Originally posted by sonhouseIn classical Newtonian mechanics, the spaceships would be travelling apart at 1.6c since you simply add the two. However, the real equation is
Ok, suppose the two spacecraft are going apart at 0.8C like we just noted. Now they are traveling in opposite directions. Suppose the two craft each have an extremely thin rope with one end spindled on on craft and the other end on craft # 2. Initially they are in close proximity and all the rope is coiled up in a huge spindle on each craft like I said. Lig ...[text shortened]... ope. When they reach 0.8C, is the length of the rope increasing faster than the speed of light?
If [spaceship] B is moving with velocity u relative to [Planet Earth] C and [spaceship] A is moving with velocity w relative to C then the velocity of A relative to B is given by,
v = (w - u)/(1 - wu/c2)
http://math.ucr.edu/home/baez/physics/Relativity/SR/velocity.html
Let's imagine the two ships are moving at 100 m/s relative to C (the Earth).
v = (100 - (-100))/(1 - (100^2)/((3x10^8)^2)
v = 200/(1 - (10^4/(9x10^16)))
v = 200/(1 - (1/(9x10^12)))
v ~ 200
because 1/(9x10^12) is very nearly zero. In classical mechanics this part of the equation is simply ignored, which is a good approximation at low speeds.
However at higher speeds you get a different result. Let's use your numbers of +/- 0.8c.
v = (w - u)/(1 - wu/c^2)
v = (1.6c)/( 1 - (-0.64c^2/c^2))
v = (1.6c)/(1.64)
And voila, 0.8c + 0.8c < c due to the Lorenz factor.
Originally posted by AThousandYoungDo you think a little weed will help me understand this?
In classical Newtonian mechanics, the spaceships would be travelling apart at 1.6c since you simply add the two. However, the real equation is
[i]If [spaceship] B is moving with velocity u relative to [Planet Earth] C and [spaceship] A is moving with velocity w relative to C then the velocity of A relative to B is given by,
v = (w ...[text shortened]... 1 - (-0.64c^2/c^2))
v = (1.6c)/(1.64)
And voila, 0.8c + 0.8c < c due to the Lorenz factor.
I must give your explaination one big, round the world, A+ Newton.
G.
Originally posted by smw6869What part didn't you understand? Just plain school arithmetics, you know, addition, subtraction, multiplication and division, oh yes, squares too.
Do you think a little weed will help me understand this?
I must give your explaination one big, round the world, A+ Newton.
G.
This was the essence of the explanation why you can't go faster than light, known for near 100 years. Well done explaining, AThousandYoung!
Originally posted by FabianFnasListen, sonny boy. It's been 80 yrs since i 've studied math. Today, all i know is, when the Soc. Sec. check arrives i go down to the Casino, deposit $100 in the slots and return home with $50, and that's on a good day. What am i doing wrong? It just doesn't add up?
What part didn't you understand? Just plain school arithmetics, you know, addition, subtraction, multiplication and division, oh yes, squares too.
This was the essence of the explanation why you can't go faster than light, known for near 100 years. Well done explaining, AThousandYoung!
Granny:'(
Originally posted by smw6869Oh, I see.
Listen, sonny boy. It's been 80 yrs since i 've studied math. Today, all i know is, when the Soc. Sec. check arrives i go down to the Casino, deposit $100 in the slots and return home with $50, and that's on a good day. What am i doing wrong? It just doesn't add up?
Granny:'(
I have an old dictionary, from the 1920ish. They say that Einstein's theory of relativity is interesting, but still a good theory. Now the theory is confirmed to that extent that it can be considered true.
You were there when the theory grew so you have 50 years more to get to know the theories. I envy you!
Originally posted by FabianFnasExactly, that's the ticket!
Oh, I see.
I have an old dictionary, from the 1920ish. They say that Einstein's theory of relativity is interesting, but still a good theory. Now the theory is confirmed to that extent that it can be considered true.
You were there when the theory grew so you have 50 years more to get to know the theories. I envy you!
I wub you Fabian, and especially those great songs you sang during the 1950's.
Granny😏
seems to me that people get all hot and bothered about the speed of light
measurement of galaxies is made to this dimensional constant, which isn't constant
and yet if it's thought of as a beam of light travelling at a constant speed, and one is shone in opposite directions, the refelected light off each beam will never catch up to that shone in the opposite direction
similarly, a light from A will never catch up with B, but one would see an image of the receding craft, just not at true speed of 1.6c
sort of like looking at a hologram or ghost image
it is the true image, just not the true craft
just as we don't see a true - current form of galaxies out yonder, but rather their image from however many thousand, million, trillion light years that they are away from us
so what we see of these galaxies is the form they took that long ago, they may well be gone now, but their image remains and is what we see today
A sees B as a light source, it sees its image - as the light from it is faster than the crafts speed, but it just cannot see the actual craft once their relative speeds are greater than c, so it sees its image, as we see those of those distant galaxies
i believe this holds true of all objects except those that don't shed light, or where gravitational effects are strong enough for warping etc, but these generate their own Lorenz type effects..
just don't shine your torch in my direction, i might go blind....
just had lunch and thought a form of simplification might be appropriate
everything we see is an image, one that we assume is in fact the object we're looking at
at normal speeds and distances this is true ( nearly )
the starting pistol at an athletics track is used to both make a noise and a puff of smoke, so that the noise starts the runners, the smoke starts the timekeepers ( in the old days and for simple meets )
what we see is not the object we are looking at but its image
for lorenz effects, this is apparently one and the same when relative distance or speeds are concerned, however as one approaches light speed, the image and the object separate relatively from the point of view of the observer travelling at the large speed
to anyone else, either nearby or at low relative speeds, the image and object remain together (almost, or at least imperceptably so...)
so at relative speeds greater than the speed of light, the image of each craft relative to the other separates from the relative objects, and each sees an image of but never the object itself
if there were an unusually flexible and very strange rubber band between the two, and it only stretched when the relative speeds btwn craft was greater than c, as they slowed, it would recoil, and the respective images and objects would approach one another relative to the other viewer
so if each reached a destination and returned, the unusual rubber band would recoil to original vision, but the return journey toward each other is but another question, and i suspect a trickier one.
i'll have a shot at that another day..
Originally posted by olddogI'm not sure you make it easier than before.
just had lunch and thought a form of simplification might be appropriate
everything we see is an image, one that we assume is in fact the object we're looking at
at normal speeds and distances this is true ( nearly )
the starting pistol at an athletics track is used to both make a noise and a puff of smoke, so that the noise starts the runners, the ...[text shortened]... but another question, and i suspect a trickier one.
i'll have a shot at that another day..
However, you wrote "but rather their image from however many thousand, million, trillion light years that they are away from us"...
An object trillion of light years away from ??? Think again. The universe isn't old eaough to be able to harbour such a beam of light trillions of light years long.
I think you should go bac to basics. The reality of relativity is often easier to understand than the fancy explanations of relativity one often sees.
Originally posted by smw6869Sorry, I have the wrong age, live in the wrong continent, perhaps in the wrong space-time reality altogether to know anything about the The Hotdog Man. Enlighten me please...
Oh Fabian, Fabian, Fabian! Please sing Granny one of your top hit songs from the '50s. I especially like " The Hotdog Man"
G.
Originally posted by FabianFnasOh, i'm sorry. I thought you were he, or maybe him. Fabian was an icon...i say, an icon of the 1950s Rock and Rollish scene in America. What a sweet lad he was. Wait one, i'm sticking to my chair. Okay, there we go. Maybe i can find him on YouTub or some such thing.
Sorry, I have the wrong age, live in the wrong continent, perhaps in the wrong space-time reality altogether to know anything about the The Hotdog Man. Enlighten me please...
Granny.
Originally posted by FabianFnas
Sorry, I have the wrong age, live in the wrong continent, perhaps in the wrong space-time reality altogether to know anything about the The Hotdog Man. Enlighten me please...
I found you Fabian. Here you are, singing your greatest hit of all time....Tiger. Wowzerroonie could you sing Rock! You were my Luv Hunk, and still are.
Granny
Originally posted by sonhouseYes, but no part of the rope is travelling faster than light.
Ok, suppose the two spacecraft are going apart at 0.8C like we just noted. Now they are traveling in opposite directions. Suppose the two craft each have an extremely thin rope with one end spindled on on craft and the other end on craft # 2. Initially they are in close proximity and all the rope is coiled up in a huge spindle on each craft like I said. Lig ...[text shortened]... ope. When they reach 0.8C, is the length of the rope increasing faster than the speed of light?
Another example:
A super strong rotating beam of light, spinning a full circle once every second.
At a distance of 100,000,000 metres there is a wall. On the wall the light comes racing past every second. The spot of light on the wall travels with a speed of 2*pi*100,000,000 > 600,000,000 metres per second!
Luckily the spot of light is not an object. It is composed out of billions of photons colliding with the wall. None of the photons travel faster than light.