We claim to separate church and state but we really don't.
Many parts of our state, beyond having their foundations in religious beliefs, have direct religious references. Our currency states "In God We Trust". Our state governments require citizens to get a marriage license. Our pledge of allegiance mentions God. The entire country operates around Christian holidays.
We did specifically forbid the government from promoting or favoring one religion over another, with the exception of the de-facto endorsement of Christianity, but that's more like a limitation rather than a separation.
If we wanted to construct a government that was truly separate from religion, how would we do it?
The main issue that comes to my mind is crime. Governments create laws and people who break the laws must be punished. But is there a difference between committing a crime and breaking a law? Or between committing a crime and sinning? Is there such a thing as a victim-less crime? Are some acts crimes in one religion but not another? Is it fair for the government to pass laws that essentially echo the laws of a specific favored religion?
I think that because religions regulate behavior, it's not possible to construct a state that is completely separate from religion - the state needs to either adopt a specific religion (or atheism) and align its laws with it, or it needs to maintain a minimal set of laws to set a basic standard of behavior and then regulate the religions that can operate within this minimal framework.
Should religious institutions have the authority to punish their members for acts that violate the laws of their religion? What maximum punishment will the state allow?
What should happen if a member of one religion commits an act that hurts a member of another religion in some way, and the two religions have different positions on the act? What if the perpetrator's religion declares it allowed and the victim's religion declares it is not allowed? What if the opposite happens - the perpetrator's religion allows the action but the victim's religion forbids it? Should the state handle these cases or should there be a regulation on how they are handled and how disagreements will be resolved?
Thursday, September 30, 2010
Wednesday, September 22, 2010
Don't Ask Don't Tell
If discussing sexuality is allowed in the military, will the government pay for gays & lesbians to have separate individual (not group) quarters and showers? Or will it, in the name of fairness and equality for all, completely abolish separate male & female quarters and showers?
Either way, it's completely unfair to force the military to deal with this issue when society at large still hasn't granted complete equality to gays & lesbians.
Congress must abolish the practice of marriage licenses and restore full authority over marriage to religious authorities.
Any two adults living together for at least a year and filing a joint return should get the same tax benefits from the IRS, and any adults filing a joint return and having custody of children should get the same benefits from the IRS.
The military must not be used as playground for social reformers. DADT allows the military to ignore the gay & lesbian issue until society resolves it, and DADT should stay in place until then.
Either way, it's completely unfair to force the military to deal with this issue when society at large still hasn't granted complete equality to gays & lesbians.
Congress must abolish the practice of marriage licenses and restore full authority over marriage to religious authorities.
Any two adults living together for at least a year and filing a joint return should get the same tax benefits from the IRS, and any adults filing a joint return and having custody of children should get the same benefits from the IRS.
The military must not be used as playground for social reformers. DADT allows the military to ignore the gay & lesbian issue until society resolves it, and DADT should stay in place until then.
Monday, September 6, 2010
Relativity of Simultaneity
So I read Relativity of Simultaneity on Wikipedia. The "train-and-platform" thought experiment is supposed to show how two events can appear to be simultaneous from one frame of reference while not appearing simultaneous in another.
Setup quote: "A popular picture for understanding this idea is provided by a thought experiment consisting of one observer midway inside a speeding traincar and another observer standing on a platform as the train moves past".
Observer on the train: "A flash of light is given off at the center of the traincar just as the two observers pass each other. The observer onboard the train sees the front and back of the traincar at fixed distances from the source of light and as such, according to this observer, the light will reach the front and back of the traincar at the same time."
BUT, I propose there's more to this observer-on-the-train scenario than was discussed. The observer can't actually know when the light hit the front and back of the traincar until the light reflects back from those surfaces and returns to the observer. Therefore the observer's measurement of when the light reached the front of the car is the time it took the light to reach the front plus the time it took the light to return from the front to the observer.
Let the first observer in the traincar be oC and the second observer on the platform be oP.
Let rCF be the ray moving from the center of the traincar, the location of oC, to the front of the traincar.
Let rCB be the ray moving from the center of the traincar, the location of OC, to the rear of the traincar.
If the car is moving forward, then the front of the car is actually moving away from the light, and so the light rCF will take longer to reach the front of the car. Let tF be the time required for the light to move a half-traincar-length in the same direction the traincar is moving. On the other hand, the light moving toward the back of the car rCB has less distance to travel because the back of the car is also moving toward the source of the light so it will get there faster. Let tB be the time required for the light to move a half-traincar-length in the opposite direction the traincar is moving.
However, once the light moving forward rCF is reflected, it will have less distance to cover on the way back since the middle of the car is moving toward it, and when the light originally moving toward the back rCB reflects it will then take longer to reach the middle because the middle will be moving away from it.
So the total time for the light moving toward the front to return to the observer is tF + tB, while the total time for the light moving toward the back to return to the observer is tB + tF. The total is the same.
The net effect is that the light moving forward and backward will appear to reach the ends of the traincar at the same time because the reflected light will reach the observer at the same time.
Now the observer on the platform: "The observer standing on the platform, on the other hand, sees the rear of the traincar moving (catching up) toward the point at which the flash was given off and the front of the traincar moving away from it. As the speed of light is finite and the same in all directions for all observers, the light headed for the back of the train will have less distance to cover than the light headed for the front. Thus, the flashes of light will strike the ends of the traincar at different times"
That's right, but that's not any different than the first half of the solution for the first observer. Since the second observer is not moving with the train, the second half of the solution is different - the second observer will see light reflected from the back and from the front of the traincar toward him. The light reflected from the back will reach the observer first because it will have less distance to travel than the light that is reflected from the front of the traincar.
BUT, what isn't accounted for in the second observer's story is the fact that the in the second half of the solution, the light rays start at different distances from the observer. This is because the light that moved from the center of the traincar toward the front actually moved more than one half traincar lengths forward before it reflected (let this be dF), and the light that moved from the center toward the back actually moved less than one half traincar lengths backward before it reflected (let this be dB). So the rays of light are no longer the same distance away from the second observer when they reflect.
The ray reflecting from the back of the traincar will reach the second observer faster because it has less total distance to travel from its origin to the back of the car than the ray moving forward travels from the origin to the front of the car, and in addition because the car has been moving forward, the back of the car is moving closer to the second observer so that the ray moving toward the back has less distance to travel from its reflection point toward the second observer than the ray that moved toward the front does when it reflects.
So while the second observer perceives rCB first, he will also observe that the origination point of rCB is closer to him than the origination point of rCF, and if he calculates the time it took rCB and rCF to reach him from their origination points he will also note that rCB started moving toward him before rCF. And he will be correct, because if you recall from the first observer oC's story, rCB did actually reach the back of the traincar and reflected before rCF reached the front of the traincar and reflected.
In other words, the "simultaneous" nature of the two events reaching the second observer is a complete misconception. While the origin of the two rays at oC was simultaneous, their reflection times and locations sending them on their path toward the second observer oP were neither simultaneous nor equidistant from the second observer oP.
And let's consider a third story that wasn't mentioned on Wikipedia: Let's assume that by some arrangement, the light originating at the center of the traincar the moment that oC and oP pass each other is equidistant from oC and oP. This could be done if we acknowledge the traincar has width and we assume that the light source is on the platform side of the car while oC is standing in the center of the traincar length-wise but on the opposite side of the traincar, one traincar-width away from the light source, while oP is standing on the platform one traincar-width away from the light source as well.
In this third story, we consider the path of two additional rays of light: rC traveling from the light source to the observer on the traincar oC, and rP traveling from the light source to the observer on the platform oP. Obviously since the traincar is much longer than it is wide, rC will reach oC much faster than either reflected ray. And since light travels the same speed regardless of of the velocity of its source, rP will reach oP at the same time that rC will reach oC's original position, because oC's original position and oP are the same distance away from the light source. Of course, because oC is moving forward with the traincar, it won't be at its original position when the light reaches it. In fact, the ray of light rC that was headed from the light source to oC's original position will never reach oC, it will simply hit the side of the traincar behind oC. Another ray of light, rC', headed at an angle somewhere between directly at oC and directly forward, is the one that will reach oC. This ray of light rC' will travel a distance longer than one traincar-width to reach the forward-moving oC because it's moving along the hypotenuse of a triangle that has its right angle at oC's original position. Because rC' travels a longer distance than rP, rC' will take longer to reach the first observer than rP will take to reach the second observer.
The origin of the light was simultaneous but the two observers will not observe the light at the same time because in fact it does not travel the same distance to them. If they compare notes on the event they will be able to calculate the speed of the traincar by using their known starting locations and the times at which they observed the light rays rC' and rP.
This explanation works for any speed of the traincar from 0 m/s up to and including the speed of light.
At the speed of light, there are some interesting results: When the traincar moves at the speed of light then rF never reaches the front of the traincar and never reflects, and rC' also never reaches oC because they start at the same time from the same track position and they're both moving at the same speed c so rC' would end up missing oC, and oC will not see any beam of light at all from the source as long as he's moving at the speed of light. Then again, as long as oC is moving at the speed of light, he won't be able to communicate with oP to compare notes on the timing of the light rays. After oC slows down or stops, the light ray rC' will catch up with him and oC will have a time measurement to compare with oP. When they calculate the speed of the traincar, the result will be below the speed of light and this accounts for the moments in which oC was slowing or stopping from the speed of light to allow rC' to reach him.
My physics teacher in college convinced the entire class that time has somehow passed more slowly for the traveler, and this is the origin of science fiction tales in which a space traveler arrives at a distant future where the world has aged faster than he. In reality, light takes longer to reach the traveler because it has to travel a much larger distance to reach him when he travels at nearly light speeds. Now, how might a traveler might cope with the fact that light doesn't even reach him from the other side of the traincar? I propose that the speed-of-light scenario isn't even possible, that only light can travel at the speed of light, and that if you want to travel at the speed of light, the universe won't let you be anything else but light.
Setup quote: "A popular picture for understanding this idea is provided by a thought experiment consisting of one observer midway inside a speeding traincar and another observer standing on a platform as the train moves past".
Observer on the train: "A flash of light is given off at the center of the traincar just as the two observers pass each other. The observer onboard the train sees the front and back of the traincar at fixed distances from the source of light and as such, according to this observer, the light will reach the front and back of the traincar at the same time."
BUT, I propose there's more to this observer-on-the-train scenario than was discussed. The observer can't actually know when the light hit the front and back of the traincar until the light reflects back from those surfaces and returns to the observer. Therefore the observer's measurement of when the light reached the front of the car is the time it took the light to reach the front plus the time it took the light to return from the front to the observer.
Let the first observer in the traincar be oC and the second observer on the platform be oP.
Let rCF be the ray moving from the center of the traincar, the location of oC, to the front of the traincar.
Let rCB be the ray moving from the center of the traincar, the location of OC, to the rear of the traincar.
If the car is moving forward, then the front of the car is actually moving away from the light, and so the light rCF will take longer to reach the front of the car. Let tF be the time required for the light to move a half-traincar-length in the same direction the traincar is moving. On the other hand, the light moving toward the back of the car rCB has less distance to travel because the back of the car is also moving toward the source of the light so it will get there faster. Let tB be the time required for the light to move a half-traincar-length in the opposite direction the traincar is moving.
However, once the light moving forward rCF is reflected, it will have less distance to cover on the way back since the middle of the car is moving toward it, and when the light originally moving toward the back rCB reflects it will then take longer to reach the middle because the middle will be moving away from it.
So the total time for the light moving toward the front to return to the observer is tF + tB, while the total time for the light moving toward the back to return to the observer is tB + tF. The total is the same.
The net effect is that the light moving forward and backward will appear to reach the ends of the traincar at the same time because the reflected light will reach the observer at the same time.
Now the observer on the platform: "The observer standing on the platform, on the other hand, sees the rear of the traincar moving (catching up) toward the point at which the flash was given off and the front of the traincar moving away from it. As the speed of light is finite and the same in all directions for all observers, the light headed for the back of the train will have less distance to cover than the light headed for the front. Thus, the flashes of light will strike the ends of the traincar at different times"
That's right, but that's not any different than the first half of the solution for the first observer. Since the second observer is not moving with the train, the second half of the solution is different - the second observer will see light reflected from the back and from the front of the traincar toward him. The light reflected from the back will reach the observer first because it will have less distance to travel than the light that is reflected from the front of the traincar.
BUT, what isn't accounted for in the second observer's story is the fact that the in the second half of the solution, the light rays start at different distances from the observer. This is because the light that moved from the center of the traincar toward the front actually moved more than one half traincar lengths forward before it reflected (let this be dF), and the light that moved from the center toward the back actually moved less than one half traincar lengths backward before it reflected (let this be dB). So the rays of light are no longer the same distance away from the second observer when they reflect.
The ray reflecting from the back of the traincar will reach the second observer faster because it has less total distance to travel from its origin to the back of the car than the ray moving forward travels from the origin to the front of the car, and in addition because the car has been moving forward, the back of the car is moving closer to the second observer so that the ray moving toward the back has less distance to travel from its reflection point toward the second observer than the ray that moved toward the front does when it reflects.
So while the second observer perceives rCB first, he will also observe that the origination point of rCB is closer to him than the origination point of rCF, and if he calculates the time it took rCB and rCF to reach him from their origination points he will also note that rCB started moving toward him before rCF. And he will be correct, because if you recall from the first observer oC's story, rCB did actually reach the back of the traincar and reflected before rCF reached the front of the traincar and reflected.
In other words, the "simultaneous" nature of the two events reaching the second observer is a complete misconception. While the origin of the two rays at oC was simultaneous, their reflection times and locations sending them on their path toward the second observer oP were neither simultaneous nor equidistant from the second observer oP.
And let's consider a third story that wasn't mentioned on Wikipedia: Let's assume that by some arrangement, the light originating at the center of the traincar the moment that oC and oP pass each other is equidistant from oC and oP. This could be done if we acknowledge the traincar has width and we assume that the light source is on the platform side of the car while oC is standing in the center of the traincar length-wise but on the opposite side of the traincar, one traincar-width away from the light source, while oP is standing on the platform one traincar-width away from the light source as well.
In this third story, we consider the path of two additional rays of light: rC traveling from the light source to the observer on the traincar oC, and rP traveling from the light source to the observer on the platform oP. Obviously since the traincar is much longer than it is wide, rC will reach oC much faster than either reflected ray. And since light travels the same speed regardless of of the velocity of its source, rP will reach oP at the same time that rC will reach oC's original position, because oC's original position and oP are the same distance away from the light source. Of course, because oC is moving forward with the traincar, it won't be at its original position when the light reaches it. In fact, the ray of light rC that was headed from the light source to oC's original position will never reach oC, it will simply hit the side of the traincar behind oC. Another ray of light, rC', headed at an angle somewhere between directly at oC and directly forward, is the one that will reach oC. This ray of light rC' will travel a distance longer than one traincar-width to reach the forward-moving oC because it's moving along the hypotenuse of a triangle that has its right angle at oC's original position. Because rC' travels a longer distance than rP, rC' will take longer to reach the first observer than rP will take to reach the second observer.
The origin of the light was simultaneous but the two observers will not observe the light at the same time because in fact it does not travel the same distance to them. If they compare notes on the event they will be able to calculate the speed of the traincar by using their known starting locations and the times at which they observed the light rays rC' and rP.
This explanation works for any speed of the traincar from 0 m/s up to and including the speed of light.
At the speed of light, there are some interesting results: When the traincar moves at the speed of light then rF never reaches the front of the traincar and never reflects, and rC' also never reaches oC because they start at the same time from the same track position and they're both moving at the same speed c so rC' would end up missing oC, and oC will not see any beam of light at all from the source as long as he's moving at the speed of light. Then again, as long as oC is moving at the speed of light, he won't be able to communicate with oP to compare notes on the timing of the light rays. After oC slows down or stops, the light ray rC' will catch up with him and oC will have a time measurement to compare with oP. When they calculate the speed of the traincar, the result will be below the speed of light and this accounts for the moments in which oC was slowing or stopping from the speed of light to allow rC' to reach him.
My physics teacher in college convinced the entire class that time has somehow passed more slowly for the traveler, and this is the origin of science fiction tales in which a space traveler arrives at a distant future where the world has aged faster than he. In reality, light takes longer to reach the traveler because it has to travel a much larger distance to reach him when he travels at nearly light speeds. Now, how might a traveler might cope with the fact that light doesn't even reach him from the other side of the traincar? I propose that the speed-of-light scenario isn't even possible, that only light can travel at the speed of light, and that if you want to travel at the speed of light, the universe won't let you be anything else but light.
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