between them? For that planet to be Earth-like? Neon Merlin 01:25, 22 June 2009 (UTC)
Is there any conversion factor between horsepower and cc of a motor car?? can these be relation in any such numerical figure?? or are these two different things?? —Preceding unsigned comment added by 119.153.21.132 ( talk) 06:22, 22 June 2009 (UTC)
Is time finite or infinite? Bus stop ( talk) 07:41, 22 June 2009 (UTC)
Why the pressures within an inverted vertical tube manometer is being substracted..? —Preceding unsigned comment added by Sreekanth awh ( talk • contribs) 08:26, 22 June 2009 (UTC)
Is there an angle that you could cast light at (in a beam) where the circle iluminated would appear the same size at all distances? Say if you shon it at a wall a foot away from you and held a ruler a couple of inches away from your eye the circle of light would appear 4" wide, and it would also appear that if you stood 10 feet away from the wall, due to perspective. Gunrun ( talk) 08:43, 22 June 2009 (UTC)
I would think so. The apparent radius of a circle goes like 1/d with d the distance between you and the circle. The actual radius of the illuminated circle is proportional to d. You might want to have a look at http://en.wikipedia.org/wiki/Gaussian_beam
My friends and i are trying to do a project in the summer, which would keep us engaged, and at the same time learn something new. We are all first year undergraduate students. The basic idea is this: You have a (computer) mouse which eats light, that is, goes to the brightest area it can. It can do cool things like following the light from a torch, etc. In addition, whenever it collides with an obstacle, it veers back a couple of meters and then zooms off in some other direction. It isn't wired. This is to be done with basic electronics. We are following this book, and you can find the circuit diagram and other details in the link. But the thing is, we are facing multiple problems, and in need of help. The first problem is the IR emitter thingy. The book says the IR emitters (removed from an old mouse) will sense the incoming light, and hence act like the "eyes" of the mouse. It has given clear instructions on how to desolder the emitters and all. My question is, how can IR emitters possibly detect light? Shouldn't you use detectors? This can't be a printing mistake, he's used it several times. Then comes another problem. According to his illustrations, his emitters have 2 terminals, whereas our emitters have 3. What do we do? Worse, our detectors have four! Are there various types of emitters/detectors used in a mouse pcb,and are we stuck with a different kind? If that is the case, would the correct IR emitters/detectors be available in any electronics shop (The major electronics hub in the city is quite some distance away)? I think we are seriously in need of help... Rkr1991 ( talk) 09:13, 22 June 2009 (UTC)
Where are you, Spinningspark ? I thought you were the resident electronics specialist... Rkr1991 ( talk) 05:22, 23 June 2009 (UTC)
How can we reach the lowest possible temperature? If something is 0 C, I can put something -5C and cool it a little. But since the absolute zero temperature does not exist, how can be cool something until the lowest existent temperature, there is nothing cooler than it...-- Mr.K. (talk) 09:56, 22 June 2009 (UTC)
Bringing an object in contact with a cooler object is not the only way of cooling it. see for example http://en.wikipedia.org/wiki/Laser_cooling
OK, forgive my lack of comprehension of science. As I understand it, because light moves extremely fast, but not infinitely quickly, whatever you see took place a fraction before you actually noticed it. And furthermore, the further away the incident is, logically, the longer ago the incident took place. So I wondered, (Q1) what happened if someone had an improbably powerful telescope and was on the moon, looking at Earth. How long ago would whatever he saw actually have taken place?
Q2 What about if the person with the telescope was even further away, say in some high-tech capsule that allowed him to survive and also get a good view from Alpha Centauri?
Q3 How far away would you need to be to see, say, the Romans invading Britain?
If there's a flaw in my logic, please point it out. -- Dweller ( talk) 10:13, 22 June 2009 (UTC)
It's probably impossible to see the romans invade britain now though, unless you're at the planet already, because to get there to see it you'd have to travel faster than than the speed of light. The invasion of the romans is moving away from our planet at light speed! Gunrun ( talk) 10:46, 22 June 2009 (UTC)
According to the article on Thymine, the molecular formula of this nucleoside is C5H6N2O2. However, in the image to the right I can only see two hydrogens and no carbons at all. Where are the four missing hydrogens and the five missing carbons? -- 83.34.187.22 ( talk) 12:00, 22 June 2009 (UTC)
Is there a scientific reason why the East Coast is getting so much rain in the past few weeks? -- Reticuli88 ( talk) 13:23, 22 June 2009 (UTC)
Large-scale movement of the universe is dominated by the metric expansion of space, making further objects recede faster. But what is the farthest object that does actually travel towards us? More generally, what it the object with the largest difference between expected and observed red shift (either way)? -- Stephan Schulz ( talk) 14:59, 22 June 2009 (UTC)
Is there an online database that lists the apparent or observed colours of night sky objects to the human eye using some sort of scientific scale? For example, Mars and Betelgeuse are redder. I know Rigel is blue in absolute terms, but is it blue to the naked eye from a human perspective? I want a version of the Hertzsprung-Russell_diagram using observed data from the human eye on Earth rather than absolute data out there in space. -- Sonjaaa ( talk) 16:53, 22 June 2009 (UTC)
Does a star or planet's B-V colour index represent its apparent colour to a human observer on Earth?-- Sonjaaa ( talk) 00:33, 23 June 2009 (UTC)
I often make spaghetti with different kinds of spaghetti sauces, and it seems that the mushroom sauce gets mold much more often than the tomato-only sauce. I can't imagine why, since both are the same brand, bought in the same amounts, stored in the same type of jar in the same place in the same refrigerator; the only difference between the types is the presence of cooked chunks of mushrooms. Obviously the mushrooms and the mold are different species, so it's not as if the mushrooms are manifesting themselves as mold, but realistically is there any possibility that the mold grows more readily on the mushrooms themselves, and/or that the presence of the mushrooms makes the sauce a better host for mold? Nyttend ( talk) 17:49, 22 June 2009 (UTC)
Are chicken eggs sterile (free of bacteria) before the shell is opened? 65.121.141.34 ( talk) 18:31, 22 June 2009 (UTC)
If we were to create a substantial population in a space station (something like Babylon 5) and ensured that the construction and all people sent there were free of all bacteria/viruses would it remain sterile indefinitely or would the human flora be likely to eventually mutate into forms that cause illness? Thanks :-) -- 87.113.12.133 ( talk) 19:58, 22 June 2009 (UTC)
Thanks all. I'm particularly interested in the fact DNA can spontaneously create a virus, I'll have a further look at that -- 87.113.128.46 ( talk) 22:15, 23 June 2009 (UTC)
Do we know of any stars whose diameter is larger then the orbit Pluto would make (at maximum distance, assuming its eccentricity was 0.0000)? What would be the angle we would be able to see if it was at the distance of Alpha Centari (sp?)? 65.121.141.34 ( talk) 20:53, 22 June 2009 (UTC)
In reading about small stars (due to an earlier question here), I found this quote: "The relatively puny body weighed in at 96 times Jupiter's mass - above the threshold of 75 Jupiter-masses required for a bona fide star, which must also burn hydrogen." So, are there hydrogen-burning planets, considered planets simply because they are less than 75 Jupiter-masses? -- kainaw ™ 22:19, 22 June 2009 (UTC)
There are accumulating unreplied remarks on that page and, of course, there is probably a bunch of you who could answer them. (is mainstream isn't it?) ~ R. T. G 22:32, 22 June 2009 (UTC)
Does an observer move relative to the light cone? Special relativity says "Special relativity incorporates the principle that the speed of light is the same for all inertial observers regardless of the state of motion of the source.", and if an observer moves relative to the light cone, the speed of light is not the same for the observer. And as, if we slide the axis of the path of the observer to enable to regard the observer not moving, then the axis of the light cone is slided accordingly, and it turns out that the speed of light is fixed to the source (like in emission theory). But if an observer does not move relative to the light cone, the plane sharing simultaneity does not seem to tilt. Like sushi ( talk) 23:18, 22 June 2009 (UTC)
(Edit conflict) (indent) The problem is that you can’t just ask if something is "moving", or talk about "the axis" of a light cone, without specifying which inertial frame of reference "motion" is defined relative to, and "the axis" of a light cone is defined in. To use a concrete example, suppose two spacecraft are moving away from each other at some constant speed v, where v is a sizeable fraction of the speed of light. Somewhere in the rough vicinity of the two spacecraft, a flashbulb goes off. Associated with each spacecraft is an inertial frame of reference such that in that frame of reference, the associated spacecraft is stationary, and the flashbulb goes off at the origin of the associated 4-D coordinate system.
The flashbulb going off is an event in spacetime. Associated with the flashbulb going off is a future light cone, which consists of the set of all events in spacetime such that light from the flash reaches that point in space at that point in time. Call the two spacecraft A and B, with associated inertial frames A and B. In inertial frame A, the future light cone associated with the flashbulb going off consists of all events (points in spacetime) such that r=c t, where r is the spatial distance from the flashbulb event as measured in inertial frame A, t is the time since the flashbulb event occurred as measured in inertial frame A, and c is the speed of light. In inertial frame B, the future light cone associated with the flashbulb going off consists of all events such that r’=c t’, where r’ is the spatial distance from the flashbulb event as measured in inertial frame B, t’ is the time since the flashbulb event occurred as measured in inertial frame B, and c again is the speed of light. The speed of light is the same constant value in both frames of reference.
The two observers agree as to which events are on the light cone, but they will disagree as to what the coordinates are of the events on the light cone. E.g., observer A might say that a given event on the light cone occurred 1 second after the flashbulb event, and is 1 light-second away from where the flashbulb event occurred. Meanwhile, observer B might say that the same event on the light cone occurred 2 seconds after the flashbulb event, and is 2 light-seconds away from where the flashbulb event occurred.
More importantly, although observers A and B agree as to which set of events are on the light cone, they do not agree as to which set of events are on the axis of the light cone. Observer A will say that the axis consists of all the events for which r=0, i.e., the world line of an object that was at the flashbulb event, and which is stationary as measured in inertial frame A. In contrast, observer B will say that the axis consists of all the events for which r’=0, i.e., the world line of an object that was at the flashbulb event, and which is stationary as measured in inertial frame B. The only event that observers A and B will agree is on the axis is the origin of the two coordinate systems.
In short, observer A will say that the axis of the light cone is parallel to spacecraft A, i.e, spacecraft A is not moving relative to the axis of the light cone, and spacecraft B is moving relative to the axis of the light cone. In contrast, observer B will say that the axis of the light cone is parallel to spacecraft B, i.e, spacecraft B is not moving relative to the axis of the light cone, and spacecraft A is moving relative to the axis of the light cone. It’s an exactly symmetrical situation, and neither observer is the "correct" one. Red Act ( talk) 05:26, 23 June 2009 (UTC)
No. I think I have found another problem. That is when the observer is out of the light cone and eventually touches its surface. The first question now makes sense? or is it still faulty?
I am confused.
Like sushi (
talk)
10:18, 23 June 2009 (UTC)
I have managed to get out of the confusion. All light cones assume axes parallel to the axis of motion of the observer in the reference frame of him. Like sushi ( talk) 11:10, 23 June 2009 (UTC) Or do they not? Like sushi ( talk) 11:15, 23 June 2009 (UTC)
Sorry,I didn't notice Mr.or Ms. Red Act has written. The axes of all light cones according to that observer are parallel. So the contents of a light cone is always the same for any observer, i.e. the light cone occupies the same spacetime, and only difference is the coordinate system which gives the event the time and location? In fact, I have posted to the math desk to confirm that two points at which observers moving parallel to the source of the cone, are the same distance away, and in a plane with the same y (the spacial axis perpendicular to the direction of motion of the observer) and the light cone meet always make a line of the same tilt, if the velocity of observers are the same (in mathematical form). But I could not be answered somehow. (About for what reference frame, I think I didn't specify. I was thinking only in one reference frame.) If all planes sharing simultaneity is inclined at the same rate in any one reference frame, no matter from what plane you start, the resulting planes are the same if any numbers of observers travel for the same time in their common reference frame, and as such, with the same velocity. Is it that it does not matter if it's the section with the light cone or not, but "from and onto the same plane" and "along parallel lines", and if not we can not simply compare them? Like sushi ( talk) 12:28, 23 June 2009 (UTC)
I think, in one reference frame, a tilted world line (I am not used to this term) of another observer moving relative to you which shows another axis of the light cone goes through the center of the ellipse which is the section of the light cone and the plane of simultaneity for that observer in the first reference frame. If that distorted cone (it is not distorted in outer cone though) can be transformed in to the right cone, making the right cone the distorted cone, then the reciprocity is shown. Like sushi ( talk) 13:27, 23 June 2009 (UTC)
I have noticed that the diagonal lines (the edges of the light cone in the plane y=z=0),are not affected by the transformation. And the outer cone is the same with and without the transformation. As I think (if it is arbitrarily set) the axis of the cone or the world line of the observer moving in respect to the right coordinate system goes through the center of the ellipse which is the section of the light cone and the plane of simultaneity for the distorted coordinate system, it just need to adjust the x-axis to make the distorted cone (of which the surface is not distorted) right.
But does the transformation to make the distorted cone the right one makes the right cone the distorted one with the opposite tilt? And does the y- or z- width of the ellipse section of the transformed light cone appears to be small than the radius of the circle section of the right cone with the centers at the same time in the reference frame of the right coordinate system? (I think that means if the observer regarding himself stationary measures the travel distance of light for the other observer moving relatively to him, in y or z in his right coordinate system, at the same time in his reference frame, it is less than his.)
(I think I have managed to understand , with the help of all of you, that the light cone is always the same if the coordinate system is adjusted to the right one, though the distance to the origin of the light cone in spacetime is different. The questions I am asking now is on the side of the original one, which was about if the shape of light cones, and thus the speed of light are always the same in all (right) coordinate systems, or for all observers who regard themselves at rest.)
Thank you very much for all of you! And I hope you will answer the side questions. Like sushi ( talk) 23:39, 23 June 2009 (UTC)
Alhough it is difficult to imagine, caliculating Lorentz transformation,
for t and x gives
.
So coordinate system A from perspective of B is coordinate system B from perspective of A just with the opposite v. It seems a light cone for A from perspective of B has just the opposite tilt of the light cone for B from perspective of A. (I changed the way of describing coordinate systems and light cones, accoring to (I hope) Mr. or Ms. Red Act's comment below. In the former way of writing, "the transformation to make the distorted cone the right one makes the right cone the distorted one with the opposite tilt.") Like sushi ( talk) 06:42, 25 June 2009 (UTC)